University of Southern California Dissertations and Theses

Modeling of continuous tiltmeter data from the 1984 rifting event at Krafla Volcano, Iceland

(USC Thesis Other)

Modeling of continuous tiltmeter data from the 1984 rifting event at Krafla Volcano, Iceland

PDF

Download a page range

Download transcript

Copy asset link

Request this asset

Transcript (if available)

Content MODELING OF CONTINUOUS TILTMETER DATA FROM THE 1984 RIFTING EVENT AT KRAFLA VOLCANO, ICELAND by Dominique Richard 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 (GEOLOGICAL SCIENCES) December 2004 Copyright 2004 Dominique Richard Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UMI Number: 1424231 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 1424231 Copyright 2005 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. ii Acknowledgements This project was possible thanks to a great collaboration with Freysteinn Sigmundsson and Thora Arnadottir from the Nordic Volcanological Institute in Reykjavik, Iceland. I would like to express my gratitude to my advisor Susan for her guidance, encouragement and understanding. Thank you to Freysteinn Sigmundsson and Scott Paterson for thoughtful reviews. Eysteinn Tryggvason kindly accepted to come down from Husavik, lead us in the field at Krafla volcano and share data recorded at the time of the latest Krafla rifting episode. Thank you to Pall Einarsson for sharing seismic data from the 1984 rifting event and to Erik Sturkell for clarifying station coordinates. This project allowed me to participate in the Ridge 2000 summer school in 2003 and interact with many scientists. These 3 years at USC were certainly a challenge, and I believe I became a better scientist and improved my thinking, writing, programming and teaching skills. I want to thank my family and my friends Claire, Quinn, Cesar, Ilene, Ken and Nedra for being there for me. Funding for this project was provided by the Fonds de Recherche sur la Nature et les Technologies. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. iii Table of Contents Acknowledgements.............................................................................................................. ii List of Tables........................................................................................................................ v List of Figures...................................................................................................................... vi Abstract...............................................................................................................................viii 1. Introduction.......................................................................................................................1 1.1. D iking P rocess........................................................................................................................................1 1.2. G eologic Setting o f Iceland................................................................................................................8 1.3. K rafla Volcanic System and M ost R ecent Rifting E pisode......................................................10 1.4. The 1984 Rifting E v en t..................................................................................................................... 13 2. D ata.................................................................................................................................. 19 2.1. The K rafla T iltm eter N etw o rk ......................................................................................................... 19 2.2. T iltm eters.............................................................................................................................................. 21 2.3. T iltm eter Recordings o f Events at K rafla................................................................................... 23 2.4. Seism icity.............................................................................................................................................. 24 2.5. A dditional D ata S ets.......................................................................................................................... 24 3. Modeling.........................................................................................................................26 3.1. Static M o d el..........................................................................................................................................26 3.2. Tim e-D ependent M odels of D ike Propagation..........................................................................31 3.3. D ike W idening and C ham ber D eflation / Inflation H istory................................................ 34 3.4. Estim ate o f M agm a Inflow R a te ....................................................................................................34 4. Results............................................................................................................................37 4.1. G eom etry o f the D ike and M agm a Cham ber based on Inversions.......................................37 4.2. End-M em ber M odels o f D ike Propagation.................................................................................47 4.3. Com bined M odels o f D ike P ropagation......................................................................................52 4.4. G eom etry o f the D ike and M agm a Cham ber based on Forw ard M o d e lin g ...................... 54 4.5. Estim ates o f D ike W idening and M agm a C ham ber Volum e during the E ruption 58 4.6. Estim ate o f M agm a Inflation R a te ................................................................................................ 60 4.7. M agm a B a la n ce.................................................................................................................................. 65 5. Discussion...................................................................................................................... 69 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 6. Conclusions., 7. Bibliography Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. V List of Tables Table 1 Results of inversions of EDM, leveling and optical leveling tilt data.........46 Table 2 Volume changes of the Mogi source during the dike propagation and eruption...................................................................................................................60 Table 3 Magma input and output......................................................................................67 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. vi List of Figures 1. Map of Iceland............................................................................................... 9 2. The Krafla volcanic system......................................................................... 11 3. Migration of earthquake epicenters away from the Krafla caldera 14 4. Fissure eruption at Krafla volcano.............................................................. 15 5. Model parameters.......................................................................................... 16 6. Vertical displacements due to point source and tensile dislocation 17 7. Graphs of the east and north tilt components recorded from September 1 to September 30, 1984................................................................................ 20 8. Networks of geodetic stations at Krafla volcano....................................... 22 9. Schematic representation of the distribution of minima and maximum when using the random cost method............................................................. 29 10. Results of inversions of EDM data only to constrain the position and strike of the dike............................................................................................. 38 11. Chi-squared values for inversions of EDM data....................................... 39 12. Results of inversions of dry tilt and continuous tilt data.......................... 41 13. Results of inversions of EDM, leveling and dry tilt data......................... 42 14. Chi-squared values associated with the parameters inverted for the inversions of the EDM, leveling and dry tilt data sets.............................. 43 15. Results of inversions of EDM, leveling, dry tilt and continuous tilt data.................................................................................................................. 44 16. Chi-squared values associated with the parameters that were inverted for the inversions of the EDM, leveling, dry tilt and continuous tilt datasets.......................................................................................................... 45 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. vii 17. Correlation between model parameters.................................................... 48 18. Vertical (a) and lateral (b) dike propagation models.............................. 49 19. Model tilt resulting from the vertical dike propagation model compared to the continuously recorded tilt data....................................... 50 20. Model tilt resulting from the lateral dike propagation model compared to the continuously recorded tilt data......................................................... 51 21. Additional dike propagation models......................................................... 53 22. Model tilt for the models combining the lateral and vertical propagation models....................................................................................... 55 23. Model tilt resulting from the oblique dike propagation model compared to the continuously recorded tilt data....................................... 56 24. Dike widening and magma chamber deflation/inflation between September 5 ,1 1 :00 and September 18, 8:30............................................ 59 25. Results of weighted least squares inversions of continuous tilt data from September 18-21, 1984...................................................................... 62 26. Results of weighted least squares inversions of continuous tilt data recorded during the eruption, September 5-7, 1984................................. 64 27. Schematic diagram of magma balance at Krafla volcano, September 4-18, 1984...................................................................................................... 68 28. Dike growth vs. deflation volume of the shallow magma chamber.......................................................................................................... 72 29. Map of the seismicity recorded during the 1984 rifting event at Krafla volcano, Iceland.......................................................................................... 75 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. viii Abstract Surface deformation at Krafla volcano during the 1975-1984 rifting event in Iceland was monitored by three continuously recording tiltmeters located around the southern end of the eruptive fissure. The tiltmeter time series was compared to models of dike propagation and magma chamber deflation by computing model tilt from a growing dislocation [Okada, 1985] and a deflating Mogi source [Mogi, 1958] in an elastic half-space. Results favored a vertical dike propagation model and indicated that the dike propagated vertically for at least the last km. Including continuous tilt data in random cost inversions confirmed the dike and magma chamber geometry, but suggested a variable along-strike dike opening. Forward models constrained the dike opening and magma chamber volume changes during the eruption. Magma balance calculations indicated that magma outflow from a shallow source was less than magma output. There may be a deeper and more extensive magma source beneath the rift zone. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 1. Introduction 1.1. Diking Process Dike intrusion is one transport mechanism of magma from an often unknown source through cracks in continental and oceanic lithosphere. This process is widely accepted as an efficient transport mechanism, but it is still poorly understood. Submarine expeditions [e.g., U.S. Geological Survey Juan de Fuca Study Group, 1986], seafloor imaging [Chadwick et al., 1991], geodetic [e.g., Anderson et al., 1997] and seismic data [e.g., Okada and Yamamoto, 1991], and data from underwater hydrophones [e.g., Dziak et al., 1995] have improved our understanding of how magma reaches the seafloor at mid-ocean ridges. Dike intrusions not only occur at divergent boundaries, but also at convergent plate boundaries [e.g., Okada and Yamamoto, 1991; Linde et al., 1993; Hayashi and Morita, 2003]. The processes are similar to those that occur at mid-ocean ridges. In both settings, the intrusions occur due to reduced compressive stresses in the oceanic crust. For example, the volcanic and seismic activity off Japan on the Philippine Sea plate, which has been studied extensively, is often explained by dike intrusions resulting from reduced compressive stresses caused by the bending of the Philippine Plate as it is being subducted along the Sagami trough [Nakamura, 1980], More easily accessible areas such as Iceland provide a direct insight on the direction and rates of dike propagation. Such information on the propagation of dikes can be useful in determining the location, depth and dimensions of magma Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2 reservoirs in the crust beneath fissure systems and central volcanoes. Tighter constraints on these 3 variables can be obtained by combining the propagation information with ground subsidence/uplift contemporaneous with diking and most likely associated with magma flow into or out of magma bodies. The analysis of dike intrusions is complex. The propagation of a dike in the lithosphere depends on several factors. The forces driving dike initiation and the consequent movement of magma through the lithosphere are most important. There must be sufficient pressure for magma to flow away from the source and to keep the walls of the dike opened. The driving forces for the propagation of magma-filled cracks are (1) excess pressure in the magma chamber, (2) magma buoyancy and (3) regional tectonic stress normal to the dike plane [Rubin, 1995]. The initial dimensions of a dike possibly influence the total duration of the propagation of a dike along with other factors [Meriaux and Jaupart, 1998]. Based on computer models of a dike propagating vertically through an elastic plate, it was found that a dike’s initial opening may control the magma flux into the dike, instead of the magma flux controlling the dike opening. They also found that magma flux in the dike increased during ascent. Sometimes, dikes freeze before reaching the surface or while melt moves along a rift zone because magma loses heat as it moves through colder crust [e.g., Fialko and Rubin, 1998]. Dike expansion during growth may prevent the freezing of dikes [Meriaux and Jaupart, 1998], This increasing Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3 magma flux implies that the source can supply the dike, which may not always be the case and can cause an eruption’s intensity to fluctuate. Whether the host rock deforms elastically or inelastically also has an effect on the dike growth [Rubin, 1993], but the amount of inelastic deformation is difficult to quantify. Some parts of the dike may behave elastically whereas other parts may behave inelastically. Therefore, most models reproducing observed surface deformation consider the host rock to behave elastically. In models of dike growth, the crust is often considered to be homogeneous and isotropic, which is not necessarily the case. For example, the crust in volcanic zones may consist of basaltic lava flows, volcaniclastic deposits and sediment, which creates strong mechanical contrasts. Layers of different composition and/or mechanical properties may affect a dike’s growth and may cause it to stop ascending/propagating in some instances [e.g., Baer, 1991; Gudmundsson, 2002]. A dike may become arrested at a weak contact, or simply be diverted. Based on outcrop exposures, dikes seem to often be in segments for which connections are not always obvious. A propagating crack fractures a host rock with specific properties, such as strength and temperature, which also influence the propagation of the crack [e.g., Baer, 1991]. Moreover, magma can flow into existing cracks, or it can flow into a new fracture. Either of these situations will influence the propagation direction of Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4 dikes because the corresponding stress field near the tip of the dike will be different. In some cases, this near-tip stress field may dictate the propagation direction. The list of controlling factors mentioned is more extensive, but the purpose of this overview was to give an idea of the complexity of dike intrusions. Therefore, a dynamic growth model of a dike intrusion should consider all of these factors, which may affect laterally- and vertically-propagating dikes differently. It is usually impossible to consider all the factors involved in the propagation of a dike and assumptions must be made. Dikes are often considered part of the plumbing of a volcanic system, which can include many magma bodies of various aspect ratios and sizes at different depths. Dikes can efficiently transport magma from one body to another, and in some instances, to the Earth’s surface. Mafic magma is mostly transported through fractures whereas granitic, more viscous, magma mostly rises through the lithosphere by other means such as diapirism [e.g., Miller and Paterson, 1998], although it is possible that viscous magma could be transported in dikes [e.g., Rubin, 1993], Mafic magma movements can occur on very short time scales of up to a few hours. Therefore, the analysis of seismic and geodetic data such as leveling, electronic distance measurements (EDM), Global Positioning System (GPS), and tilt has proven to be useful in resolving the temporal and spatial evolution of these magma plumbing systems. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5 The seismicity often recorded during diking events is directly related to the growth of dikes [e.g., Einarsson and Brandsdottir, 1980; Hayashi and Morita, 2003], even though the crustal deformation may go on longer than the seismicity associated with the same intrusion [Aoki et al., 1999]. Stresses in the crust may be such that earthquakes occur at the beginning of dike propagation and become much smaller or imperceptible as the dike continues to grow. Also, the correlation between the location of epicenters and the location of a dike front is unknown because the causes of these earthquakes are not well understood [Rubin, 1993; Rubin and Gillard, 1998], Therefore, the seismicity associated with dike intrusions may provide information on part of a diking event (e.g., propagation direction, rate of propagation), but may only represent a partial record of the dike growth. For example, Einarsson and Brandsdottir [1980] observed earthquakes that migrated away from the Krafla magma chamber during the July 1978 rifting event in Iceland. There was a gap on July 11 between 10:00 and 11:00 where seismicity stopped and started again further north. Therefore, the seismicity did not track the whole dike propagation. Surface deformation measurements have been able to document the entire propagation of a dike [eg., Aoki et al., 1999]. Aoki et al. [1999] modeled the spatio-temporal evolution of a 9-day long intrusion. Earthquakes migrated vertically in about 12 hours, but modeling of tilt and GPS measurements indicated that the dike propagated vertically for several days. Surface deformation lasted about 10 days, whereas 80% of the seismic moment was released during the first 2 days of the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 6 event. There might have been other sources of deformation other than the dike propagation, but the amplitude and timing of the deformation signal indicated that it was most likely associated with the ongoing intrusion. These dike intrusion studies support the idea that seismicity does not necessarily record the complete evolution of a propagating dike. Seismicity mostly reflects stress, which is released when magma forces its way through the crust. It is probably normal not to observe complete correspondence between dike evolution and seismicity. The propagation direction of dikes, whether in oceanic or continental lithosphere, on land or under water, is still an unresolved question even though ground deformation and seismic data, where available, have provided strong constraints. Because seismic events at mid-ocean ridges can be very small (M<4), they are often undetected. A seismic swarm that started on June 26, 1993 and that propagated along the CoAxial Segment of the Juan de Fuca Ridge, was recorded by a recently installed real-time monitoring system. There was a localized initial burst of seismic activity, which lasted ~8 hours. Five hours later, seismic activity increased and the epicenters migrated north for the next ~14 hours. The seismic swarm then focused at a northern site, about 25 km NNE of the southern swarm site. This first recorded seismic swarm at a mid-ocean ridge was interpreted as evidence for a lateral dike injection into faults and fissures [Dziak et al., 1995]. Other seismic swarms have been detected since then. Dziak et al. [2002] reported a seismic swarm Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 7 at the Lucky Strike Segment along the Mid-Atlantic Ridge, but a migration of earthquakes was not observed. Magma transport processes through dike propagation has also been studied by looking at ancient dikes now exposed at the surface. Flow indicators observed mostly at the dike margins [e.g., Philpotts and Asher, 1994] and magnetic fabrics [e.g., Ernst and Baragar, 1992] have helped to determine the flow direction of magma and the propagation direction of tensile fractures. Some field studies support the lateral flow of magma in fractures. Studies of mega-swarms (hundreds of kilometers along strike) support a magma flow pattern that is vertical some distance from the magma source and lateral for larger distances [e.g., Ernst and Baragar, 1992], Philpotts and Asher [1994] found an example where magma rose in the middle of an en-echelon segment (-10 km long) of a giant diabase feeder dike and spread laterally toward the ends of the segment. However, whether or not these mega-swarms of dike intrusions are similar to the smaller scale dike intrusions is undetermined. The scale of dikes is certainly an important factor to consider when discussing their propagation. Many dike propagation models have been suggested through the years and have been reviewed in Rubin [1995], All of these models attempt to describe the shape of a dike’s leading edge [e.g., Maaloe, 1998], a dike’s dimensions, and a dike’s direction and rate of propagation. It is difficult to attribute a dynamic model to the emplacement of a specific dike because it is often a challenge to gather enough Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. evidence to discriminate between models. A dike may propagate laterally, vertically, or obliquely. It can possibly ascend in the lithosphere and then propagate laterally when it reaches a level of neutral buoyancy or when the excess magma pressure is insufficient to feed the dike. When magma pressure from the source is insufficient to be the driving force, the dike walls may close and the dike grows as an isolated pulse. Determining magma sources and their distributions is a challenge in itself. As mentioned above, field studies suggest that magma may rise as several ‘fingers’, forming a series of en echelon dike segments from a source capable of producing magma of the same composition over hundreds of kilometers [e.g., Fink and Pollard, 1985; Philpotts and Asher, 1994], Early work by Pollard et al. [1975] suggested that offset vertical dike segments were parallel to the propagation direction and that dikelets vertically growing off of the segments were perpendicular to the propagation direction. This interpretation could be challenged. There is still much to learn about dike intrusions and Iceland has been an ideal location for many workers attempting to better understand the diking process. 1.2. Geologic Setting of Iceland Iceland, a volcanically active ocean island, is located along the Mid-Atlantic Ridge, between the Reykjanes and Kolbeinsey Ridges (Figure 1). Iceland owes its existence to the presence of a mantle plume at latitude ~65° under central east Iceland beneath Vatnajokull; therefore its crust is unusually thick, up to 40-41 km thick over the plume [Darbyshire et al., 2000], compared to normal oceanic crust. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 9 336°40’ 340°00' 343°20' 346°40' 66°40' 63°20’ Kolbeinsey Ridge Tjomes Fracture Zone Reykjanes Peninsula 'Si 0 50 100 Q Volcanic center with a caldera # Glacier )t< Faults in transform zone Fissure swarm 66° 40' 63°20' 336°40' 340°00' 343°20’ 346°40' Figure 1. Map of Iceland. Outlined are the fissure swarms within the neovolcanic zone with their associated central volcano and caldera. In light grey are the ice caps. The largest ice cap is the glacier Vatnajokull. The Reykjanes Ridge is to the southwest o f the island, just off o f the Reykjanes Peninsula. The Kolbeinsey Ridge is to the north of the island, with the Tjomes Fracture Zone as a transform joining the ridge with the Theistareykir fissure swarm. The main volcanic systems in northern Iceland are Theistareykir (Th), Krafla (K), Fremri-Namur (F), Askja (A), and Kverkfjoll (Kv). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 10 Most of the igneous activity, occurring as dike intrusions and fissure eruptions, is focused in the “neovolcanic zone”, which is composed of the East, West, and North Rift Zones, and the Reykjanes Peninsula. Each rift zone consists of en-echelon fissure systems, which generally consist of fissures dipping vertically at the surface, normal faults, grabens, and a central volcano sometimes with a collapsed caldera. Rifting events, occasionally associated with eruptions, occur periodically to release strain accumulated due to the tensional tectonic stress caused by the divergence of the North American and Eurasian plates at a full-spreading rate of ~1.9 cm/yr. Excess pressure in the magma chamber possibly triggers the propagation of dikes [Einarsson and Brandsdottir, 1980]. There are many features observed in Iceland, such as rifting events, which are analogous to mid-ocean ridges that are not affected by hot spot magmatism. En-echelon segments are present, mostly in the North Rift Zone and Reykjanes Peninsula. A rift is propagating to the southwest in the East Rift Zone [Gudmundsson and Brynjolfsson, 1993]. The geologic record indicates that there were several ridge jumps toward the hot spot as the tectonic plates drifted to the west. At present, the West Rift Zone and the East Rift Zone are two parallel spreading centers that overlap in south central Iceland [Gudmundsson, 2000]. 1.3. Krafla Volcanic System and Most Recent Rifting Episode The Krafla volcanic system, ~100 km long and ~6 km wide, in northeast Iceland, has been active for at least 300 ka (Figure 2). The Krafla central volcano and fissure system is bounded by normal faults to the east and west. The caldera is Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 11 17°00'W 16°50'W 16°40'W 17°00'W 16°50'W 16°40'W Figure 2. The Krafla volcanic system. The inset shows the location of the Krafla volcanic system (star), which consists of many fissures and normal faults that transect the caldera. The 1984 lava flow is a dark shade of grey and the fissure (black dashed line), which fed the 1984 eruption, consists of many segments. Lava erupted outside the caldera was primitive, but the lava erupted within the caldera rim was more evolved. Shown are the 100 m elevation contours. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 12 located at the center of a 15 km diameter shield volcano, and is transected by numerous north-south striking fissures. The Myvatn Fires rifting episode (1724-1729) was the oldest historically recorded episode [Bjomsson et al., 1977]. Rifting occurred mostly to the south of the caldera. The most recent and second historical rifting episode at Krafla began in 1975 and ended in 1984 [Tryggvason, 1986]. This episode consisted of 22 rifting events that were characterized by rapid deflation and longer inflation events in the center of the caldera. Most rifting events occurred north of the caldera, even though a few occurred south of the caldera. Only 9 of the events led to volcanic eruptions. By the end of the rifting episode, there was a total horizontal extension of 9 m across the fissure zone [Tryggvason, 1986], Magma intruded, in some instances, away from the magma chamber at a distance of up to ~40 km from the center of the caldera (~14 events), but 7 intrusions were within 1 km of the magma chamber. The intrusions associated with the rifting events often did not propagate to the surface. In fact, the first half of the episode was characterized by numerous intrusions and the majority of eruptions occurred during the second half of the episode. This episode was the subject of seismic, geodetic, structural and petrological/geochemical studies that focused on determining the magma source(s) and the geometry of eruptive fissures. Petrological studies [Nicholson, 1990; G ronvold, pers. comm., 2002] revealed that primitive lava was erupted from most of the fissures’ length; however, the lava composition within the caldera was more evolved due to differentiation in Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 13 the reservoir(s) prior to eruption. The bimodality of the lava, which was characteristic of both the Myvatn and the Krafla fires [Gronvold, pers.comm., 2002], favored a vertically propagating dike transporting magma from a source other than the Krafla shallow magma chamber. This reasoning stemmed from the idea that the more primitive magma came from a different and deeper source, contrarily to the more evolved magma that most likely came from the shallow magma chamber located within the caldera. Earthquakes observed during most intrusive events of the 1975-1984 rifting episode, migrated laterally away from the shallow magma chamber (Figure 3) [Einarsson and Brandsdottir, 1980], except for the 1984 event. Also, the deflation of the caldera magma chamber during all the intrusions indicated that magma may have traveled laterally from this central source during the formation of the fissures. The Krafla seismic swarm has been cited in many studies as evidence that dikes propagate mainly laterally from their source. 1.4. The 1984 Rifting Event The last rifting event, the subject of this study, began on September 4, 1984 and ended on September 18, 1984. There were 2 years and 9 months of quiescence between the 1984 event and the previous event. At ~20:20 on September 4, there was rapid deflation of the magma chamber followed by volcanic tremor, and the eruption began nearly 4 hours later at 23:49 that same day [Tryggvason, 1986], The first fissure vent erupted ~6 km north of Leirhnjukur, and a second vent erupted within a minute ~3 km south of the first segment [McClelland et al., 1989], The 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. Distance from the center of the Krafla caldera (km) Figure 3. Migration of earthquake epicenters away from the Krafla caldera. It occurred on July 10th and July 11th during the July 1978 deflation event, with no associated eruption. This pattern has been observed for many rifting events during the 1975-1984 rifting episode. Dots represent epicenters that have an error of 1 km and less and open circles represent epicenters with errors between 1 and 2 km [Einarsson and Brandsdottir, 1980]. • • 0 % ° o o * * = <*>« „ . s *> V ° . • ° 0 O ° < P • 0 -* o fif* o o ° ° o O 0 o ° . ° » • o 0 J U \ V Oo° o o o H • O • ° o o • O ° ° O & •o C D 18 19 20 21 22 23 24 1 July 10 July 11,1978 15 vents joined within an hour to form an 4). erupted, forming a ‘curtain of fire’ (Figure 8.5 km long fissure from which lava Over 110 x 106 m3 of lava erupted, Figure 4. Fissure eruption at Krafla volcano [7V V 7]. which was the largest amount of lava erupted during any one given eruption of the 1975-1984 rifting episode [Rossi, 1997]. The eruption rate was high along the whole fissure for the first few hours, but then the intensity of the eruption greatly decreased in some sections of the fissure [Tryggvason, 1986]. From September 6 until the end of the eruption, the volcanic activity was focused in the northern part of the fissure at one crater. The eruption was relatively vigorous at this vent until the afternoon on September 18 where it stopped [McClelland et a l, 1989]. Because of the abrupt way that the eruption ended, it was possibly stopped by the blockage of the magmatic conduit, instead of the magma supply being insufficient [Tryggvason, 1986]. The dike dimensions and position, as well as the magma chamber location, were evaluated by inverting EDM, leveling, and optical leveling tilt measurements [Arnadottir et al., 1998]. The static model that reproduced the observed surface deformation consisted of (1) a deflating magma chamber at the southern end of the eruptive fissure and (2) a vertical dike that transported magma to the surface. The magma chamber was modeled as a Mogi point source [Mogi, 1958]; the dike, as a 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. Strike North Height Point source deflation/inflatioi volume Figure 5. Model parameters. Tensile dislocation [Okada, 1985] and point source [Mogi, 1958], both in an elastic, homogeneous, isotropic half-space. The radius of the point source must be small compared to its depth. This is the preferred model to reproduce the surface deformation during the 1984 rifting event at the Krafla volcanic system [Arnadottitr et al., 1998]. os 17 Mogi point source parameters - depth: 3 km - volume change: -0.01 km^ Vert, exagg. ~ 27000 § 0.05 - 6 o o 0.1 - c u 05 5 0.15- W ■ g 0,2 > 0.25 Dislocation parameters - length: 9 km - height: 7 km - depth: 7 km opening: 1 m strike: 0° dip: 90° Vert, exagg. ~ 62000 e « 0.15 - -e 0.05 - Dislocation ' ' Mogi source § « 0.05 - SUSP* 55000 Vert, exagg. a - 0 .0 5 . - 5 km 5 1 0 ' Figure 6. Vertical displacements due to point source and tensile dislocation. Theoretical deformation caused by a tensile dislocation [Okada, 1985] and a Mogi point source [Mogi, 1958] in a homogeneous, isotropic, and elastic half-space. The figure illustrates the deformation caused by a Mogi source and a dislocation alone, and then the combined deformation. Tilt is the gradient of vertical displacements. Parameter values are arbitrary. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 18 type I dislocation, both in a homogeneous, isotropic and elastic half-space [Okada, 1985] (Figures 5-6). Dike parameters that resulted in the best fit of these data were: 9 km length along strike, 7 km depth, 1 m opening, ~5° strike, and 90° dip [ . Arnadottir et al., 1998]. The dike depth was however not well constrained. The magma chamber, located at (65.7151°N, 16.8056°W), was 2.8 km deep with 0.032 km3 of deflation. The volume change of the magma chamber was evaluated from a maximum ground subsidence of 0.98 m. In the present study, continuous tilt data were compared to elastic dislocation and point source models of the surface deformation using results from Arnadottir et al. [1998] as a starting model. Dynamic models tested the direction of dike propagation. Continuous tilt data from three stations located around the southern end of the eruptive fissure spanned the entire time of the September 1984 dike propagation [Tryggvason, 1986]. These data represented a unique insight in the diking processes because they documented the ground deformation every 30 seconds between dike initiation (~20:20) and eruption (23:49). The other data sets consisted of data measured up to 5 months before and up to 1 1/2 years after the rifting event and so were affected by deformation that occurred before and after the dike propagation. The geometry of the dike and magma sources had been investigated [Tryggvason, 1986, Arnadottir et al., 1998], but the dike propagation itself had not been modeled. Our results showed that a vertically-propagating dike could be distinguished from a laterally-propagating dike. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 19 The dike widening and chamber deflation history throughout the dike propagation and eruption were also modeled to evaluate whether the modeled total magma flow out of the chamber was consistent with the volume of lava erupted and emplaced as a dike. It is unlikely that the shallow magma chamber provided the totality of the magma. Findings on the propagation direction of the feeder dike and magma budget could have direct implications for the understanding of magma accretion at mid-ocean ridges and on the spatial distribution of magma bodies along rift zones. 2. Data 2.1. The Krafla Tiltmeter Network Continuous tilt data recorded by the Nordic Volcanological Institute (NVI), now the Nordic Volcanological Centre, during the September 1984 fissure eruption at Krafla volcano, northern Iceland, represented a unique data set spanning the entire rifting event. Three electronic tiltmeters, located both around the center of deflation and the southern end of the fissure, recorded north-south and east-west components of tilt (Figure 7) with a precision of 1-3 /<rad [Tryggvason, 1986]. This degree of precision was sufficient given the large tilt variations during the 1984 diking event. Tilt records for the September 4 eruption contain tilt values at all 3 stations for the 3.5 hours of propagation, recorded at 1-minute intervals. 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. 50 £,□-50 □-too □ -150 Tiltmeter at Station Litli Leirhnjukur Tiltmeter at Station Viti ■ north ■ east down to north + down to east - 5 10 15 20 Time (days) km 0 5 • Electronic tiltmeters north east down to north + down to east + 5 10 15 20 Time (days) Tiltmeter at Station Krafla Litli Leirhnjukur down to north - down to east + Krafla □ 100 5 10 15 20 Time (days) Figure 7. Graphs of the east and north tilt components recorded from September 1 to September 30, 1984. Tilt data are plotted such that the tilt rate is negative during magma chamber deflation. A fissure eruption started on September 4, which was observed as an abrupt change in tilt at all 3 stations. The 3 continuously recording tiltmeters were located around the southern end of the eruptive fissure. Indicated on the figure are the approximate location of the shallow Krafla magma chamber, and the areal extent of the lava erupted during the 2 weeks of the eruption. g 21 2.2. Tiltmeters Magnetoresistor electronic tiltmeters [Tryggvason, 1982] were designed by NVI to closely monitor the deformation at Krafla volcano. Four of these electronic instruments were operating at Krafla volcano in Iceland, but only three were close enough to be useful in modeling the September 1984 rifting event: Krafla (powerhouse), Litli Leirhnjukur, and Viti (Figure 8). The 4th tiltmeter, Bjarnaflag, was located ~10 km south of the deflation/inflation center, east of Lake Myvatn, but its data were not considered in this study because the station was too distant from the caldera to record significant tilt associated with the event. The first electronic tiltmeter was installed at the powerhouse in mid-August 1977. The instrument consisted of a pendulum tiltmeter with a magnetoresistor transducer. Although the instruments were sensitive to ground freezing (thermal strain), the data recorded were still useful for monitoring magmatic activity at Krafla because the magmatic and thermal signals acted on different time scales. In the present study, seasonal and daily thermal effects on the tiltmeter data were not significant because the propagation time was only ~3.5 hours. A water tube tiltmeter had been installed at the Krafla powerhouse, but readings were made once a day, which was insufficient to observe tilt changes during rapid deformation events. The Krafla tiltmeter was located in a concrete cellar below the transformer platform under a i m layer of scoria at the Krafla powerhouse. The floor of the cellar was 3.4 m below the ground surface. The Viti tilt station was installed in Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 22 17°00'W 16°50'W 16°40’ W caldera ♦ ♦ ♦ ▲ ▲ 0 km - 65°50'N ▲ Optical tilt stations ♦ Leveling benchmarks ■ EDM stations • Electronic tiltmeters - 65°40'N 17°00'W 16°50'W 16°40'W Figure 8. Networks of geodetic stations at Krafla volcano. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 23 September 1978 in a 2 m deep hole in young volcanic rocks (lava and scoria). The Litli Leirhnjukur tilt station was installed in February 1979, and its depth and rock type were similar to the Viti installation. 2.3. Tiltmeter Recordings of Events at Krafla As discussed by Tryggvason [1982 and 1986], the Litli Leirhnjukur tilt station showed the most fluctuations in its tilt record. Extremely rapid tilt changes were observed at the Litli Leirhnjukur station during subsidence events in March 1980 and October 1980, and these changes may have been associated with the movement on nearby fissures or faults. The geothermal activity in the area also possibly contributed to the tilt signal in other magmatic events, including the September 1984 event. A shallow low-velocity zone about 500 m thick was detected in 1988 around Leirhnjukur [Brandsdottir and Menke, 1992] and interpreted as the result of hydrothermal alteration of the rocks. These slower waves were a secondary phase modeled as a compressional to shear wave conversion at the base of the zone. The Viti station had systematic 24-hour period oscillations of up to 3 prad possibly due to temperature variations in the box covering the tiltmeter. The Krafla tilt station recorded a smooth signal associated mostly with the chamber deflation because of its proximity to the chamber. In order to achieve the best results, the modeling focused on fitting the Krafla and Viti tilt data. It was impossible to fit the tilt data from Litli Leirhnjukur station reasonably well with a simple dike and magma chamber model that was consistent with other geodetic data. Since Litli Leirhnjukur was most likely Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 24 influenced by local geothermal activity, we do not include it in our determinations of the best-fitting models; however, for completeness, we do show how the various models compared to the tilt recorded at this station. The time period of the dike propagation was set to be from 20:20 to 23:49. The onset of the dike propagation did not necessarily coincide with the beginning of the chamber deflation, but it was probably close. It is possible that the dike began growing before the shallow magma chamber began deflating. This scenario would support an additional and deeper source. 2.4. Seismicity The number of earthquakes at Krafla volcano started to increase at 20:59 on September 4, 1984. An earthquake occurred at 20:20, but the epicenter was ~100 km west of the rift zone. Most of the epicenters were located around the northern end of the fissure. It is also worth noting that there were significantly fewer earthquakes for this event than for previous events [Einarsson, pers. comm., 2003]. 2.5. Additional Data Sets Leveling, optical leveling tilt (or dry tilt) and EDM data (Figure 8) were used in this study. Leveling data are height differences between identified benchmarks usually arranged in a grid. For measuring optical leveling tilt, 5 markers formed a circle 25 m from a mark in the center of the circle. Tilt values were measured for each marker on the circle relative to the center mark and combined to find a east and north tilt components. EDM data are distance measurements between benchmarks. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 25 These data sets were collected before and after the 1984 rifting event they were used to constrain the dike geometry and the location of the magma chamber for the 1984 eruption. When finding models that fit the continuous tilt data, we required that these models also closely fit the EDM, leveling and optical leveling tilt data sets. Each data set by itself is insufficient to solve for the geometry of the dike and the magma chamber during the September 4-18 period due to the extended time period between observations (EDM data) or due to the network geometry (optical leveling tilt and leveling). Therefore, a combination of the data sets is necessary to obtain the most realistic estimate of the dike and magma chamber geometry. The leveling data were collected on April 10, 1984 and September 7, 1984 [Bjornsson et al., 1985]. The EDM data set used in this study consisted of 49 data obtained from measurements in March 13-28, 1984 and March 6-17, 1986 [Tryggvason, 1993]. The geodimeter network is mostly to the east of the fissure and north of the center of deflation, which is an inadequate network to locate the magma chamber. Optical leveling tilt stations are mostly located around the southern end of the 1984 fissure and south of the caldera. Readings of east and north tilt components from 16 stations in June 1984 and September / October 1984 [Tryggvason, 1995] are also part of the data used in this study. The dry tilt data set by itself is insufficient to constrain the dike position, since most stations of the network are located south of the 1984 fissure. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 26 3. Modeling The 1984 feeder dike was modeled as a rectangular tensile dislocation [Okada, 1985] with a uniform opening. The shallow magma chamber was modeled as a Mogi point source [Mogi, 1958], A Mogi source gives a good approximation to a spherical source when the source radius is small compared to its depth. Otherwise, modeled values may not be accurate. Both deformation sources were assumed to be in a homogeneous, isotropic and elastic half-space. The theoretical surface displacements are a non-linear function of the changes in the dislocation parameters (3-dimensional position, length, height, strike, and dip) and the Mogi source parameters (3-dimensional position). However, the deformation field is a linear function of the changes in the dislocation opening and in the Mogi source volume. Although volume changes of a volcanic edifice are linear as a source inflates/deflates, they do not exactly reflect subsurface magma chamber volume changes (-150%, [Delaney and McTigue, 1994]) because of the elastic properties of the country rocks. 3.1. Static Model Using the dislocation and Mogi source model just described, total surface deformation measurements (EDM, leveling and optical leveling tilt data) were inverted with the random cost method [Berg, 1993] to test the reproducibility of the Arnadottir et al. [1998] results, which were found using a different non-linear optimization algorithm. The inversions were used to infer the final dike position and Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 27 geometry, and the shallow magma chamber position associated with the 1984 rifting event. The parameters were found by looking for a model that minimized the misfit to the data. Reduced chi-squared values (x2 ) were used to evaluate the “goodness” of the fit to the data, where the x2 was defined as: 1 X 2 = ~ y . w h robs - 'm odel)! Where y = N - M V The calculation of a chi-squared value consisted mainly of calculating residuals between N data points (r0 b S ) and N model values (rm o dei)5 and multiplying each residual by a certain weight factor (w0. i represents each individual observed or predicted value and M represents the number of model parameters that were inverted for. The complete matrix W of values W j was obtained by doing a Cholesky factorization of the inverse covariance matrix of each data set. When inverting data to find a best set of model parameters, it is advantageous to set tighter bounds on parameters when possible, or to reduce the number of varying parameters to simplify the inversions. Each parameter is resolved more quickly when the number of parameters is smaller. Reasonable values can also be assigned to some parameters that are already better constrained by other data sets. The dip of the dike and the bounds on the dike length and strike were estimated based on the surface expression of the eruptive fissure. Inversions were conducted using the random cost method, which tested model parameters within specified bounds. These bounds were tested with a few Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 28 inversions to make sure that these bounds were wide enough. A x 2 value was calculated for each geometry tested and the distribution of the x 2 values for each parameter was plotted to define the appropriate bounds. The minimum x2 value had to be between the upper and lower bounds. However, when the lowest x2 value was about the same for all reasonable parameter values, it meant that the data set could not constrain that parameter. The random cost method first consisted of randomly picking a starting set of parameters, and calculating the x2 value associated with the set. Subsequently, based on this starting model, a grid of models to test was generated and each model was kept if it passed a series of tests. A x 2 value was calculated for each set of parameters that passed the tests. The x2 values were compared to the value of the starting model to look for a local maximum or local minimum (Figure 9). Next, based on each model’s x2 value, the models were divided into a pool of models that fit the data worse than the starting model and a pool of models that fit the data better than the starting model. Then, the next set of parameters to test was randomly picked from one of the pools, based on statistical probabilities. The set of new starting parameters picked could have been worse or better than the starting model. This method prevented the process from being trapped in a local minimum and improved the likelihood of finding a global minimum. Each subsequent model tested depended partly on the previous model tested. The difference between the models Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 29 2 Figure 9. Schematic representation of the distribution of 4 minima (1,2,3 and 4) and a maximum (6) when using the random cost method [Berg, 1993], The minimum with the lowest y-axis value is the global minimum. decreased as the models converged toward the global minimum. The models generated and their associated x2 were saved in a table. A new starting model was then totally randomly picked and everything just described was repeated. There were a total of 98 new randomly picked starting models, thus each inversion resulted in 98 tables. After -25 inversions, the likelihood of finding a best-fitting model with a global minimum x2 value was high. The x2 values were useful for means of comparison between parameter sets rather than for determining absolute x2 values. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 30 The random cost method was chosen because a set of best-fitting parameters could be found relatively quickly compared to other methods such as Monte Carlo, and the probability that it found the best-fitting model was very high. The Monte Carlo method consists of purely randomly picking a very large number of trial models within the defined parameter space in order to find a global minimum, which is time consuming. Berg [1993] estimated that the random cost method is 101 1 faster than the pure random sampling method. The gradient-based method consists of randomly picking a trial model and then conducting iterations that lead down a path of lower x 2 values, which means the inversion process may cause a steep descent toward a local minimum, without a chance of finding another minimum. This process must be repeated many times to make sure to find a global minimum, and not only local minima. The random cost method is one of the methods that combine the Monte Carlo and gradient-based methods. EDM, leveling, dry tilt and electronic tilt data were used in the inversions. The geodetic stations where measurements had been made were distributed over the area of the Krafla volcanic system. Each data type was associated with a specific network of stations, and the geometry and location of the networks influenced the outcome of the inversions. The EDM data and the dry tilt data were inverted individually to evaluate how each data set constrained the various model parameters. However, the leveling and continuous tilt data sets were too small to be inverted individually. Because the EDM benchmarks were located mostly east and north of Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 31 the dike, the EDM data set was used to determine the best location and strike of the dike. The EDM, leveling, and optical leveling tilt data were then inverted together to find a best set of parameters, while maintaining the location and strike of the dike fixed to the values found with the inversions of the EDM data. If these parameters were not fixed for the inversions, the dike’s position was many kilometers to the west of the surface expression of the eruptive fissure. The other data sets did not constrain the dike’s position well because the stations were to the south and around the southern end of the fissure. Inversions that included the continuous tilt data (Sept. 4-18) in the data set were conducted to confirm that the parameter values that resulted from inversions of the EDM, leveling and dry tilt data would also be consistent with the continuous tilt data. 3.2. Time-Dependent Models of Dike Propagation Time-dependent models of the dike intrusion involved testing a series of forward models that reproduced most closely the continuous tilt data recorded during the ~3.5 hour-long dike propagation. The intent was to determine the propagation direction of the dike. Preliminary modeling entailed testing two end-member time- dependent models of different propagation directions using the dike and magma chamber geometry from the co-eruptive inversions of EDM, leveling and optical leveling tilt data. The 2 end-member models were the vertical and lateral propagation models, which were compared to the continuous tilt data recorded between 20:20 and 23:49 on September 4. The tilt values recorded at 20:20 were Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 32 subtracted from the tilt values recorded during this time interval in order to only consider tilting that occurred during the dike propagation. Some dike and magma chamber parameters (e.g., dike opening, Mogi source location and deflation volume) were adjusted to improve the fit to the tilt data because the dike opening and the volume change of the magma chamber were obviously different for the dike propagation period than for the whole September 4-18 event. The Mogi source was moved ~1 km because the Krafla tilt record could not be fit otherwise. Subsequent modeling investigated the resolution of the end-member models and involved combining these two end-member models. The purpose was to determine whether the deformation recorded by the tiltmeters was sufficient to constrain the propagation direction along the entire length of the dike and from the time of dike initiation to eruption. The tiltmeter data were divided into 15 equal time intervals for all tested models. However, for no specific reasons, the tiltmeter data was divided into 18 equal time intervals for the lateral propagation model. Modeling involved modifying existing modeling code that was based on the Okada code [1985] to reproduce the surface deformation from dislocations in an elastic half-space. Tilt resulting from volume changes of a Mogi source in an elastic half-space were also calculated with a modified existing code. The modifications enabled us to calculate a series of model tilt values at specific stations and to plot these values as a function of time. These 2 modified codes were combined to add the tilt values from both sources of deformation. The resulting propagation model, Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 33 divided into equal time intervals, provided a resolution sufficiently detailed to track the progression of the propagation and compare the tilt to observations for the 3 tilt stations. The dike opening was, at all times, proportional to the dike area (length x height), based on the final area:opening ratio. The propagation rate was assumed constant and magma flux into the dike was not considered in the modeling of the dike propagation [e.g., Okada and Yamamoto, 1991], Magma supply to growing dikes is still a poorly understood matter and it was decided to emphasize on the mechanical properties of the dislocation. Early modeling results indicated that the magnitude of the tilt data at Litli Leirhnjukur was significantly different from the magnitude of the model values. As mentioned earlier, recorded tilt at Litli Leirhnjukur possibly resulted from movement along faults and/or fractures. Therefore, various strategies to fit the data were tested, assuming a local fault or fracture was also contributing to the signal at Litli Leirhnjukur. The models tested were unsuccessful in reproducing the surface deformation observed at all 3 tilt stations. It is possible that more diffuse geothermal activity was partly responsible for the observed deformation at Litli Leirhnjukur. Due to these large discrepancies between the data and the model tilt, and the likelihood that localized fractures or geothermal activity affected the signal, modeling efforts focused on fitting tilt data from the Viti and Krafla stations. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 34 3.3. Dike Widening and Chamber Deflation / Inflation History After the dike intrusion, the 1984 eruption lasted ~2 weeks, from September 4, 23:49 to September 18, between 16:00 and 17:00. To accurately estimate the volume change of the magma chamber during the eruption, it was necessary to also estimate the change in the dike opening. Forward modeling using a Mogi source and a tensile dislocation was done to reproduce the surface deformation recorded at the Krafla, Viti and Litli Leirhnjukur tiltmeter stations during the eruption. The dislocation represented the fully-grown dike and the Mogi source represented the shallow magma chamber located in the middle of the caldera. The dike height, length, location, strike and dip and the magma chamber position were fixed to the values used for the modeling of the dike propagation to optimize the fit between the observed and predicted tilt. The dike opening and the volume change of the magma chamber were then adjusted to fit the tiltmeter data. The time of the eruption was divided into 15 equal time intervals (~22 hr intervals) to reproduce the surface deformation observed as the volcanic system evolved during this eruption. 3.4. Estimate of Magma Inflow Rate In addition to the bimodality of the lava [Gronvold, pers. comm., 2002], it was estimated in previous studies [Tryggvason, 1986; Arnadottir et al., 1998] that the amount of lava erupted and emplaced as a dike could not have come from a single magma source, the Krafla shallow magma chamber. It is possible that there was a deeper source of magma below the shallow magma chamber, which could Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 35 have fed ongoing eruptions at Krafla volcano. The existence of a second magma reservoir is also supported by the fact that there was a period of inflation during the eruption (Sept. 5-9), indicating inflow of magma into the shallow magma chamber. Such a source would be difficult to detect with the existing geodetic data sets. However, modeling of InSAR data from 1993 to 1999 indicated that there was a deflating shallow magma reservoir, and also that magma accumulated at a depth of 21 km at the crust-mantle boundary [de Zeeuw-van Dalfsen et al., 2004]. Based on electronic tiltmeter, lake level measurements, EDM and optical leveling tilt data, Tryggvason [1986] suggested that there were several additional magma sources. A first reservoir below the shallow magma chamber would have been at less than 10 km depth, possibly 5 km, and a second reservoir would have been at more than 20 km deep. A third reservoir would have supplied magma to the shallow reservoir for 2 years previous to the eruption and would have been at greater depth than the second, although existing observations did not provide any constraints on this third reservoir. The suggestion of a third reservoir was based on ground deformation recorded during the 2 years previous to the 1984 rifting event. The horizontal location of the reservoirs was however not constrained. Arnadottir et al. [1998] concluded there had to be an additional magma source to explain the amount of magma that was extruded and emplaced as a dike. Based on their results, at least 40 x 106 m3 of magma had to come from a second reservoir, but the geodetic data used could not constrain the location and depth of this source. However, it was Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 36 estimated that the second reservoir was at a minimum depth of 5 km because volume changes of a shallower reservoir would have produced a signal large enough to be detected by the existing network of geodetic stations. In order to obtain better constraints on the magma balance during the eruption, we attempted to determine the amount of magma that was supplied by a suggested second reservoir to the shallow magma chamber. The expression ‘magma balance’ refers to the amount of magma erupted and emplaced as a dike versus the amount of magma that flowed out of the shallow magma reservoir. Continuous tilt data recorded during the first 3 days after the eruption were used to estimate the amount of magma inflow from a deeper source into the shallow Krafla magma chamber. This amount was converted to a rate and was then used to infer the magma input from a deeper source throughout the eruption. The magma inflow rate was therefore estimated during the time period where the inflation rate was highest and approximately constant, which was immediately after the eruption stopped on September 18. The inflow rate was also calculated for the first 2 days of a 5-day inflation period during the eruption where the tilt rate at the Krafla electronic tiltmeter was highest [Tryggvason, 1986]. However, magma was still leaving the system during the ongoing eruption. Assuming the inflow rate was constant throughout the eruption, this rate was considered a minimum estimate. For an initial estimate of the amount of magma from the deeper source, it was assumed that the dike was static after the eruption stopped. Continuous tilt data were Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 37 used in the weighted least squares inversions to find the volume change of the Mogi source. It is possible that the dike opening increased as the magma chamber inflated after the eruption stopped. Therefore, opening of the dike during the September 18-21, 1984 period was taken into consideration. A weighted least squares inversion was used to determine the opening of the dike and the volume change of the Mogi source. It was assumed that the Mogi source location and depth remained the same after the eruption ceased, and so the geometry and location parameters were kept the same as those determined by prior forward models. Station Litli Leirhnjukur was included in the data set because there would have been very few data points otherwise to proceed with the inversions. 4. Results 4.1. Geometry of the Dike and Magma Chamber based on Inversions EDM, leveling, optical leveling tilt and continuous tilt data were used to invert for the best set of parameter values. The fit to the data as well as the x2 values are shown on figures 10 to 16. Including the continuous tilt data set resulted in a larger dike opening than the 1.2 m opening found with the inversions of the EDM, leveling and dry tilt data (Table 1). Because the electronic tiltmeter network was located at the southern end of the fissure, the 1.6 m estimate was not necessarily representative of the whole dike. Therefore, the 1.2 m opening estimate was considered a better estimate. These inversions indicated that the dike was over ~6.5 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 38 343°00' 343° 10' 343°20' km Model EDM 0.5 m ► EDM data 0.5 m ^ Mogi source Q length 8.5km depth 5.7km dip 90° strike 5° opening 1.1m Mogi source depth 4.5km vol. change -0.02km3 65°50' 65°40' 343°00' 343°10' 343°20' Figure 10. Results of inversions of EDM data only to contrain the position and strike of the dike. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Length (kmj Depth (km) th Height (km) Strike (°) Dike mid-point (east west, km) Dike mid-point (north-south, km) Figure 11. Chi-squared values for inversions of EDM data, (a) Values are shown for 6 of the parameters that were inverted for. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Opening (m) Latitude (km) •0.03 0.02!: C > 0" -G 015 -C G 1 -0 C O ? Mogi source volume change (km3 ) -J S o < 1 5 Longitude (km) i.-i 2 5S « i ,15 Mogi source depth (km) Figure 11. (continued) (b) Chi-squared values for 5 of the parameters that were inverted for with the inversions of EDM data. The Mogi source location is given in the local coordinate system. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 41 343° 00' 343° 10' 343° 20' k m o MODEL TILT 100 urad TILT DATA 100 urad Mogi source 65° 50' 343° 00' length 6 km depth 3 km dip O o strike 2° opening 2.3 m Mogi source depth 2.8 km vol. change -0.02 km3 343° 10' 343° 20' 65° 40 ' Figure 12. Results of inversions of dry tilt and continuous tilt data. Error attributed to station Litli Leirhnjukur was 30 urad. The only fixed parameter was the dip (90°) of the dike. As apparent on the figure, this data set did not constrain the position of the dike. K, V and L.L. identified on the figure are the continuous tilt stations Krafla, Viti and Litli Leirhnjukur. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 42 343°00' 343°1 O ' 343°20' km Tilt lOOurad obs ------ ► calc ------ EDM 0.5m obs ----- *- calc ----- ► 'f o Mogi source length 8.7 km depth 9.6 km dip v O o o strike 5° opening 1.2 m Mogi source depth 3.4 km vol. change -0.02 km3 343°00' 343°10' 343°20' Figure 13. Results of inversions of EDM, leveling and dry tilt data. The dip, strike and mid-point of the dike were fixed using the results of inversions of the EDM data alone. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 65°50' 65°40' Length (km) Depth (km) Height (km) « 1 ; .t ' * * * 1 I * , i Mogi source latitude (km) ' I ».■1 ■ v Opening (m )’‘ ■ ‘ « ’ • >, i t 1 Mogi source longitude (km) .!• S M ‘ »»* :: v -W rT ij* » » 1 ;Jr t.- U f a -8$ : * * 1 * ill Mogi source depth (km) Mogi source volume change (km3 ) Figure 14. Chi-squared values associated with the parameters inverted for the inversions of the EDM, leveling and dry tilt data sets. The Mogi source location is given in the local coordinate system. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 44 343°00' 343°1 O ' 343°20' Tilt lOOurad calc ------► obs ------ ► EDM 0.5m c a lc ► obs ----- ► source length 8.5 km depth 9.8 km dip 90° strike 5° opening 1.6 m Mogi source depth 2.8 km vol. change -0.02 kn 65°50' 65°40' 343°00' 343°1 O ' 343°20' Figure 15. Results of inversions of EDM, leveling, dry tilt and continuous tilt data. The dip, strike and mid-point of the dike were fixed using the results of inversions of the EDM data alone. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 45 * '* n ? * * * 4 Length (km) r- t* ;W flW r). *;•.? 'Mf 'J.H 3 • • - * • . : • . J s f ’ .ja. • • • *%,»• f s-i ; . .: jj. ,• ." % ' ■ * ’ " / • '■ **.".! ! F Height (km) : ? M ’ ’’ ;in * Latitude (km) I \f * y • J #t§£lti! • • • • tv. i. it. ,;>j .?. >{,:?•■’ t - i 1 • - i * ' ,v 4? Depth (km) 1 - ■ s. • j * 1 Opening (m) I i Longitude (km) Depth (km) (j? \ * . Volume change (km) Figure 16. Chi-squared values associated with the parameters that were inverted for the inversions of the EDM, leveling, dry tilt and continuous tilt data sets. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 46 km deep. The location of the magma chamber was somewhat better constrained to within ~250 m of the best-fit position. The x2 value for the best fit of EDM, leveling and optical leveling tilt data was 15.5. Models below a x 2 of 19.5 were within a confidence level of 95%. However, dike opening and Mogi source volume changes were optimized after the inversions to reduce the x2 value to 14.5. The x2 values plotted on the graphs of figures 11, 14 and 16 have not been optimized. Values plotted on graphs of figure 14 are between 15.5, the minimum x 2 value obtained, and 65.5, a reasonable upper bound. Therefore, it is difficult to evaluate which models are within the confidence interval when looking at the dike opening and Mogi source volume. There were no clear indications of a correlation between most of the parameters (Figure 17); however, the Mogi source depth and volume change had an inverse correlation. Table 1. Results o f inversions o f EDM , leveling and optical leveling tilt data PARAMETERS VALUES Length 8.7 km Depth 9.6 km Dip 90° Strike 5° Opening 1.2 m Mogi source depth 3.4 km Mogi source volume change -0.02 km 3 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 47 4.2. End-Member Models of Dike Propagation This part of the project involved determining whether it was theoretically possible, based on continuous tilt data from 3 stations around the southern end of the fissure, to distinguish between the following end-member models of the dike propagation: a purely vertical propagation and a purely lateral (horizontal) propagation. The vertical propagation model consisted of a 8.5 km long dike that propagated vertically from beginning to end (Figure 18a). By a similar approach, the lateral propagation model consisted of a 7 km high dike that propagated laterally only (Figure 18b). These two end-member models are not likely to occur in nature but, in the context of this study, they provided insight as to what type of tilt signals could be expected from different propagation directions. It was also an initial resolution test because there would not have been any incentive to continue with modeling the tilt data if the end-member models resulted in similar tilt values. The 2 end-member models indicated that the geometry of the continuous tiltmeter network at the Krafla fissure swarm could distinguish between a purely vertical and a purely lateral dike propagation (Figures 19-20). Two features in the tilt record of station Viti distinguished a vertically propagating dike from a laterally propagating dike: (1) a sign change of the tilt rate of the east component and (2) a greater increase of the east component compared to the north component. Moreover, the tilt signal from Viti station at the beginning of the dike growth could distinguish between the 2 propagation directions, contrarily to the Krafla and Litli Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 48 a D . U Q M Q • r S • • « f* fv *■{»*. A % ,V » • • • \ 10 Dike length (km) Dike opening (m) g W ) c ’ g 8. o •• 00 02 * • * • % •• 5 Mogi source depth (km) Dike Length (km) • / M • - • * • _ %_ Opening (m) F igure 17. Correlation betw een model param eters. M odels used were the result of inversions of EDM , leveling, dry tilt and continuous tilt and had chi-squared values betw een the m inim um value 43 and m axim um value 73. There is an obvious inverse correlation betw een the depth and the volum e change o f the M ogi source. There seem s to be an inverse correlation betw een the opening and the length of the dike, but it is unclear. The other param eters do not seem to influence each other. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 49 Dike Length F ig u re 18. Vertical (a) and lateral (b) dike propagation models. For each model, the dike propagates purely laterally, or purely vertically. The direction of propagation is indicated by the white arrows, (a) The dike length is fixed during the whole propagation, (b) The dike height is fixed during the whole propagation. In both (a) and (b), the dike opening: area ratio is m aintained constant and the dike height, or length, increases by equal increments, i.e. the rate o f propagation is fixed. 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. K rafla tiltm eter Time (hrs) n G *3 c « I S o s East com ponent N orth com ponent 1 3 5 7 9 n 13 15 Viti tiltm eter Time intervals Time (hrs) o n C c d •3 c d u o t-H ( J H East com ponent North com ponent Change in tilt sign 3 5 7 9 11 13 15 11 13 Time intervals Litli Leirhnjukur tiltm eter Tim e (hrs) -o c d U i i O s-, o 1 € 6 0 • — ' East com ponent North com ponent 3 9 5 7 11 13 15 Time intervals F igure 19. M odel tilt resulting from the vertical dike propagation m odel com pared to the continuously recorded tilt data. M odel tilt values are shown as circle m arkers. The dike propagation began at ~20:20 on Septem ber 4, 1984 based on the onset of the deflation above the K rafla shallow m agm a chamber, and the eruption began ~23:49 based on visual observations. The following dike param eters produced a best fit: 8.5 km length, 7 km depth, 90° dip, 7° strike, and 0.6 m opening. The m agm a cham ber param eters were a 3 km depth and a 0.015 km 3. The dike opening was m aintained proportional to the dike area throughout the propagation. The K rafla tiltm eter recorded a tilt signal mainly caused by the m agm a cham ber deflation because it was located farther away from the dike than the other tiltmeters. The fit o f the Viti and Krafla tilt data is satisfactory, but the Litli Leirhnjukur m odel tilt poorly fits the data. o Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without permission. Krafla tiltmeter Time (hrs) W 5 G c d 2 O s H East component North component 1 4 7 10 13 t6 Time intervals Viti tiltmeter Time (hrs) (A § o U e H East component North component 13 7 1 0 16 Time intervals Litli Leirhnjukur tiltmeter Time (hrs) O E H ' — ■ East component North component 1 0 13 16 4 Time intervals Figure 20. Model tilt resulting from the lateral dike propagation model compared to the continuously recorded tilt data. Model tilt values are shown as circle markers. The dike propagation began at ~20:20 on September 4, 1984 based on the onset o f the deflation above the Krafla shallow magma chamber, and the eruption began -23:49 based on visual observations. The following dike parameters produced a best fit: 8.5 km length, 7 km depth, 90° dip, 7° strike, and 1 m opening. The magma chamber parameters were a 3 km depth and a 0.015 km3 volume change. The dike opening was maintained proportional to the dike area throughout the propagation. The fit o f the Krafla tilt data is satisfactory, but the Litli Leirhnjukur and Viti model tilt poorly fit the data. 52 Leirhnjukur tilt stations. For all 3 stations, the end of the propagation yielded a tilt signal that is unique to a vertical propagation. The model north component at Viti increased from beginning to end, but the east component tilt rate reversed its sign towards the end of the propagation. Litli Leirhnjukur experienced a similar reversal as the north component continued to decrease. 4.3. Combined Models of Dike Propagation A model combining the vertical and lateral propagation models (Figure 21a) tested whether the continuous tilt data was sufficient to determine the depth at which the dike propagation was mostly vertical or lateral. The dike parameters were the same as for the best-fitting model obtained with the vertical propagation model. The first combined model consisted of a 3.5 km high dike that propagated laterally until it reached its full 8.5 km length, after which the dike propagated vertically and reached the surface. Another combined model, with the same final dimensions, consisted of a 5.25 km high dike propagating laterally for 3/4 of the propagation time, or vertical distance, to its full 8.5 km length, after which it propagated vertically to the surface. This model was similar to the previous model except for the fact that the dike propagated vertically only for 1/4 of the propagation time instead of 1/2 the propagation time. Additional combined models tested an initial dike height of ~6 km and ~6.5 km. The final dike dimensions for all combined models were length (8.5 km), height (7 km), and opening (0.6 m), which were the same for the vertical propagation model. An oblique propagation model, Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 53 ‘ Eruption Eruption 0 8.5 km < Dike Length ^ Figure 21. Additional dike propagation models. White arrows indicate propagation direction of the dike, (a) Models testing the depth resolution of the vertical component to the dike propagation. The model combines the vertical and lateral dike propagation models. The propagation is first purely lateral, then purely vertical. This model was tested for different initial dike height, (b) The propagation is both lateral and vertical simultaneously. The rectangles within the diagram illustrate the geometry of the dike as it is propagating. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 54 which is a more geologically realistic model, consisted of a dike propagating obliquely directly to the opposite end of the dike (Figure 21b). Forward modeling was also used to test how sensitive the tiltmeter network was to a dike propagating vertically a specific distance away from the network. These tests were accomplished by shortening the dike from its southern end to observe how far north the dike intrusion was detected by the tiltmeters. Assuming a constant propagation rate, the combined dike propagation models (Figure 22) yielded tilt values that were similar to the purely vertical propagation model, except for the last 2 depths tested. Thus, with continuous tilt data and the given station network geometry, the direction of dike propagation was resolved best at depths less than 1 km. The oblique propagation model also yielded a good fit (Figure 23). Finally, we infer from the modeling that at least 3-4 km of the southern end of the dike propagated vertically, and also that the tiltmeter network was insensitive to the deformation caused by the intrusion farther north. 4.4. Geometry of the Dike and Magma Chamber based on Forward Modeling Forward modeling of the dike propagation provided a set of parameter values that produced a model that best fit the continuous tiltmeter data. Subsequently, the constraints on each dike and magma chamber parameter were evaluated. In the following discussion of the resolution of parameters, a significant misfit refers to a misfit of at least 6 prad. When first testing the resolution of a parameter, the rem aining dike- and magma cham ber-param eters were held constant. 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. Viti East Tilt Component -V - 6.5/7 □100 5 10 15 20 25 30 35 40 Time intervals Krafla East and North Tilt Components H 020 V - 6.5/7 5 10 15 20 25 30 35 40 Time intervals Viti North Tilt Component 10 15 20 25 30 35 40 5 Time intervals Figure 22. Model tilt for the models combining the lateral and vertical propagation models. Propagation was first purely lateral and became purely vertical once the dike reached its full ~ 8.5km length. 5 models were tested while only 2 of these resulted in noticebly differents curves. Each curve represents a dike propagating vertically for a specific fraction of the time period. Tiltmeter Krafla was not sensitive to the depth at which the dike started propagating vertically. Tilt is positive downward. Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without permission. Krafla tiltmeter Time (hrs) o S H East component North component Time intervals Viti tiltmeter Time (hrs) •a a s u i O u H East component North component Time intervals Tilt (micro-radians) Litli Leirhnjukur tiltmeter Time (hrs) ■ — • East component North component 13 15 3 5 7 9 Time intervals Figure 23. Model tilt resulting from the oblique dike propagation model compared to the continuously recorded tilt data. Model tilt values are shown as circle markers. The following dike parameters produced a best fit: 8.5 km length, 7 km depth, 90° dip, 5° strike, and 0.7 m opening. The magma chamber parameters were a 3 km depth and a 0.0145 km3 volume change. The dike opening was maintained proportional to the dike area throughout the propagation. The fit of the Krafla and Viti tilt data is satisfactory. The fit of the Krafla tilt with this model is better than for the vertical propagation model. os 57 Subsequently, if the fit to the tilt data was significantly worse for a parameter value, some parameters, such as the opening, were adjusted in an attempt to improve the fit to the data. Because the amplitude of the surface deformation is sensitive to the total amount of magma intruded in the crust, and not necessarily to a specific geometry, it is often possible to fit the data equally well with different parameters as long as the dike volume is constant among the various models. Constraints on the dike length and strike were mostly from the surface expression of the fissure. The tiltmeter network did not constrain the length north of the end of the fissure. Assuming the dike grew at a constant rate, the depth of the dike had to be between 6 and 8 km. However, the depth could have been between 8 and >15 km when only considering the net tilt at the end of the propagation. Tilt at station Krafla remained unchanged with dike initiation depth because its tilt signal mostly reflected the magma chamber deflation. A dike opening between 0.5 and 0.7 m resulted in a good fit of the net tilt. The amount of magma chamber deflation during the dike propagation was mainly constrained by station Krafla because, of the 3 tiltmeters, it was located closest to the magma chamber and furthest away from the dike intrusion. Its recorded smooth and continuously decreasing tilt signal resulted mostly from the chamber deflation rather than from the dike propagation. The magma chamber had deflated ~0.0145 km3 by 23:49 on September 4. If a total deflation volume of 0.0155 km3 was used in the modeling with a fixed depth of 3 km, results were significantly Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 58 different. The depth of the shallow reservoir was constrained between 2 and ~4.5 km and its position was constrained within a radius ~0.5 km from the position used in forward models. In summary, the dike parameters that differed from the parameters found with the inversions of the EDM, leveling, optical leveling tilt and continuous tilt data were the dike opening, the magma chamber location and the volume change of the chamber. The dike opening and the dike depth were better constrained using forward models of the tiltmeter data. The volume changes of the magma chamber and the dike opening changes throughout the dike propagation and the eruption were documented in more detail. Forward models of tiltmeter data also indicated that the center of inflation/deflation possibly moved during the period between EDM, leveling, dry tilt and continuous tilt measurements. 4.5. Estimates of Dike Widening and Magma Chamber Volume during the Eruption Dike widening and shallow magma chamber volume changes during the eruption were estimated to calculate the amount of magma that left the shallow reservoir. The eruption was defined as the time period between the end of the dike propagation and when lava stopped flowing at the surface. A forward model reproduced continuous tilt variations during the eruption (Figure 24). The parameters that resulted in a best fit of the data when using the vertical propagation model were used for this modeling. However, the dike opening and the 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. Krafla Time (days) G O § O s East component North'component' Time intervals Viti Time (days) C O § 1 V - I 2 O '§ P East component 'North component Time intervals Litli Leirhnjukur Time (days) o B P — ■ East component —- ' North component Time intervals Figure 24. Results obtained with forward models using model tilt to compare with data between September 5, 11:00 and September 18, 8:30 tilt data. Opening 0.4 m, length 8.5 km, dip 90°, depth 7 km, strike 5°, Mogi position (0.75, -0.05), depth 3 km. Net volume change of the source was -0.003 km3. It seemed logical to keep the same position for the magma chamber, although it is possible that the inflation/deflation center was not spatially fixed. The tilt data consists of one data point every half-hour. Tilt + down to north + down to east Ux vo 60 Mogi source volume were allowed to vary. Based on this model, the total amount of deflation of the shallow chamber (AVM ) during the eruption was ~0.0278 km3 and the amount of inflation of the chamber during the September 5-9 period was ~0.0033 km3 (Table 2). The east component of model tilt at station Viti was significantly too small when the dike opening was fixed, which justifies the widening of the fissure following the dike propagation. The dike widened ~0.4 m between September 5, 11:00 and September 18, 8:30. Table 2. Volume changes of the Mogi source during the dike propagation and eruption. Time period Volume change of Mogi source (x 106m3 ) (-) deflation, (+) inflation September 4, 20:20 to 23:49 -14.5 September 4, 23:49 to September 5, 11:00 -7.0 September 5, 11:00 to September 10, 1:00 + 3.3 September 10, 1:00 to September 18, 8:30 -6.3 Total volume change (deflation) -27.8 4.6. Estimate of Magma Inflation Rate In order to find a maximum rate of magma inflow into the magma chamber during the time of the eruption, the amount of inflation during the 3 days following Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 61 the end of the eruption was estimated. Given the model used, weighted least squares inversions revealed that the dike widening did not contribute significantly to the tilt signal. The standard deviation of the opening was as large as the opening itself. The data could be fit equally well by the Mogi source model and the dike and Mogi source model (Figure 25 ab). However, a dike opening increase should not be discarded. The Mogi source-only model was favored because there was no evidence that there was widening of the dike after the eruption stopped and the Mogi source model results could not be distinguished from the dike and Mogi source model results. It should also be noted that the two models resulted in a similar amount of inflation. Based on these inversions, the inflation volume for these 3 days was 0.002 km3. The inflation rate of the Mogi source was then ~7.7 m3 /s. If we assume that this rate was constant, this amounted to a total theoretical volume of inflation of -9.3 x 106m3 for the 14 days of eruption. As a test, continuous tilt data recorded during the September 5-9 inflation period were used to find an inflation rate. There was a -2-day period, September 5- 7, where the tilt rate was fixed and largest [Tryggvason, 1986], This was an attempt to obtain a more accurate minimum estimate of the inflow rate of magma into the shallow magma chamber. Even though the fissure widened by about 0.1 m during this time period, the effect of the dike was not included in the model. The Mogi source model was used (Figure 26). The inflation volume was 0.0024 km3 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 62 a) 343° 00' 343° 10' 343° 20 ' 65° 50' 65° 40 ' km MODEL TILT 10 urad TILT DATA 10 urad Mogi source L.L. / 65° 50' Mogi source depth Volume change 3 km -0.002 km3 65° 40 ' 343° 00' 343° 10' 343° 20 ' F igure 25. Results of weighted least squares inversions of continuous tilt data from September 18-21, 1984. Error attributed to station Litli Leirhnjukur was 30 urad. K, V and L.L. identified on the figure are the stations Krafla, Viti and Litli Leirhnjukur. (a) Mogi source model. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 63 b) 343° 00' 343° 10' 343° 20 ' 65° 50' 65° 40 ' km MODEL TILT 10 urad TILT DATA 10 urad 'jij- Mogi source L.L. / Mogi source depth Volume change Dike opening 2.8 km -0.02 km3 0.45 m 343° 00' 343° 10' 343° 20' Figure 25. (continued) (b) Mogi source and dike model. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 65° 50' 65° 40' 64 343° 00' 343° 10 ' 343° 20' 65° 50' 65° 40 ' km MODEL TILT 20 urad TILT DATA 20 urad Mogi source / Mogi source depth Volume change 65° 50' 3 km +0.0024 km3 65° 40' 343° 00' 343° 10 ' 343° 20' Figure 26. Results of weighted least squares inversions of continuous tilt data recorded during the eruption, September 5-7, 1984. Error attributed to station Litli Leirhnjukur was 30 urad. K, V and L.L. identified on the figure are the stations Krafla, Viti and Litli Leirhnjukur. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 65 over 2 days, which resulted in ~14.3 m3 /s. This rate is probably a better estimate and it was used in the calculations of magma balance during the eruption. 4.7. Magma Balance The volume change of a magma chamber estimated from Mogi source modeling does not necessarily represent accurately the volume of magma that left or entered the magma chamber. The compressibility of the magma has to be considered in order to correctly estimate the volume of magma (AVm) that left or entered a magma chamber. When magma leaves a magma chamber, the pressure inside the chamber drops and magma expands. Therefore, the volume change of the chamber is less than the volume of magma that left the chamber. Johnson (1987) estimated this discrepancy between the volume change of a magma reservoir and the volume of magma entering or leaving a reservoir. Gravity and geodetic data collected during 15 deflation events at Kilauea volcano were used to calculate ratios of magma chamber volume change to the subsidence volume at the surface (edifice volume change, AVe). The volume changes due to magma removal were in fact mass changes detected by gravity changes. These gravity changes were converted to volume changes based on a non-compressed magma of fixed density 2.75 g/cm3 . The 15 ratios calculated were averaged and the relation AVm = 2.4 AVe (2) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 66 resulted. The difference between AVm and AVe results from any process that might be occurring when magma leaves the chamber, such as the expansion of the magma remaining in the chamber caused by pressure release. In this study, the upper bound for the magma volume that left the chamber was set to 2.4 AVe and the lower bound, to 2/3 AVe, from which resulted the relation 2/3 AVe < AVm < 2.4 AVe (3) This relation is consistent with that used in Arnadottir et al. [1998]. Even though the ratio minimum and maximum were 1.2 and 4.5 [Johnson, 1987], 2.4 was considered a reasonable average upper bound. These results are used here because, to the best of our knowledge, similar work on magma compressibility has not been done at Krafla volcano. For the simple Mogi source model, the following relation applies: AVm = 2/3AVe [Delaney and McTigue, 1994] (4) where (AVM ) is a Mogi source volume change. 2/3AVe is in fact the AVm lower bound mentioned above. This equation was also used in Arnadottir et al. [1998]. The relations mentioned above were applied to the Krafla volcanic system in order to calculate a balance between magma input into and output out of the system. Magma input into the Krafla volcanic system was considered as magma that left the magma chamber from September 4 to 18, 1984. A ~ constant inflow of magma into the magma chamber, which is consistent with Tryggvason [1986], and an equal amount of magma leaving the chamber was assumed. In addition, there was more magma leaving the chamber, causing deflation of the chamber and subsidence Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 67 at the surface. Magma input consisted of these two components. Magma output was magma that flowed into the rift zone and onto the surface. Table 3. Magma input and output. Balance between the magma that was erupted and emplaced as a dike, and the magma that flowed out of the shallow crustal magma chamber. The outflow of magma was estimated as the amount of deflation plus the magma that flowed into in the magma chamber from a deeper source. Volume of Magma Input (x 106m3 ) Volume of Magma Output (x 106m3 ) Volume of magma from deflation [28 -100] Magma erupted >110 [Rossi, 1997] Volume of magma inflow [1 7-62] Magma emplaced as a dike (op = 1.2 m) [6 1 -8 2 ] Total magma input [45 - 162] Total magma output [171 - 192] An estimate of an inflation rate (~14.3 m3 /s) was used to calculate the total magma volume resulting from inflow into the shallow magma chamber during the 14 days of the eruption (Table 3). The inflation rate was converted to a magma volume per second. Magma flux into the shallow reservoir was between 14.3 and 51.5 m3 /s, which means a total magma increase between 17 x 106 and 62 x 106 m3 for the 14 days. Tryggvason [1986] had estimated a ~20 m3 /s increase in the inflation bulge when the eruption stopped on September 18. This rate results in a total volume of magma inflow of ~24 x 106 m3 during the 14 days of the eruption. This inflow rate 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. YU -caldera Erupted lava: >110 km3 Magma volume from i ? . chamber deflation: I 28 - 100 km3 Magma emplaced as a dike: 61 - 82 knP Magma inflow into shallow magma chamber from deeper source: 17 - 62 km3 ? ? Deeper magma source of unknown depth and dimensions Total Input: 45 - 162 km3 Total Output: 171 - 192 km3 M agm a Balance ------ ► Output - Input = + [9 - 147] km3 Figure 27. Schematic diagram of magma balance at Krafla volcano, September 4-18, 1984. Total magma input consists of the magma resulting from chamber deflation and magma inflow from a deeper source. Total magma output consists of the magma emplaced as a dike and magma that flowed onto the surface. as 00 69 was based on the assumption that the uplift volume was equal to the volume of magma influx, and that the location of the magma chamber was fixed [Tryggvason, 1980]. Thus, the estimate that 1 prad of uplift equaled 0.2 x 106 m3 was derived. Even though the calculation was based on an inflation event that occurred in 1977, this estimate was assumed valid during the 1984 event. Because of these differences in calculating magma inflow, it is difficult to use his estimates for comparison with our estimates. After calculating the magma balance (Figure 27) for the 1984 eruption, I found that the total magma input was less than the total magma output by a minimum of 9 x 106 m3 . 5. Discussion The geometry found for the dike and the shallow Krafla magma chamber (Table 1) was consistent with earlier results [Arnadottir et al., 1998], Adding the continuous tiltmeter series to the EDM, leveling and dry tilt data sets resulted in different estimates of the position of the magma chamber and the dike opening. The dike opening found (1.6 m) was larger than that found with previous inversions; the dike possibly had a variable opening along its strike. The continuously recording tiltmeters were located at the southern end of the dike, within the caldera, and were therefore more sensitive to dike widening at the southern end of the fissure. The dike volume was used to determine whether an additional magma source was needed to achieve a magma balance. Therefore, it would be important to know whether the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 70 opening was variable. Using a variable-opening static model could possibly improve the fit to the four data sets and would provide a better estimate of the dike volume. Forward models of the dike during its propagation and the eruption indicated that the dike continued to widen during the eruption, possibly not uniformly along the strike of the dike. The dike propagated vertically for at least the last ~1 km. Few studies have been able to resolve this much about the propagation direction of dike intrusions. Based on our results for the geometry of the dike, a vertical propagation model and a constant rate of propagation, the propagation rate was -2 km/hr (0.6 m/s), which is close to, but somewhat larger than, results of previous studies. A propagation rate was calculated for the July 1978 intrusion using the migration of the seismicity observed [Einarsson and Brandsdottir, 1980]. The dike propagated at a rate of ~1.6 km/hr for the first 9 hours, which is close to the rate calculated for the 1984 event. Fox et al. [1995] reported a seismic swarm that migrated about 65 km in 2 days, which was -1 .4 km/hr. Hayashi and Morita (2003) indicated that part of an intrusion process was tracked by hypocenters migrating upward at a rate of 1 km/hr. A variable-opening propagation model would be useful for modeling future rifting events at Krafla volcano and other volcanoes if a network of geodetic instruments (tiltmeters, strainmeters, GPS) was extensive enough. At Krafla volcano, a better resolution of a dike’s propagation direction could be achieved if the continuous tiltmeter network extended further north and some distance away from Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 71 the eruptive fissure in areas not affected by geothermal activity. The network of geodetic stations and seismometers was not originally meant to monitor the propagation of eruptive fissures, but to follow the deflation / inflation cycles of the magma chamber. Instruments of higher precision would also improve the modeling potential of the data. Additional data sets now available such as GPS and InSAR will certainly improve the surface deformation coverage of the area if another rifting event occurs and will facilitate the interpretation of future events. InSAR would help resolving the depth of the dike intrusions while continuous GPS, tiltmeters and strainmeters would help tracking the propagation of the dikes. The continuous tiltmeters were efficient in monitoring deflation and inflation events. Most of the magma chamber deflation occurred during the dike propagation, even though the chamber continued to deflate and inflate throughout the eruption. A more accurate total deflation volume (27.8 x 106 m3 ) was obtained with forward models for the time of the whole rifting event. In comparison, inversions resulted in 20.9 x 106 m3 of deflation. However, the total deflation volume was insufficient to supply the growing dike during the dike propagation and during the eruption (Figure 28). Forward models also indicated that the center of deflation/inflation of the magma chamber possibly moved during the time period between geodetic observations. The center of deflation was located ~1 km southeast of the position found with inversions of EDM, leveling, dry tilt and continuous tilt data. The best- Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 72 Dike growth and chamber volume changes during the dike propagation 40 -^D eflation H P - D i k e v o lu m e S 20 a 1 5 ’o > 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Time intervals (unitless) b) Dike growth and chamber volume changes during the eruption D e fla tio n D ik e v o lu m e 40 30 O 20 10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Time intervals (unitless) Figure 28. Dike growth vs. deflation volume of the shallow magma chamber, (a) During the dike propagation, (b) During the eruption. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 73 fitting model that resulted from inversions could not fit the Krafla data whereas forward modeling focused on fitting Krafla because it was most likely the best record of subsidence and uplift events. The Mogi source closely reproduced the deformation observed at the continuous tiltmeters Krafla and Viti. This location difference supports the evidence suggesting that the magma chamber was not perfectly spherical, but that it can be modeled as a Mogi source for deformation events of relatively short duration. Mogi source modeling was a good approximation to reproduce the deformation field caused by volume changes of the magma chamber during the rifting event. Although the network of tiltmeters monitored the volume changes of the magma chamber, the instruments are no longer in operation. Ideally, monitoring this volcanic system would best achieved if there were instruments in the northern part of the rift zone, in the southern part of the rift zone as well as in the caldera to study the propagation of future feeder dikes. Magma balance calculations indicated that the input of magma from the Krafla shallow magma chamber was insufficient to produce the amount of magma that was erupted and emplaced as a dike. We suspect there is an extensive magma body underneath the rift zone, and it would be important to have a better grasp of its shape and location. The shape of the shallow magma reservoir and the depth of the feeder dikes should also be resolved in order to understand the Krafla volcanic system and to determine which parts of the system the monitoring efforts should be focused on. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 74 The seismic data recorded during the ~4 hours previous to eruption (Figure 29) indicated that there were fewer earthquakes and no lateral migration of the earthquake epicenters observed, compared to the other dike intrusions that occurred during the 1975-1984 rifting episode. These differences may represent evidence that the propagation direction was vertical for the last event. The crust was probably not as brittle as in the previous events because of a temperature increase due to the numerous intrusions. Rubin [1995] hinted that it is possible that not all intrusions produce a large number of detectable earthquakes, mentioning the 1991 Hekla intrusion as an example. The evidence presented in this study support the idea that the 1984 eruptive fissure propagated vertically from a deeper magma source, or possibly obliquely. The evidence included the bimodality of the lava composition, the absence of earthquakes migrating away from the magma chamber, the northern location of the earthquake epicenters, the focus of the eruption in the northern end of the fissure, the vertical propagation of the dike for at least the last km, and the need for an additional source of magma other than the inflow of magma into the shallow magma chamber. Consequently, the plumbing system beneath the Krafla volcanic system may include a deeper and more extensive magma body underlying the rift zone. The surface deformation observed at Krafla volcano could not be totally explained using the simple Mogi source and tensile dislocation model. There is Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 75 65°50' 65°40' Figure 29. Map of the seismicity recorded during the 1984 rifting event at Krafla Volcano, Iceland. Earthquakes located by less than 4 stations or with more than 4 km horizontal error were excluded. Most of the seismicity was located at the northern end of the fissure. The magma chamber (solid circle) and dike (straight line) shown on the map were the results of inversions. 343 00 343 10 343 20 0 hr 20 hr 24 hr 343°00' 343°1 O ' 343°20' Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 76 more to be learned from this volcanic system and a more complex model to be constructed. However, the results obtained from this study may be applicable to mid ocean ridge systems because magma accretion occurs mostly as dikes. There may be several magma bodies feeding any given dike; some may be shallow, others may be deeper. The reservoirs may not only be located at one end of a dike, but also along its base. These results could have an impact on the dynamic models chosen to represent magma traveling through the oceanic crust. The mechanical and thermal evolution of a dike would then vary depending on the model chosen. Based on our results, the propagation direction of dikes at Krafla volcano may have been mainly lateral during the first half of the rifting episode, but it may have become mainly vertical during the second half of the episode. A volcanic system evolves and stresses in the crust most likely change with time. Consequently, the factors that control dike propagation change with time. 6. Conclusions The dike and magma chamber geometry was well constrained with inversions of EDM, leveling, dry tilt and continuous tilt data. The dike was 8.5 km long, mostly aligned with the surface expression of the fissure, with a strike of 5° and within a depth range of 6-8 km for a constant propagation rate. However, the opening value that resulted in the lowest chi-squared value was 1.6 m, which was much larger than Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 77 what resulted from the inversions of EDM, leveling and dry tilt data. This could mean that the southern end of the dike widened more than the rest of the dike. The magma chamber was located at the southern end of the fissure at ~3 km depth. These results are consistent with what was found by [Arnadottir et al., 1998] using a different inversion algorithm. The results of this study indicated that the feeder dike for the September 4- 18, 1984 fissure eruption propagated vertically for at least the last ~1 km before reaching the surface and that the tiltmeter network was sensitive to the direction of propagation for the southern ~3-4 km of the fissure. Assuming a constant rate of propagation, the dike ascended at a rate of 2 km/hr. The oblique propagation model also yielded a good fit to the tiltmeter data. Magma balance calculations indicated that the magma that flowed out of the shallow reservoir was less than the volume of magma that was emplaced as a dike and erupted by 9 x 106 m3 . It is unsure whether magma flowed only through the shallow magma chamber and not directly from a deeper source. However, based on the evidence, the dike likely propagated vertically from a deeper magma source and some magma flowed directly from it into the dike. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 78 7. Bibliography Anderson, G., S. Constable, H. Staudigel, and F.K. Wyatt, A seafloor long-baseline tiltmeter, Journal o f Geophysical Research, 102 (9), 20 269-20 285, 1997. Aoki, Y., P. Segall, T. Kato, P. Cervelli, and S. Shimada, Imaging magma transport during the 1997 seismic swarm off the Izu Peninsula, Japan, Science, 286 (5441), 927-930,1999. Amadottir, T., F. Sigmundsson, and P.T. Delaney, Sources of crustal deformation associated with the Krafla, Iceland, eruption of September 1984, Geophysical Research Letters, 25 (7), 1043-1046, 1998. Baer, G., Mechanisms of dike propagation in layered rocks and in massive, porous sedimentary rocks, Journal o f Geophysical Research, 96 (B7), 11911-11929, 1991. Berg, B.A., Locating global minima in optimization problems by a random-cost approach, Nature, 361, 708-710, 1993. Bjomsson, A., Dynamics of Crustal Rifting in NE Iceland, Journal o f Geophysical Research, 90 (B12), 10151-10162, 1985. Bjomsson, A., K. Saemundsson, P. Einarsson, E. Tryggvason, and K. Gronvold, Current rifting episode in North Iceland, Nature, 266, 318-323, 1977. Brandsdottir, B., and P. Einarsson, Volcanic tremor and low-frequency earthquakes in Iceland, IAVCEI Proceedings in Volcanology, 3, 212-222, 1992. Chadwick, W.W.J., R.W. Embley, and C.G. Fox, Evidence for volcanic eruption on the southern Juan de Fuca Ridge between 1981 and 1987, Nature, 350, 416-418, 1991. Darbyshire, F.A., R.S. White, and K.F. Priestly, Structure of the crust and uppermost mantle of Iceland from a combined seismic and gravity study, Earth and planetary sciences letters, 181, 409-428, 2000. de Zeeuw-van Dalfsen, E., R. Pedersen, F. Sigmundsson, and C. Pagli, Satellite radar interferometry 1993-1999 suggests deep accumulation of magma near the crust- mantle boundary at the Krafla volcanic system, Iceland, Geophysical Research Letters, 31 (L13611), 5, 2004. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 79 Delaney, P.T., and D.F. McTigue, Volume of magma accumulation or withdrawal estimated from surface uplift or subsidence, with application to the 1960 collapse of Kilauea, Bulletin o f Volcanology, 56, 417-424, 1994. Dziak, R.P., C.G. Fox, and A.E. Schreiner, The June-July 1993 seismo-acoustic event at Coaxial segment, Juan de Fuca Ridge: Evidence for a lateral dike injection, geophysical research letters, 22 (2), 135-138,1995. Dziak, R.P., C.G. Fox, D. Smith, M. Tolstoy, H. Matsumoto, D. Bohnensteihl, J. Haxel, and M. Fowler, Evidence of a probable magmatic episode at the Lucky Strike segment, Mid-Atlantic ridge, March 2001, InterRidge News, 11 (2), 29-31, 2002. Einarsson, P., and B. Brandsdottir, Seismological evidence for lateral magma intrusion during thr July 1978 deflation of the Krafla volcano in NE Iceland, Journal o f Geophysics, 47, 160-165, 1980. Ernst, R.E., and W.R.A. Baragar, Evidence from magnetic fabric for the flow pattern of magma in the Mackenzie giant radiating dyke swarm, Nature, 356, 511-513, 1992. Fialko, Y.A., and A.M. Rubin, Thermodynamics of lateral dike propagation: Implications fro crustal accretion at slow spreading mid-ocean ridges, Journal of Geophysical Research, 103 (B2), 2501-2514, 1998. Fink, J., and D. Pollard, Inyo dike rotation, Science, 228 (4706), 1382-1383, 1985. Gudmundsson, A., Dynamics of volcanic systems in Iceland: Example of tectonism and volcanism at juxtaposed hot spot and mid-ocean ridge systems., Annual Reviews o f Earth Planetary Sciences, 28, 107-140, 2000. Gudmundsson, A., and S. Brynjolfsson, Overlapping rift-zone segments and the evolution of the south Iceland seismic zone, Geophysical Research Letters, 20 (18), 1903-1906, 1993. Gudmundsson, A., Emplacement and arrest of sheets and dykes in central volcanoes, Journal o f Volcanology and Geothermal Research, 2462, 1-20, 2002. Hayashi, Y., and Y. Morita, An image of a magma intrusion process inferred from precise hypocentral migrations of the earthquake swarm east of the Izu Peninsula, Geophysics Journal International, 153, 159-174, 2003. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 80 Johnson, D.J., Elastic and inelastic magma storage at Kilauea volcano, in Volcanism in Hawaii, pp. 1297-1306. Linde, A.T., K. Agustsson, I.S. Sacks, and R. Stefansson, Mechanism of the 1991 eruption of Hekla from continuous borehole strain monitoring, Nature, 365, 737- 740,1993. Maaloe, S., Shape of ascending feeder dikes, and ascent modes of magma, Journal of Volcanology and Geothermal Research, 81, 207-214, 1998. McClelland, L., T. Simkin, M. Summers, E. Nielsen, and T.C. Stein, in Global Volcanism 1975-1985, 1989. Meriaux, C., and C. Jaupart, Dike Propagation through an elastic plate, Journal of Geophysical Research, 103 (B8), 18,295-18,314, 1998. Mogi, K., Relations between the eruptions of various volcanoes and the deformation of the ground surfaces around them., Bull. Earthq. Res. Inst., 36, 99-134, 1958. Nakamura, K., Tectonics in the Izu Peninsula and plate bending, Mon. Earth, 2, 94- 102,1980. Nicholson, H., The magmatic evolution of Krafla, NE Iceland., Unpublished Ph.D. Thesis, Edinburgh University, 1990. Okada, Y., Surface deformation due to shear and tensile faults in a half-space, Bulletin o f the Seismological Society o f America, 75 (4), 1135-1154, 1985. Okada, Y., and E. Yamamoto, Dyke intrusion model for the 1989 seismovolcanic activity off Ito, Central Japan., Journal o f Geophysical Research, 96 (B6), 10,361 - 10,376, 1991. Paterson, S.R., and R.H. Vernon, Bursting the bubble of ballooning plutons: a return to nested diapirs emplaced by multiple processes, Geological Society o f America Bulletin, 107 (11), 1356-1380, 1995. Philpotts, A.R., and P.M. Asher, Magmatic flow-direction indicators ina giant diabase feeder dike, Connecticut, Geology, 22 (April), 363-366, 1994. Pollard, D.D., O.H. Muller, and D.R. Dockstader, The form and growth of fingered sheet intrusions, Geological Society o f America Bulletin, 86, 351-363, 1975. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 81 Rossi, M.J., Morphology of the 1984 open-channel lava flow at Krafla volcano, northern Iceland, Geomorphology, 20, 95-112, 1997. Rubin, A., On the thermal viability of dikes leaving magma chambers., Geophysical Research Letters, 20, 257-260, 1993. Rubin, A., Propagation of magma-filled cracks, Annual Reviews o f Earth Planetary Sciences, 23, 287-336, 1995. Rubin, A., and D. Gillard, Dike-induced earthquakes; theoretical considerations, Journal o f Geophysical Research, B, Solid Earth and Planets, 103 (5), 10017- 10030, 1998. Rubin, A., M., Dikes vs diapirs in viscoelastic rocks., Earth and Planetary Sciences Letters, 119 (4), 641-659, 1993. Tryggvason, E., Subsidence events in the Krafla area, North Iceland, 1975-1979, Journal o f Geophysics, 47, 141-153, 1980. Tryggvason, E., The NVI magnetoresistor; tiltmeter results of observations 1977- 1981, pp. 44, Nordic Volcanological Institute, University of Iceland, Reykjavik, 1982. Tryggvason, E., Multiple magma reservoirs in a rift zone volcano: ground deformation and magma transport during the September 1984 eruption of Krafla, Iceland, Journal o f Volcanology and Geothermal Research, 28, 1-44, 1986. Tryggvason, E., Distance measurements in the Krafla-Gjastykki area 1983-1993, pp. 200, Nordic Volcanological Institute, University of Iceland, Reykjavik, 1993. Tryggvason, E., Optical levelling tilt stations in the vicinity of Krafla and the Krafla fissure swarm: Observations 1976 to 1994, pp. 218, Nordic Volcanological Institute, University of Iceland, Reykjavik, 1995. U.S. Geological Survey Juan de Fuca Study, G., Submarine fissure eruptions and hydrothermal vents on the southern Juan de Fuca Ridge: Preliminary observations from the submersible Alvin, Geology, 14, 823-827, 1986. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

Linked assets

University of Southern California Dissertations and Theses

Conceptually similar

PDF

Management of large earthquake data using the Antelope Relational Database and seismicity analysis of the 1999 Turkey earthquake sequences

PDF

Simulating nonplanar fault surfaces using stochastic branching

PDF

Numerical modeling of long period events at the Piton de la Fournaise by the use of object-oriented scientific computing

PDF

Three-dimensional reconstructions of fold growth using growth strata: An example from the Catalan Coastal Ranges, northeast Spain

PDF

Seafloor precipitates and carbon-isotope stratigraphy from the neoproterozoic Scout Mountain member of the Pocatello Formation, Southeast Idaho: Implications for neoproterozoic Earth history

PDF

A tectonic model for the formation of the gridded plains on Guinevere Planitia, Venus: Implications for the thickness of the elastic lithosphere

PDF

Using small events to measure the evolution of the strain and stress fields before the 1992 Landers, California earthquake

PDF

Multi-proxy studies of climate variability in central China: Subdecadal to centennial records in stalagmite from Budda Cave

PDF

Paleoenvironments and paleoecology of the disaster taxon Lingula in the aftermath of the end-Permian mass extinction: Evidence from the Dinwoody Formation (Griesbachian) of southwestern Montana...

PDF

Paleoseismology and geomorphology of the eastern Sierra Madre fault: Evidence for a >8ka age of the most recent event

PDF

Structural evolution of the southwestern Daqing Shan, Yinshan Belt, Inner Mongolia, China

PDF

Oxygen-related biofacies in slope sediment from the Western Gulf of California, Mexico

PDF

Lower Cambrian trace fossils of the White-Inyo Mountains, eastern California: Engineering an ecological revolution

PDF

The origin of enigmatic sedimentary structures in the Neoproterozoic Noonday dolomite, Death Valley, California: A paleoenvironmental, petrographic, and geochemical investigation

PDF

Late Holocene depositional history of western shelf margin, Gulf of California, Mexico

PDF

Magma mingling/mixing in a heterogeneous, multi-pulse magmatic system: An example from the Jackass Lakes pluton, central Sierra Nevada batholith

PDF

Reinterpreting the tectono-metamorphic evolution of the Tonga Formation, North Cascades: A new perspective from multiple episodes of folding and metamorphism

PDF

Application of spectral ratios as a forward modeling technique in the comparison of crustal and upper mantle structures beneath the Rio Grande Rift and the Oslo Garden (i.e. Graben]

PDF

Numerical simulation of whole core squeezer radon pore water profiles: Methodological considerations and evaluation of benthic fluxes and rates of bio-irrigation and advection

PDF

Construction of a gabbro body in the Trinity Complex, northern California

Asset Metadata

Creator Richard, Dominique (author)

Core Title Modeling of continuous tiltmeter data from the 1984 rifting event at Krafla Volcano, Iceland

Degree Master of Science

Degree Program Geological Sciences

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

Tag geophysics,OAI-PMH Harvest

Language English

Contributor Digitized by ProQuest (provenance)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c16-321645

Unique identifier UC11326964

Identifier 1424231.pdf (filename),usctheses-c16-321645 (legacy record id)

Legacy Identifier 1424231.pdf

Dmrecord 321645

Document Type Thesis

Rights Richard, Dominique

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