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Active deformation at Canyonlands National Park: Distribution of displacements across the grabens using spaceborne geodesy

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Active deformation at Canyonlands National Park: Distribution of displacements across the grabens using spaceborne geodesy

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Content ACTIVE DEFORMATION AT CANYONLANDS NATIONAL PARK: DISTRIBUTION OF DISPLACEMENTS ACROSS THE GRABENS USING SPACEBORNE GEODESY by Scott Douglas Marsic A Thesis Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree MASTER OF SCIENCE (EARTH SCIENCES) December 2003 Copyright 2003 Scott Douglas Marsic Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UMI Number: 1420385 INFORMATION TO USERS The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleed-through, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. ® UMI UMI Microform 1420385 Copyright 2004 by ProQuest Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. ProQuest Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, Ml 48106-1346 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UNIVERSITY O F SOUTHERN CALIFORNIA THE GRADUATE SCHOOL UNIVERSITY PARK LOS ANGELES, CALIFORNIA 90689-1695 This thesis, written by approved by all its members, has been presented to and accepted by the Director o f Graduate and Professional Programs, in partial fulfillment o f the requirements for the degree of Master of Science in Geological Sciences S c o t t Douglas Marsic under the direction o f h -* -s thesis committee, and Director Date 1 0 /2 9 /2 0 0 3 Thesis Committee Chair Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ACKNOWLEDGEMENTS Thanks to everyone that made this possible. Special thanks go out to my advisor Susan Owen allowing me the opportunity to work on this project. I would not have finished this thesis if it were not for her valuable time and assistance. Thanks to USC students Ross Hartleb and Shari Christofferson for helping me through the tremendous learning curves of graduate school. Utmost thanks to James Dolan, Greg Davis, Tim Wright, Juliet Crider, and Charlie Sammis for their tremendous support on many aspects of this thesis and my education. I am also indebted to my parents, sister, friends and fish, Turkish, for standing by me during the ups and downs of graduate school. Research associated with this thesis was supported by a grant from the National Science Foundation. All interferograms were processed using the Repeat Orbit Interferometry Package (ROI_Pac) from the NASA Jet Propulsion Laboratory in Pasadena, California. Thank you to Matt Pritchard, David Sandwell, and Evelyn Price for the time and assistance with this powerful program. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE OF CONTENTS ACKNOLEDGEMENTS ii LIST OF FIGURES v ABSTRACT x 1. INTRODUCTION 1 2. BACKGROND 5 2.1. Geologic Setting 5 2.2. Previous Investigations 13 3. DATA SOURCES: ANALYSIS AND RESULTS 24 3.1. The Global Positioning System (GPS) 24 3.1.1. GPS Results 27 3.2. Interferometric Synthetic Aperture Radar 30 3.2.1. InSAR Data Processing Procedure 35 3.2.2. Topographic Errors 39 3.2.3. Observed Atmospheric Effects 44 3.2.4. Interferometric Stacking 49 3.2.4.1. Descending Interferogram Stack 52 3.2.4.2. Ascending Interferogram Stack 61 3.2.5. Orbital Errors 66 3.2.6. Decomposition of InSAR Displacement Vector 72 3.2.6.1, Decomposition Assumption: Angle o f Extension 77 3.3. Decomposition Results 90 3.3.1. Horizontal Deformation 94 3.3.2. Vertical Deformation 102 4. DISCUSSION 109 5. CONCLUSIONS 116 6. REFERENCES CITED 118 iii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 7. APPENDIX 126 A l. Processing Interferograms Using NASA/JPL ROI_Pac 126 A2. Creating ROI_Pac Compatible DEM from SDTS Data 132 A3. Systematic Removal of Suspected Orbital Ramp 134 A4. MATLAB Analysis Programs 137 iv Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. LIST OF FIGURES Figure 1. Map of faults in Canyonlands National Park, southeastern Utah. Inset shows location. Redrawn from Huntoon et al. (1992) with additional annotations. Home Springs Anticline and Meander Anticline redrawn from Huntoon (1982). 2 Figure 2. Typical Canyonlands graben wall. Notice the simple “layer cake” stratigraphy. Image from west wall of Cyclone Canyon (Marsic, 2002). 6 Figure 3. Major regional structures associated with the Paradox Basin. Adapted from Nuccio and Condon (1996). The study area pertinent to this thesis is delineated on the north end of the Monument Upwarp. 9 Figure 4. Generalized Canyonlands stratigraphy after Grosfils et al. (2002). 11 Figure 5. North-facing view of Colorado River and Green River confluence. The downcutting of this river system has effectively unbuttressed the Pennsylvanian and Permian sediments, allowing them to move northwestward above the ductile Paradox salt substrate. Height of cliffs above the rivers is approximately 1000 ft. (305 m). Photo by Marsic, 2002. 14 Figure 6. Orthorectified Landsat-5 Thematic Mapper image of the Needles District of the Canyonlands. Three spectral bands are represented. Mid-infrared is displayed as red, near-infrared is displayed as green, and visible green is displayed as blue. The pixel resolution is 28.5 m. Fault nomenclature from Stromquist, 1976. URLC = Upper Red Lake Canyon, UC = Unnamed Canyon, (photo from NASA, 2003). 16 Figure 7. Generalized cross section profile across the northern portion of the grabens. The profile extends from the west (Cataract Canyon) to the east (Devil’s Pocket). Modified from Moore and Schultz, 1999. 18 Figure 8. Cross-section from Schultz-Eia and Walsh (2002). Finite element derived passive material deformation lines of overburden (dark) and the salt (light) for both dipping (c) and near-horizontal models (d). As a reference, deformation lines in a driving flow scenario (a) depict “pipe” like flow with a maximum flow rate within the salt and slower rates near the salt/overburden interface. Deformation lines in a resisting flow scenario (b) depicts a maximum rate near the salt/overburden interface. 21 Figure 9. (a) East-facing panoramic view of Devil’s Lane . (b) North facing view of the actively deforming east graben wall, (c) South facing view of the actively Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. deforming east graben wall. Recent deformation Is depicted as the lineage on the left side of (c). Photos by Marsic, 2002. 23 Figure 10. The GPS satellite constellation provides accurate and precise position, velocity and time information to users worldwide (FAA, 2003). 25 Figure 11. GPS derived horizontal displacement vectors (2000-2002). Blue vector without error ellipse Is equal to 1 cm/yr of displacement. Deformation is relative to the GPS base station location (WEII) 30 Figure 12. Illustration of ERS flight path. Satellite has a right looking range direction swath of approximately 100 km. Redrawn from ESA website illustration (ESA, 2003). 32 Figure 13. SAR image footprint of both ascending and descending tracks. Track 363 is ascending (south to north travel). Tracks 227 and 456 are both descending (north to south travel). Grabens study area is highlighted in the center of the image. 38 Figure 14. Tandem pair interferograms from ascending (2) and descending (1) tracks illustrating total slant range deformation (cm). Deformation is relative to the GPS base station location (WEI1;Figure 11) 43 Figure 15. Descending Interferograms used in pair-wise logic atmospheric test. Deformation (cm/yr) is relative to the GPS base station location (WEI1; Figure 11). Dark blue patches, corresponding to the darkest color on the color scale, represent regions of no correlation. Note the effect of atmosphere on the above interferograms, illustrated by the cross section profiles. 46 Figure 16. Location of 10 km by 25 km test swath. 47 Figure 17. Descending interferograms illustrating annual slant range deformation (cm/yr). Deformation is relative to the GPS base station location (WEI1; Figure 11). Dark blue patches, corresponding to the darkest color on the color scale, represent regions of no correlation. 57 Figure 18. Descending interferograms illustrating annual slant range deformation (cm/yr). Deformation is relative to the GPS base station location (WEI1; Figure 11). Dark blue patches, corresponding to the darkest color on the color scale, represent regions of no correlation. 58 Figure 19. Descending interferogram stack. Deformation is in the slant range (cm) per year. No orbital ramp was suspected; consequently no orbital ramp has been removed. Deformation is relative to the GPS base station location (WEI1; Figure 11). Dark blue patches, corresponding to the darkest color on the color vi Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. scale, represent a mosaic of no correlation regions from ail contributing interferograms. 59 Figure 20. Effect of deformation on right-looking radar line of sight. The first image in interferogram will have a path length represented by the observed phase (p) for a particular object on the ground (A). If A moves away from satellite (to right; A ” ), the path length will increase and observed phase will be p + 8p. If A moves toward satellite (to left; A ’), the path length will decrease and the observed phase will be p - 8p. 60 Figure 21. Ascending Interferograms illustrating annual slant range deformation (cm/yr). Deformation is relative to the GPS base station location (WEI1; Figure 11). Dark blue patches, corresponding to the darkest color on the color scale, represent a mosaic of no correlation regions from all contributing interferograms. 64 Figure 22. Ascending interferogram stack. Deformation is in the slant range (cm) per year. Deformation is relative to the GPS base station location (WEI1; Figure 11). Dark blue patches, corresponding to the darkest color on the color scale, represent a mosaic of no correlation regions from all contributing interferograms. 65 Figure 23. Suspected orbital ramp removed from the 930721-960209 interferogram. 69 Figure 24. Ascending interferogram stack. Deformation is in the slant range (cm) per year. Suspected orbital ramp has been removed. Deformation is relative to the GPS base station location (WEI1; Figure 11). Dark blue patches, corresponding to the darkest color on the color scale, represent a mosaic of no correlation regions from all contributing interferograms. 71 Figure 25. Illustration o f pointing vector grid (3x3) and the generalized graben trend setup based on the extensional angle assumption in equation 4. A unique pointing vector was calculated for each cell in the grid based on the center coordinates of each cell. The assumed direction o f overburden extension is perpendicular to the trend of the grabens. 74 Figure 26. Diagram illustrating relationship of east displacement (de ) to north displacement (dn). 75 Figure 27. Illustration of pointing vector grid (3x3) and generalized graben trends (bold curved line) used for extensional angle assumption in equation 4. A unique pointing vector was calculated for each cell in the grid based on the center coordinates o f each cell. 79 vii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 28. Illustration of pointing vector grid (3x3) and generalized graben trends (bold dashed line) used for extensional angle assumption in equation 4. A unique pointing vector was calculated for each cell in the grid based on the center coordinates of each cell. 83 Figure 29. Comparison of GPS derived horizontal displacement vectors (2000-2002) to InSAR horizontal displacement vectors. Note that both east and north displacements are utilized for this plot, therefore Inadequacies in the extension direction assumption are not taken into account. Index vectors equal to 1 cm/yr o f displacement. Deformation is relative to the GPS base station location (WEI1). 92 Figure 30. Relative total horizontal deformation (cm) per year. Profiles and GPS locations are removed from bottom image. Suspected orbital ramp has been removed from the contributing ascending interferogram stack. Deformation is relative to the GPS base station location (WEI1). Dark blue patches, corresponding to the darkest color on the color scale, represent a mosaic of no correlation regions from all contributing interferograms. 96 Figure 31. Relative horizontal deformation plots for profiles A through D. Profiles are west (left) to east (right) oriented. Deformation relative to the GPS base station (WEI1) is located on the y-axis of each plot (cm/yr). Lateral profile distance (km) on the x-axis. RLC = Red Lake Canyon; CC = Cyclone Canyon. 101 Figure 32. Relative horizontal deformation plots for profiles E (Red Lake Canyon) and F (Devil’s Lane). Profiles are north (left) to south (right) oriented. Deformation relative to the GPS base station (WEI1) Is located on the y-axis of each plot (cm/yr). Lateral profile distance (km) on the x-axis. 102 Figure 33. Relative vertical deformation (cm) per year. Profiles and GPS locations are removed from bottom image. Suspected orbital ramp has been removed from the contributing ascending interferogram stack. Deformation is relative to the GPS base station location (WEI1). Dark blue patches, corresponding to the darkest color on the color scale, represent a mosaic of no correlation regions from all contributing interferograms. 106 Figure 34. Relative vertical deformation plots for profiles A through D. Profiles are west (left) to east (right) oriented. Deformation relative to the GPS base station (WEI1) is located on the y-axis of each plot (cm/yr). Lateral profile distance (km) on the x-axis. RLC = Red Lake Canyon; CC = Cyclone Canyon. 107 Figure 35. Relative vertical deformation plots for profiles E (Red Lake Canyon) and F (Devil’s Lane). Profiles are north (left) to south (right) oriented. viii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Deformation relative to the GPS base station (WEI1) is located on the y-axis of each plot (cm/yr). Lateral profile distance (km) on the x-axis. 108 Figure 36. Chosen points for orbital plane coefficient determination. Point 1 steps to the right from the top left comer along row 100. Point 2 steps to the bottom along the right side of the image (row 850) from the top right comer. Point 3 steps to the left from the bottom right comer along row 700. 135 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ABSTRACT The Needles District of Canyonlands National Park in southeastern Utah is a unique geologic region in which gravitationally induced extension can be observed. Prior to our study, knowledge of Canyonlands deformation rates was limited to long term geologic averages between 2 mm/yr and 2 cm/yr that assumed spatial and temporal uniformity. Our research utilizes two geodetic techniques, Global Positioning System (GPS) and Interferometric Synthetic Aperture Radar (InSAR), to observe a clearer picture of current deformation rates across the entire study area. Results indicate relative regional subsidence of up to 3 mm/yr within the graben system. The interferograms additionally show spatially varied rates of horizontal deformation, with a maximum rate of deformation (6 mm/yr) near the eastern margin of the faulted region. Observations of deformation along several profiles support prior modeling efforts that suggest basal salt flow regulates overburden deformation. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1. INTRODUCTION "...the splendor of the landscape, the perfection o f the silence" Edward Abbey, 20th century writer, reflecting on the Canyonlands National Park (Abbey, 1984) The Needles District of Canyonlands National Park in southeastern Utah is a unique geologic region in which gravitationally induced extension above a ductile substrate can be observed. The arcuate, northwest-trending systems of faults that define the grabens region of the Needles District have simple stratigraphy and excellent exposure, therefore permitting the study of normal fault evolution under relatively simple conditions. There has been scientific interest in the grabens since the 1800’s, originally due to it’s unique landforms and more recently because of its similarities to more complicated extensional systems on the earth as well as other planets (Grosfils et al., 2003). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A h M o a b 0 J n 20 73 STUDY AREA % Y i I 2 kilometers r ^ - 1) ^ KEY TO SYMBOLS N | ^ Home Springs Anticline axis {Huntoon, 1S82J Normal fault,bar on down-thrown side (Huntoon et al., 1982). Meander Anticline (along Cataract Canyon) (Huntoon, 1982) Location o f 65 kaThermolujmnescence date on grabaa-fillsedlm ent (Biggar & Adams, 1987) Figure 1. Map o f faults in Canyonlands National Park, southeastern Utah. Inset shows location. Redrawn from Huntoon et al. (1992) with additional annotations. Home Springs Anticline and Meander Anticline redrawn from Huntoon (1982). 2 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The grabens, located in the Needles District of the Canyonlands National Park, consist of an approximately 450 meter-thick Pennsylvanian to Permian sedimentary section that is underlain by the Pennsylvanian Paradox evaporites. This entire package lies on the northern flank of the north-south trending Monument Uplift (Condon, 1996). The general consensus in the scientific community is that once the adjacent Colorado River incised down into the Paradox salt substrate, the upper sedimentary sequence became unbuttressed and consequently slid toward the Colorado River incision along the 4° northwest dip of the Monument Uplift's northern flank (Stromquist, 1976; McGill and Stromquist, 1979) with resulting internal extension. Workers in a variety of disciplines such as petroleum exploration, planetary geology, rock mechanics and extensional tectonophysics have demonstrated interest in how the grabens have evolved to their present state. Studies of spatially varying fault complexities (Stromquist, 1976; McGill and Stromquist, 1979; McGill and Schultz, 2000), normal fault displacement versus length analysis (Moore, 1997; Moore and Schultz, 1999), even plane-strain finite-element modeling (Walsh and Schultz-Ela, 1999; Schultz-Ela and Walsh, 2002; Walsh and Schultz-Ela, 2003) have facilitated understanding o f this still evolving system (Stromquist, 1976; McGill and Stromquist, 1979; Moore and Schultz, 1999). To date, no precise geodetic measurements have been conducted within the region to capture present day deformation. Long term extensional rate estimates have been calculated, ranging from 2 mm/yr to 2 cm/yr, based a balanced cross- 3 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. section extension estimate combined with an age estimate of the graben system (Biggar, 1987; Biggar and Adams, 1987; Schultz and Moore, 1999). Ultimately, deformation rates computed based on these processes assume uniform extension across the grabens, thus yielding spatial and temporal averages that do not assign unique rates to any particular region (Moore and Schultz, 1999; Grosfils et al., 2003) This thesis utilizes two geodetic techniques, Global Positioning System (GPS) and Interferometric Synthetic Aperture Radar (InSAR), to observe deformation rates across the entire grabens field area. Rates from these two techniques are independently derived, thereby allowing a robust means of comparison and error estimation. A discussion of results allows a comparison with published estimated rates using both field data (Biggar, 1987; Biggar and Adams, 1987; Schultz and Moore, 1999) and finite-element analysis modeling efforts (Walsh and Schultz-Ela, 1999; Schultz-Ela and Walsh, 2002; Walsh and Schultz-Ela, 2003). Specific emphasis in this thesis will be placed on the use and analysis of ascending and descending track InSAR data, which is ideal in this region due to predominately arid weather conditions, regionally broad terrain and relatively low vegetation density. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2. BACKGROND In the southeastern comer of Utah State sits a nearly pristine wilderness known today as Canyonlands National Park. Water and gravity have been the principal architects of this land, carving smooth shallow dipping layers of sedimentary rock into the dynamic landscape seen today (Figure 2). Evolving to its present state over a period of tens of thousands of years, scientists have only just begun to understand the origins of its unique beauty and the scientific value of its magnificent landforms. Perhaps no portion of the Canyonlands is more interesting and perplexing, than the grabens, the subject o f this research. 2.1. Geologic Setting "We glide along through a strange, weird grand region. The landscape everywhere, away from the river, is o f rock." John Wesley Powell - explorer commenting on the Canyonlands (1869) In 1859, the United States Army sent Captain John N. Macomb into the region to explore the Colorado Plateau for possible wagon routes to the west. His maps were the first geographic and geologic representations of the area. Ten years 5 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. later, M ajor John Wesley Powell led an expedition through the area, traveling down the Green and Colorado Rivers to the Grand Canyon. A second Powell expedition in 1871, produced maps that stood as the most detailed and accurate geologic and topographic information at the time (Herbert, 2003). Members of the Powell river expeditions in 1869 and 1871 were the first to lead a detailed investigation into the geology o f this unique region. In particular, they were the first to describe what came to be known as the Meander anticline (Stromquist, 1976), a differentially unloaded salt diapir at the base of Cataract Canyon (Huntoon, 1982) through which the Colorado River traverses. Additionally, they were the first to observe and study the grabens (Stromquist, 1976), laying the foundation upon which subsequent geologic studies (Harrison, 1927; Baker, 1933, 1946) were based. The Canyonlands are located in the western portion of the Colorado Plateau within the sediment filled Paradox Basin (Hunt, 1956; Rigby, 1977, Nuccio and Condon, 1996). Rigby (1977) has characterized this portion of the Plateau as consisting of deeply incised canyons, large monoclines and laccolithic mountains Figure 2. Typical Canyonlands graben wall. Notice the simple “layer cake” stratigraphy, image from west wall o f Cyclone Canyon (Marsic, 2002). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (Figure 3). This characterization of the western Plateau and Paradox Basin is the result o f a history of regional orogenic uplift and subsidence, cycles of inland sea regression and transgression, as well as periods o f extensive peripheral erosion and sediment transport and deposition (Nuccio and Condon, 1996). Sedimentary strata exposed within the Paradox Basin lie unconformably above an Early Proterozoic basement of metamorphic gneiss and schist that in some areas has been intruded by Proterozoic granite (Nuccio and Condon, 1996). The stratigraphy within the Canyonlands portion of the basin is a relatively simple succession of Pennsylvanian to Early Permian clastic sedimentary rocks and evaporites (Lewis and Campbell, 1965; Condon, 1997). The Paradox Basin region was located between the Cambrian and Devonian periods on a stable primarily shallow marine shelf (Burchfiel et al., 1992). These stable shelf conditions extended from central Colorado to the northeast-southwest trending Wasatch hinge in central Utah (Burchfiel et al., 1992). Sediment west of the Wasatch hinge line formed a large, west-thickening miogeocline that encompassed western Utah, eastern Nevada, and adjacent areas (Nuccio and Condon, 1996). The end of this stable period saw a change in the regional structural setting with the onset of the Late Devonian/Mississippian Antler Orogeny (Burchfeil and Royden, 1991). Occurring far west of the Paradox Basin, this orogenic event uplifted the north-trending Antler highland in Nevada and adjacent regions (Turner et al., 1989) that consequently produced significant terrigineous sediment flow into Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the Paradox Basin region (Pooie and Sandberg, 1991). Sub-Pennsylvanian rocks in the Basin, which have correlative units throughout the Plateau, contain a wide variety o f marine and non-marine originating elastics such as quartzite, shale, carbonates and sandstones (Nuccio and Condon, 1996). Pre-Pennsylvanian Paradox Basin strata thicken westward, from 300 feet to 2,600 feet. In the Canyonlands portion o f the Basin, these rock thickness range from 1,800 feet to 2,000 feet (Nuccio and Condon, 1996). Prior to the Pennsylvanian, the majority of present-day North America was contained on the supercontinent Laurentia (Scotese and McKerrow, 1990). The collision of Laurentia with the southern supercontinent Gondwana in the Pennsylvanian and Permian led to significant changes in the Paradox Basin region (Scotese and McKerrow, 1990; Nuccio and Condon, 1996). Most significant was the rapid large-scale uplift of the Uncompahgre Plateau, situated to the north - northeast of the current basin location. Concurrently, the Paradox Basin was formed as the region was subjected to rapid subsidence (Figure 3; Nuccio and Condon, 1996). During this time large amounts of Cambrian through Mississippian sediments, as well as an unknown thickness of Precambrian basement, were eroded from the Uncompahgre Plateau and deposited into the Paradox Basin (Nuccio and Condon, 1996). The deposited sediments created what are now referred to as the Hermosa, Honker Trail and Cutler Formations (Nuccio and Condon, 1996). During deposition of the Pennsylvanian Hermosa Formation, a series of repeated desiccation and 8 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. marine flooding cycles resulted in the formation of a varied unit consisting of dolostone, black shale, anhydrite, halite and other salts (Hite and Buckner, 1981). 1 1 0 ° 0 0 ‘ 1 1 f0 0 ' 1Q7°30' ] 09*30' S an Rafael Swell / La Sal M tns S tu d y A rea S an M ig u el £■ N ee d le M tn s 37°30 La P lata - M tns Lake Pow ell San Utah C olorado Arizona N ew Mexico E x ten t o f Basin 25 Km 36°30' Figure 3. Major regional structures associated with the Paradox Basin. Adapted from Nuccio and Condon (1996). The study area pertinent to this thesis is delineated on the north end o f the Monument Upwarp. Today some authors recognize this unit as the Paradox Formation (Molenaar, 1981), whereas other authors have differentiated it as the Paradox Member of the Hermosa Formation (Lewis and Campbell, 1965; Figure 4). 9 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Eroded sediments originating from the Uncompahgre Precambrian basement contributed to formation of the alternating marine carbonates and arkosic redbeds of the strati graphically higher Permian Rico Formation (Lewis and Campbell, 1965; Lower Cutler Formation in Molenaar, 1981) and the Cedar Mesa Sandstone of the Cutler Formation (Lewis and Campbell, 1965; Molenaar, 1981). The total thickness of sediments deposited in the basin during this period ranges from 2,000 feet in the west to nearly 12,000 feet in the north (Nuccio and Condon, 1996). In the immediate region o f the Canyonlands, basin subsidence was less significant, therefore resulting in a lesser Pennsylvanian and Permian sediment thickness of roughly 4,000 feet (Nuccio and Condon, 1996). Based on the investigation of Woodward-Clyde Consultants (1983), the thickness of the Paradox salts within the grabens area has been estimated to be approximately 300 m. These salts, which behave in a ductile manner under the weight of overlying sediments, are considered by many authors to have played a major role in the overall evolution of the grabens (Stromquist, 1976). 10 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Age Unit Name Permian Cedar Mesa Member (Cutler Formation) Cedar Mesa Sandstone (Cutler Group) Rico Formation lower Cutler beds Pennsylvanian Upper Hermosa Formation Honaker Trail Formation (Hermosa Group) Paradox Member (Hermosa Fm.) Paradox Formation (Hermosa Group) (Lewis & Cambell 1965) (Condon 1997) rrrp " f meters Figure 4. Generalized Canyonlands stratigraphy after Grosftls et al. (2002). During the Jurassic and Cretaceous, the Nevadan and Sevier orogenies west of the Paradox Basin produced uplifted highlands that discharged large volumes of sediment onto the Colorado Plateau. The last sediments to be deposited of marine origin are Cretaceous in age, thereby constraining the general elevation of the Plateau during this time to sea level (Rigby, 1977). While stratigraphic profiles around the Paradox Basin can be correlated to define a history of Middle Mesozoic through Cenozoic deposition, much o f this rock is missing from the Canyonlands field area, particularly in the grabens region. Cenozoic erosion and possibly Middle 11 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Triassic non-deposition led to the absence of some these older units, not only within the Canyonlands, but also in other areas in southwestern Utah (Stewart et al., 1972). The Cretaceous through Early Tertiary saw the creation of the central and southern Rocky Mountains and the Colorado Plateau by way of the Laramide Orogeny (Nuccio and Condon, 1996). This orogenic event caused relatively gentle deformation throughout the Plateau, resulting in the creation of several monoclines and normal faults (Rigby, 1977). The Monument Uplift was one such structure that was produced during this time (Figure 3). Once horizontal Pennsylvanian and Permian sediments situated on the north end of this north-south trending upwarp were effectively tilted to the northwest (Rigby, 1977; Nuccio and Condon, 1996). As a result of the new Rocky Mountain highland to the east, sediment was once again shed onto the Plateau, consequently covering many of the aforementioned Laramide derived structures. Many of these early Cenozoic sedimentary units are not evident in the immediate region of the grabens, presumably due to Tertiary overland flow and erosion by the adjacent Colorado and Green Rivers during late Cenozoic plateau uplift (Nuccio and Condon, 1996). Oligocene volcanic activity throughout the region resulted in basaltic laccoliths that formed many of the mountain ranges surrounding the Paradox Basin (Figure 3; Nuccio and Condon, 1996; Rigby, 1977). Holocene deformation, related primarily to overburden erosion and the consequential diaprism of the Paradox salts, has resulted in the formation of several salt-cored anticlines (Huntoon, 1982). The Meander Anticline, which trends 12 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. along Cataract Canyon, and the Home Springs Anticline, located immediately south of the grabens, are both unloading structures related to the diapiric behavior of the Paradox salts (Figure 1; Huntoon, 1982). 2.2. Previous Investigations Many researchers have used the grabens as a natural laboratory to study analogous less-exposed and more-complicated extensional systems. It has been theorized that faulting at Canyonlands began when the Colorado River cut through the sedimentary section to the depth of the Paradox evaporites. This process released the restaining buttress on the western margin of the Canyonlands region, thereby permitting the overlying sedimentary section to slide into Cataract Canyon along the 4° NW dip of the northern margin o f the Monument Uplift (Baker, 1933; Lewis & Campbell, 1965; McGill and Stromquist, 1979; Huntoon, 1982). The 450-meter-thick sedimentary overburden has undergone brittle deformation, accommodated by normal faulting and graben formation above the ductily deforming Paradox Formation. The faults are generally steep (greater than 70° dip) and laterally segmented (Trudgiil & Cartwright, 1994). Fault segments range in length from hundreds of meters to several kilometers. They show tapered slip distributions (Cartwright & Mansfield, 1998) and a variety of linkage structures (Trudgiil & Cartwright, 1994). The grabens are commonly asymmetrical (Schultz & Moore, 13 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. it. Figure 5. North-facing view of Colorado River and Green River confluence. The downcutting o f this river system has effectively unbuttressed the Pennsylvanian and Permian sediments, allowing them to move northwestward above the ductile Paradox salt substrate. Height of cliffs above the rivers is approximately 1000 ft. (305 m). Photo by Marsic, 2002. 1996), and they have depths ranging from a few meters to greater than 100 m (Trudgill & Cartwright, 1994). The faults commonly display a component of Assuring or dilation in addition to dip slip (McGill & Stromquist, 1979). Prior research has suggested that within the grabens there is an eastward decrease in graben age due to 1) a general eastward decrease in graben size and complexity and 2) an eastward increase in bounding fault asymmetry (Stromquist, 1976). The total duration of deformation has been estimated utilizing two methods: Biggar et ah (1981) estimated long-term incision rates of the Colorado River through the sedimentary overburden. Utilizing a minimum estimated rate of incision of 0.17 meters per 1000 years suggests an initiation of graben development at approximately 590 ka. This age estimate is foreseeably an overestimate because o f the higher 14 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. incision rates at Cataract Canyon due to 1) the combined erosive strength of both the Colorado and Green Rivers (Figure 5), and 2) the formation of diapiric anticlines caused by the unroofing of salt at Cataract Canyon (Huntoon, 1982). In a related study, Biggar (1987) and Btggar and Adams (1987) used thermal luminescence dating o f youthful graben sediments located roughly a quarter of the distance from the Colorado River to the eastern margin of the graben system. These Quaternary sediments have been dated at 65,370 ± 4,530 years (Biggar and Adams, 1987). Based on required graben formation prior to the deposition o f sediment, Biggar (1987) suggests a minimum age for graben initiation at 85 ka. 15 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 6. Orthorectified Landsat-5 Thematic Mapper image o f the Needles District of the Canyonlands. Three spectral bands are represented. Mid-infrared is displayed as red, near- infrared is displayed as green, and visible green is displayed as blue. The pixel resolution is 28.5 m. Fault nomenclature from Stromquist, 1976. URLC = Upper Red Lake Canyon, UC = Unnamed Canyon, (photo from NASA, 2003). While no contemporary deformation measurements have been previously published, workers have estimated rates assuming uniform deformation in time and space. Deformation within the region is of an extensional nature and as such has been assumed to be predominantly orthogonal to the graben trend except in 16 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. "accommodation zones" where interaction between offset rifting segments perturbs the stress field (Moore and Schultz, 1999). Combining the aforementioned dates of estimated graben initiation and an estimation of 25% extension across the northern section o f the grabens (Moore and Schultz, 1999; Figure 7), a uniform extension rate of between 2 mm/yr (using a river incision rate derived age) and 2 cm/yr (using a thermal luminescence derived age; Moore and Schultz, 1999) has been determined. This range of rates assumes that extension rates are temporally and spatially uniform across the Moore and Schultz (1999) balanced cross-section profile. Modeling efforts by Schultz-Ela and Walsh (2002) along a similar profile also estimate rates w ithin these bounds, yet they incorporate an evolutionary progression of graben formation from the west to the east. In their evolutionary model, the grabens near Cataract Canyon formed first (Stromquist, 1976; Moore and Schultz, 1999) and regressed from major to minor contributors to the total extension rate as eastern grabens begin to develop (Schultz-Ela and Walsh, 2002). As the system evolved, an eastward acceleration in extensional rate for each graben was postulated, yet the maximum rate of deformation of each respective graben decreased eastward (Schultz-Ela and Walsh, 2002). It should be noted that field and modeling-based rate estimates are unique to the region immediately adjacent to the Moore and Schultz (1999) profile and do not necessarily represent deformation in surrounding regions. 17 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Colorado River/ Red Lake Cyclone Devil's Devil's elevation (m) Cataract Canyon Canyon Canyon Lane Pocket / v 1500J , / 1000- i -----------------------: --------------------------------------------------------------- i i I Q Q Q m | Figure 7. Generalized cross section profile across the northern portion of the grabens. The profile extends from the west (Cataract Canyon) to the east (Devil’s Pocket). Modified from Moore and Schultz, 1999. A ll workers to date agree that the Paradox salt has played a critical role in the evolution of the grabens system (Baker, 1933, Huntoon, 1982, Moore and Schultz, 1999, W alsh and Schultz-Ela, 2003). Current prevailing opinion claims that the down-dip extension of sedimentary strata occurs above a ductile Paradox evaporate unit (Baker, 1933, McGill and Stromquist, 1974; Stromquist, 1976). Evidence of Paradox salt flow is in the form of the numerous salt-cored diapirs that exist throughout the Paradox Basin (Huntoon, 1982; Nuccio and Condon, 1996). These include differential unloading structures, most notably the Meander Anticline which winds along the base of Cataract Canyon, through which the Colorado River flows (Figure 1; Huntoon, 1982). Comparable anticlines occur along deep canyons tributaries adjacent to Cataract Canyon (Huntoon, 1982). Halite and other evaporites in the Paradox salts deform due to the relatively shallow brittle-ductile transition experienced in both dry and wet conditions (Hansen and Carter, 1984; Weijermars et al., 1993). For dry salt, this transition occurs at depths between 10 m and 130 m by means of dislocation creep assuming a strain rate of 10"1 4 s'1 and a geothermal 18 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. gradient o f 30 K/km. The presence of brine, fresh water, or increased temperatures has the effect of increasing the ductility of salt and subsequently shallowing the ductile transition (Gussowi, 1968). Wet salt flows by means of dissolution creep and experiences a brittle-ductile transition at approximately 2-10 m (Hansen and Carter, 1984; W eijermars et ah, 1993). The aforementioned transitions also assume a differential stress of between 1 Mpa and 2 Mpa. Assuming that the weight of the overburden is the key driving force of deformation, this stress can be calculated using cjxx ~ pgh. Using an overburden layer density of 2400 kg/m3 (Walsh and Schultz-Ela, 2003) and an average overburden thickness of 450 m, this stress is found to be approximately 10.5 Mpa. This stress far exceeds the requirements for ductile salt flow (Hansen and Carter, 1984; Weijermars et al., 1993). Several hypotheses of salt-related deformation have been published, included salt dissolution and subsequent graben collapse (Stokes, 1948; Baars and Mlenaar, 1971; Hite, 1982), salt/overburden detachment and simple down-dip gravity sliding (Huntoon, 1982). Both analogue (McGill and Stromquist, 1979; Childs et al., 1993) and computer finite element model experiments (Schultz-Ela and Walsh, 2002) have been created in attempts to reproduce the salt-related extensional and diapiric geomorphology of the grabens. Recent computer modeling, in collaboration with prior field observations, concludes that deformation likely occurred due to a combination o f gravitational forces and regulated salt flow (Schultz-Ela and Walsh, 2002; Walsh and Schultz-Ela, 2003). In this sense, salt drives extension, yet 19 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. prevents (or regulates) runaway deformation that one might expect along a frictionless surface once the overburden failure criterion is reached (Figure 8; Schultz-Ela and Walsh, 2002). The result of salt regulation is non-uniform deformation in both a temporal and spatial sense (Schultz-Ela and Walsh, 2002; Walsh and Schultz-Ela, 2003). Based on this model, rates of extension can be expected to be relatively high east of Cataract Canyon where salt flow drives deformation, and relatively slower near the canyon where salt restricts deformation. Both dipping and near-horizontal finite element models were used by Schultz-Ela and W alsh (2002) to illustrate this behavior (Figure 8). Furthermore, a downward flexure east of Cataract Canyon and an upward flexure at Cataract Canyon are expected as a result o f gravity driven overburden subsidence and consequential salt expulsion at Meander Anticline, respectively (Walsh and Schultz-Ela, 2003). While estimates of vertical deformation rates have not been made in earlier literature, Walsh and Schultz-Ela (2003) estimate approximately 40-60 meters of topographic subsidence west of Red Lake Canyon, with decreasing subsidence to the east. This observation suggests subsidence and salt expulsion near the older grabens in the west is higher than what one might find near the more recently formed grabens in the eastern portions of the field area (Walsh and Schultz-Ela, 2003). The work of Walsh and Schultz-Ela (2003) additionally noted the subsidence of horst blocks across the grabens, an observation that hinders support for a single surface salt decollement model. In such a model, one would expect stratigraphic layers to remain relatively planar (Walsh and Schultz-Ela, 2003). 20 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5 km (a) Driving flow (c) S io p e m odel P p a . S ^ S s i L (d) H o i> o ta! Tiedei _ , I S R esistin g flow sssbi vrij V \ \ \ V*W \\V :V W : Figure 8. Cross-section from Schultz-Ela and Walsh (2002). Finite element derived passive material deformation lines of overburden (dark) and the salt (light) for both dipping (c) and near-horizontal models (d). As a reference, deformation lines in a driving flow scenario (a) depict “pipe” like flow with a maximum flow rate within the salt and slower rates near the salt/overburden interface. Deformation lines in a resisting flow scenario (b) depicts a maximum rate near the salt/overburden interface. 21 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Field based observations have suggested that deformation across the grabens is continuing today. Geologists have observed modem Assuring (Trudgill and Cartwright, 1994; Biggar and Adams, 1987, Schultz and Moore, 1996), Quaternary sediment deformation (Oviatt, 1988), as well as topple failures and dilating cracks along several graben faces (Adhikary et al., 1997; Biggar and Adams, 1987; Ely, 1987). Modem Assuring at Devil’s Lane (Biggar and Adams, 1987; Schultz and Moore, 1996) was recently observed in the field by workers from a joint USC and Western Washington research group (2002). Measurements made at Devil’s Lane in 2001 and 2002 by the same research group observed extensional growth on the order of several centimeters. The group additionally observed recent bounding fault Assuring and sinkhole formation at Cow Canyon. Interestingly, because no seismicity has been reported in the grabens field area in recent times (Wond et al., 1987; Wong et ah, 1996), aseismic creep along some faults has been inferred (Huntoon, 1982; Lewis and Campbell, 1965; Moore and Schultz, 1999). 22 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without permission. M H i ■ H I —■B B B il ®B1 S M S B P w r ^ .. < c ) (b) Figure 9. (a) East-facing panoramic view of Devil’s Lane . (b) North facing view of the actively deforming east graben wall, (c) South facing view o f the actively deforming east graben wall. Recent deformation is demoted as the lineage on the left side o f (c). Photos by Marsic, 2002. U J 3. D A T A SO U R C E S: A N A L Y S IS A N D R E SU L T S Deformation data for this project were generated from two types of spacebome geodesy. The bulk of the work in this thesis falls under the category of Interferometric Synthetic Aperture Radar (InSAR). Campaign Global Position System (GPS) data, collected by geologists at the University of Southern California and W estern Washington is additionally Included. Together, these data sets have allowed us to observe deformation on similar spatial scales using two unique views. This allows us to cross check observations from both sources thereby mitigating any anticipated sources of error. 3.1. The Global Positioning System (GPS) Initially developed by the United States Department of Defense, the Global Positioning System (GPS) is a satellite-based radio-navigation system. The original concept of the system was that it be used for navigation and positioning purposes by both the military and civilian population. In addition to this achievement, GPS has additionally become the primary geodetic tool for studying a wide range of geophysical phenomena Including but not limited to volcanic and tectonic derived deformation, mass wasting, glacial flow, and temporal and spatial variations of both atmosphere and sea level (Segall and Davis, 1997). The high accuracy, simplicity 24 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. and speed of the GPS system have allowed a revolution to take place within the geodetic community. Where the aforementioned deformation measurements were once collected using laborious methods such as trilateration and spirit leveling, GPS allows small groups with relatively small budgets to collect and assemble data more efficiently and with greater spatial coverage (Segal! and Davis, 1997). The current GPS satellite constellation consists of 24 L-band communication satellites orbiting the earth at an elevation of 20,200 km. Satellites are equally spaced in one of six circular orbital planes (FAA, 2003). Each GPS satellite make one revolution around the earth every 12 W V : Y / \ \ i . 1 11 *A ' / W i a V i hours at an inclination of 55° relative to the earth’s equator (FAA, 2003). Users of the GPS system are able to obtain accurate and precise position, velocity and time measurements anywhere in the world and in any weather condition. A minimum of four satellites is required to Figure 10. The GPS satellite constellation . . . „ „ „ provides accurate and precise position, velocity in ^P S receivers view at any one and time information to users worldwide (FAA, 2003). time to obtain position (latitude, longitude and altitude) and time information. The excellent sky view and lack of obstructing features (topographic or cultural) within the Canyonlands permits the observation of between 6 to 8 satellites at any one time. Signals from the satellites 25 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. are carried in two codes, a civilian code (Course Acquisition Code, or C/A-code) and a m ilitary code (Precise Code, or P-Code). For instantaneous position observations, the C/A code is accurate (2a error) to roughly 10 meters (Strang and Borre, 1997; Table 1). The P-code, which is more accurate, is encrypted by the U.S. Department of Defense and has an accuracy (2a error) of roughly 5 meters (Strang and Borre, 1997; Table 1). S tandard Error Source Single Frequency Double Frequency Ephemeris Data 2 m 2 m Satellite Clock 2 m 2 m Ionosphere 4 m 0.5 - 1 m Troposphere 0.5 - 1 m 0.5 - 1 m Multipath 0 - 2 m 0 - 2 m User Equivalent Range Error (rms) 5 m 2 - 4 m Its Error 10 m 4 - 8 m Table 1. Standard Errors with Instantaneous GPS (from Strang and Poire, 1997). Single frequency (LI) errors account for civilian receivers that only utilize the C/A code. Double frequency (LI and L2) errors account for receivers that utilize both the C/A code and P code. JPL based ephemeris and dock information, combined with differential processing, reduces most of these errors. The accuracy of GPS results is not always easy to quantify due to the possible existence of several errors. Campaign GPS specifically encounters errors due to multipath interference, antenna centering errors, and antenna height measurement errors (Strang and Borre, 1997; Table 1). These errors sources can be 26 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. dealt w ith by carefully setting up receivers and by conducting long observation sessions. Observing stations over several hours can effectively average out m ultipath errors. Satellite orbit trajectory (ephemeris) data and satellite clock data error, w hich are common to both campaign and permanent station GPS, can be reduced by obtaining accurate data from NASA/JPL. Atmospheric (ionospheric and tropospheric) variability can be estimated and errors reduced with GIPSY-OASIS during processing. When simultaneously observing multiple stations within a local reference frame, also known as differential GPS, 2a errors can in effect be reduced to 2-3 mm in the horizontal direction and 1 cm in the vertical direction. Campaign differential GPS therefore provides much more accurate results than instantaneous positioning. 3.1.1. GPS Results Over a period of three years (2000 - 2002), geologists from the University of Southern California (USC) and Western Washington University (WWU) conducted a series of differential GPS survey campaigns. In 2000, research members installed a total of seven (7) GPS benchmarks within the Canyonlands grabens district (Table 2, Figure 11). All stations were marked with 2.5” brass monuments secured with epoxy into stable rock. Vehicle and helicopter access to many parts of the grabens region is prohibited, hence requiring that most sites be approached by foot. Sites were chosen 27 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. based o n their spatial distribution and apparent rock stability. Due to the extensive jointing, faulting and block toppling that exists throughout the field area, the GPS results m ay be affected by local rock movements. A total of four campaigns took place during the summer months of 2000, 2001 and 2002 (Table 3). All surveys utilized the Ashtech GPS Z-12 receiver and choke ring antenna. Several sites during the 2002 campaign utilized the more compact Trimble 5700 GPS receiver and Zephyr antenna. Data was collected for at least one full day at each station. All data was processed at USC using the National Aeronautics and Space Administration (NASA) Jet Propulsion Laboratory (JPL) GIPSY-OASI8 differential GPS data analysis program. Results from three years of Canyonlands GPS campaign surveys are presented in Table 4. Horizontal velocity vectors (cm/yr) and error ellipses are presented in Figure 11. General GPS Station Location Inform ation WEI1 Survey Base Station, Eastern grabens Region POOL Beef Basin DEEP Mid Deep Canyon, Eastern Horst DEVL Mid Devil’s Lane, Eastern Horst PLNQ Mid Cow Canyon, East Horst CYCL Southern Cyclone Canyon at Southern Ramp COLR East o f Cataract Canyon Table 2. Canyonlands GPS campaign stations and general location information. 28 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Y ear Survey Month Notes 2000 May All sites installed. Only C O LR not observed 2001 May Only COLR and POOL observed 2001 September All sites observed except COLR 2002 September All sites observed except POOL Table 3. Canyonlands campaign GPS surveys, 2000 - 2002. East (cm /yr) 2a Error (cm ) North (cm /yr) 2e Error (cm ) Horizonta 1 (cm /y) 2a Error (cm ) Vertical (cm /y) 2o Error (cm ) W EI1 0.00 ±0.00 0.00 ±0.00 0.00 ±0.00 0.00 ±0.00 POOL 0.19 ±0.38 -0.39 ±0.46 0.43 ±0.60 -1.23 ± 1.66 D EEP -0.30 ±0.14 0.38 ±0.16 0.48 ±0.22 0.12 ±0.58 DEVL -0.20 ±0.12 -0.09 ± 0.12 0.21 ±0.16 0.70 ±0.44 PLNQ -0.22 ±0.12 0.20 ±0.12 0.30 ±0.16 0.13 ±0.44 CY CL -0.32 ±0.18 -0.13 ±0.20 0.34 ±0.26 -0.25 ±0.72 C O L R -0.09 ±0.22 0.22 ±0.24 0.23 ±0.32 3.47 ±0.88 Table 4. GPS solutions for Canyonlands campaign stations. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. POOL 2-sigma error -110 0 -109 55' Figure 11. GPS derived horizontal displacement vectors (2000-2002). Blue vector without error ellipse is equal to 1 cm/yr of displacement. Deformation is relative to the GPS base station location (WEI1) 3.2. Interferometric Synthetic Aperture Radar Interferometric synthetic aperture radar (InSAR) is a relatively new geodetic technique that can be used to obtain high spatial resolution surface deformation maps and digital elevations models (Biirgmann et ah, 2000; Rosen et ah, 2000; Hanssen, 30 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2001). In a period of just over thirty years, radar interferometry has evolved from a theoretical concept to a viable geodetic technique with unique promise for the physical sciences. Today, InSAR is used worldwide for a variety o f earth system observation tasks, including, but not limited to, tectonic deformation, volcanic inflation and deflation, glacial migration, and mass wasting (Rosen et ah, 2000; Biirgmann et al., 2000). The synthetic aperture radar (SAR) images that are used in this project were taken by the European Space Agency (ESA) European Remote Sensing platforms (ERS-1 and ERS-2). Initially launched in 1992, ERS-1 became a highly accomplished earth observational tool with its array o f varied wavelength sensors (ESA, 2003). This success prompted the subsequent launch of ERS-2 in 1995. Together, these satellites have been part of the spacebome imaging boom In the 1990’s and have consequently fostered the evolution of InSAR into the technology that it is today. InSAR utilizes the active ERS C-band microwave SAR sensor, operating at a wavelength of 5.66 cm. Images taken at this wavelength are capable of penetrating cloud cover, making them useful in all weather and lighting conditions. The SAR onboard the ERS-1 &2 satellites creates two-dimensional complex images along a right-looking line of sight. This view has an incidence angle of 23° from vertical at the center of the image (Figure 12). The curvature of the earth’s surface causes this angle to vary between -20° and 26° as one moves laterally away from the center of the image (ESA, 2003). 31 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ER S SAR images contain two distinct bands of information. The first is an am plitude band that contains information on target reflectivity. The second is a phase band that encodes a term proportional to the target range (Biirgmann et al., 2000; Tsay and Lu, 2001). While the ultimate resolution of a SAR image is impressive (20 m across track, or range, and 4 m along-track, or azimuth) the true power of this geodetic technique is fully realized when the considering spatial coverage. The processing of synthetic aperture data allows the formation of a roughly 100 km wide by 100 km image (Hanssen, 2001; Figure 12). To date, no other geodetic technique rivals this robust spatial capability (Hanssen, 2001). It is the fact that InSAR uses the phase of contributing SAR images that allows the determination of surface topography as well as sub-centimeter surface deformation. If two SAR images can be aligned to within sub-pixel spacing, relative information about the change in phase for each pixel can be extracted, thus producing an interferogram. Differences in satellite locations will yield two unique 32 Figure 12. Illustration o f ERS flight path. Satellite has a right looking range direction swath o f approximately 100 km. Redrawn from ESA website illustration (ESA, 2003). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. viewing angles of the ground, thus yielding an interferogram containing phase change due to surface deformation and topography. If the geometry of the two satellites can be determined precisely, relative elevation information for the image can be extracted. This process can be used to create digital elevation models (DEM) with the required condition that the temporal span between the two SAR images is short. This serves to minimize the potential of surface deformation occurring between the contributing SAR images. The first applications of this process did not involve terrestrial observations, but rather of observations of Venus (Rogers and Ingalls, 1969) and soon thereafter, the earth’s moon (Zisk, 1972). If there is surface deformation between the time span of the two images, the relative change in phase range will then contain both elevation and deformation information. In a process known as differential interferometry, or D-InSAR (Gabriel et al., 1989; Tsay and Lu, 2001), the topographic portion o f the observed phase change is removed from the interferogram, leaving behind deformation information. This process was originally developed by Gabriel et al (1989) to measure soil swelling caused by irrigation in the Imperial Valley of California. D-InSAR can be conducted by way of either a two-pass approach (using two SAR images for deformation and an external DEM; Massonnet et al., 1993), a three-pass approach (using two SAR images for deformation and one additional SAR image common to one of the other two for topography; Gabriel, et al., 1989; Zebker et a l, 1994; Rosen et al., 2000; Biirgmann et al., 2000) or a four-pass approach (using two SAR images 33 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. for deformation and an additional two SAR images for topography; Rosen et al., 2000). Today, each o f these D-InSAR processes is used by a wide variety of scientists in many disciplines to observe spatial and temporal surface deformation. All displacements are scalars representing the projection of the three displacement components (Ax, Ay and Az) onto the radar line of sight. Users must be careful as to how they interpret line of sight range changes. Often it is helpful to use interferograms from both ascending (south to north trajectory) and descending (north to south trajectory) tracks to give a better sense of the displacement field. Even then, a prior understanding of a region’s deformation field must exist to allow a full three dimensional visualization of the deformation field (Fialko et al., 2001; Hanssen, 2001). Users must also be careful to not interpret a variety of errors that can and do exist in processed InSAR images as surface deformation. When used in concert with other geodetic techniques, such as GPS or tiltmeters, many of these errors (atmospheric, topographic and orbital) can be mitigated (Hanssen, 2001). GPS is used in this thesis to assist in the computation of the three displacement components (decomposition) of the InSAR images and to compare with final decomposition results. 34 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3.2.1. InSAR Data Processing Procedure Spacebome radar imagery is particularly apt for the grabens of the Canyonlands due to an estimated rate of deformation agreeable with InSAR technology (Massonnet & Feigl, 1998) and the availability of ascending and descending SAR data. Assuming a rate of horizontal extension between 2 mm/yr and 2 cm/yr, InSAR should expect to see between 0.5 and 3.5 radians of slant range phase change per year. Furthermore, the region’s desert terrain, which consists of relatively little topographic relief, snow, vegetation, or seasonal vegetation variations, increases the probability of interferometric coherence (Massonnet and Feigl, 1998). Vegetation throughout the field area is comprised primarily of cryptobiotic soil and native grasses (Ehleringer, 2003) that in general have a density below the ERS C-band threshold for vegetative microwave interference of 0.5 kg/m2 (Ulaby et al., 1996). Using both ascending and descending ERS-1 and ERS-2 SAR data obtained from Eurimage in Italy, thirteen (13) SAR interferograms have been successfully produced (Table 5; Figure 13). The footprint of each satellite track is illustrated in Figure 13. All interferograms were processed using a two-pass approach with the Repeat Orbit Interferometry Package (ROIJPac), written and distributed by NASA Jet Propulsion Laboratory and Caltech. Ten (10) of the interferograms depict 35 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. deform ation over a time span of between 21 and 79 months. To observe deformation, the two-pass approach requires the use of an external elevation data set to rem ove the topographic signal from each image. For this purpose we used United States Geological Survey (USGS) 7.5-minute quad OEMs. Each DEM has 30-meter pixel spacing and covers a total area of approximately 11 km by 14 km. Because this region o f coverage is not adequate for our field area, mosaicing an array of twelve (12) adjacent DEMs became necessary. The final DEM mosaic was then converted from a native USGS DEM format into a double precision binary format so as to be compatible with R O IPac. A discussion of this process is presented in Appendix A2. 36 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Interferogram L ab el Date 1 Date 2 Track/ Scene T rack Direction Elapsed Time (days) Elapsed Time (years) 920726-990120 920726 990120 227/2835 2369 6.48 921124-961018 921124 961018 456/2835 1424 3.90 930622-950824 930622 950824 456/2835 M ss 793 2.17 930622-970516 930622 970516 456/2835 1424 3.90 930622-961227 930622 961227 456/2835 1 1284 3.51 930622-990312 930622 990312 456/2835 o 2089 5.72 950824-970516 950824 970516 456/2835 631 1.73 950824-950825 950824 950825 456/2835 3 .1 : 0.00:;.. 930512-960210 930512 960210 363/756 1004 2.74 930721-960209 930721 960209 363/756 •S 962 2.63 930721-960210 930721 960210 363/756 T3 1 963 2.63 930512-930721 930512 930721 363/756 < : 70 0.19 960209-960210 960209 960210 : 363/756 / ;/i , 0.00 .. . Table 5. Successfully produced interferograms using the two-pass approach. Interferograms highlighted in gray are short time span interferograms used for topographic residual analysis. 37 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 38 40‘ 38 20’ Study Area 38 00' 10 km 37 40' 249 20’ 249 40' 250 00’ 250 20’ 250 40’ 251 00' Figure 13. SAR image footprint o f both ascending and descending tracks. Track 363 is ascending (south to north travel). Tracks 227 and 456 are both descending (north to south travel). Grabens study area is highlighted in the center of the image. To resolve how effectively ROIJPac removes topography during processing, three (3) additional interferograms were constructed from pairs of tandem SAR images. These image pairs span a short time interval (1 day to 1 month), thus permitting an assumption that no deformation is present in the interferogram. Once the topographic signature is removed from the tandem pair interferograms, they can be used to quantifying the amount of topographic residual one might expect to find in a longer time span interferogram. This also assumes that any residual is not of an 38 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. atmospheric or orbital nature. A more in depth discussion of this error source and is presented in the following sections. A ll final interferograms are geocoded by ROI_Pac in a Universal Transverse Mercator projection (UTM) according to the World Geodetic System 1984 fixed global reference frame (WGS-84) ellipsoid datum. Analysis was conducted using both the Interactive Data Language (IDL) driven Research Systems, Inc. Environment for Visualizing Images (RSI-ENVI) and the Math Works, Inc. Matrix Laboratory Program (MATLAB). Final images in this report are presented in a Latitude-Longitude coordinate system. 3.2.2. Topographic Errors For differential interferograms, it is advantageous to use a SAR pair in which the perpendicular baseline (fix, the component of the separation vector between the two satellite locations perpendicular to the ERS line of sight) is small enough so that topographic errors do not overwhelm the observed signal. To quantify this, a term known as the height of ambiguity (ha) is used. 3 9 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. h a = (X p sin 0) / (2 Bj_) ~ 9122.5 m2 / Bjl, (1) h a = height of ambiguity (meters) X = radar wavelength, 5.66 cm for ERS C-band p = range of the master scene, 825 km 0 = look angle, using 23° for center of ERS scene B-l = perpendicular baseline (meters) This term is a measure of the change in height required to create a 2% phase change in the interferogram. A 2n phase change is equal to one half a wavelength of slant range displacement, or 28 mm. An observed 2iz cycle difference between two images is the culmination of an outgoing signal and a reflected signal, hence one half of a wavelength. The only topographic error remaining at the end of the two-pass procedure is that of the USGS 30-meter posting DEMs that were used. By comparing the calculated height of ambiguity for each interferogram to a 2a standard deviation DEM error we can estimate the maximum DEM noise we might observe. Although the vertical RMS error of the USGS DEMs is 7 m, a conservative 95% confidence of 30 m was chosen to represent the 2a DEM error for the height of ambiguity analysis. (2a DEM error / ha ) * QJ2) = 2a DEM noise [in m m ], (2) ha = height of ambiguity (meters) I = radar wavelength, 5.66 cm (use 56.6 mm in calculation) for ERS C-band 2a DEM error = 30 m 40 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Depending on the perpendicular baseline between contributing SAR images, the interferograms may have between 0.1 and 2.5 mm/yr of topographic noise (Table 6). These values should be considered to be a worst-case scenario as the height of ambiguity calculation is using the 2a DEM error of 30 m. An example of this is seen in the tandem pair interferograms, where the signal to DEM noise ratio is less than one (Table 6). The maximum signals obtained from the majority of these interferograms are significantly higher than the 2a DEM noise. As shown in Table 6, the maximum interferogram signal to noise ratio (SNR) is significantly larger than one (1). Topographic residuals from DEM error can be additionally evaluated by observing the tandem pair interferogram signals relative to the calculated 2a DEM error. The low signal to noise ratio (~ 1.5) of two of the tandem pair interferograms (Figure 14) suggests that the topographic residual is well approximated by the calculated 2a DEM error. The one tandem pair that has the higher SNR (930512 - 930721) has an average image signal of less than 5 mm. Using this value instead of the maximum range change value for the interferogram brings the signal to noise ratio down below the SNR of all other deformation interferograms (~2.5). The large signal in this image is unique and could be due to an isolated atmospheric anomaly, rapid deformation event (e.g. block toppling), or a phase unwrapping error. 41 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Date 2 Track Direction A Perpendicular Baseline (m) Height of Ambiguity (m) 2 a D E M Noise (mm) Possible Annual DEM noise (mm/yr) M ax Image Signal (mm) Signal / D E M Noise — ... .... ...... 920726 990120 © ft 0 5 n 6 e ra -53 -172 5 0.8 70 14 921124 961018 +67 + 136 6 1.5 30 5 930622 950824 +31 +294 2.5 3.2 35 14 930622 970516 +56 +162 5 1.3 16 3.2 930622 961227 -7 -1195 0.5 0.1 20 40 930622 990312 +15 +608 1.5 0.3 50 34 950824 970516 +40 +209 1 0.6 30 30 950824 950825 -81 (tandem . -102 8 'v : n/a ■ 4 2 w- 1-5 930512 960210 Ascending +52 +175 5 1.8 30 6 930721 960209 -40 -315 2.5 0.9 30 12 930721 960210 +74 +123 6.5 2.5 25 4 930512 930721 '+,-22 (landenf:: pair) . -414 n/a : 20 + .10 . 960209 960210 +117 ■ (tandem- pair) +780:; .10 n/a 15 1.5 Table 6. Tabular analysis o f topographic effect on interferometry. Perpendicular baselines give insight into the height o f ambiguity for each image. This can be used to determine the how topography will effect the phase observation of each interferogram. Since the look angle varies across the scene (eq. 1), height of ambiguity values are only valid for the scene center. DEM noise calculations in this table are left as absolute values. Note that possible annual DEM noise is not shown for the tandem pairs due to their high topographic sensitivity. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Z J CD ■ o — i o Q _ C o CD Q . ■ o CD C / ) ( /) CD O O ■ o 950824 ~ 950825 - Descending 3. CD CD ■ o - 5 O Q . C a o ■ o o CD Q . ■ o CD C / ) C / ) 00.- O u > 00 u > 00 ~11 o'O' ...........-109’ 55' 960209 - 960210- Ascending 00. o u » 0 0 0 0 . I u o a » D l"+ X & < 2 C D g s a . 930512 - 930721 - Asc U ) 0 0 . . U ) O S -110*0’ i3 1 -109° 55’ C M s s? 3 to CD g S' c ? . o 3 -no'0‘ -109'55' Figure 14. Tandem pair interferograms from ascending (2) and descending (1) tracks illustrating total slant range deformation (cm). Deformation is relative to the GPS base station location (WEI1 ;Figure 11) ■ t * . U J 3.2.3. Observed Atmospheric Effects Often the most significant source of error in differential interferometry is atmospheric noise (Biirgmann et ah, 2000; Hanssen, 2001). It has been shown that temporal and spatial atmospheric variations can account for significant percentages of interferometric phase change. Recent studies have shown that atmospheric anomalies could explain upwards of 10 cm of deformation error in differential interferometry (Goldstein, 1995; Zebker et ah, 1997). The cause of the atmospheric signals, as discussed by Hanssen (2001), are localized changes in refractive index due in large part to weather induced humidity variances in the troposphere. Fortunately, tropospheric errors do not always dominate a SAR image, yet they must be considered, especially when conducting sub-centimeter deformation mapping (Biirgmann et ah, 2000) as the signal to noise ratio is more susceptible to degradation. One process by which atmospheric noise can be evaluated is an analysis of multiple interferograms known as “pair-wise logic” or using linear combinations of images (Massonnet and Feigl, 1995; Hanssen, 2001). This process involves comparing two interferograms where one contributing SAR image is common to both o f the interferograms. In this way, the SAR image acts as a master in one interferogram and as a slave in the other. If a contributing image has no atmospheric error and the deformation rate across the scene is considered to be constant, no dramatic rate changes should be observed in any interferogram. On the other hand, if a contributing image does have an atmospheric error, the two 44 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. interferograms that this image contributed to should have an equal and opposite phase change as a result of the anomaly (Massonnet and Feigl, 1995). T o illustrate this process, we can look at a group of interferograms that have common images between them (Figure 15). In this case, 930622-950824 shows a large positive signal within the grabens while the 950824-970516 image shows a large negative signal across the same region. We can arguably rule out a significant atmospheric anomaly within the 930622 and 970516 images since deformation from their respective interferogram (930622-970516) is consistent with deformation observed in other interferograms (Figure 17). Based on this, we deduce that the signal difference between 930622-950824 and 950824-970516 is due to an atmospheric artifact in the common 950824 image. Results from the National Climatic Data Center (NCDC) archive (2003) for the “Island in the Sky” weather station (<5 km north of the grabens) showed that 930622 and 970516 were both dry days. In fact, there was no precipitation for several weeks prior to the images being collected. The 950824 image, on the other hand, had significant precipitation the day of the image (0.9 inches) as well as precipitation during the week prior to the image. 45 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without permission. 930622 - 950824 950824-970516 u > 8 U l u > 0 0 . o U i -110‘ O ' -109*55' 930622-970516 W\ * fz U i 00 0 0 3 3 3 o > D . iG m •S’ S' C f . I S £ Q J 3 * • * } • 3 0 a i n f D S ' QJ o 3 00,. o U ) 0 0 0 0 o" -110 O' i 09" 55' C f l § p * #930622-950824 i ■ 950824-970516 ! 930622-970510 5 3.00 - 1.00 -2 .0 0 5 10 0 15 Kilometers -110 O ' -109' 55' Figure 15. Descending interferograms used in pair-wise logic atmospheric test. Deformation (cm/yr) is relative to the GPS base station location (WEI1; Figure 11). Dark blue patches, corresponding to the darkest color on the color scale, represent regions of no correlation. Note the effect of atmosphere on the above interferograms, illustrated by the cross section profiles. 4 5 . 0\ A n additional test for atmospheric noise involves a standard deviation of range changes contained within a specified swath in the original interferogram. The swath th at was chosen is located west of the grabens where no deformation is believed to be occurring. Assuming topographic error is low and deformation Is not occurring, deviations in range, change for this swath should be a good first order approximation for atmospheric noise. 38 40' Test Swath' 38 20' Study Area 38 00' 10 km 37 40' 249 20' 249 40' 250 00' 250 20' 250 40' 251 00' Figure 16. Location o f 10 km by 25 km test swath. 47 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. o 8 3 a S' S' M T rack Direction © w 1 S' 1 ' I I 950825 921124 961018 0.25 930622 970516 0.32 930622 961227 1 0.33 930622 990312 a B 0.33 920726 990120 T O 0.34 950824 970516 0.41 930622 950824 0.52 960209; : : 96021 (T; p : 930512 ■ 930721; 0.21 930721 960209 e e 3 a 0.33 930512 960210 B * ( T Q 0.33 930721 960210 0.39 Table 7. Standard deviation calculations for test swath in processed interferograms. Interferometric pairs are sorted by track direction, from lowest to highest standard deviation. Tandem pair interferograms (highlighted) yield the lowest deviations. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A s shown in Table 7, nearly every interferogram has roughly the same standard deviation for a sampled 10 km by 25 km test swath. Exceptions found were: a) Tandem pairs: All three tandem pairs have lower standard deviations than m ost deformation interferograms, presumably due to a lack o f surface deformations that may have occurred over the given time span. b) Interferograms identified using pair-wise logic: The two interferograms that contain the 950824 image that were analyzed in the pair-wise logic exercise both have the largest standard deviations. Considering that atmospheric error is random in occurrence, results of this rough test estimate that atmospheric noise is not significant in the majority of interferograms, at least within the region of and on the spatial scale of the test swath. 3.2.4. Interferometric Stacking While pair-wise logic is a powerful technique for dealing with potential atmospheric artifacts, one of the most promising is a process known as interferogram stacking, or interferogram averaging. Stacking interferograms simply involves the 49 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. averaging of multiple similar interferograms in an attempt to remove potential or suspected atmospheric error. This process makes the assumptions that (1) deformation across an imaged region is constant, and (2) that atmospheric errors are random occurrences due to tropospheric weather patterns. With this assumption in mind, stacking independent images should yield an average deformation map. The more independent images that are included in the stacking process, the less significant atmospheric error should become. Unfortunately, there are drawbacks to the stacking procedure that need to be considered. The first is availability of independent pairs available for interferometric processing. In some regions, especially in the southern hemisphere, SAR data is not available in the quantities that it is in other areas of the world (ESA, 2003). This has to do primarily with how frequently data is downloaded from the ERS satellite, which often has to do with how close downloading stations are to the respective field area. The fewer interferograms that are included in the stacking procedure, the less effective the overall process will be in the removal of atmospheric artifacts. The second consideration with stacking is whether the noise from a scene is always positive or negative. To illustrate this point, consider two interferograms that use a common image. If this common image is the sole carrier of an atmospheric anomaly, the position of the scene will be of great importance. Using the scene as 50 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the m aster image (first, or primary position that the other image is “relative” to) in both interferograms, stacking will effectively result in the atmospheric error being added to the average twice. Likewise, if the erroneous image is in the slave position (second position, relative to the master), the error will be subtracted twice from the average. The solution in this situation is to either (1) only use this image once in your stack (either in the slave or master position), or (2) use the image in both a master and slave position in two separate interferograms. The first solution makes use o f the stacking philosophy that the noise will be smoothed out by the other independent interferograms. The second solution effectively removes the noise simply by adding it once to the stack in the master position, then subtracting it back in the slave position. Each interferogram contributing to the stack contains observed phase changes referenced to the location of the GPS base station, WEIL This location was chosen as it is assumed to be unaffected by the grabens extension due to it’s distance (>10 km) from the edge of the grabens field area. Stacks were formed dividing the sum of the contributing phase changes by the sum of the individual interferogram time spans (eq. 3; Appendix A4). In this way, the stack weighs equally both the time dependent surface deformation component and the non-time dependent atmospheric component of the contributing interferometric phase changes. 51 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (d<D/d/)av e rag e= X A<p / £ At, , (3) / = 1 i = 1 €> = interferometric phase change (radians) 1 . = number of interferograms in stack t = time (days) Regions of no-correlation have been “masked,” or removed from the stack. In this way, each un-masked pixel in the stack receives phase change values from all contributing interferograms, not just one or two. When assembled, this mask is an Image the same size of the contributing interferograms, consisting of ones and zeros for each pixel. A one represents the total correlation of every contributing interferogram for a particular pixel. A zero illustrates that one or more interferograms do not have correlation for a particular pixel. Multiplying the stack by the mask systematically assigns a value of zero (later changed to N/A) to all masked pixels. These values are assigned the color of dark blue in the subsequent images. 3.2.4.1. Descending Interferogram Stack We processed a total o f eight (8) descending Interferograms utilizing ten (10) SAR images (Table 8). Seven o f the eight interferograms have long enough temporal spans between contributing SAR images to be used for deformation studies. 52 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The one tandem pair interferogram is useful in determining the potential effect of topography on the deformation interferograms. All interferograms are shown in Figure 17 and Figure 18. Regions that contain no interferometric correlation are masked out in the color of the smallest color bar value (dark blue). The observed slant range phase change between contributing SAR images is depicted in centimeters. Using the aforementioned stacking strategy and discussion of foreseeable interferogram errors, a list of three usable interferograms was compiled (Table 9). These interferograms contain minimal observable atmospheric noise in addition to having short perpendicular baselines that allow for a relatively high signal to DEM-noise ratio. Four interferograms that were processed use a common master image (930622) that, if used in the stack, could foreseeably multiply any errors contained within the image. An observational comparison of interferograms that use this image in addition to the pair-wise logic was used to evaluate the potential promise of this image. Interferograms with this image that do not utilize a slave suspected of containing atmospheric errors are observed as exhibiting similar deformation patterns to other independent descending interferograms. By virtue of this, both the 930622-970516 and 930622-990312 images were included in the descending stack (Figure 19). The 930622-950824 interferogram was not chosen as the 950824 image contains a suspected atmospheric error (Section 4.2.3). The 930622-961227 was not chosen because it has a shorter temporal span than the remaining interferograms. 53 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Interferograms with longer time spans between images are advantageous due to the small annual deformations of the region. Based on this reasoning, both the 920726-990120 and the 921124-961018 interferograms were also included in the descending stack (Table 9). T o check the strength of this stack (Table 10; Stack #1), several other interferometric combinations were assembled and analyzed (Table 10). One combination (Stack #2) involved removing the 921124-961018 image from the stack. Another combination (Stack #3) retained the above interferogram, yet replaced the 930622-970516 image with the 930622-961227 image. Both o f these stacks yielded essentially the same result as stack #1, with no more than a 0.5mm/yr difference at any one point. Additionally, the perpendicular baseline for each o f the three stacks was calculated to estimate the amount how each would be affected by DEM error. This baseline, which is equal to the sum of the individual perpendicular baselines, reflects a relatively large height of ambiguity, or low sensitivity to DEM errors in all three combinations. While stack #3 has a lower SNR than stack #1, the 930622- 961227 image used in this stack has a slightly larger standard deviation (section 4.2.3) than the 930622-970516 image used in stack #1. Ultimately, these observations had little bearing on the final products since all three combinations produce roughly the same result. For this reason, the original stack formed, stack #1, was maintained as the final descending stack. 54 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Date 1 Date 2 Track/ Scene A Perpendicular Baseline (m) Height of Ambiguity (m) 2 o D E M Noise (nun) M ax Image Signal (mm) Signal / D E M Noise 920726 990120 227/2835 -53 -172 5 70 14 921124 961018 456/2835 +67 +136 6 30 5 930622 950824 456/2835 +31 +294 2.5 35 14 930622 970516 456/2835 +56 +162 5 16 3.2 930622 961227 456/2835 -7 -1195 0.5 20 40 930622 990312 456/2835 +15 +608 1.5 50 34 950824 970516 456/2835 +40 +209 1 30 30 -81 950824 950825 456/2835 (tandem -102 . 8 20 1.5 pair) Table 8. List o f eight processed descending track interferograms (8) based on ten (10) individual ERS SAR images. Maximum image signal is in mm, not mm/yr. Date 1 Date 2 A Perpendicular Baseline (m) Height of Ambiguity (m ) 2« DEM Noise (mm) Max Image Signal (mm) Signal / DEM Noise 920726 990120 -53 -172 5 70 14 921124 961018 +67 +136 6 30 5 930622 970516 +56 +162 5 16 3.2 930622 990312 +15 +608 1.5 50 34 Table 9. List of processed descending track interferograms used in descending interferogram stack. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Stack N um ber C ontributing Interferogram s in Stack £ A Perpendicular Baseline (m) H eight of Ambiguity (m) 2o DEM Noise (mm) ' 920726-990120 921124-961018 930622-970516 930622-990312 +85 +107 7 2 920726-990I20 930622-970516 930622-990312 +18 +506 1.5 3 920726-990120 921124-961018 930622-961127 930622-990312 +22 +414 2 Table 10. List of different descending interferogram stacks and their associated height o f ambiguity calculations. The perpendicular baseline o f a stack is the sum of the contributing perpendicular baselines. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without permission. 920726-990120 9211?/ < : ; -110" O ' -109'55' 930622 - 961227 m m 1 I O J D s - 33 & ? ! •«? 3 O f d. o D & O * U J 0 0 © q o ’ ‘ /V -11 O 'O ' -109'55' 930622-990312 o s.. 00. o ' & > D 3 3 f t ) r » S i i e u 5' 3 -110 0 ’ -109'55' -110*0' -109'55' Figure 17. Descending interferograms illustrating annual slant range deformation (cm/yr). Deformation is relative to the GPS base station location (WEI1; Figure 11). Dark blue patches, corresponding to the darkest color on the color scale, represent regions of no correlation. U l -4 Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without permission. 930622-950824 U » 0 0 o ’ -110 0‘ -109" 55* 930622-970516 w 00. u > 0 0 U 3 00 I I 950824-970516 i/i 5T 3 S’ 3 9 * - S' * -11 O'O' -109'55' I £ f i i 3 (H* 3 0 O i _ 3 I s 3 a > C f . o 3 - 110“ 01 -109° 551 Figure 18. Descending interferograms illustrating annual slant range deformation (cm/yr). Deformation is relative to the GPS base station location (WEI1; Figure 11). Dark blue patches, corresponding to the darkest color on the color scale, represent regions of no correlation. U \ DO Figure 19. Descending interferogram stack. Deformation is in the slant range (cm) per year. No orbital ramp was suspected; consequently no orbital ramp has been removed. Deformation is relative to the GPS base station location (WEI1; Figure 11). Dark blue patches, corresponding to the darkest color on the color scale, represent a mosaic o f no correlation regions from all contributing interferograms. Highest values of deformation are seen along the Colorado River (trending Northeast-Southwest and denoted by the high concentration of no-correlation pixels). Slant range deformation is positive along the Colorado River and consequently decreases laterally both east and west. Phase change continually decreases southeast 59 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. of the grabens. Positive phase changes for descending track images suggest lateral or vertical motion away from the satellite. Negative phase changes suggest lateral vertical towards the using lateral surface displacements toward and away from the radar sensor. Figure 20 illustrates this effect using lateral surface displacements toward and away from the sensor. Figure 20. Effect of deformation on right-looking radar line of sight. The first image in interferogram will have a path length represented by the observed phase (p) for a particular object on the ground (A). If A moves away from satellite (to right; A ” ), the path length will increase and observed phase will be p + 5p. If A moves toward satellite (to left; A ’), the path length will decrease and the observed phase will be p - dp. Considering that the descending satellite track direction is approximately SO W , negative range change values from aright looking sensor suggest ground motion is either west-northwest directed, vertical (uplift), or a combination of the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. two. Conversely, positive range change values suggest that ground motion is either east-southeast directed, vertical (subsidence), or a combination of the two. GPS data com bined with ascending track interferograms permit a more robust evaluation of the three-dimensional ground displacement vector. 3.2.4.2. Ascending Interferogram Stack Whereas the archive of available descending SAR scenes from Eurimage is roughly 70, the number of ascending SAR scenes is only 10. Because this archive is less complete, the number of possible interferometric pairs is significantly less for the ascending track. As a result, only five differential interferograms were processed from a set of four ascending track SAR images (Table 11). O f these interferograms, three have a long enough temporal span for the observation of deformation. The other two have short temporal spans, covering a period o f 1 day and 70 days. These interferograms are useful in determining the topographic residual from the DEM that may remain after processing (Section 4.2.2). All processed ascending interferograms are shown in Figure 21. Regions that contain no interferometric correlation are masked out in the color of the smallest colorbar value (dark blue; see Section 4.2.4.1). Observed slant range phase change between contributing SAR images is depicted in centimeters. 61 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A gain using the aforementioned stacking strategy and discussion of foreseeable interferogram errors, a list o f two usable interferograms was assembled (Table 12). The selection pool of ascending interferograms was not substantial, thus it seem ed prudent to create a stack that did not multiply any errors from contributing SAR images. Thus the one image that was left out (930721-960210) was done so because it utilized SAR scenes from the other two interferograms. The two remaining interferograms contain a minimum of observable atmospheric noise in addition to having perpendicular baselines that allow for a good signal to DEM noise ratios. A calculation of the perpendicular baseline of this stack reveals a large height of ambiguity, thus a low sensitivity to DEM noise (Table 13). Date 1 Date 2 Track/ Scene Perpendicul a r Baseline (m) Height of Ambiguity (in) 2 o DEM Noise (mm) M ax Image Signal (mm) Signal / D E M Noise 930512 960210 363/756 +52 175 5 30 6 930721 960209 363/756 -40 315 2.5 30 12 930721 960210 363/756 +74 123 6.5 25 4 930512 930721 363/756 -22 (tandem pair) tv 414 : ' 2 . ,25-: , + 10 966209 960210 363/756 ■ ■ ' + 117' / : (tandem pair) 78' . / 10 ' : 20.:■ " 1.5' Table 11. List o f five processed ascending track interferograms (5) based on four (4) individual ERS SAR images. Maximum image signal is in mm, not mm/yr. 62 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. D ate 1 Date 2 A Perpendicular Baseline (m ) Height of Ambiguity (m) 2® DEM Noise (m m ) M ax Image Signal (nun) Signal / DEM Noise 930512 960210 +52 175 5 30 6 930721 960209 -40 315 2.5 30 12 Table 12. List of processed ascending track interferograms used in descending interferogram stack. Contributing Interferograms in Stack E A Perpendicular Baseline (m ) Height of Ambiguity (m ) 2® DEM Noise 930512-960210 930721-960209 +12 +760 1 Table 13. Descending interferogram stack topographic noise analysis. The perpendicular baseline of a stack is the sum o f the contributing perpendicular baselines. 63 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without permission. 930512-960210 u » , 05.- O "110 O ' -109" 55’ 930721 -960210 O D 930721 - 960209 m m IH : U ) o».. -110' O ’ -109* 55* 5 T 1 " H U > 0 5 . - * . U 1 00 o* & ) f a * 3 u f " n " , 3 £ „ 3 g . 3 O l e r . o 3 -110*0' -109*55' Figure 21. Ascending interferograms illustrating annual slant range deformation (cm/yr). Deformation is relative to the GPS base station location (WEI1; Figure 11). Dark blue patches, corresponding to the darkest color on the color scale, represent a mosaic of no correlation regions from all contributing interferograms. £ ■105^55' Figure 22. Ascending interferogram stack. Deformation is in the slant range (cm) per year. Deformation is relative to the GPS base station location (WEI 1; Figure 11). Dark blue patches, corresponding to the darkest color on the color scale, represent a mosaic o f no correlation regions from all contributing interferograms. The most striking observation one can make regarding the ascending interferograms and the stack they create is the decrease in phase change across the image. Positive range changes are observed in the north and northwest portions of the image, whereas extreme negative values are observed in the south and southeast portions of the image. Often when trends such as this are observed in interferograms 65 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Slant Range Change (cm/yr) they are the result of an incorrect calculation of baseline information derived from satellite orbit information. A possible method for identifying and removing this trend w ill be discussed further in the following section. Regardless of this suspected orbital trend or ramp across the image, various regions of range change can be pointed out that agree with observations from the descending interferograms. The most significant of these is the peak of relative positive range changes along the Colorado River. Immediately east and west o f the river these changes are observed to decrease. Subsequent chapters will combine the ascending and descending interferograms in order to estimate a 2-D displacement vector. GPS based surface deformation information will also be utilized in this process to 1) optimize the decomposition process, and 2) to provide a second geodetic data set with which InSAR values can be directly compared. 3.2.5. Orbital Errors ROfyPac automatically estimates the baseline length between satellite passes for use in determining differential phase interferometry. While the differential phase shift between SAR scenes is usually of deformational, topographic or atmospheric origins, there is a fourth source of phase change which must be considered. Even in 66 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the absence of topography, there exists a phase term that is due to the spherical curvature o f the earth. Using the Precise Orbit Product (PRC) obtained through the ESA, ROI_Pac calculates this as a function of the estimated baseline. €>fiat = (4tiA,)[B sin (0 - a) - B sin (0q - a)] , (4) €>fiat - phase correction for “curved earth” effect % = radar wavelength (5.66 cm) B = baseline length 0 = look angle 0O = look angle to each point in the image, assuming zero local height a = angle of baseline with respect to horizontal at the satellite If the baseline estimated from the satellite orbits is not exactly the actual baseline, the curved earth phase correction (Ofiat) will be incorrect and the subsequent displacement maps will show distortions (Zebker et ah, 1994). These distortions appear as a phase gradient across the scene. Sometimes these gradients can be empirically removed after the interferogram is processed. A gradient in the range direction is due to this baseline mis-estimation. It is difficult to remove this error post-processing by just fitting a plane to the interferogram (E. Price, personal communication, 2003). ROI_Pac re-estimates the baseline using a script called “phase2base.pl” using a non-linear procedure in an attempt to mitigate the effect of range direction orbital errors. 67 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A gradient in the azimuth direction can be due to a mis-estimation of the rate of change of the baseline along the image. This gradient appears as a linear ramp and can b e modeled with a plane of best fit through an interferogram (E. Price, personal communication, 2003). A sample orbital ramp that was extracted from the 930721 — 960209 interferogram is illustrated in Figure 23. The ramp was removed by calculating best-fit planes through a series of three image data points. The final ramp w as determined by averaging the ramp plane coefficients of the calculated best-fit planes (Appendix A3). In this way, the final ramp is not dependent on any one set o f points, but rather the entire image. To make sure that there is a consistent ramp to remove, the tilt and rotation of the normal vector is calculated for each estimated plane. 68 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. -IlC f O' -1 0 ^ 5 5 ' Figure 23. Suspected orbital ramp removed from the 930721-960209 interferogram. The standard deviation of every tilt and rotation is taken to observe any significant variability. The 930721-960209 interferogram was seen as possessing an azimuth direction ramp with the lowest deviation (Table 14). The ramp results in a range direction slope of 0.1 radians/km, or 15.7 mm across our cropped interferogram image. This ramp was consequently removed from the 930721- 960209 interferogram. The resultant ascending stack is shown in Figure 24. 69 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Slant Range Change (radians) Date 1 Date 2 T rack Direction Rotation Standard Deviation (°) Tilt S tandard Deviation f) Range A Across Image (cm) 920726 990120 0.14 54 2 921124 961018 0.20 56 1 930622 950824 a n 0.21 54 2 930622 970516 .3 "0 a 0.22 56 1 930622 961227 4 » u 8 0.21 53 6 930622 990312 Q 0.17 55 2.5 950824 970516 0.23 55 1 950824 950825 0.20 ' 56 V 2.; 930512 960210 0.10 20 2 930721 960209 sf 0.09 19 2 930721 960210 -a 0.09 27 2 9305:12 930721 m < -'v: 0.03 56 ■ ' " ■ "I 960209 960210 : 0.07 1 ' .:56:::; : 1 ■ Table 14. Orbital plane removal analysis. Tilt and rotation standard deviation for approximately 800 extracted planes are used to determine robustness of removal procedure. Low variability suggests the true existence of a plane. High variability suggests the opposite. Interferograms in bold are suspected of containing an orbital ramp. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. -ncPo’ -lOSf 55' Figure 24. Ascending interferogram stack. Deformation is in the slant range (cm) per year. Suspected orbital ramp has been removed. Deformation is relative to the GPS base station location (W EI1; Figure 11). Dark blue patches, corresponding to the darkest color on the color scale, represent a mosaic of no correlation regions from all contributing interferograms. With the removal of the suspected 930721-960209 orbital ramp, we observe an interferometric stack that has the same deformation characteristics, yet appears slightly flattened with lower maximum and minimum deformation values. Range change values again in the south and southeast are negative, yet they do not appear to dominate the image as they did in the unaltered ascending stack. 71 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3.2.6. Decomposition of InSAR Displacement Vector The radar signal that we observe is only capable of measuring path length differences in the satellite line o f sight, also called the slant range direction (23° from vertical at the scene center). It is therefore not possible to retrieve the M l displacement vector with one interferogram (Fialko et ah, 2001; Hanssen, 2001). Using a combination of ascending and descending interferograms, two components can be retrieved. To retrieve the third component, we need to make assumptions about the direction of the resulting displacement. In the Canyonlands, we make the assumption that horizontal deformation is perpendicular to the trend of the graben bounding normal faults. This is a fairly safe assumption based on the simple style of faulting observed. Regardless, since an assumption is being made, final horizontal results will be presented in terms of total deformation, not east and north displacements. The programs that developed for this purpose were coded in MATLAB and are presented in Appendix A4. To ultimately solve for the individual components of the displacement vector using InSAR, we must create a system of linear equations. The equation relating the observations to the surface displacement is 72 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. -pv • d = r (5) d = displacement vector [east (de), north (dn), vertical (dv )] p v = ERS line of sight pointing vector [east, north, vertical] r = range change along observed in interferograms A s stated above, two of the three components can be determined based on the evaluation of the range change observations from ascending and descending interferograms. The key here is that each track direction has a unique perspective of our field area, allowing a form of “stereo vision.” Using a C based code (calcpv) written by Dr. Tim Wright at the University of Oxford, we can determine the pointing vector for specific locations along each track. Knowing this information, we can establish the following equations: "pVascending * d — f ascending ( 6 ) "pVdescending * d — rdescending ( 2 ) The pointing vector varies across the ascending and descending SAR scenes, so we must therefore modify this value accordingly throughout. Since the pointing vector varies slowly from pixel to pixel, the analysis can be simplified by setting up a 3x3 grid on the cropped interferogram (Figure 25). The dimensions of this cropped image are approximately 27 km wide by 29 Ion long. While this is area is effectively less than i/9th o f the total interferogram area (100 km wide by 100 km long), it is still 73 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. large enough to cover the entire Canyonlands field area. Furthermore, the pointing vector throughout this area does not change dramatically. By computing nine unique pointing vectors for each of the 9 cells cropped image grid, the pointing vector for every pixel within each cell has been averaged. u > ° 9 > o U J U 1 o Figure 25. Illustration o f pointing vector grid (3x3) and the generalized graben trend setup based on the extensional angle assumption in equation 4. A unique pointing vector was calculated for each cell in the grid based on the center coordinates o f each cell. The assumed direction of overburden extension is perpendicular to the trend o f the grabens. 7 4 -110° O ' -109° 55' Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Recovering the third parameter of the displacement vector requires that we make the aforementioned assumption regarding the direction of graben overburden extension (Figure 26). This assumption allows us to establish a relationship between the two horizontal displacement components, east (de ) north (dn) as shown: -de = dn tan(0) (8) 0 = local graben trend (angle between normal and north Figure 26. Diagram illustrating relationship of east displacement (de) to north displacement (dn ). In the northern end of the field area the graben trend runs approximately north-south (approximately N10°E, or 0 = 80°). The southern end o f the grabens defines a more east-west trending segment (approximately N75°E, or 0 =25). A more detailed discussion of the extensional angle that was used in the decomposition is presented in Section 4.2.6.1. 75 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Using equations 6 and 7, the final set o f linear equations that will allow us to solve for the three components of the displacement vector can be established. ("P^asc (e a st) de)+ (“PV asc (n o rth ) dn ) + (-pva sc (v e rtic a l) dv ) rise (9) (_ pV(je c (e a st) de ) + (-pv<jec (n o rth ) dn ) + (-pV(je c (v e rtica l) dy) riec (10) -de - dntan(0) + 0 dv = 0 (11) Discussions of horizontal deformation will reflect the total horizontal deformation (dh), where dh is: Within the grabens region, there are most likely certain zones that do not behave as we have assumed. The ductility o f the Paradox salts surely enables graben extension. Integrating additional salt flow behaviors into the decomposition algorithm is beyond the scope of this thesis yet the implications of these occurrences will be addressed in a subsequent section. Future work should attempt to integrate salt deformation modeling efforts with observed geodetic signals to more fully understand spatial deformation variations. (12) overburden deformation to deviate from the hypothesized overall northwestward 76 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3.2.6.1. Decomposition Assumption: Angle of Extension As discussed previously, even when using both ascending and descending satellite track InSAR data, extraction of the M l three-component displacement vector requires an assumption. While this assumption is based on the premise that extension is predominantly orthogonal to the trend of the graben bounding normal faults axes, it is not without its inadequacies. This assumption does not take into account stress field perturbations near fault “accommodation zones,” or localized salt dependent deformation variations (i.e. diaprism, salt/overburden interface slope variations, etc.). To aid in determining how the direction of horizontal deformation varies throughout the field area, we will use the available GPS velocities. By projecting the GPS displacement vector [de d„ du] for a given GPS location onto the a corresponding pointing vector of both the ascending and descending tracks, we obtain GPS magnitudes equivalent to the temporal ascending and descending slant range, respectively. These GPS derived range change values can then be decomposed using equations 5, 6 and our assumption equation, 7. By modifying the angle of extension (0), an attempt is made to obtain the smallest variation between the decomposed GPS data [de dn djops and the original GPS displacement vector. This angle should be considered the “best” angle to use in the decomposition. 77 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. This process can be taken a step further by comparing the original GPS displacement vector with the InSAR based decomposition vector using the same angle. The goal here is to verify that the angle chosen works well with both GPS and InSAR resulting in a minimal difference between the two data sets. An angle that meets these tests should be considered to be a good approximation o f the direction of localized extension. A consideration in this second comparison is whether or not external errors (atmospheric, topographic or orbital) exist in our InSAR data. While these factors have been mitigated in prior sections, they nevertheless must not be ruled out, especially when dealing with relatively low signal to noise ratio data. Initially a variable angle of extension is applied to the field area. As illustrated in Figure 27, a curvilinear trend is used that attempts to match both the general graben trend and the trend of the Colorado River. This second qualification, matching the trend of the Colorado River, is used because this feature is the free surface into which the overburden theoretically extends. Using an appropriate range of extensional angles (degrees (0) between -10 and -50) we calculated both GPS based and InSAR based displacements at corresponding GPS locations (Table 15). This curvilinear angle estimation varies the angle by row. Cells across a particular row are of a constant angle for simplicity. As previously mentioned, we are 78 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. interested in the difference between both 1) the original GPS displacements and the GPS based decomposition displacements, and 2) the original GPS displacements and the InSAR based decomposition. Differences below 1.5 mm/yr are highlighted in bold. e = -io o - 1 1 0 ° O' -109° 55' Figure 27. Illustration o f pointing vector grid (3x3) and generalized graben trends (bold curved line) used for extensional angle assumption in equation 4. A unique pointing vector was calculated for each cell in the grid based on the center coordinates o f each cell. The assumed direction of overburden extension is perpendicular to the trend o f the grabens. In this example, the angle of extension varies by row in an attempt to match graben trend and the Colorado River trend. A comparison o f decomposed GPS data and InSAR data using these angles is used to determine the best angle approximation. 79 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. G PS Station Displacement Direction Angle Used (degrees 0) GPS Actual Solution ± 2 o error (cm/yr) Decomposed G PS Data (cm/yr) Absolute Difference G P S A ctual versus. G P S Decomposition (cm) Decomposed S A R Data (cm/yr) Absolute Difference G P S A ctual versus InSAR D ecom position (cm) POOL East 0.19 ± 0.38 0.20 0.01 -0.49 0.68 N orth -10° -0.39 ± 0.46 -1.13 0.74 2.80 3.19 H o rizo n tal 0.43 ± 0.60 1.15 0.72 2.85 2.41 V ertical -1.23 ± 1.66 -1.30 0.07 0.49 1.72 DEEP -23.5° E ast -0.30 ± 0.14 -0.30 0.00 -0.43 0.13 North 0.38 ±0.16 0.70 0.32 0.98 0.60 Horizontal 0.48 ± 0.22 0.76 0.28 1.07 0.58 Vertical 0.12 ±0.58 0.15 0.03 0.23 0.11 DEVL -42° East -0.20 ±0.12 -0.20 0.00 -0.36 0.16 North -0.09 ± 0.12 0.23 0.32 0.40 0.49 Horizontal 0.21 ±0.16 0.31 0.09 0.53 0.31 Vertical 0.70 ± 0.44 0.73 0.03 0.12 0.58 PLN Q -20° East -0.22 ±0.12 -0.23 0.01 -0.35 0.13 North 0.20 ±0.12 0.62 0.42 0.98 0.78 H orizontal 0.30 ± 0.16 0.66 0.37 1.04 0.74 Vertical 0.13 ±0.44 0.17 0.04 0.28 0.15 CYCL ! j 1 o 1 O ! "sh 3 East -0.32 ±0.18 -0.33 0.01 -0.25 0.07 North -0.13 ±0.20 0.39 0.52 0.31 0.44 Horizontal 0.34 ± 0.26 0.51 0.17 0.40 0.05 Vertical -0.25 ± 0.72 -0.20 0.05 0.02 0.27 C O LR East -0.09 ± 0.22 -0.09 0.00 -0.35 0.26 North -25° 0.22 ± 0.24 0.19 0.03 0.76 0.54 Horizontal 0.23 ± 0.32 0.21 0.03 0.84 0.60 Vertical 3.47 ± 0.88 3.47 0 . 0 0 -0.12 3.59 Table 15. Summary o f decomposition analysis results using a variable angle o f extension: GPS actual solution (column 1), decomposition with GPS data (column 2), absolute difference between column 1 and column 2 (column 3), decomposition with SAR data (column 4), and absolute difference between column 1 and column 4 (column 5). All values are in cm/yr. Bold denotes low deviations (<1.5 mm/yr). 80 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. G PS Horizontal (cm/y) G PS 2a Error (cm) InSAR Horizontal (cm/y) Absolute Horizontal Difference G P S Actual versus InSAR Decomposition (cm) G PS Vertical (cm/y) G PS 2a Error (cm) InSA R Vertical (cm/y) Absolute Vertical Difference G P S Actual versus InSAR Decomposition (cm) W EI1 0.00 ±0.00 0.00 0.00 0.00 ± 0.00 0.00 0.00 PO O L 0.43 ±0.60 2.85 2.41 -1.23 ± 1.66 0.49 1.72 D EEP 0.48 ±0.22 1.07 0.58 0.12 ±0.58 0.23 0.11 DEVL 0.21 ±0.16 0.53 0.31 0.70 ± 0.44 0.12 0.58 PLN Q 0.30 ±0.16 1.04 0.74 0.13 ±0.44 0.28 0.15 CYCL 0.34 ±0.26 0.40 0.05 -0.25 ±0.72 0.02 0.27 COLR 0.23 ±0.32 0.66 0.84 3.47 ±0.88 -0.12 3.59 Table 16. Comparison of GPS results and InSAR decomposition results. InSAR values determined using a variable angle o f extension. All values are in cm/yr. Bold denotes deviation within GPS 2o error. When using a variable extension model for the decomposition, Table 15 illustrates that 62% of the GPSActuai/GPSoecomposed deviations are below a 1.5 mm baseline versus 20% of the GPSActuaidnSARoecomposed deviations. While noting that there are innate variations in the deformation field that are not accounted for with our extension assumption, decomposing only 62% of the GPS slant range magnitudes within 1.5 mm/yr of the actual GPS value is disappointing, considering that the only variables introduced into this procedure are the calculated pointing vectors (which are considered to be relatively accurate) and the angle o f extension. Furthermore, the observation that over half of the InSAR derived values deviate more than 4mm/yr 81 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. from the actual GPS values leads one to conclude that 1) the decomposition angle was poorly chosen, and/or 2) external sources of error may have tainted the Interferograms contributing to the ascending and descending decomposition stacks. The second possibility was mitigated In prior sections. The first possibility requires modifying the decomposition angle, a process that will either simplify or greatly complicate our model of system extension. Accounting for deformation direction variability across the entire field area could result in a more accurate representation of grabens deformation, yet would present an arduous task due to the foreseeable variability o f basal salt flow. Therefore, instead o f complicating our ideal extensional model, the model of extension has been greatly simplified. The easiest way to do this is by a linear approximation taking into account 1) the average graben trend, and/or 2) the trend of the Colorado River. To achieve this, several generalized “trends” (-40°, -50, and -60°) were utilized in the decomposition process (Figure 28). Values and implications of each respective decomposition angle will be discussed below. 82 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. < 9 = -i Q . ■ i u > % o - 1 1 0 ° O' -1 Q9°55' Figure 28. Illustration of pointing vector grid (3x3) and generalized graben trends (bold dashed line) used for extensional angle assumption in equation 4. A unique pointing vector was calculated for each cell in the grid based on the center coordinates o f each cell. The assumed direction of overburden extension is perpendicular to the trend o f the grabens. Several constant extensional angles were used to best approximate this trend. Three o f these approximations are shown (-40°, -50° and -60°). A comparison of decomposed GPS data and InSAR data using these angles is used to determine the best angle approximation. 83 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. GPS Station | Displacement Direction Angle Used (degrees 0) GPS Actual Solution ± 2 a error (cm/yr) Decomposed G PS Data (cm/yr) Absolute Difference G P S Actual versus. G P S Decomposition (cm) Decomposed S A R Data (cm/yr) Absolute Difference G P S Actual versus InSAR Decomposition (cm) PO O L E a st 0.19 ±0.38 0.19 0.00 -0.46 0.65 North -40° -0.39 ± 0.46 -0.22 0.17 0.55 0.94 H o rizo n tal 0.43 ± 0.60 0.29 0.14 0.72 0.29 V ertical -1.23 ± 1.66 -1.22 0.02 0.28 1.51 DEEP E ast o o -0.30 ±0.14 -0.30 0.00 -0.42 0.12 N o rth 0.38 ±0.16 0.36 0.02 0.50 0.12 H orizontal 0.48 ± 0.22 0.47 0.02 0.66 0.17 Vertical 0.12 ±0.58 0.12 0.00 0.19 0.07 DEVL -40° East -0.20 ±0.12 -0.20 0.00 -0.36 0.16 N orth -0.09 ±0.12 0.24 0.33 0.42 0.51 H orizontal 0.21 ±0.16 0.32 0.10 0.55 0.34 Vertical 0.70 ± 0.44 0.73 0.03 0.12 0.58 PLNQ 1 O o East -0.22 ±0.12 -0.22 0.00 -0.35 0.13 North 0.20 ±0.12 0.26 0.06 0.41 0.21 Horizontal 0.30± 0.16 0.34 0.05 0.54 0.24 Vertical 0.13 ±0.44 0.14 0.01 0.22 0.09 CYCL E ast -0.32 ±0.18 -0.33 0.01 -0.25 0.07 North -40° -0.13 ± 0.20 0.39 0.52 0.30 0.43 Horizontal 0.34 ±0.26 0.51 0.16 0.39 0.05 Vertical -0.25 ± 0.72 -0.20 0.05 0.02 0.27 COLR East -0.09 ± 0.22 -0.09 0.00 -0.35 0.26 N orth -40° 0.22 ± 0.24 0.11 0.12 0.42 0.20 Horizontal 0.23 ± 0.32 0.14 0.10 0.54 0.31 V ertical 3.47 ±0.88 3.46 0.01 -0.16 3.63 Table 17. Summary of decomposition analysis results using constant -40° angle o f extension: GPS actual solution (column 1), decomposition with GPS data (column 2), absolute difference between column 1 and column 2 (column 3), decomposition with SAR data (column 4), and absolute difference between column I and column 4 (column 5). All values are in cm/yr. Bold denotes low deviations (<1.5 mm/yr). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. G PS Horizontal (cm/y) G PS 2® Error (cm) InSA R Horizontal (cm/y) Absolute Horizontal Difference G P S A ctual versu s InSAR D ecom position (cm) G PS Vertical (cm/y) G PS 2a Error (cm) InSAR Vertical (cm/y) Absolute Vertical Difference G P S A ctual versu s InSAR D ecom position (cm) W E I1 0.00 ±0.00 0.00 0.00 0.00 ±0.00 0.00 0.00 P O O L 0.43 ±0.60 0.72 0.29 -1.23 ± 1.66 0.72 1.51 D E E P 0.48 ±0.22 0.66 0.17 0.12 ±0.58 0.19 0.07 D E V L 0.21 ±0.16 0.55 0.34 0.70 ±0.44 0.12 0.58 P L N Q 0.30 ±0.16 0.54 0.24 0.13 ± 0.44 0.22 0.09 CYCL 0.34 ±0.26 0.39 0.05 -0.25 ±0.72 0.02 0.27 COLR 0.23 ±0.32 0.54 0.31 3.47 ±0.88 -0.16 3.63 Table 18. Comparison o f GPS results and InSAR decomposition results. InSAR values determined using a constant -40° angle o f extension. All values are in cm/yr. Bold denotes deviation within GPS 2o error. Using an extension angle of -40° in the decomposition model, Table 17 illustrates that 83% of the GPSActuai/GPSoecomposed deviations are below a 1.5 mm baseline. This is a substantial increase from the 62% observed using variable extension angles in our decomposition. Furthermore, we now observe that 29% of the GPSActuai/InSARoecomposed deviations are below the 1.5 mm baseline, a significant increase from the variable angle model. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. G P S Station | Displacement D irection Angle Used (degrees 0) GPS Actual Solution ± 2 o error (cm/yr) Decomposed G PS Data (cm/yr) Absolute Difference G P S A ctual versus. G P S Decomposition (cm) Decomposed S A R Data (cm/yr) Absolute Difference G P S A ctual versus InSAR Decom position (cm) P O O L E ast 0.19 ±0.38 0.19 0.00 -0.46 0.65 N o rth O O tn i -0.39 ± 0.46 -0.16 0.23 0.39 0.78 H o rizo n tal 0.43 ± 0.60 0.24 0.19 0.60 0.17 Vertical -1.23 ± 1.66 -1.21 0.02 0.27 1.50 D E E P E ast -50° -0.30 ±0.14 -0.30 0.00 -0.42 0.12 North 0.38 ± 0.16 0.25 0.13 0.35 0.03 H orizontal 0.48 ± 0.22 0.39 0.10 0.55 0.06 Vertical 0.12 ±0.58 0.11 0.01 0.17 0.05 DEVL -50° East -0.20 ±0.12 -0.20 0.00 -0.35 0.15 North -0.09 ±0.12 0.17 0.26 0.30 0.39 H orizontal 0.21 ± 0.16 0.27 0.05 0.46 0.24 Vertical 0.70 ± 0.44 0.72 0.02 0.11 0.59 PLNQ U l o o E ast -0.22 ±0.12 -0.22 0.00 -0.34 0.12 North 0.20 ± 0.12 0.18 0.02 0.29 0.09 Horizontal 0.30 ±0.16 0.29 0.01 0.45 0.15 Vertical 0.13 ± 0.44 0.13 0.00 0.21 0.08 CYCL -50° East -0.32 ±0.18 -0.33 0.01 -0.25 0.07 North -0.13 ±0.20 0.27 0.40 0.21 0.34 H orizontal 0.34 ± 0.26 0.43 0.08 0.33 0.02 V ertical -0.25 ± 0.72 -0.21 0.04 0.01 0.26 COLR East -0.09 ± 0.22 -0.09 0.00 -0.35 0.26 North -50° 0.22 ± 0.24 0.07 0.15 0.29 0.07 Horizontal 0.23 ± 0.32 0.12 0.12 0.45 0.22 Vertical 3.47 ±0.88 3.46 0.01 -0.17 3.64 Table 19. Summary o f decomposition analysis results using constant -50° angle of extension: GPS actual solution (column 1), decomposition with GPS data (column 2), absolute difference between column 1 and column 2 (column 3), decomposition with SAR data (column 4), and absolute difference between column 1 and column 4 (column 5). All values are in cm/yr. Bold denotes low deviations (<1.5 mm/yr). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. G PS Horizontal (cm/y) G P S 2 a Error (cm) InSAR Horizontal (cm/y) Absolute Horizontal Difference G P S A ctual versu s InSAR D ecom position (cm) G PS Vertical (cm/y) G PS 2e Error (cm) InSAR Vertical (cm/y) Absolute Vertical Difference G P S A ctual versu s InSAR D ecom position (cm) WEI1 0.00 ±0.00 0.00 0.00 0.00 ± 0.00 0.00 0.00 P O O L 0.43 ±0.60 0.60 0.17 -1.23 ± 1.66 0.27 1.50 D E E P 0.48 ±0.22 0.55 0.07 0.12 ±0.58 0.17 0.05 DEVL 0.21 ±0.16 0.46 0.24 0.70 ± 0.44 0.11 0.59 P L N Q 0.30 ±0.16 0.45 0.15 0.13 ± 0.44 0.21 0.08 C Y C L 0.34 ±0.26 0.33 0.02 -0.25 ±0.72 0.01 0.26 COLR 0.23 ±0.32 0.45 0.22 3.47 ±0.88 -0.17 3.64 Table 20. Comparison of GPS results and InSAR decomposition results. InSAR values determined using a constant -50° angle of extension. All values are in cm/yr. Bold denotes deviation within GPS 2a error. Using an extension angle of -50° in the decomposition model, Table 19 illustrates that 80% of the GPSActuai/GPSoecomposed deviations are below a 1.5 mm baseline. This represents a slight decrease from the 83% observed using an approximation of -40°. A more significant observation is the 45% of GPSActuai/InSAR-Decomposed deviations that are below the 1.5 mm. This represents an improvement of 16% from results that use an angle o f -40°. Additionally, Table 20 illustrates that 75% of the decomposed InSAR values (total horizontal and vertical) are within the 2a (95 percentile) GPS error of the actual GPS values. Only 58% of these values were within the 2a GPS error when using an extension angle o f-40°. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. GPS Station Displacement Direction Angle Used (degrees 0) GPS Actual Solution ± 2 a error (cm/yr) Decomposed G PS Data (cm/yr) Absolute Difference G P S Actual versus. G P S Decomposition (cm) Decomposed S A M Data (cm/yr) Absolute Difference G P S Actual versus InSAR Decomposition (cm) POOL E ast 0.19 ± 0 .3 8 0.19 0.00 -0.46 0.65 N o rth -60° -0.39 ± 0.46 -0.11 0.28 0.27 0.66 Horizontal 0.43 ± 0.60 0.22 0.22 0.53 0.10 Vertical -1.23 ± 1.66 -1.20 0.03 0.26 1.49 DEEP East 1 O h o o -0.30 ±0.14 -0.30 0.00 -0.42 0.12 North 0.38 ± 0.16 0.17 0.21 0.24 0.14 H orizontal 0.48 ± 0.22 0.34 0.14 0.48 0.00 V ertical 0.12 ± 0 .5 8 0.10 0.02 0.16 0.04 DEVL -60°° East -0.20 ± 0 .1 2 -0.20 0 . 0 0 -0.35 0.15 North -0.09 ± 0 .1 2 0.12 0.21 0.20 0.29 Horizontal 0.21 ± 0 .1 6 0.23 0.02 0.41 0.19 Vertical 0.70 ± 0.44 0.72 0.02 0.10 0.60 P L N Q t O h O o East -0.22 ± 0 .1 2 -0.22 0.00 -0.34 0.12 North 0.20 ± 0 .1 2 0.13 0.07 0.20 0.00 Horizontal 0.30 ± 0.16 0.25 0.04 0.40 0.10 Vertical 0.13 ±0.44 0.12 0.01 0.20 0.07 CY CL East -0.32 ± 0.38 -0.32 0.00 -0.25 0.07 N orth -60° -0.13 ± 0 .2 0 0.19 0.32 0.15 0.28 H orizontal 0.34 ± 0.26 0.37 0.03 0.29 0.06 V ertical -0.25 ± 0.72 -0.22 0.03 0.01 0.26 CO LR East -0.09 ± 0.22 -0.09 0.00 -0.35 0.26 N orth -60° 0.22 ± 0.24 0.05 0.17 0.20 0.02 H orizontal 0.23 ± 0.32 0.10 0.14 0.40 0.16 V ertical ...... ...... 3.47 ± 0 .8 8 3.45 0.02 -0.18 3.65 Table 21. Summary o f decomposition analysis results using constant -60° angle of extension: GPS actual solution (column 1), decomposition with GPS data (column 2), absolute difference between column 1 and column 2 (column 3), decomposition with SAR data (column 4), and absolute difference between column 1 and column 4 (column 5). AH values are in cm/yr. Bold denotes low deviations (<1.5 nun/yr). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. G PS Horizontal (cm/y) G P S 2o Error (cm) InSA R H orizontal (cm/y) Absolute Horizontal Difference G P S Actual versus InSAR Decomposition (cm) G PS Vertical (cm/y) G P S 2a Error (cm) InSA R Vertical (cm/y) Absolute Vertical Difference G P S Actual versus InSAR Decomposition (cm) W EI1 0.00 ± 0 .0 0 0.00 0.00 0.00 ± 0 .0 0 0.00 0.00 P O O L 0.43 ± 0.60 0.53 0.10 -1.23 ± 1.66 0.26 1.49 D E E P 0.48 ± 0 .2 2 0.48 0.00 0.12 ± 0 .5 8 0.16 0.04 D E V L 0.21 ± 0 .1 6 0.41 0.19 0.70 ± 0 .4 4 0.10 0.60 P L N Q 0.30 ± 0 .1 6 0.40 0.10 0.13 ± 0 .4 4 0.20 0.07 C Y C L 0.34 ± 0 .2 6 0.29 0.06 -0.25 ± 0 .7 2 0.01 0.26 C O L R 0.23 ± 0 .3 2 0.40 0.16 3.47 ± 0 .8 8 -0.18 3.65 Table 22. Comparison o f GPS results and InSAR decomposition results. InSAR values determined using a constant -60° angle of extension. All values are in cm/yr. Bold denotes deviation within GPS 2o error. Using an extension angle of -60° in the decomposition model, Table 21 illustrates that 75% of the GPSActuai/GPSoecomposed deviations are below 1.5 mm. This represents a slight decrease from the 80% observed using a linear approximation o f - 50° in the prior decomposition ran. A slight increase in GPSActuai/InSAR-Decomposed deviations that are below 1.5 mm are observed when changing the angle from -50° to -60° (45% to 50%, respectively). Additionally, Table 22 illustrates that 67% of the decomposed InSAR values (total horizontal and vertical) are within the 2o 89 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (95 percentile) GPS error of the actual GPS values when using an angle of -60°. This represents no change from a decomposition using a linear extension angle o f -50°. 3.3. Decomposition Results Based on the decomposition tests discussed above, a linear angle o f-50° across the field area appears to be the simplest yet most robust assumption of extension direction. Not only does it result in velocity values that are consistent with the actual GPS resuls, a -50° extension angle (i.e. a graben trend o f N40°E) is consistent with the average fault trend for the field area. Subsequent sections will consequently utilize InSAR results that have been decomposed using this angle (Table 23). 9 0 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. G PS Horizontal (cm/y) G PS 2o Error (cm) InSAR Horizontal (cm/y) Absolute Horizontal Difference G P S Actual versus InSAR Decomposition (cm) G PS Vertical (cm/y) G PS 2 e Error (cm) InSAR Vertical (cm/y) Absolute Vertical Difference G P S Actual versus InSAR Decomposition (cm) WE11 0.00 ± 0 .0 0 0.00 0.00 0.00 ± 0 .0 0 0.00 0.00 P O O L 0.43 ± 0 .6 0 0.60 0.17 -1.23 ± 1.66 0.27 1.50 DEEP 0.48 ± 0 .2 2 0.55 0.07 0.12 ± 0 .5 8 0.17 0.05 D EV L 0.21 ± 0 .1 6 0.46 0.24 0.70 ± 0 .4 4 0.11 0.59 PLNQ 0.30 ± 0 .1 6 0.45 0.15 0.13 ± 0 .4 4 0.21 0.08 C Y C L 0.34 ± 0 .2 6 0.33 0.02 -0.25 ± 0.72 0.01 0.26 COLR 0.23 ± 0 .3 2 0.45 0.22 3.47 ± 0 .8 8 -0.17 3.64 Table 23. Final comparison o f GPS results and InSAR decomposition results. InSAR values determined using a constant -50° angle of extension. All values are in cm/yr. Bold denotes deviation within GPS 2cr error. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. yCYCL InSAR 1 cm /yr 2-sigma error -110 0 -109 55' Figure 29. Comparison of GPS derived horizontal displacement vectors (2000-2002) to InSAR horizontal displacement vectors. Note that both east and north displacements are utilized for this plot, therefore Inadequacies in the extension direction assumption are not taken into account. Index vectors equal to 1 cm/yr of displacement. Deformation is relative to the GPS base station location (WEI1). As previously pointed out, this assumption neglects possible spatial variations of deformation. This is mostly a problem in regions to the north and south of our GPS array where we do not have GPS data to verify that the horizontal deformation is roughly perpendicular to the graben trend. Nevertheless, GPS and 92 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. InSAR derived horizontal deformation vectors are relatively consistent across the field area, with the notable exception of POOL. While the variability between GPS and InSA R rates at POOL is high, the GPS 2a errors for this station is significantly larger than the other five (5) stations (Table 23). Once the MATLAB based decomposition algorithm (Appendix A4) calculates the velocity vectors for each pixel in the cropped interferogram, vertical and total horizontal deformation images are then assembled. These images, which illustrate deformation rates in cm/yr, are georeferenced ASCII matrices of either dv values (for the vertical image) or dh values (for the total horizontal image) computed from the interferogram stacks. Any region in any interferogram that had no correlation is effectively omitted from both the vertical and horizontal images. These regions, which exist predominantly along the rivers and in the southern portion o f the images, are illustrated as dark blue patches to distinguish them from adjacent correlated regions that depict ground deformation. All images depict average annual deformation rates relative to the GPS base station WEI1 for direct comparison with GPS based rate information. The estimation that WEI1 is stable relative to the rest of the field area is supported by InSAR which shows no discemable range change around WEI1 (Figure 18; Figure 21; Figure 22). 93 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3.3.1. Horizontal Deformation Total horizontal deformation was computed across the entire field area and is illustrated in Figure 30. Horizontal results at GPS stations for both GPS and InSAR are listed below in Table 24. Six cross-sectional profiles across Figure 30 were chosen to help look in detail at the deformation across the grabens. Profiles A through D (Figure 31) are orthogonal to the local graben direction, trending roughly northwest to southeast. The locations of these profiles were chosen to best represent deformation variability across the field area. Profile A was chosen as it corresponds to the both the balanced cross section profile location chosen by Moore and Schultz (1999) and the finite element analysis profile chosen by Schultz-Ela and Walsh (2002). This allows us to directly compare our results to the observations and theories o f past workers. While the implication of these profiles will be addressed in the discussion section of this thesis, in general, Profiles A through D are bounded by a relatively stable rate of deformation on the west (far left side of profile) and east (far right side of profile) of the Needles fault zone. Adjacent to the intersection of the profile and Cataract Canyon, rates tend to be low. To the east of Cataract Canyon, Profiles A, B and D see an increase in rate that reaches a maximum before decreasing and stabilizing further to the east. Based on GPS results, our extensional direction 94 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. assumption, and the theories of the evolution of this area, these profiles imply extension to the east and compression to the west of the maximum. The steeper the profile rate gradient, the greater the extension or compression. This observation can also be applied to Profile C that does not observe the same distinct maximum that is observed in the other profiles. Like other profiles, Profile C observes a steep increase in rate immediately east of Cataract Canyon, implying that compression exists within this southwestern zone of the grabens. GPS Horizontal (cm/y) G PS 2c Error (cm) InSAR Horizontal (cm/y) Absolute Horizontal Difference G P S Actual versus InSAR Decomposition (cm) W E I1 0.00 ± 0 .0 0 0.00 0.00 P O O L - 0.43 ± 0 .6 0 0.60 0.17 D E E P 0.48 ± 0 .2 2 0.55 0.07 D E V L 0.21 ± 0 .1 6 0.46 0.24 PLNQ 0.30 ± 0 .1 6 0.45 0.15 C V C L 0.34 ± 0 .2 6 0.33 0.02 C O L R 0.23 ± 0 .3 2 0.45 0.22 Table 24. GPS and InSAR decomposition results for total horizontal deformation. InSAR values determined using a constant -50° angle of extension. All values are in cm/yr. Bold denotes deviation within GPS 2a error. 95 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 30. Relative total horizontal deformation (cm) per year. Profiles and GPS locations are removed from bottom image. Suspected orbital ramp has been removed from the contributing ascending interferogram stack. Deformation is relative to the GPS base station location (WEI1). Dark blue patches, corresponding to the darkest color on the color scale, represent a mosaic o f no correlation regions from all contributing interferograms. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A ll profile maximums were approximately 7mm/yr relative to WEIL Using a distance of 8 km between WEI1 and Cyclone Canyon (Figure 6) near Profile A, an extensioxial strain rate of 2.7 x 10-1 4 s'1 can be calculated. A notable increase in extension is observed in Profile A near Devil’s Lane. Between Devil’s Lane and Cyclone Canyon, strain rate increases to approximately 7.6 x 1G "1 4 s i . Several authors (Biggar and Adams, 1987; Schultz and Moore, 1996), including workers from the University of Southern California and Western Washington University, have observed signs o f active Assuring within this particular graben. High deformation rates are additionally observed along the margins of the Colorado River. Significant rates (-5-7 mm/yr) are seen on the north and south sides of Profile A, as well as near the intersection of Profile B and the Colorado River. This implies rapid extension near the free surface of Cataract Canyon. Between the Cyclone Canyon and Cataract Canyon, horizontal deformation decreases to the west by approximately 4-5 mm/yr. A decrease in horizontal rate across a given distance implies compression. Using a distance of 3.5 km between Cyclone Canyon and Cataract Canyon (Figure 6) along Profile A, a compressional strain rate o f 10'1 4 s"1 can be calculated. All strain rates calculated above agree with realistic published geologic strain rates (Pfiffner and Ramsay, 1982; Campbell-Stone, 2002) as well as strain rates estimated across the grabens (Moore and Schultz, 1999; Schultz-Ela and Walsh, 2002). 97 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. High rates of deformation in the southern reaches of the field area have been evaluated for noise potential (topographic, atmospheric or orbital). This strong signal appears in most contributing interferograms so is unlikely to be due to an atmospheric anomaly. Additionally, the signal does not appear in tandem pair interferograms, suggesting that the signal is not due to topography. GPS signals from POOL, the furthest GPS station to the south, deviates greatly from the assumed model o f deformation. It should be noted that results from POOL are based on only two observations, whereas most other stations have been observed three times. The SAR pointing vector, which is predominantly east-west facing for both ascending and descending images, is very sensitive to changes in the assumed angle of extension. Faults in this region are principally east-west trending, making the assumed extension direction north-south. While we chose an extension angle of - 50°, to increase this value serves to increase both the north component of deformation and consequently the total horizontal deformation value. Based on this, an assumed extensioml direction o f -50° for this region appears to produce conservative results for the east-west trending normal faults of this region. The location o f high deformation rates across this region (between 4 and 9 relative mm/yr) correlates well with the existing fault mapping o f Huntoon (1982; Figure 30). 98 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Profiles E and F traverse the lengths of Red Lake Canyon and Devil’s Lane, respectively (Figure 32). These two profiles were chosen to represent deformation along tw o significant and well developed graben systems. Past workers have expressed an interest in observing deformation rate changes at various locations along the graben in the hope of learning more about the evolution and development fault systems (Moore and Schultz, 1999). While this has been attempted, it should be noted that the relatively narrow width of these grabens (-100-200 meters) corresponds to only 3-6 pixel widths and can be difficult to precisely observe due to the fine line one must look at when constructing profiles. Additionally, the small deviations in deformation that are o f interest along the profiles may be below the threshold of InSAR resolution when considering the effect of topography and atmosphere. Atmospheric noise, as discussed in Section 4.2.3, is due to tropospheric anomalies that are random and difficult to quantify (Hanssen, 2001). Attempts have been made to mitigate this source of noise. As discussed in Section 4.2.2, height of ambiguity calculations and tandem pair interferometry suggest the presence of 2.6 mm/yr of topographic noise in our decomposition results. This should be considered a worst-case scenario as the height of ambiguity calculation may overestimate the amount o f topographic noise seen in an image. Profile E (Red Lake Canyon) contains significant scatter, due in part to significant blocks of no-correlation between correlated pixels. The average trend across the correlated points suggests a low relative deformation rates near the center 99 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. of the profile adjacent to Upper Red Lake Canyon. Rates approximately 2-4 mm/yr higher are observed at the ends of the profile near the mapped edges of Red Lake ' Canyon, suggesting a strain rate of approximately 3.1 x 10’1 4 s'1 between the center and tip o f the profile. Profile F (Devil’s Lane) Illustrates a region of extremely good correlation, along which a wave-like pattern of deformation is observed. There is an observable deformation rate Increase to the north of the profile. Maximum points, which are approximately 1.5-2 mm/yr larger than their adjacent minimums, are observed to occur at the ends of continuous fault segments (Figure 32). Mapping by Huntoon (1982) illustrates overlapping fault segments and step-over at these locations along Devil’s Lane (Profile F; Figure 30). The strain rate between the northern most stepover and its adjacent minimum deformation measurement 2 km to the south is 3.1 x 10'1 4 s'1 . 100 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Kilometers 0.90 ? 0.80 0.70 S3 J 0.80 R ! a 0.50 S3 0.40 O & Q > 0.30 0.20 0.10 0.00 Colorado River Red Lake Oinyon Deep Canyon ,* Y . ■ X 4 6 Kilometers < £ > * g & 0.90 E y C U ./U • | 0.60 § 0.50 I 0 ,0 9 0.30 0.20 0.00 1 2 14 10 0 2 4 6 8 Kilometers '• s O i o .s o 1 0.80 1 ° - 7 ° | 0.60 | 0.50 | M 0 2 0.30 M 0.20 =4 0.10 0.00 Colorado River Imperial Fault * * ' i . 4 6 6 Kilometers Figure 31. Relative horizontal deformation plots for profiles A through D. Profiles are west (left) to east (right) oriented. Deformation relative to the GPS base station (W EI1) is located on the y-axis of each plot (cm/yr). Lateral profile distance (km) on the x-axis. RLC = Red Lake Canyon; CC = Cyclone Canyon. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Kilometers i U s o 0.50 0.30 0.20 - 0.10 0.00 Kilometers Figure 32. Relative horizontal deformation plots for profiles E (Red Lake Canyon) and F (Devil’s Lane). Profiles are north (left) to south (right) oriented. Deformation relative to the GPS base station (WEI1) is located on the y-axis o f each plot (cm/yr). Lateral profile distance (km) on the x- axis. 3.3.2. Vertical Deformation Vertical deformation was computed across the entire field area and is illustrated in Figure 33. Vertical deformation for both GPS and the InSAR decomposition at each o f the six GPS stations is listed in Table 25. Six cross- Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. sectional profiles across were chosen to help exemplify the spatial variability in deformation. As discussed in the section on horizontal deformation, Profiles A through D (Figure 34) are orthogonal to the local graben direction, trending roughly northwest to southeast. The locations of these profiles were chosen to best illustrate spatial deformation variability. Absolute H orizontal Difference G P S Actual versus InSAR Decomposition (cm) G PS Vertical (cm/y) G PS 2a Error (cm) InSAR Vertical (cm/y) Absolute Vertical Difference G P S Actual versus InSAR Decomposition (cm) WEI1 0.00 0.00 ± 0 .0 0 0.00 0.00 PO O L 0.17 -1.23 ± 1.66 0.27 1.50 D E E P 0.07 0.12 ± 0.58 0.17 0.05 DEVL 0.24 0.70 ± 0 .4 4 0.11 ■ 0.59 PLNQ 0.15 0.13 ± 0 .4 4 0.21 0.08 CYCL 0.02 -0.25 ± 0 .7 2 0.01 0.26 C O LR 0.22 3.47 ± 0 .8 8 -0.17 3.64 Table 25. GPS and InSAR decomposition results for vertical deformation. InSAR values determined using a constant -50° angle of extension. All values are in cm/yr. Bold denotes deviation within GPS 2o error. Profiles A through D (Figure 34) illustrate the key feature of the vertical deformation image, that of subsidence along Cataract Canyon relative to far-field regions northwest and southeast of the Colorado River. The rate of relative subsidence reaches a maximum point immediately east o f the Colorado River in all 103 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. profiles. Profile A exhibits the largest subsidence of approximately 3 mm/yr. The rate o f vertical deformation decreases to both the west and east, generally decreasing slower to the east than to the west. Vertical deformation appears to decrease to zero in the far-field of Profiles A and B, suggesting that these regions are relatively stable. In the southern region of the field area, deformation rates continue to increase to the east, as reflected in east of Profiles C and D. Possible sources of InSAR signal error within the southern high deformation rate regions of the deformation image were evaluated and mitigated in prior sections. GPS signals from POOL, the southernmost GPS station, has large uncertainties (-1.23 ± 1.66 cm/yr) and does not help constrain vertical deformation in this region. Nevertheless, the strong signal seen in this area is present in most contributing interferograms and has therefore been accepted as real. The contributing interferograms and subsequent decomposition suggests uplift in this region relative to WEI1. Vertical deformation decreases to the northeast from a maximum of approximately 4 mm/yr, where coincidentally, there is also a decrease in the density and extent of faults mapped by Huntoon (1982; Figure 33) As stated previously, Profiles E and F illustrate deformation along both Red Lake Canyon and Devil’s Lane, respectively (Figure 35). Profile E (Red Lake Canyon) contains significant scatter, due in part to significant blocks of no correlation between correlated pixels. The average trend across the correlated points 104 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. suggests a maximum rate of subsidence (-1-1.5 mm/yr; 1.5 -2 .3 x 10'1 4 s'1 ) adjacent to U pper Red Lake Canyon (kilometer 2 on Profile E) relative to the rest of the profile. Profile F detects the north to south increase in uplift that is seen in Figure 33. W hile this trend appears to dominate the profile, a few local rate changes can be observed. Unfortunately, these changes do not amount to much more than 0.25 mm/yr, well below the signal-to-noise ratio of the contributing interferograms (Section 3.2.2). 105 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. -10SP55' Figure 33. Relative vertical deformation (cm) per year. Profiles and GPS locations are removed from bottom image. Suspected orbital ramp has been removed from the contributing ascending interferogram stack. Deformation is relative to the GPS base station location (WEI1). Dark blue patches, corresponding to the darkest color on the color scale, represent a mosaic of no correlation regions from all contributing interferograms. 106 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. RLC CC Devil's I-ane Colorado River 0.50 0.40 o 0.30 0.10 c • | -0.10 & -0.20 -0.30 12 10 4 6 g 0 2 Colorado River Red Lake Canyon Deep Canyon 0.50 % 0.40 tC < £ . O - 1 0 0 0.00 1 '° - 1 0 < 2 -0.20 -0.30 0 2 4 5 8 10 Kilometers 0.50 S 0.40 o a 0.30 JU P 0.20 C < 2 0.10 o 5 - O 0.00 > 1 3 -0.10 < 2 -0.20 -0.30 Colorado River Deep Canyon imperial Fault 0.50 0.30 0.20 0.10 0.00 5 8 Kilometers Figure 34. Relative vertical deformation plots for profiles A through D. Profiles are west (left) to east (right) oriented. Deformation relative to the GPS base station (W EI1) is located on the y-axis of each plot (cm/yr). Lateral profile distance (km) on the x-axis. RLC = Red Lake Canyon; CC = Cyclone Canyon. 107 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 0.15 0.10 0.05 0.00 -0.05 -0.10 Kilometers - s E p D ( S 0.15 0.10 - 0.05 - 0.00 -0.05 I 2 4 6 8 10 Kilometers Figure 35. Relative vertical deformation plots for profiles E (Red Lake Canyon) and F (Devil’s Lane). Profiles are north (left) to south (right) oriented. Deformation relative to the GPS base station (WEI 1) is located on the y-axis of each plot (cm/yr). Lateral profile distance (km) on the x- axis. 108 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4. DISCUSSION A primary concern with the analysis of interferometric data from the Canyonlands is the relatively low signal-to-noise ratio (SNR). While this value is not easily quantified, several methods have been discussed that attempt to mitigate the key forms of noise (topographic, orbital, and atmospheric) that exist in InSAR data. A n analysis of the effect of topography has been conducted utilizing a parameter known as the “height o f ambiguity,” which showed that the differential interferograms have an average SNR of 8 (section 4.2.2; Table 6). Orbital errors, which are usually due to a mis-calculation of the baseline between contributing satellite locations, were mitigated during both the processing (in ROI Pac) and post processing stages (Section 4,2.5; Appendix A3). Atmospheric error, which often produces the most significant data noise, has been alleviated using both pair-wise logic (section 4.2.3) and interferometric stacking (section 4.2.4). Finally, horizontal and vertical displacements were extracted from the InSAR stacks using the assumption that the extensional direction is N 50° W. GPS data were used to both help determine this angle, as well as to provide a comparative data set for the decomposed InSAR results. Ultimately, results between the two data sets are closely aligned, with 75% of the total horizontal and vertical InSAR values within the 2a error range of the GPS results. 109 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. In addition to estimating when graben formation was initiated (Biggar, 1987; Biggar and A dam s, 1987; Moore and Schultz, 1999, Schultz-Ela and Walsh, 2002), past researchers have expressed interest in the evolutionary kinematics of the system. When combined with cross sectional reconstructions (Moore and Schultz, 1999), graben initiation dates have provided a uniform extension rate of 2 mm/yr to 2 cm/yr (Moore and Schultz, 1999). While this was a solid first estimate of extensional rates across the system, even Moore and Schultz (1999) contended that it was inadequate for a system that arguably had a complex, non-uniform evolutionary history. That history, as discussed by Stromquist (1976) was one in which extension evolved eastward from the free surface near Cataract Canyon. This conclusion was based on evidence o f an eastward decrease in graben size, complexity and bounding fault symmetries (Stromquist, 1976), which suggested an eastward decrease in graben age. Using this information and a similar northern cross-sectional profile to that of Moore and Schultz (1999), Schultz-Ela and Walsh (2002) calculated extensional rates within the 2 mm/yr to 2 cm/yr bounds based on finite element models. Both these rates and geodetic observations from this thesis agree with the extensional rate calculation of Moore and Schultz (1999). Schultz-Ela and Walsh (2002) observe an evolution of eastward graben extension that is consistent with prior field observations (Stromquist, 1976, Moore and Schultz, 1999). This suggests that over time younger grabens in the eastern 110 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. portion o f the field area begin to account for a larger percentage of the system’s total deformation. They conclude that not only is ductile salt flow crucial for overburden deformation, but more importantly that salt flow regulates the evolution of the system. Further modeling by Walsh and Schultz-Ela (2003) indicates the importance of vertical deformation throughout the system, due in large part to the westward extrusion of ductile salt from beneath brittlaly deforming overburden. While vertical deformation rates are not identified in their paper, Walsh and Schultz-Ela (2002) identify a maximum of 60 m of subsidence within the grabens, as reflected in their USGS topographic profiles, total station profiling, and finite element modeling. Assuming uniform deformation and a graben initiation date of between 85 ka and 595 ka, a maximum rate of subsidence of between 1 and 7 mm/yr is anticipated. While GPS is not particularly sensitive to vertical deformation, InSAR does suggest localized subsidence within the grabens that is consistent with these rates. All prior work in Canyonlands acknowledges that the presence of salt is necessary for deformation and subsequent faulting (Stromquist, 1976; Huntoon, 1982; Moore and Schultz, 1999; Schultz-Ela & Walsh, 2002), yet there is no agreement as to the amount of salt flow and whether this flow drives or resists deformation. Several authors have concluded that the salt-overburden interface acts as a decollement, along which failure is allowed to propagate (Huntoon, 1982; Ely, 1987). Schultz-Ela & Walsh (2002) argue, based on their modeling, that salt flow regulates deformation rather than strictly driving it. InSAR and GPS results support 111 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. a model o f salt regulation, at least within the GPS array where the InSAR decomposition has better control. This observation was first made in 2002 (Marsic et ah) when decomposed InSAR deformation values were observed along a profile similar to the profile used by Moore and Schultz (1999) and Schultz-Ela and Walsh (2002). In this thesis, this profile Is illustrated as Profile A. Both horizontal (Figure 31) and vertical (Figure 34) profiles are bounded by relatively stable deformation. The horizontal profile (A) shows increased extension while the vertical profile shows increased subsidence immediately west of Devil’s Lane. Horizontal deformation increases to the west from 4 mm/yr to a maximum profile deformation rate of approximately 7 mm/yr, relative to GPS base station WEIL Field based observations of active Assuring along the eastern margin of Devil’s Lane (Biggar and Adams, 1987; Schultz and Moore, 1996) support the geodetic and finite element modeling observations of high rates of extension occurring at this location. These observations agree with the kinematic hypothesis of Schultz-Ela and Walsh (2002) that salt flow under the eastern-most grabens drives deformation, allowing overburden extension to increase until it reaches a maximum velocity compatible with the basal salt flow. Once extension reaches a maximum rate, salt flow begins to resist overburden deformation. If this did not occur, overburden extension would tend to runaway and grow infinitely large once the failure criterion was reached. Horizontal deformation rates in Profiles A, B, and D are observed as decreasing west of the maximum rate. Assuming westward extension towards the 112 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. free surface, this decrease in horizontal deformation indicates compression across the western grabens. Vertical profiles across the same regions suggest relative subsidence of up to 3 mm/yr. (Figure 34). Additional modeling and detailed topographic mapping by Walsh and Schultz-Ela (2003) supports the observation of subsidence within the grabens region. While many models of salt-driven deformation have been developed for this region, many, including Walsh and Schultz-Ela (2003), believe that salt extrusion towards the free surface plays a part in the deformation process (Baars and Molenaar, 1971; Stromquist, 1976). The flow of salt beneath the overburden is supported by the presence of the Meander Anticline (Huntoon, 1982) and the lack of observable subsidence beyond the grabens region (Walsh and Schultz-Ela, 2003). Schultz-Ela and Walsh (2002) integrated the extrusion o f salt into their finite element modeling by means of differential unloading. They observed that horizontal extension accelerated during events of increased erosion and subsequent salt extrusion. Two significant InSAR observations support basal salt flow Into Cataract Canyon. The first is the subsidence of overburden due to the theorized expulsion of salt to the west (Baars and Molenaar, 1971; Stromquist, 1976). The second is the overburden compression that is observed west of the maximum rate. The diapiric behavior of the salt at the free surface (Cataract Canyon) due to differential unloading allows the formation of a “ridge” of salt at which extension of the overburden would be resisted. Schultz-Ela and Walsh (2002) discuss this in their 113 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. m odeling, stating that their modeled extension rate was observed to be slightly negative east of the free surface. If overburden subsidence rates, and therefore salt flow rates, were truly high, this would serve to support the phenomena of salt upwelling and possibly overburden compression. Upwelling along Meander Anticline at the free surface is not observed with InSAR due to a lack of interferometric correlation. Past workers have expressed an interest in observing deformation rate changes at various locations along the grabens in the hope of learning more about the evolution and development of fault systems (Moore and Schultz, 1999). Profiles E and F traverse the lengths of Red Lake Canyon and Devil’s Lane, respectively (Figure 32), in the hope of observing changes in deformation rate along the grabens. The average trend across the correlated points shows the lowest rates near the center of the profile trend, adjacent to Upper Red Lake Canyon. Rates approximately 2-4 m m /y r higher are observed at the ends of the profile near the mapped edges of Red Lake Canyon. Vertical deformation (Figure 35) illustrates a maximum rate of subsidence (-1-1.5 mm/yr) adjacent to Upper Red Lake Canyon (kilometer 2 on Profile E). This location, while not at the tip of the Red Lake Canyon profile, is still close to the northern reach of the graben. Profile F (Devil’s Lane) similarly illustrates high rates and subtle increases in deformation at the ends of continuous fault segments. These deformation peaks, which are approximately 1.5 - 2 mm/yr larger than their adjacent minimums, occur adjacent to overlapping fault segments or 114 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. stepovers (Huntoon, 1982). These higher rates of deformation may reflect the cumulative displacement of overlapping fault segments. The large signals in the southern region of the field area are intriguing. Not only are they consistently observed in most interferograms, they do not agree with prior deformation models or observations. One caveat is the aforementioned inadequacies of the linear extensional direction assumption in the decomposition process. No GPS sites exist in the southern region of the field area to verify these results. Deformation may occur within this region because of many factors, one of which is gravity-induced extension along the northwest gradient o f the Monument Upwarp (Stromquist, 1976). Huntoon (1982) suggests that the grabens system can continue to grow updip to the south until it reaches the axis of the Home Springs anticline (Figure 1). This anticline, which trends east-west and is slightly concave to the north, is situated in the southern end of our displacement images. Additionally, researchers have estimated that this region is near the southwest pinch out of the Paradox Formation salts (Nuccio and Condon, 1996; Schulz-Ela and Walsh, 2002). Based on these findings, the strong signals in the region south o f the grabens may be explained in the following three ways. First, this region, which is located a significant distance from the free surface, is likely one o f the youngest parts of the system and therefore may be experiencing high rates o f salt-driven extension. This explanation is consistent with the previous modeling efforts of Schutz-Ela and Walsh 115 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (2002). A second explanation is that the base station (WEI1) is subsiding relative to the far-fteld, yet at a faster rate than this southern region. This would cause this region to be uplifted relative to WEI1, yet still subside in an absolute sense. A third possibility is that the high rate of extension is due to the unloading effect of a thin extended overburden. Vertical signals, relative to base station WEI1, are prominent in this area, and suggest a high rate of uplift of up to 4 mm/yr. While there is no modeling to prove or disprove the spatial behavior of salt flow in this region, it is possible that salt could be both expelled towards the free surface and back towards an extended and thinned overburden as grabens more adjacent to Cataract Canyon subside. A third option involves deformation related directly to the Home Springs Anticline. Assuming that this anticline formed in a similar manner to other anticlines in the vicinity of the Needles District, salt diaprism may be actively uplifting this region. Interestingly, deformation rates decrease dramatically to the northeast and appear to correlate with the pattern of faults that are mapped in this region. 5. CONCLUSIONS Deformation across the grabens of the Canyonlands as observed using InSAR and GPS coincide well with earlier estimates of extension rates and directions. Across an analogous profile (Profile A) to that of Moore and Schultz (1999) and 116 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Schultz-Ela and Walsh (2002), it is observed that relative rates of extension reach a m axim um of 6 mm/yr. Extension along the east and compression along the west side of this profile is consistent with basal salt flow regulating overburden deformation. A westward decrease in extensional rate is foreseeably due both salt regulation and the upwarping of the overburden tip at Meander Anticline. Strong subsidence rates of up to 3 mm/yr along the eastern side of Cataract Canyon support the conclusion of eastward salt flow and subsequent salt expulsion at Meander Anticline. Profiles of displacements along two major grabens, Red Lake Canyon and Devil’s Lane, suggest that high rates of deformation, both total horizontal and vertical, are situated at both the tips and overlapping regions of the bounding faults. Large signals in the southern region of the field area appear to be consistent across most processed interferograms, suggesting high rates of extension (up to 8 m m /yr) and high rates of relative uplift (4 mm/yr). These large signals can be explained in three ways. The first postulates that salt is actively driving deformation in this newly deforming region of the grabens. A second explanation is that the GPS base station WEI1 is subsiding relative to the far-field at a rate faster than the southern grabens. A third explanation postulates that as this region is being extended, the overburden is being thinned, resulting in localized differential unloading and consequential salt diapirism. 117 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 6. REFERENCES CITED Abbey, Edward, 1984, Beyond the Wall. New York, NY. Holt, Rinehart, and Winston, 203 pp. Baars, D.L., and Molenaar, C.M., 1971, Geology of Canyonlands and Cataract Canyon: Four Comers Geological Society, 6th Field Conference Guidebook, 99 pp. Baker, A.A., 1933, Geology and oil possibilities of the Moab district, Grand and San Juan Counties, Utah, U.S. Geological Survey Bulletin 841. Barnes, F.A., 1988, Canyonlands National Park: Early History and First Descriptions, Canyon Country Publications, UT, 160 pp. Biggar, N.E., 1987, Quaternary studies in the Paradox Basin, southeastern Utah. Battelle Memorial Institute, Office of Nuclear Waste Isolation Technical Report ONWI-622, Columbus, OH. Biggar, N.E., and Adams, J.A., 1987, Dates derived from Quaternary strata in the vicinity of Canyonlands National Park, In: Campbell, J.A. (Ed.), Geology of Cataract Canyon and Vicinity, p. 127-136. Four Comers Geological Society Guidebook, 10th Field Conference. Burchfiel, B.C, Lipman, P.W., and Zoback, M.L., eds., The Cordilleran Orogen, Conterminous U.S.: Geologic Society of America, The Geology o f North America, V. G-3, p. 9-56. Burchfiel, B. C. and Royden, L. H., 1991, Antler orogeny: A Mediterranean-type orogeny, Geology, v. 19, p. 66-69 118 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Biirgmarm, R., Rosen, P.A., and Fielding, E.J., 2000, Synthetic Aperture Radar Interferometry to Measure Earth’s Surface Topography and Its Deformation, Annual Review Earth Planet Science, v. 28, p. 169 - 209. Campbell, J.A. (Ed.), Geology of Cataract Canyonlands Vicinity, p. 69-73, Four Comers Geological Society Guidebook, 10th Field Conference. Campbell-Stone, E., 2002, Realistic Geologic Strain Rates, 2002 GSA Annual Conference, Paper no. 165-33. Cartwright, J.A., Tradgill, B.D., Mansfield, C.S., 1995, Fault growth by segment linkage: an explanation for scatter in maximum displacement and trace length data from the Canyonlands grabens of SE Utah, JSG, v. 17, p. 1319- 1326. Condon, S.M., 1997, Geology of the Pennsylvanian and Permian Cutler Group and Permian Kaibab Limestone in the Paradox basin, southeastern Utah and southwestern Colorado, U.S. Geological Survey Bulletin 2000-P, 46 pp. Crider, J G, S E Owen & S D Marsic, 2002, Monitoring active deformation in the grabens of Canyonlands National Park (for the special session on Geology in the National Parks), Abstracts with Programs - Geological Society of America, 34(6), p.458; Geological Society o f America, Annual Meeting, Denver, CO, Oct. 27-30. Davis, G.H., and Reynolds, S.I., 1996, Structural Geology o f Rocks and Regions, Wiley & Sons, pp. 776. Ehleringer, J.R., 2003, Nitrogen Deposition and UV Stressor Impacts in Canyonlands National Park as Affected by Climatic Pulse Events, http://www.forestry.umt.edu/research/MFCES/programs/primenet/Assets/Pri menet%20Projects/Belnap/Part%204,%20Ehleringer%20text.pdf Ely, R.W., 1987, Colluvium-filled fault fissures in the Needles fault zone, Cataract Canyon, Utah. In: 119 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. European Space Agency (ESA), 2003, European Remote Sensing (ERS) SAR Design, http://earth.esa. int/eeo3.298 Federal Aviation Administration (FAA), 2003, Global Positioning System Rasies, http://gps.faa.gov/FAQ/faq-gps-text.html. Fialko, Simons, M., Agnew, D., 2001, The complete 3-D surface displacement field in the epicentral area of the 1999 Mw 7.1 Hector Mine earthquake, California, from space geodetic observations, Geophysical Research Letters, v. 28., no. 16, p. 3063 - 3066. Gabriel, A.K, Goldstein, R.M, and Zebker, H.A., 1989, Mapping Small Elevation Changes over Large Areas: Differential Radar Interferometry, Journal of Geophysical Research., v. 94, n. B7, p. 9183-9191. Goldstein, R.M, 1995, Atmospheric limitations to repeat-track radar interferometry, Geophysical Research Letters, v. 22, no. 18, p. 2517-2520. Grosfiis, E.B., Schultz, R.A., Kroeger, G., 2003, Geophysical exploration within northern Devils Lane graben, Canyonlands National Park, Utah: implications for sediment thickness and tectonic evolution, Journal of Structural Geology, v. 25, p. 455-467. Hanssen, R.A., 2001, Radar Interferometry: Data Interpretation and Error Analysis. Kluwer Academic, Dordrecht, The Netherlands, 308 pp. Hansen, F.D., and Carter, N.L., 1984, Creep of Avery Island Rocksalt. In: R.H. Hardy Jr. and M.Langer (Editors), The Mechanical Behaviour of Salt. Trans. Tech. Pub!., Cluausthai, p. 53 - 69. Heidler, D.S., and Heidler, J.T., 1996, Old Hickory’s War: Andrew Jackson and the Quest for Empire. Mechanicsburg, Pa., Stackpoie, 308 pp. 120 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Herbert, N ., 2003, Canyonlands National Park, National Park Service Website, http://www.nps.gov/cany/. Hite, R .J., and Buckner, D.H., 1981, StratigrapMc correlations, facies concepts, and cyclicity in Pennsylvanian rocks of the Paradox Basin, Geology of the Paradox Basin Field Conference, Rocky Mountain Association of Geologists, p. 41 - 159. Huntoon, P.W., 1982, The Meander Anticline, Canyonlands, Utah: An unloading structure resulting from horizontal gliding on salt. GSA Bulletin, v. 93, p. 941-950. Huntoon, P.W., Billingsley, G.H., Breed, W.J., 1982, Geologic Map o f Canyonlands National Park and Vicinity, Utah, Canyonlands Natural History Association, Moab, Utah, scale 1:62,500. Kelly, Shannon, 2003, Land Use History o f the Colorado Plateau - Canyonlands National Park, Utah, http://cpluhna.nau.edu/Places/canyonlands.htm. Lewis, Sr, R.Q., Campbell, R.H., 1965, Geology and uranium deposits of Elk Ridge and vicinity, San Juan County, Utah, U.S. Geological Survey Professional Paper 474-B, 69 pp. Lyons, S., Sandwell, D., 2003, Fault Creep Along the Southern San Andreas from InSAR, Permanent Scatters, and Stacking, Journal of Geophysical Research, v. 108 (Bl), 2047, doi: 10.1029/2002JB001831. Marsic, S D, S E Owen, J G Crider, 2002, Active deformation at Canyonlands National Park: Distribution of displacement across grabens using InSAR, Eos Trans. AGU, 83(47), Fall Meet. Suppl., Abstract G61B-0988. Massonnet D., Rossi, M., Carmona, C., Adragna, F., Peltzer, G., Fiegi, K., and Rabaute, T., 1993, The displacement field of the Landers earthquake mapped by radar interferometry, Nature, v. 364, p. 138-142. 121 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. M assonnet, D. and Feigl, K.L., 1995, Discrimination of geophysical phenomena in satellite radar interferograms. Geophysical Research Letters, 22, p. 1537- 1540. McGill, G.E. and Stromquist, A.W., 1979, The grabens of Canyonlands National Park, Utah - geometry, mechanics, and kinematics, JGR, v. 84, p. 4547- 4563. Molenaar, C. M., 1981, Mesozoic stratigraphy of the Paradox Basin-an overview, in 1981 Field Conference on the Geology of the Paradox Basin: Rocky Mountain Association of Geologists, p. 119-127. NASA (National Aeronautics and Space Administration), 2003, Earth Sciences Applications Directorate Multi-resolution Seamless Image Database (MrSID), Landsat-5 Imagery (http://zulu.ssc.nasa.gov/mrsid/). National Climatic Data Center (NCDC), 2003, NOAA Weather Archive, http://www.ncdc.noaa.gov/oa/ncdc.html. Nuccio, V.F. and Condon, S.M., 1996, Burial and Thermal History of the Paradox Basin, Utah and Colorado, and Petroleum Potential of the Middle Pennsylvanian Paradox Formation, U.S. Geological Survey Bulletin 2000-0, 41 pp. Oviatt, C.G., and Huntoon, P.W., 1988, Evidence for Quaternary deformation in the Salt Valley Anticline, southeastern Utah, Bulletin - Utah Geological and Mineral Survey, v. 122, p. 61 - 76. Pfiffiier, O.A. & Ramsay, J.G., 1982, Constraints on geological strain rates: arguments from finite strain states o f naturally deformed rocks, J. geophys. Res., v. 87/Bi, p. 311-321. 122 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Poole, F.G ., and Sandberg, C.A., 1991, Mississippian paleogeography and conodont biostratigraphy of the Western United States, in Cooper, JD., and Stevens, C.H., eds.. Paleozoic Paleogeography of the Western United States - II: Pacific Section, Society of Economic Paleontologists and Mineralogists Book 67, v. 1, p. 107 - 136. Rogers, A.E.E., and Ingalls, R.P., 1969, Venus: Mapping the surface reflectivity by radar interferometry, Science, v. 165, p. 797 - 799. Rosen, P.A., Hensley, S., Joughin, I.R., Li, F.K., Madsen, S.N., Rodriguez, E., Goldstein, R.M., 2000, Synthetic Aperture Radar Interferometry, Proceedings of the IEEE, v. 88, no. 3, 49 pp. Schultz-Ela, D.D., and Walsh, P., 2002, Modeling of grabens extending above evaporites in Canyonlands National Park, Utah, JSG, v. 24, p. 247-275. Segall, P., and Davis, J.L., 1997, GPS Applications for Geodynamics and Earthquake Studies, Annual Review of Earth Planet Science, v. 25, 35 pp. Stewart, J.H., Poole, F.G., and Wilson, R.F., 1972, Stratigraphy and origin of the Triassic Moenkopi formation and related strata in the Colorado Plateau region: U.S. Geological Survey Professional Paper 691, 195 pp. Strang, G., and Borre, K., 1997, Linear Algebra, Geodesy, and GPS, Wellesley- Cambridge Press, Wellesley, MA, 400 pp. Stokes, W.L., 1948, Geology of the Utah-Colorado salt dome region with emphasis on Gypsum Valley, Colorado: Utah Geological Society Guidebook, no. 3, 50 pp. Stromquist, A.W., 1976, Geometry and Growth of grabens, Lower Red Lake Canyon Area, Canyonlands National Park, Utah, Contribution no. 28, Department of Geology and Geography, University of Massachusetts, Amherst. 123 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Tsay, J., and Lu, C., 2001, Quality Analysis on Height Displacement Values Determined by Three-Pass Method and Some Test Results in Urban Area in Taiwan, 22n d Asian Conference on Remote Sensing, 5-9 November, 2001, Singapore, www.crisp.nus.edu.sg/~acrs2001/pdf/103tsay.pdf Turcotte, D.L., and Schubert, G., 2002, Geodynamics, Second Edition, Cambridge University Press, New York., 456 pp. Turner, R.J.W., Madrid, R.J., and Miller, EX., 1989, Roberts Mountains allochton: Stratigraphic comparison with lower Paleozoic outer continental margin strata of the northern Canadian Cordillera, Geology, v. 17, p. 341 - 344. Ulaby, F.T., Dubois, P.C., and van Zyl, J., 1996, Radar mapping o f surface soil moisture, Journal of Hydrology, v. 184, p. 57 - 84. Walsh, P., and Schultz-Ela, D.D., 2003, Mechanics of graben evolution in Canyonlands National Park, Utah, GSA Bulletin, v. 115, no. 3, p. 259 - 270. Weijermars, R., Jackson, M.P.A., and Vendevilie, B., 1993, Rheological and tectonic modeling of salt provinces, Tectonophysics, v. 217, no. 1/2, p. 143 - 174. Wong, I.G., Ely, R.W., Nelson, R.A., and Olsen, P.E., 1988, Seismicity, tectonics, and the state of stress in the Paradox Basin, southeastern Utah, EOS Transactions, AGU Fall Meeting, v. 63, p. 1102. Woodward-Clyde Consultants, 1983, Overview of the regional geology of the Paradox Basin study region: Battelle Memorial Institute Office o f Nuclear Waste Isolation, ONWI-92, 433 pp. Wong, I.G., Olig, S.S, and Bott, J.D.J., 1996, Earthquake potential and seismic hazards in the Paradox basin, southeastern Utah, in Huffman, A.C., Jr., Lund, W.R., and Godwin, L.H., eds., Geology and resources of the Paradox basin: Utah Geological Association Guidebook, v. 25, p. 241 - 250. 124 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Zebker, H.A., Rosen, P.A., Goldstein, R.M., Gabriel, A., Wemer, C.L., 1994, On the derivation of coseismic displacement fields using differential radar interferometry: The Landers earthquake, JGR, v. 99, p. 19,617 - 19,634. Zebker, H. A., P. A. Rosen, and S. Hensley, 1997, Atmospheric effects in interferometric synthetic aperture radar surface deformation and topographic maps, Journal of Geophysical Research - Solid earth, v. 102, no. BIO, p. 7547-7563. Zisk, S.H., 1972, A new earth-based radar technique for the measurement of lunar topography, Moon, v. 4, p. 296 - 300. 125 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 7. APPENDIX A l. Processing Interferograms Using NASA/JPL ROIJPac The process described below is specific for machines at the University of Southern California. Directories, files and results will vary depending upon the analysis location and data set used. 1. From your home directory, you need to "cd" into your working directory: albite.usc.edu(lO): cd /home/albite-01 /practice/sar 2. Type "Is" to see what is there. You will find the following directories and files: SAR_CONFIG (file that you will need to source) 920726-990120.pro (processing file that ROIJPac references) orbit (directory that contains subdirectories with orbit information) DEM (directory containing the Digital Elevation Model) 920726 (SAR data for the date July 26, 1992) 990120 (SAR data for the date January 20, 1992) note: When you run ROIJPac, other files and directories will be created, such as GEO, SIM and 920726-990120. 3. "cd" into the first SAR directory (cd 920726). Notice the files listed: 126 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. DAT_01.001 « this is the actual SAR data VDFJDAT.001 « Volume Descriptor File (this is data containing order information) MULJ3AT.0O1 « Not important to the processing procedure LEA_01.001 « Sar Leader File (Header file containing important information about the DAT) 4. Change the files into names that ROIJPac can read. Do this using the mv command: albite.use.edu( 10): mv DAT_01.001 IMAGERY920726 « notice the date after IMAGERY if you typed "Is" now, instead of seeing DAT_01.001, you would see IMAGERY920726. Do this for two of the other files. Change them as follows: mv VDFJM T.0Q1 VDF920726 mv LEA SARLEADER920726 don't change NUL*. This stays as is. Do this for the files in the other data directory (920120). Remember, you are in /home/albite-01 /practice/sar/920726. So, type: 5. cd ../ « to get back to /home/ablite-01/practice/sar 127 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. THEN cd 990120 and change those files. Remember to put the correct date in the filenames. 6. After you have changed the file names, cd into the working director}’ (*/practice/sar). 7. Source the SAR_CONFIG file. I have set this up for you, so it should work properly. albite.usc. edu( 10): source SAR_C0NF1G 8. Check out the *.proc file that is in the working directory. I have set this up for you, but notice how it is set up for future reference. Check out Dave Schmidts website (at Berkeley) for more information on what is contained within. * * * * * * * * Y o u are now ready to process interferograms!******** 1. Convert the raw SAR data into a format that can be read by ROIJPac a) cd into the directory 920726. b) type the following command: albite.usc.edu(lO): make_raw.pl PRC SARLEADER920726 920726 A A A A PERL script orbit typ SAR info date 128 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. c) the process should take -1-2 minutes, maybe more. Let it finish. d) go into the other SAR directory (990120) and do the same thing there. **note: the orbit files are already set up for you so no need to do anything in the orbit directories. 2. Process the Interferogram a) cd into the working directory (*/practice/sar). b) type the following command: albite.usc.edu(lO): process_2pass.pl 920726-990120.proc c) the process here creates: **the Single Look Complex image (SLC) »S ingle-look complex image (amplitude and phase data encoded as complex numbers »Projection: Slant Range, » P ix e l size: 7.9 m in range (perpendicular to ground track) and 4 m in azimuth (along ground track) » S L C I full scene: 100 km x 100 km **the correlation image between master & slave **the differential interferogram (master + slave phase change) **the synthetic DEM (converts double binary format DEM into phase representation compatible with R O IP ac 129 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. **the final interferogram (subtracts the SIM DEM from the differential interferogram, geocodes and unwraps the 2*PI phase ambiguity) 3. Display your results To view the final geo_920726-990120.unw interferogram (which will be in the directory /home/albite-01/practice/sax/920726-990120 directory), you will need to run a program called dgx.pl. When you get to this stage, you will need to either berunning x-win (a UNIX emulator) on a PC or be on a SUN workstation. You will need to set your Display environment variables to view what is being put out by albite. If you are on a SUN, you will need to logout, then log back in, using following syntax: whatever your prompt is( 10): xhost + « th is allows clients to send information to your computer whatever your prompt is(l 1): rlogin albite.usc.edu login: « y o u r name here password: « y o u r password here aibite.usc.edu(l): setenv DISPLAY your_computer_name_here.usc.edu:0.0 « th is allows albite to display images from albite on to your computer 130 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. example: if your computer name is fast.usc.edu, then you would type: setenv DISPLAY fast.usc.edu:0.0 albite.usc.edu(2): cd /faome/albite-01 /practice/sar albite.usc.edu(3): source SAR_CONFIG Now, you can view images... a!bite.usc.edu(4): cd 920726-990120 albite.usc.edu(5): dgx.pl geo_920726-990120.unw « th is should be the name of the final interferogram A display will appear on your computer. Use dgx.pl to view any image from ROIJPac (including the DEM) on your computer. 131 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A2. Creating ROIJPac Compatible DEM from SDTS Data 1. Download *.tar.gz SDTS files from www.geocomm.com 2. U nzip and untar these files into separate directories for each DEM 3. Assemble the DEM using ENVL File > Open Exeremal File > USGS > SDTS DEM 4. Save the assembled file as an ENVI image file. Give file a simple name and save in same directory as SDTS files. 5. ENVI tends to bog down or crash when assembling multiple SDTS dems. You might need to close ENVI down occationally and resart it. 6. Open each newly created ENVI image file. View the file to make sure it looks good. 7. Mosaic adjacent DEMS (the ENVI image files you created). Map > Mosaicking > Georeferenced 8. Import each DEM file individually Import > Import Files and Edit Properties It is important to not just import files as you will need to adjust input parameters (ie: overlap). 9. Diologue box will pop up. Set "Background See Through data value to ignore" to zero (0). 10. Hit OK 11. Do this for all adjacent DEMs. 132 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 12. A pply the mosaic if the thumbnail representation looks adequate. File > Apply 13. Chech "output x" and "output y" values. Save file here. Do not output result to memory. Even if you do this and save the image later, the result will cot be compatible with ROI_Pac. 15. Once the file is saved, take note of several important DEM parameters you will need for the *.dem.rsc file. View the header information for the mosaic'd DEM. Note the following information: Samples (this will be Width) Lines (this will be Length) go to Edit Attributes > Map Info Datum: Make sure you note this. For SDTS DEMs, Datum will be NAD27 Projection: Should be UTM. Note the Zone. E and N: This is the upper left hand comer. Lat (E) and Lon (N). 15. Change the name of the output (once saved in ENVI) to <filename>.dem 16. Create the <filename>.dem.rsc file. 17. Verily that ROIJPac will read the file by using dgx.pl <ftlename>.dem 13 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A3. Systematic Removal of Suspected Orbital Ramp Note: The process described below has been coded as ‘removeramp.m.’ (Appendix A4 - MATLAB Analysis Programs) using the MATLAB language. A suspected orbital ramp with a gradient in the range direction is typically due to baseline mis-estimation (pers. comm., E. Price, 2003). It is difficult to remove this by just assuming a plane. There is a script in ROIJPac called ''phase2base.pl" that is does the baseline re-estimation using a non-linear procedure. The result of which has second order effects, producing a parabolic ramp with the parabola axis oriented in the range direction (pers. comm., E. Price, 2003; Hanssen, 2001). A ramp in the azimuth direction can be due to mis-estimation of the rate of change o f the baseline along the image. This ramp can be modeled with a plane after the interferogram is processed (pers. comm.., E. Price, 2003). The removal a suspected azimuth gradient orbital ramp requires finding the best-fit plane through an Interferometric image (latitude, longitude, and deformation). To accomplish this task, three points are chosen, PI, P2 and P3. Next, the equation o f the plane through these three points (xn, yn, zn ) is found (eq. A31). 134 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Ax + By + Cz - -D (A3-1) This process is done repeatedly for a variety of three point sets across the image by calculating the coefficients of the plane. Points for each set are chosen sequentially in approximately 900 steps (roughly the pixel width o f the image), as illustrated below in Figure 36. C D Q C O 03 O -109 55' -110 0 Figure 36. Chosen points for orbital plane coefficient determination. Point 1 steps to the right from the top left comer along row 100. Point 2 steps to the bottom along the right side of the image (row 850) from the top right comer. Point 3 steps to the left from the bottom right comer along row 700. 135 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Coefficients are equal to the determinant of a 3x3 matrix, consisting of x,y and z values for the three data points (eq. A3-2). I y 2zt y i 1 y , y 2 1 y i y 2 2 1 A = l y 2z 2 B = y , l z 2 c = y ty 21 D = y , y 2z 2 1 y 2 2 3 y i l z 3 J i J A 1 J l k 2Z3 (A3-2) The average of the plane coefficients (A,B,C,D) is determined to find an "average ramp." To make sure that there really is a consistent ramp to remove, the tilt and rotation of a normal vector to each plane is calculated. The normal is found by taking the cross product of two vectors parallel to the planar surface. Tilt and rotation angles are computed by finding the dot product between the normal vector and the vertical and horizontal (y-axis) unit vectors (0,0,1) and (0,1,0), respectively. The standard deviation of the computed list of tilt and rotation is then taken to quantify the amount o f planar variability. If there is significant variability (o > 20°), then our confidence that a ramp exists is reduced. If the variability is low, our confidence is increased. 136 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A4. MATLAB Analysis Programs The following set of programs was written for the purpose of loading interferograms, decomposing a three-dimensional displacement vector, displaying and analyzing results. Interferograms processed by ROI_Pac are in a floating-point binary format, which can be easily opened in the IDL driven Environment for Visualizing Images Program (ENVI). Within ENVI, the images are georeferenced and saved. Coded in MATLAB, the following programs require these saved interferograms are (1) in an ASCII format, and (2) are of Identical dimensions and spatial coverage. Suspected orbital ramps can be evaluated and removed using ‘removeramp.m’ prior to the decomposition of the displacement vector. Once this is completed for each interferogram, Toad_data.m’ allows users to define which interferograms are to be loaded for analysis. This is accomplished by altering a master ASCII text file that contains all available scenes and associated directories. The program then loads the appropriate interferograms and assembles an ascending and descending stack. ‘Slant_gps.nT integrates GPS data into the decomposition process by allowing the user to determine the most appropriate extensional angle to use in the decomposition. Once this is determined, ‘ decomposition.!!!’ computes the displacement vector components for each pixel. Results are presented and saved 137 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. using ‘dispiay_figures.m.5 The entire loading and decomposition process is regulated by the program ‘ start.m.’ % removeramp.m % by Scott Maxsic, 6/10/03 % this program removes any artificial ramp (usually assumed to be derived from % orbital PRC error). See notes below regarding ramp calculation. % remove comment on interferogram you wish to analyze %int = load('/home/albite- 00/RESULTS/DECOMP/2D/DATA_LARGE/large930512_960210.txt'); %int = load('/home/albite- 00/RESULTS/DECOMP/2D/DATA_LARGE/large930721_960209.txt'); %int = load('/home/albite- 00/RESULTS/DECOMP/2D/DATA_LARGE/large920726_990120.txt'); %int - load('/home/albite- 0Q/RESULTS/DECOMP/2D/DATA_LARGE/large930622_990312.txt'); %int = load('/home/albite- 00/RESULTS/DECOMP/2D/DATA_LARGE/large930622_970516.txt'); %int = load('/home/albite- 00/RESULTS/DECOMP/2D/DATA_LARGE/large960209_960210.txt’ ); %int = load(Vhome/albite- 00/RESULTS/DECOMP/2D/D AT A_L ARGE/large930721_960210.txf); %int = load('/home/albite- 00/RESULTS/DECOMP/2D/D ATA_LARGE/large921124_961018 .txt'); %int = load('/home/albite- 00/RESULTS/DECOMP/2D/D ATA_LARGEZlarge930622_961227.txt'); %int = load('/home/albite- 00/RESULTS/DECOMP/2D/DATA_LARGE/large930512_930721.txt’ ); %norm = int(l,l); %int = int-norm; num = 0; clear ramp; clear norm; clear normal; clear list xnormavg = 0; ynormavg = 0; znormavg = 0; aavg = 0; bavg = 0; cavg = 0; davg = 0; width = size(int,2); length = size(int,l); Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. % based on equation of a plane, ax + by + cz + d = 0, this program finds three points % on interferogram and computes a, b, c, and d. The three points are as follows: % pt. 1 => starts at top left comer and moves to right % pt. 2 => starts at top right comer and moves down % pt. 3 => starts at bottom right comer and moves left % pt. 4 => starts at the middle right and moves left % Points were chosen to get an array of plane coefficients that best approximates a plane % through the image. These values are then averaged. The equation of a plane is then % subtracted from the interferogram image. for i = 1: width-1; % point 1 (x l,y l,zl) x l = i; yl = 100; zl = int(100,i); % column,row % point 2 (x2,y2,z2) x2 = (width-100); y2 - i; z2 = int(i,width-100); % column,row % point 3 (x3,y3,z3); x3 = (width-i); y3 = (length-100); z3 = int((length-100),(width-i)); % column,row % point 4 (x4,y4,z4); x4 = (width-i); y4 = (widfh/2+0.5); z4 = int((width/2+0.5),(width-i)); % column, row % solve for plane coefficients a = det ([ 1 ,y 1 ,z l; 1 ,y2,z2; 1 ,y3 ,z3j); b = det ([xl,l,zl;x2,l,z3;x3,l,z3]); c = det ([xl ,y 1,1 ;x2,y2,1 ;x3,y3,1 ]); 139 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. d = -d et ([xl ,y 1 ,zl ;x2,y2,z2;x3,y3,z3]); % disregard any point that has a z = 0.00 (no correlation) if z l= — 0.00 || z2==0.00 || z3==0.00 num = num; % if all points have z ~=0.00, form coefficient sum else num - num+1; aavg - aavg + a; bavg = bavg + b; cavg = cavg + c; davg = davg + d; % and make list of tilt and rotation z l = (d-(a*xl)-(b*yl))/c; z2 = (d-(a*x2)-(b*y2))/c; z3 = (d-(a*x3)-(b*y3))/c; z4 = (d-(a*x4)-(b*y4))/c; % v l = pt. 3 minus pt. 1; v2 = pt. 4 minus pt. 2; v l = [x3 ,y3 ,z3 ] - [x4,y4,z4]; v2 = [x2,y2,z2] - [x 1 ,y 1 ,z 1 ]; normal = cross(vl,v2); normal = normal/(norm(normal)); zaxis = [0,0,1]; tilt = acos(dot(normal,zaxis)); tilt = tilt*(l 80/pi); list(num,l) = tilt; yaxis = [0,1,0]; rotation = acos(dot(normal, yaxis)); rotation = rotation*(l 80/pi); !ist(num,2) = rotation; 140 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. % compile list of normals xnormavg = xnormavg + normal(l); ynormavg = ynormavg + normal(2); znormavg = znormavg + normal(3); end end % find standard deviation of plane orientation disp('calculating plane orientation variance') disp(' Tilt Rotation'); s = std(list,Q); disp(s) % compute average plane coefficients a = aavg/num; b = bavg/num; c = cavg/num; d = davg/num; % form average plane (ramp) fory = l:size(int,l); for x = 1 :size(int,2); ramp(y,x) = ~(d+(b*x)+(a*y))/c; % column,row (y,x) end end % form interferogram with ramp removed intramp = int-ramp; a = input('Print ramp and figures?: (1/0)'); if a == 1 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. figure; image(int,! cdatamappingVscaled'); colorbar; title('unaltered interferogram'); yiabelfmeters *30'); x!abe!('meters *30'); figure; image(ramp,'cdatamapping7scaled! ); colorbar; title('ramp'); ylabel('meters *30'); xlabel('meters *30'); % Locates regions of no correlation from original interferogram % and adjusts intramp to reflect this. dec = zeros(size(int)); testdec = ones(size(int)); ind = fmd(int— 0.00); intramp(ind) = 0.00; % displays interferogram with ramp removed. figure; imagesc(intramp); colorbar; title('interferogram with ramp removed'); ylabel('meters *30'); xiabel('meters *30'); else end save intramp.txt intramp -ascii; 142 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. % slant_gps.m % by Scott Marsic, 5/15/03 % % this program projects observed GPS values (vectors) onto ascending and % descending pointing vectors. The result is a scalar that is in the slant % direction of the satellite path. The computed scalars are then decomposed % using linear system of equations. Decomposed vectors are then displayed for % comparison to decomposed InSAR derived values. load pv.txt; pv = pv*(-l); % GPS results (7/20/2003 - S. Owen) % de, dn, du (vertical columns) % POOL, DEEP, DEVL, PLNQ, CYCL, COER (stations) load gps_res.txt; % results are from stacked interferograms, ascending ramp removed % ascending and descending values(vertical columns) % POOL, DEEP, DEVL, PLNQ, CYCL, COLR (stations) load InSAR_res.txt; sitel = input('Would you like to specify an extensional angle? (1/0)'); if sitel = 1; ang_ext = inputfEnter angle relative to north (negative for west extension)\n'); else end angle = load('/home/albite-00/RESULTS/DECOMP/2D/angle.txf); for num = 1:6 gps = [gps_res(num,l), gps_res(num,2), gps_res(num,3)j; if num = 1 % POOL % pv cell is number 8, pv lines are 15 and 16 143 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. pvasc = [pv(15,l), pv(15,2), pv(15,3)]; pvdec = [pv(16,l), pv(16,2), pv(16,3)j; else % pv cell is number 5, pv lines are 9 and 10 pvasc = [pv(9,l), pv(9,2), pv(9,3)]; pvdec = [pv(10,l), pv(10,2), pv(10,3)]; end % i is the line number of the particular GPS station if num == 1 disp('POOL') angle_i = 732; elseif num = 2 disp('DEEP') angle_i = 567; elseif num == 3 disp('DEVL') angle_i = 354; elseif num == 4 disp('PLNQ') angle_i = 590; elseif num == 5 disp('CYCL') angle_i = 342; elseif num == 6 disp('COLR') angle_i = 259; end if sitel == 1 ang = tan(ang_ext*(pi/l 80)); elseif sitel = 0 ang_ext = angle(angle_i,2); ang = -tan(ang_ext*(pi/l 80)); Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. end fprintf('Extension angle is %2.3f,ang_ext) proj_asc = dot(gps,pvasc); % slant range (asc) projection of gps vector proj_dec = dot(gps,pvdec); % slant range (dec) projection of gps vector B = [proj_asc, proj_dec, 0]; X = [InS AR_res(num, 1), InSAR_res(num,2), 0]; A = [pvasc(l), pvasc(2), pvasc(3); pvdec(l), pvdec(2), pvdec(3); -1, ang, 0]; C = A\B'; D = A\X'; % Decomposition of GPS data e = G(l); % east n = C(2); % north v = C(3); % vertical h = sqrt((eA 2)+(nA 2)); % Decompostion of SAR data einsar = D (l); % east ninsar = D(2); % north vinsar = D(3); % vertical hinsar = sqrt((einsarA 2)+(ninsarA 2)); % GPS data (total horizontal) gpshor = sqrt((gps( 1) A 2)+(gps(2)A 2)); % Difference between GPS (real) and InSAR ediff = abs(gps( 1 )-einsar); ndiff = abs(gps(2)-ninsar); vdiff = abs(gps(3)-vinsar); hdiff = abs(gpshor-hinsar); 145 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. % Difference between GPS (real) and GPS Decompostion gpsdiff_e = abs(e-gps(l)); g p sd iffn = abs(n-gps(2)); g p sd iffji = abs(h-gpshor); gpsdiff_v = abs(v-gps(3)); fprintf('\n GPS Actual GPS Based GPS Diff (abs) InSAR Based GPS/InS AR Diff (abs)\n') fprintf('East %3.3f %3.3f %3.3f %3.3f %3.3£Vn’ ,gps( 1 ),e,gpsdiff_e,einsar, ediff) fprintf(f North %3.3f %3.3f %3.3f %3.3f %3.3f\n',gps(2),n,gpsdiff_n,ninsar,ndiff) fprintf('Horizontal %3.3f %3.3f %3.3f %3.3f %3.3f\n',gpshor,h,gpsdiff_h,hinsar,hdiff) fprintff Vertical %3.3f %3.3f %3.3f %3.3f %3.3f\n\n\n',gps(3),v,gpsdiff_v,vinsar,vdiff) end S t : * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * % start.m % by Scott Marsic, 4/15/03 % this program regulates the decomposition process fprintf(‘ 'n\nInterferogram Decomposition Program\n'); l^rintf('Would you like to: \n (1) load data for analysis \n (2) decompose data \n (3) find InSAR values \n (4) display current imagesVnW) val = input(' enter your choice (1,2,3,4):'); p = input('Are you dealing with small(O) or large(l) interferograms? '); ifp — 0 xstart = 582996; 146 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ystart = 4232849.5; elseif p = 1 xstart = 581996; ystart = 4232849.5; end if val — 1 load_data elseif val — 2 decomposition elseif val == 3 findval elseif val — 4 display_figures end val = input('Quit? (1/0) ’ ); if val = 0 start elseif val — 1 end * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * % ioad_data.m % by Scott Marsic, 3/15/03 % load_data.m loads interferometric data into MATLAB for decomposition. % files need to be set up as follows: % (1) Format: ASCII, 1 band. This can be done in MATLAB or ENVI. % (2) All files need to have the same dimentions. More importantly, % the pixel coordinates should match for all images. % load_data.m also requires 2 input files, asc_mt_list.txt (ascending input) % and dec_int_list.txt (descending input). Both files need to be setup % as follows: 147 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. % (1) Format: ASCII, 1 space delimited. % (2) Three columns. Column 1 - interferogram dates (yymmddjyymmdd). % Column 2 - filename and path % Column 3 - total days between interferogram dates % ioad_data.m will load interferograms and assemble stacks for both ascending % and descending tracks. If contributing element to the summed stack contains % a 0.00 value, that element location will be eliminated from the stack. clearallbut p xstart ystart disp('reading input files'); % p - input(''Would you like to load small or large data? (0=small, l=large):'); % p is specified in start.m if p = 0 q - input('Would you like to load ascending interferograms with ramp removed? (1/0):'); if q = 0 [decfile,decdir,decdays] = textread('/home/albiteOO/RESULTS/DECOMP/2D/INTLISTS/small_dec_int _list.txt','%s %s % f, -1); [ascfile,ascdir,ascdays] = textread('/home/albiteOO/RESULTS/DECOMP/2D/INTLISTS/small_asc_int_ list.txt','%s %s % f, -1); elseif q = 1 [decfile,decdir,decdays] = textread('/home/albiteOO/RESULTS/DECOMP/2D/INTLISTS/small_dec_int _list_ramp.txt','%s %s % f, -1); [ascfile,ascdir,ascdays] = textread('/home/albiteOO/RESULTS/DECOMP/2D/INTLISTS/small_asc_int_ list_ramp.txt','%s %s % f, -1); end elseif p = 1 q = input('Would you like to load ascending interferograms with ramp removed? (1/0):'); if q = 0 148 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. [deefile.decdir.decdays] = textread('/home/dbiteOO/RESULTS/DECOMP/2D/INTLISTS/large_dec_int Hst.txtV%s %s % f, -1); [ascfile,ascdir,ascdays] = textread('/home/albiteOO/RESULTS/DECOMP/2D/INTLISTS/large_asc_int_ JIsttxty% s %s % f, -1); elseif q = 1 [decfile,decdir,decdays] = textread(7home/albiteOO/RESULTS/DECOMP/2D/INTLISTS/large_dec_int list.txt';%s %s % f, -1); [ascfile,ascdir,ascdays] = textread('/home/albiteOO/RESULTS/DECOMP/2D/INTLISTS/large_asc_int_ list_ramp .txt’ ,'%s %s % f, -1); end % load ascending interferograms disp('loading ascending interferograms'); for i = 1 :size(ascdir,l); disp(i); disp(ascfile(i)); a = char(ascdir(i)); clear int; clear days; int = load(a); days = ascdays(i); if i — 1; % these initialization steps only need to be done once, hence they % are not ran again in the descending stack assembly xnorm = inputfZero Easting Value (suggest 608076.4368 for WEL1): '); ynorm = input('Zero Northing Value (suggest 4224031.2806 for WEL1: '); xstep = 30; ystep = 30; width = size(int,2); length = size(int,l); 149 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. i f xnorm<xstart | xnorm>(xstart+(30*width)-30) | ynorm>ystart ynorai<(ystart-(3 0* length)+3 0); disp('UTM values outside of image bounds'); else for i - 1: length; northutm(i) = ystart-(i*ystep)+ystep; end for j = 1: width; eastutm(j) = xstart+(j *xstep)-xstep; end row = find (northutm>=ynorm & northutm<: =(ynorm+29)); column = find (eastutm<=xnorm & eastutm>=(xnorm-29)); disp('normalize to row'); disp(row); disp('normalize to column'); disp(column); norm = int(row,column); end disp('initializing matricies'); asc = zeros(size(int)); testasc = ones(size(int)); totdays = 0; end disp('fmding bad values'); ind = find(int=0.00); testasc(ind) = 0; totdays = totdays + days; int = int-(norm); asc = asc + int; end % form ascending interferogram stack Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. disp('forming ascending stack'); astack = asc./totdays; astack = astack*365.25; astack = astack. *testasc; astack = astack.*(5.66/(4*pi)); % load descending interferograms disp('loading descending interferograms'); for i - 1 :size(decdir,l); disp(i); disp(decfile(i)); a = char(decdir(i)); clear int; clear days; int = load(a); days = decdays(i); norm = int(row, column); if i = 1; dispfinitializing matricies'); dec = zeros(size(int)); testdec = ones(size(int)); else end disp('finding bad values'); ind = fmd(int==0); testdec(ind) = 0; int = int-(norm); totdays = totdays + days; dec = dec + int; end % form descending interferogram stack disp('forming descending stack'); dstack = dec./totdays; dstack = dstack*365.25; Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. dstack = dstack. *testdec; dstack = dstack.*(5.66/(4*pi)); % decomposition.m % by Scott Marsic, 3/15/03 % decomposition requires the creation of astack (ascending) and dstack (descending) % prior to initiation. Once created, decomposition can run independently. q = inpttt('Would you like to load data? (y/n) Vs'); if q = V; Joad_data else end % User either defines an angle (usually -50) or chooses to use the % predefined variable angle estimation (saved in angle.txt). This % estimation varies the angle by row to best match the graben trend. % Angles are between normal to graben and north (west is negative) ext = input('Would you like to use linear (0) or variable angle estimation (l)?\n! ); if e x t= 0 ext_ang = inputfDefine extension angle relative to north (west is negative)\n'); elseif ext — 1 load angle.txt; end dispfdecomposing displacement vector’ ); length = size(astack,l); width = size(astack,2); load(Vhome/albite-00/RESULTS/DECOMP/2D/INTLISTS/pv.txt') % pv.txt is set up as ascending pv followed by descending pv for each section 152 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. % 1 through 9. We multiply pv by -1 because the pointing vector is ground % directed. SAR signal is satellite directed. pv = pv*(-l); % initialization of horizontal and vertical matricies horizontal = zeros(size(astack)); vertical = zeros(size(astack)); % decompostion rlc l, rlc2, rlc3,...,r2cl, r2c2,... for i = 1 :length; disp(i); % angle exists between direction of assumed extension (normal to grabens) % and north. This angle should be negative, as the normal will be pointing % to the west (negative de will therefore come out of the decomposition). for j = 1: width; % picks values from ascending and descending stacks for decompostion. Sets % up solution matrix. ascval = astack(ij); decval = dstack(ij); B=[ascval, decval, 0]; if l<=i<(length/3) & l<=j<( width/3) % area 1 of 9 xasc = p v(l,l); yasc = pv(l,2); zasc = pv(l,3); xdec = pv(2,l); ydec = pv(2,2); zdec = pv(2,3); elseif !<=i<(length/3) & (width/3)<=j<((width/3)*2) % area 2 of 9 xasc = pv(3,l); yasc = pv(3,2); zasc = pv(3,3); xdec = pv(4,l); ydec = pv(4,2); zdec = pv(4,3); elseif l<=i<(length/3) & ((width/3)*2)<=j<=width % area 3 of 9 xasc = pv(5,l); yasc = pv(5,2); zasc = pv(5,3); xdec = pv(6,l); ydec = pv(6,2); zdec = pv(6,3); elseif (length/3)<=i<((length/3)s ! : 2) & l <=j<(width/3) % area 4 of 9 xasc = pv(7,l); yasc = pv(7,2); zasc = pv(7,3); Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. xdec = pv(8,l); yasc = pv(8,2); zasc = pv(8,3); elseif (length/3)<=i<((length/3 )* 2) & (width/3)<=j<((v/idth/3)*2) % area 5 of 9 xasc = pv(9,l); yasc = pv(9,2); zasc = pv(9,3); xdec = pv(10,l); ydec = pv(10,2); zdec = pv(10,3); elseif (length/3 )<=i<((length/3) *2) & ((width/3) *2)<=j <=width % area 6 of 9 xasc = p v (ll,l); yasc = pv(l 1,2); zasc = pv(ll,3); xdec = pv(12,l); ydec = pv(12,2); zdec = pv(12,3); elseif ((length/3)*2)<=i<=length & l<=j<(width/3) % area 7 of 9 xasc = pv(13,l); yasc = pv(13,2); zasc = pv(13,3); xdec - pv(14,l); ydec = pv(14,2); zdec = pv(14,3); elseif ((length/3)*2)<=i<=length & (width/3)<=j<((width/3)*2) % area 8 of 9 xasc = pv(15,l); yasc = pv(15,2); zasc = pv(15,3); xdec = pv(16,l); ydec = pv(16,2); zdec = pv(16,3); elseif ((length/3)*2)<=i<=length & ((width/3)*2)<=j<=width % area 9 of 9 xasc = pv(17,l); yasc = pv(17,2); zasc = pv(17,3); xdec = pv(18,l); ydec - pv(17,2); zdec = pv(18,3); end if ext==0 ang = tan(ext_ang*(pi/l 80)); elseif ext— 1 ext__ang = angle(i,2); ang = -tan(ext_ang*(pi/l 80)); end % creates image of used angle of extension angjm age(ij) = ext_ang; % previous angle sheet is in */2D/extend.dat A = [xasc, yasc, zasc; xdec, ydec, zdec; -1, ang, 0]; C = AYB'; de(i,j) = C(1); dn(ij) = C(2); du(i,j) = C(3); horval = sqrt((C( 1 )A 2)+(C(2)A 2)); dh(ij) = horval; 154 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. vertvai = du(ij); if horval == 0; horizontal(ij) = NaN; else horizontal(ij) = horval; end if vertvai = 0; vertical(ij) = NaN; else vertical(ij) = vertvai; end end end vertical = vertical. *testasc. *testdec; horizontal = horizontal. *testasc.*testdec; % saves the ascending and descending stacks % saves the decomposed vertical and horizontal images disp('saving ascending and descending stacks'); delete /home/albite-00/RESULTS/DECOMP/2D/FINAL/astack.dat save /home/albite-00/RESULTS/DECOMP/2D/FINAL/astack.dat astack -ascii delete /home/albite-00/RESULTS/DECOMP/2D/FINAL/dstack.dat save /home/albite-00/RESULTS/DECOMP/2D/FINAL/dstack.dat dstack -ascii disp('saving horizontal and vertical images’ ); delete /home/aibite-00/RESULTS/DECOMP/2D/FINAL/horizontal.dat save /home/aIbite-00/RESULTS/DECOMP/2D/FINAL/horizontal.dat horizontal - ascii delete /home/albite-00/RESULTS/DECOMP/2D/FINAL/vertical.dat save /home/albite-00/RESULTS/DECOMP/2D/FINAL/vertical.dat vertical -ascii % creates log file of contributing interferograms dispfcreating log file'); delete/home/albite-OG/RESULTS/DECOMP/2D/FINAL/log.txt Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. diary /home/albite-00/RESULTS/DECOMP/2D/FINAL/log.txt -ascii disp('descending interferograms used’ ) for i = l:size(decdir,l); disp(char(decdir(i))) end disp('ascending interferograms used') for i = 1 :size(ascdir,l); disp(char(ascdir(i))) end diary o ff % gives option of printing the decomposed images p = input('Would you like to print images? (yin) Vs'); if p = 'y'; display_figures else end frndval l i e * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * % findval.m % by Scott Marsic, 3/15/03 % displays du, de, dn and dh for a particular UTM value within decomposed % interferometric image. fjprintf(rWould you like to: \n (1) find InSAR values at GPS locations \n (2) find another locations InSAR values \n (3) none of the above \n') val = input(' enter your choice (1,2,3):'); switch val case 1; 156 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. [name5 lonJat,UTMx,UTMy] = textread(7home/albite- 00/RESULTS/DECOMP/2D/FINAL/GPS.txt',... ! %s % f % f % f % f, -1); clear east north up totaJ_horizontai c for c = l:size(UTMx,l) xstep = 30; ystep = 30; width = size(horizontal,2); length = size(vertical, 1); if UTMx(c)<xstart | UTMx(c)>(xstart+(3 0 * width)-3 0) | UTMy(c)>ystart UTMy(c)<(ystart-(3 0 * length)+3 0); disp('UTM values outside of image bounds'); else for i = 1 dength; northutm(i) = ystart-(i*ystep)+ystep; end for j = 1 :width; eastutm(j) = xstart+(j *xstep)-xstep; end a = find (northutm>=UTMy(c) & northutm<=(UTMy(c)+3 0)); b = find (eastutm<=UTMx(c) & eastutm>=(UTMx(c)-3 0)); east(c) = de(a,b); north(c) = dn(a,b); up(c) = du(a,b); total_horizontal(c) = dh(a,b); avalue(c) = astack(a,b); dvalue(c) = dstack(a,b); end end name=char (name); iprmtf('\n'); Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. disp('Station East North Vertical Horizontal'); for c = 1 :size(UTMx) fprintf('%s % .2f % .2f %.2f %.2f\n',name(c, 1:4),east(c),north(c),up(c),totaI__horizontal(c)); end dispC'Station Ascending Value Descending Value'); for c = 1 :size(UTMx) fprintf('%s %.2f %.2f\n',name(c, 1:4),avalue(c),dvalue(c)); end case 2 UTMx - input('input easting UTM location (WGS 84): '); UTMy = input('input northing UTM location (WGS 84): '); xstart = 581996; ystart = 4232849.5; xstep = 30; ystep = 30; width = size(horizontal,2); length = size(vertical,l); if UTMx<xstart | UTMx>(xstart+(3 0 * width)-3 0) | UTMy>ystart | UTMy<(ystart- (30*length)+30); disp('UTM values outside of image bounds'); else for i = 1: length; northutm(i) = ystart-(i *ystep)+ystep; end for j = 1: width; eastutm(j) = xstart+(j *xstep)-xstep; end a = find (northutm>=UTMy & northutm<-(UTMy+3 0)); b = find (eastutm<=UTMx & eastutm>=(UTMx-3 0)); fprintf('\n\n This location is found at \n row %i \n column %i\n\n! ,a,b); east = de(a,b); 158 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. fprintf('easting deformation is %.2f\n',east); north = dn(a,b); fprintf('northing deformation is %.2f\ri,north); up = du(a,b); fprintf('vertical deformation is %.2f\n',up); total_horizontal = dh(a,b); fprintfftota! horizontal deformation is %.2f\n’ ,total_horizontal); end otherwise end % display_figures % by S. Marsic dear pro sv pro = input('Would you like profile lines drawn on the images? (1/0):'); gps = input('Would you like GPS points plotted on images? (1/0):'); sv = inputfWould you like to save images? (1/0):'); gray = input('Would you like images saved in color (0) or greyscale (1)?:'); if gps = 1 [UTMx,UTMy,station] = textread('/home/albite- 00/RESULTS/DECOMP/2D/FINAL/GPSplot.txt'/%f % f %s', -1); else end dispCprinting figures') figure(l) for i = l:size(int,l); forj = l:size(int,2); if dstack(ij) = 0.00; dstack(ij) = NaN; else end 159 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. end end imagesc(dstack); if gray = == 0 colormap('default'); elseif gray == 1 colormap('gray'); end colorbar; title('Descending Stack'); ylabel('meters *30'); xlabel('meters *30'); if pro — 1 draw_profile else end if gps = 1 hold; place_GPS hold; else end if sv == 1 saveas(figure( 1 ),'dstack','epsc2'); else end figure(2) for i = l:size(int,l); for j = l:size(int,2); if astack(ij) = 0.00; astack(ij) = NaN; else end end end imagesc(astack); if gray == 0 colormap('defaulf); elseif gray == 1 colormap('gray'); end 160 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. colorbar; title('Ascending Stack'); yiabel('meters *30’ ); xlabel('meters *30'); if pro — 1 drawjprofile else end if gps = 1 hold; place_GPS hold; else end if sv == 1 saveas(figure(2),'astackVepsc2'); else end figure(3) for i = l:size(int,l); for j - 1 :size(int,2); if verticai(ij) = 0.00; vertical(ij) = NaN; else end end end imagesc(vertical); if gray = 0 colormap('default'); elseif gray — 1 colormap('gray'); end colorbar; title('Vertical Deformation'); ylabel(’ meters *30'); xlabel(! meters *30'); if pro — 1 draw__profile else end Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. if gps = 1 hold; place_GPS hold; else end if sv — 1 saveas(figure(3),VerticalVepsc2'); else end figure(4) for i = l:size(int,l); for j = l:size(int,2); if horizontal(ij) == 0.00; horizontal(ij) = NaN; else end end end imagesc(horizontaI); img = horizontal; if gray = 0 colormap('defauif); elseif gray = 1 colormap(’ gray'); end colorbar; title('Horizontal Deformation'); ylabel('meters *30'); xlabel('meters *30'); if pro — 1 draw_profile else end if gps = 1 hold; place_GPS hold; else end if sv = : 1 162 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. saveas(%we(4),'hoFizoiitaiyepsc2'); else end if pro — 1 ql = input('Would you like to extract these profiles? (1/0):! ); if q l = 1 extract_profile q2 = input('Would you like to view these profiles? (1/0):'); if q2 — 1 display_profile else end else end else end disp('done!'); * * * * * * * * * H e * * * * * * * * * * * % extract_profile.m % by Scott Marsic, 4/15/03 % extracts predefined profiles from both the vertical and horizontal displacement images %clearallbut vertical horizontal astack dstack pro length = size(vertical,l); width = size(vertical,2); %xstart = 582996; %ystart = 4232849.5; xstep = 30; ystep = 30; 163 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. for 1 = 1 .-length; northutm(i) = ystart-(i*ystep)+ystep; end for j = 1: width; eastutm(j) = xstart+(j *xstep)-xstep; end % Profile(l): Schultz clear profx profy profxnew profynew verprofile horprofile profile = textread('/home/albite- 00/RESULTS/DECOMP/2D/PROFILE/schultz.mat'); profx=profile(l,:); profy=profile(2,:); compute_draw_profile verprofile - improfi!e(vertical,profxnew,profynew); horprofile = improfile(horizontal,profxnew,profynew); zero = find(verprofile==0); verprofile(zero) = NaN; zero = find(horprofile==0); horprofile(zero) = NaN; save/home/albite-00/RESULTS/DECOMP/2D/FINAL/PROFILE/schultzver.txt verprofile -ascii; save /home/albite-00/RESULTS/DECOMP/2D/FINAL/PROFILE/schultzhor.txt horprofile -ascii; % Profile(2): E-W2 clear profx profy profxnew profynew verprofile horprofile profile = textread('/home/albite-00/RESULTS/DECOMP/2D/PROFILE/ew2.maf); profx=profile(l profy=profiIe(2,:); compute_draw_profile verprofile = improfile(vertical,profxnew,profynew); horprofile = improfile(horizontal, profxnew, profynew); zero = find(verprofile==0); verprofile(zero) — NaN; zero = fmd(horprofile==0); horprofile(zero) = NaN; save /home/albite-00/RESULTS/DECOMP/2D/FINAL/PROFILE/ew2ver.txt verprofile -ascii; 16 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. save /home/albite-00/RESULTS/DECOMP/2D/FINAL/PROFILE/ew2hor.txt horprofile -ascii; % Profile(3): E-W3 clear profx profy profxnew profynew verprofile horprofile profile = textread('/liome/albite-00/RESULTS/DECOMP/2D/PROFILE/ew3 .mat'); profx=profile( 1,:); profy=profile(2,:); compute_draw_profile verprofile = improfile(vertical,profxnew,profynew); horprofile = improfile(horizontal, profxnew, profynew); zero = find(verproflle=0); verprofile(zero) = NaN; zero = find(horprofile=0); horprofile(zero) = NaN; save /home/albite-00/RESULTS/DECOMP/2D/FINAL/PROFILE/ew3ver.txt verprofile -ascii; save /home/albite-QO/RESULTS/DECOMP/2D/FINAL/PROFILE/ew3hor.txt horprofile -ascii; % Profile(4): E-W4 clear profx profy profxnew profynew verprofile horprofile profile = textread('/home/albite-00/RESULTS/DECOMP/2D/PROFILE/ew4.mat'); profx=profile( 1,:); profy=profile(2,:); compute_draw_profile verprofile = improfile(vertical,profxnew,profynew); horprofile = improfile(horizontal,profxnew,profynew); zero = find(verprofile==0); verprofile(zero) = NaN; zero = find(horprofile==0); horprofile(zero) = NaN; save /home/albite-00/RESULTS/DECOMP/2D/FINAL/PROFILE/ew4ver.txt verprofile -ascii; save /home/albite-00/RESULTS/DECOMP/2D/FINAL/PROFILE/ew4hor.txt horprofile -ascii; % Profiie(5): N-S Red Lake Canyon clear profx profy profxnew profynew verprofile horprofile profile = textread(Vhome/albite-00/RESULTS/DECOMP/2D/PROFlLE/rlc.mat'); profx^profileCl,:); profy=profile(2,:); compute_draw_profile 165 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. verprofile = improfile(vertical,profxnew,profynew); horprofile = improfile(horizontal, profxnew, profynew); zero = find(verprofile=0); verprofile(zero) = NaN; zero = find(horprofile=0); horprofile(zero) = NaN; save /home/albite-00/RESULTS/DECOMP/2D/FINAL/PROFILE/rlcver.txt verprofile -ascii; save /home/albite-00/RESULTS/DECOMP/2D/FINAL/PROFILE/rlchor.txt horprofile -ascii; % Profile(6): N-S Devil's Lane clear profx profy profxnew profynew verprofile horprofile profile - textread('/home/albite-00/RESULTS/DECOMP/2D/PROFILE/dl.mat'); profx=profile(l,:); profy=profile(2,:); compute_draw_profile verprofile = improfile(vertical,profxnew, profynew); horprofile = improfile(horizontal,profxnew,profynew); zero = find(verprofile=0); verprofile(zero) = NaN; zero = find(horprofile=0); horprofile(zero) = NaN; save /home/albite-00/RESULTS/DECOMP/2D/FINAL/PROFILE/dlver.txt verprofile -ascii; save /home/albite-00/RESULTS/DECOMP/2D/FINAL/PROFILE/dlhor.txt horprofile -ascii; clear profx profy profxnew profynew Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

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Asset Metadata

Creator Marsic, Scott Douglas (author)

Core Title Active deformation at Canyonlands National Park: Distribution of displacements across the grabens using spaceborne geodesy

School Graduate School

Degree Master of Science

Degree Program Earth Sciences

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag Geodesy,Geology,geophysics,OAI-PMH Harvest

Language English

Contributor Digitized by ProQuest (provenance)

Advisor Owen, Susan (committee chair), Davis, Gregory (committee member), Dolan, James (committee member), Wright, Tim (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c16-312281

Unique identifier UC11327929

Identifier 1420385.pdf (filename),usctheses-c16-312281 (legacy record id)

Legacy Identifier 1420385.pdf

Dmrecord 312281

Document Type Thesis

Rights Marsic, Scott Douglas

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the au...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus, Los Angeles, California 90089, USA