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Source Parameters Of The Joshua Tree Aftershock Sequence

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Source Parameters Of The Joshua Tree Aftershock Sequence

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Content INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. 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 bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UMI 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. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand comer and continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the back of the book. Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6” x 9” black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order. UMI A Bell & Howell Information Company 300 North Zeeb Road, Ann Arbor MI 48106-1346 USA 313/761-4700 800/521-0600 SOURCE PARAMETERS OF THE JOSHUA TR EE AFTERSHOCK SEQUENCE by Periklis Beltas A Thesis Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree MASTER OF SCIENCE (Earth Sciences) May 1996 UMI Number: 1380456 UMI Microform 1380456 Copyright 1996, by UMI Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. UMI 300 North Zecb Road Ann Arbor, MI 48103 UNIVERSITY O F SOUTHERN CALIFORNIA THE GRADUATE SCHOOL UNIVERSITY PARK LOS ANGELES. CALIFORNIA 0 0 0 0 7 This thesis, written by PtRJLKLK £ e l j a s under the direction of h.CJ. Thesis Committee, and approved by all its members, has been pre sented to and accepted by the Dean of The Graduate School, in partial fulfillment of the requirements for the degree of MaweV; ot Giv-t-iu ITct'cMf r Dtm* THESIS COM M ITTEE D edication This dissertation is dedicated to my family Panagiota, George and M aria Beltas, and my aunt Spyridoula Chorti, who was always a second mother to me. ITHAKA As you set out for Ithaka hope the voyage is a long one, full of adventure, full of discovery. Laistrygonians and Cyclops, angry Poseidon-don’t be afraid of them; you ’ 1 1 never find things like that on your way, as long as you keep your thoughts raised high as long as a rare excitement stirs your spirit and your body. Laistrygonians and Cyclops, wild Poseidon-you won’ t encounter them unless you bring them along inside your soul, unless your soul sets them up in front of you. Hope that your voyage is a long one. May there be many a summer morning when, with what pleasure, what joy you come into harbors seen for the first time; may you stop at Phoenician trading stations to buy fine things mother-of-pearl and coral, amber, ebony, sensual perfume of every kind as many sensual perfumes as you can; and may you visit many Egyptian cities to gather stores of knowledge from their scholars Keep Ithaka always in your mind. Arriving there is what you are destined for But not hurry your journey at alL Better if it lasts for years, so you are old, by the time you reach the island, wealthy with all you have gained on the way, not expecting Ithaka to make you rich. Ithaka gave you the marvelous journey Without her you would not have set it out. She has nothing left to give you now. And if you find her poor, Ithaka won ’t have fooled you. Wise as you will have become, so full of experience, You will have understood by then what these Ithakas mean C.P. Cavafy Translated by Edmund Keeley ©The Ecco Press Acknowledgm ents W ithout the support and help of many individuals this thesis would not have been possible. First of all I’d like to thank my supervisor Keiiti Aki. Before I m et him I knew him only as one of the greats in seismology. These years that I was at USC he kept me surprised me and he was a source of inspiration for me. His advice and comments were like diamonds, rare but invaluable, always accurate and more than helpful. But the most im portant thing that I learn from him is the way of thinking and how nice it is to be alive. I 'd like also to thank Yong Gong Li for supporting me the last two years of my program under National Science Foundation grant EAR 9404762 and his daily advice, as well as for the opportunity that he gave me to know the country side of Southern and Central California. It would have been very difficult, if not impossible, to come in USA without the help of Mr. Larry Patsouras. His support during the first difficult year and later was invaluable and I cannot express my gratitude to him. Deserving of special mention are Profs. Ta-Lang Teng, who was my supervisor in the first year, and Charles Sammis who had allowed me to learn a lot about earth quakes, Thanks are also due to Rachel Abercrombie for being the devil's advocate, and to Jiakang Xie who taught me how similar two earthquakes can be, if you know how to search for them. My graduate fellows in the Department of Earth Science deserve my thanks for making my life interesting and for their help with various problems. David Adams for his help in the field work, his effort to improve my English, his British sense of humor and the endless discussions about science and life. Michael Forrest, Jinbo Chen and Hongping Ouyang with whom I shared the same office for three years. Helpful discussions with James Chin, XiaoFei Chen, Anshu Jin, Linji An are very much appreciated. Anne Petrenko and Yoshiaki Hisada for being my friends and always inspire me for a better life. Avijit Chakraborty and Joyjeet Bhowmik for their help with com puter problems. I could not forget my friends outside the Departm ent, with whom I shared many beautiful moments. Em m a Avakyan for all the poetry, Gilberto Kuzuhara, Apos- tolos Kountouris, Xialing Liu, Phillip Mihopoulos, Fernando and Luciana Moreira, Carmen Perez, Guido Preparata, Anastasia Tsingotsidou, Christina Vagelopoulou, Dimitris Vatakis, all of them gave me something in their way. Last but not least I ’d like to thank Rene Kirby for her invaluable help with the bureaucracy of the graduate school and Mushtaq Khan for m aintaining the computer network of our departm ent. C ontents D edication ii Acknowledgm ents v List O f Tables ix List Of Figures x A bstract xii 1 Introduction 1 1.1 B a c k g ro u n d ......................................................................................................... 1 1.2 The Joshua Tree e a rth q u a k e .......................................................................... 2 1.3 Thesis R ev iew ..................................................................................................... 3 2 Theoretical Background 5 2.1 In tro d u ctio n ........................................................................................................ 5 2.2 Kinematic M odels.............................................................................................. 5 2.3 Dynamic models .............................................................................................. 7 2.4 Source D im e n sio n s........................................................................................... 9 2.5 Scaling relations................................................................................................... 12 3 Sim ultaneous Inversion of Source and Path Effects 19 3.1 In tro d u ctio n ........................................................................................................ 19 3.2 Formulation of the In v ersio n .......................................................................... 20 3.3 D ata A n aly sis..................................................................................................... 23 3.4 Results and D iscu ssio n .................................................................................... 29 4 Em pirical G reen’s Function 61 4.1 In tro d u ctio n ........................................................................................................ 61 4.2 M ethod of a n a ly s is ........................................................................................... 62 4.3 Results and D iscussion............................. 63 vii 5 Conclusions R eference List List O f Tables 3.1 Date, time, location, and magnitude of the earthquakes that were used in the in v e rs io n ........................................................................................ 47 3.2 Corner frequencies / c, high frequency fall off 7 and source dimension R from the in v e rs io n ........................................................................................ 54 4.1 Date, time, location and magnitude of the earrthquakes that we used with the EGF m e t h o d .................................................................................... 77 4.2 Corner frequencies and source dimensions of the earthquakes that we used with the EGF method .......................................................................... 79 ix List O f Figures 1.1 Spatial and temporal development of the Joshua Tree sequence . . . . 4 2.1 Propagating dislocation with slip Au and P-wave displacement up at an observation p o i n t ........................................................................................ 10 2.2 Seismic moment with source dimensions, including borehole data [l] . 15 3.1 Detail of m atrix equation 3 .3 ......................................................................... 21 3.2 Detail of m atrix equation 3 .4 ......................................................................... 22 3.3 Locations of earthquakes and stations that were used in the inversion 26 3.4 Seismograms (displacement) of an earthquake magnitude 1.60 and the S-wave spectrum. The noise level (dash line) was calculated from a three seconds window before the P arrival................................................... 27 3.5 An earthquake magnitude 2 . 5 ...................................................................... 28 3.6 Corner frequencies with Q=150 •, and Q=300 + . . . ....................... 30 3.7 Examples of source spectrum, vertical c o m p o n e n t................................. 32 3.8 Examples of source spectrum, E-W com ponent....................................... 33 3.9 examples of source spectrum, N-S component ....................................... 34 3.10 Amplification factor at station C O V F ...................... 35 3.11 Amplification factor at station SDCE . ..................................................... 36 3.12 Amplification factor at station K E Y V ........................................................ 37 3.13 Corner frequencies with seismic m o m e n t.................................................. 38 3.14 Seismic moment and source d im e n s io n ..................................................... 39 3.15 High frequency fall off with corner frequency....................................... 40 3.16 High frequency fall off with m a g n itu d e ................................................. 41 3.17 High frequency fall off with d e p t h ........................................................... 42 3.18 Corner frequency with depth for different magnitude ranges, N-S com ponent .................................................................................................................. 43 3.19 Corner frequency with depth for different m agnitude ranges, E-W com ponent............................................................................................................ 44 3.20 Corner frequency with depth for different magnitude ranges, vertical com ponent........................................ 45 3.21 Location of the earthquakes with depth more than 7 km and corner frequencies higher than 18 Hz (solid circles) and those with depth less than 6 km and corner frequencies less than 16 k m .................................. 46 x 4.1 The earthquakes that we used with the EGF m e t h o d ...............................64 4.2 Pair of earthquakes that was used with the EGF method. For every component the first window is the seismogram of the large earthquake (displacement), and the second window is the waveform of the small earthquake. The third and fourth windows are the same events after being band passed. All windows start from the P wave arrival . . . . 65 4.3 Example of an earthquake p a ir...................................................................... 66 4.4 Example of an earthquake p a ir...................................................................... 67 4.5 Example of an earthquake p a ir...................................................................... 68 4.6 Examples of spectral ratios with the best fit curve. On the right of each example the distribution of the residuals is shown for all the calculated pairs of corner frequencies. The optimum pair of corner frequencies is shown with an asterisk. Pairs with residuals within 25% of the optimum are shown with crosses. Circles represent pairs with residuals between 25% and 50% of the optimum. Pairs with larger residuals are represented with d o t s ................................................... 70 4.7 Examples of spectral ratios ......................................................................... 71 4.8 Corner frequencies with seismic moment, as they were calculated with the EGF m e t h o d .............................................................................................. 72 4.9 Seismic moment with source d im en sio n ..................................................... 73 4.10 Corner frequencies with depth, N-S com ponent....................................... 74 4.11 Corner frequencies with depth, E-W c o m p o n e n t.................................... 75 4.12 Corner frequencies with depth, vertical com ponent................................. 76 5.1 Corner frequencies of earthquakes with depth less than 7 km (o) and depth larger than 7 km (+) .......................................................................... 84 xi A bstract We examined the source parameters of the Joshua Tree aftershocks that were recorded by a temporal network in the area of Joshua Tree. For this analysis we used a joint inversion of source and site factors and the Empirical Green’s Function method. We found that there is no upper limit in the corner frequency of small earthquakes down to m agnitude 1.0. Our data show a decrease of stress drop with decreasing seismic moment with earthquakes of magnitude 3.5 having stress drops around 1000 bars and earthquakes of magnitude 1.0 having stress drops around 10 bars, sup porting nonsimilarity between large and small earthquakes. We also find a depth dependence of the stress drops, with deep earthquakes having higher stress drops than shallow earthquakes. We believe th at this is due to the increase if the confining pressure with depth or material heterogeneities in the source area of the earthquakes. C hapter 1 Introduction 1.1 Background The study of the source mechanism of earthquakes 3s one of the most im portant subjects of seismology and has evolved into a large field, to which numerous contri butions have been made. The origin and cause of earthquakes has fascinated man since antiquity. The experience of the catastrophic consequences of large earthquakes that shake the foundations of the stable earth has excited m an’s quest for explana tions of such phenomena. The earliest explanations took recourse to legends and mythology, and many of them were embellished with an amount of beauty. Greek natural philosophers were the first to search for natural causes of earthquakes. The frequent occurrence of earthquakes in the Hellenic region forced these authors to dedicate part of their work in the explanation of these phenomena. The purpose of the present thesis is to deduce the source param eters of small earthquakes and more specifically their relationship with m agnitude (scaling law) and the tectonic environment. Knowledge of the scaling law has crucial implications in high frequency seismology. It can be used as the basis for predicting strong motion of a large earthquake, using the data from smaller earthquakes, since they are more frequent than the large ones. It can be used also for the discrimination of nuclear explosions from small earthquakes, the understanding of high frequency energy propagation in near surface rocks and the possible mapping of spatial and tem poral variations in tectonic stress using microearthquake stress drops. For this study we use the aftershocks of the Joshua Tree earthquake. These events were recorded from a temporal network which was deployed by the Southern 1 California Earthquake Center (SCEC) hours after the mainshock. The proximity of the stations to the source region of the events and the high dynamic range of the instrum ents allowed us to examine earthquakes in a magnitude range from 4.0 down to 1.0. 1.2 T he Joshua Tree earthquake The April 23 1992 Joshua Tree earthquake (Mw = 6.1) occurred along a previously unmapped north trending fault located about 20 km south of the Pinto Mountain fault and about 10 km northeast of the Mission Creek branch of the San Andreas fault system. It was the first of a series of events that constitute the Landers earthquake sequence. Seismicity in this area is characterized by frequent earthquake swarms [46]. A se quence of moderate earthquakes had occurred in this area between 1940 and 1948 [83] which included the 1940 Covington Flat (Mj,5.3), 1947 Morongo Valley (A-f/,5.4) and 1948 Desert Hot Springs (AZ/,6.5) earthquakes. The Covington Flat earthquake probably ruptured the same fault as the Joshua Tree earthquake. North trending faults in this area lie in the Eastern California Shear Zone (ECSZ), a zone of intracontinental right-lateral shear, extending northwestward from the southern San Andreas fault zone into the Mojave Desert where it turns north- northwest into Death Valley. About 9% to 23% of the total Pacific-North American relative plate motion is accommodated within this zone [87],[26]. In order to ex plain the high strain rates, in the ECSZ, Savage suggested [91] th at some flaw in the lithosphere controls it. Nur [72] suggested th at the Joshua Tree and Landers earthquakes are due to the creation of a new fault trending Ar10°H'r and extending roughly 100 km across the Mojave desert. The Joshua Tree mainshock nucleated at a depth between 12 and 15 km. By June 1992 it had been followed by over 6000 aftershocks. No surface breakage from this seismic activity was found [85]. The fault plane solution of the mainshock shows a right lateral fault striking A^20°iy, with a dip of 90° and a rake of 160° [46]. The aftershocks extended to the north and south of the mainshock area from the southern San Andreas fault to the Pinto Mountain fault (Fig. 1.1). During the month of April the southern part of the aftershock zone had a N 2W W direction while 2 the northern part had a north direction. In May the north trend became prominent while aftershocks started to occur with a E-W direction around a latitude of 34°. Many of the aftershocks are right lateral with nodal planes either subparallel to the mainshock plane or auxiliary nodal planes striking at high angles. This predominance of the strike-slip faulting, which was one of the main char acteristics of the Landers sequence, was also seen in background seismicity of the region [46] and it is related to the deformation along the San Andreas fault. The earthquakes occurred in the area of the Big Bend, where the strike of the San An dreas faults changes from iV35°W to iV65° — 75°W. The strike of the Landers fault zone is very close to the direction of the plate motion vector in the area. These earth quakes provided a mechanism for the transformation of the slip across the ECSZ. The slip transferred from the San Andreas fault, across the Little San Mountains to the Landers fault zone with the breakage of multiple parallel right-lateral faults striking north to northwest. 1.3 T hesis R eview Chapter 2 includes a review of the earthquake source theory. We also present the results of others work on the earthquake scaling law, and the related problems. In chapter 3 we present a simultaneous inversion of site and source effects. We explain the formulation of the inversion problem, the procedure that we followed in the analysis of the earthquakes, and finally the results. In chapter 4 we present the Empirical Green’s Function method. We explain the method, the procedure that we used to select the earthquakes, and our results In Chapter 5 we compare the results of the two methods and present the final conclusions. 3 f A) 22 - 30 A pril 1992 Joshua Tree Mi/ ( B > 5 T T 20’ \ % 1 f ,N* * ’ • L V . O ,j M 6 . I J o i h u o T r t f 50* '% V \ \ W ' ' X * u A illU jJ. 7\ \ V m a g n i t u d e ^ ! 1 1 V ' T \ \ V T T ' 11 r 3 'J-n \ V ' f k \ \ ; V V '■ ' Q * ■ i < ' ’ • : ■ \ • h t k : \ . ; V. N « M + • 1 * ' 'A * * ' T* ** '«*_ M . d S P * ' '' v M O flT • ‘ s * Blvt rut Foull*': X n B s ' 10 KMV< V t'. 1 1 a 1 1 n i i i iJ \ , X . i ■ * . . . , ■ (C J 1- 2 8 J u n e \V < O '1' A \ N> £ * • v \ 0 v ■ > . \ M7.3 i 1 Lon d»r» * ■ t Mainihocli V. < L F N * r » -v 1 ---------------- N ; 10 KM 116*20' 10 ' 116*20' 10 ' 116*20’ 10 ' Figure 1.1: Spatial and temporal development of the Joshua Tree sequence [46] 4 C hapter 2 T heoretical Background 2.1 Introduction The mechanism of an earthquake has been considered as a slip across a fault plane and m athem atical and physical models have been formulated based on the linear elastic theory. These source models or representations were defined by a small num ber of param eters which were constrained by the observed elastic displacement field for a particular earthquake. In general the faulting phenomenon can be considered from two different points of view: kinem atic and dynamic. T he kinem atic models are those th at assume the space-time characteristics of the slip or displacem ent dis continuity at the fault plane. The dynam ic models try to relate the fracture process to the stress conditions and the m aterial properties at the source region. 2.2 K inem atic M odels For earthquakes characterized by displacement discontinuities at fault surfaces, and the traction continuity across the fault surface, the elastic displacement field [9] is generally represented by the following equation [9] u,-(®, t) = J m pq * GipfidE (2.1) This is an integral superposition of the impulse response of a medium (G reen’s tensor derivatives G ,-Pt9) weighted with the moment density tensor m pq. The superposition is over the ruptured fault area S . 5 The m om ent density tensor, is given by m p? = [UtWjCijpq where [u,-] is the displacement discontinuity between the two sides of the fault area, i/j is the normal vector to the fault area and c;jpq are com ponents of the fourth order tensor of elastic moduli. In order to find the displacements tq we need to know G reen’s function.The Green tensor derivatives are equivalent to solutions produced by force couples. In case of an unbounded isotropic homogeneous elastic medium an exact analytical expression of G{p is available [9] Gip{x ,t;i,r) = 1 (7*7p - £p )rsd - (2-2) 4irp/32 ,p tp/r v (3‘ Here x is the observation point, is the source point, r = x — £ is the distance between source and observation points, 7 is the unit vector, a, (3 are the P wave and the S wave velocities, p the density, Sip is Kronecker’s delta and S is the tem poral Dirac delta function. The first term in equation. 2.2 decays more rapidly (r -2 ) than the other two term s (r “ l ), is called the near field term , and describes a wave field not separated into P and S waves. The other two term s describe the P and S waves separately. Using equation 2.2 to derive G,p(9 and equation 2.1 we can obtain the displace m ent field due to a point source, in an infinite homogeneous medium. This field in spherical polar coordinates centered on the source has the form [9] 6 1 v 1 r/P u(x, t) = -— A — I rM 0{t — t )(It Airp r'1 Jr/a An pa? r2 a 4wp(32 r2 /?' - : > + s k ' 1 " ; * * * - j )ocm rs ( 2 - 3 ) where M 0{i) is the tim e dependent seismic moment and A are the radiation patterns for the near field (N), interm ediate field P and S (IP, IS), and far field P and S (FP, FS). 2.3 D ynam ic m odels Laboratory studies of fracture and frictional behavior of rocks provide the physical basis for understanding the phenomena of earthquake rupture. It is now generally accepted th at crustal earthquakes are caused by a sudden drop in shear stress accom panied by unstable slip on a fault. The mechanism of rupture in unstable slip can be described either as a brittle fracture or as a stick-slip friction instability. These two approaches are mathematically equivalent in relating motion in the medium to a drop in shear stress on the fault surface, but the rupture process is considered differently [92], For the crack propagation a fracture energy per unit area to create a new crack surface is required while in the stick slip model rupture the stress on the fault reaches the static friction value leading to the condition for dynamic instability. The simple case of a plane Mode III crack is discussed by Andrews [12], Consider a crack on the y = 0 plane extending from z — — L to z = L. The shear stress a\ is constant far from the crack and on the fault plane equals the sliding friction value ttj. Then the displacement on the crack is u = - *»)■/> (2.4) The change in strain energy is AC/e = - crj)L2 (2.5) & p. 7 The net energy available to supply surface energy which is the sum of the strain energy and the work against friction is - A Uc - A U} = - a j f L 2 (2.6) As the crack half-length increases an am ount dL the increment of available energy is t?(AUe - AC//) = ^{<7t - a jfL d L (2.7) At the critical half-length Lc this must be just sufficient to supply the fracture energy for both ends of the crack, 2GcdL = (2.8) f t ( f f ! - ( 7 / ) 2 This model has the non physical result of a stress singularity at the crack tip. This is usually avoided assuming that the crack breakdown occurs over some finite distance which smears out the stress drop and its associated stress concentration. In crack theory this corresponds to the development of a process zone while in friction to the breakdown between the static and the dynamic friction, which requires a critical slip distance. Andrews [12] shows the model of Ida [52],[53] where the initial stress < 7i is less than the yield stress < tu initially, and then it breaks down to a friction stress 07 over some critical slip distance d0 In this case the fracture energy is Gc - ~ (2.9) This model corresponds to a slip weakening model. When the half-length exceeds Lc the rupture will accelerate up to some limiting value which is the shear velocity of the medium for the mode III case. The rupture propagation depends on a dimensionless strength param eter S [92] defined as the ratio of the stress increase required to initiate slip to the dynamic stress drop. S - ?v ~ gl (2.10) a x - 07 8 2.4 Source D im ensions The point source approximation does not consider the finite dimension of the source region. The complete representation of the seismic source m ust include its shape and dimensions. M aruyam a [67] was the first to show th a t the force equivalent for fault slip is a double couple distribution over the fault plane. Burridge and Knopoff [23] studied the case of propagating dislocations over a certain finite length and showed again its equivalence to propagating double couples. Ben Mehanem [16] [17] de term ined solutions for surface and body waves from extended sources consisting in point forces of the single and double couple type propagating in one direction with a finite velocity. T he model of the fault is a rectangular fault of finite length (L) and width (W). He shows th at the effects of finite dimensions can be isolated by means of the directivity function ratio of the spectral amplitudes radiated from the source in opposite directions. Haskell [42] [43] [44] presented a model of the source with finite dimensions of rectangular shape of length L and width W , in which the slip has the form of a rupture front th at propagates in one dimension with velocity «, along the length. The slip depends on tim e in such a way that it takes a tim e r to reach it’s maximum value D, in the form of a ram p function, from t= 0 to r . Savage [88] presented a model of an elliptical fault and Hirasawa and Stauder [49] investigated the radiation from several models of rectangular faults with fracture initiating at a point and propagating unilaterally and bilaterally. The radiation of P waves in the far field from a simple rectangular fault can be w ritten in the form (Fig. 2.4) where 72(7,-, n,•,/,■) is the radiation pattern of a point source, constant for E if r is very large in comparison with the dimensions of the source. If in the course of 9 D L Figure 2.1: Propagating dislocation with slip Ati and P-wave displacement up at an observation point 1 0 the propagation the fracture moves with velocity u along the length of fault L, the integral can be written in the form D f l A«[t - £ - £(cos 0 - £)]df (2.12) Jo a a u For the tim e dependence of A u the following function was proposed by Ben Menahem and Toskoz [18] Au(f) = A u //(i)(l — e ~ ) (2.13) where r is the rise tim e . In this case the Fourier transform of the displacements in equation 2.11 is given by rrP/ , uAu(LW) _ 1 sinA' .wr 7 r, Uf(u) = , K . JR-------------- — e x p j( h A - - ) (2.14) 1 v ' 47rpa3r 1 + iu r A 1 v a 2 1 y ’ where X is given by A' = — ^(cos£l ) (2.15) 2a u In equation 2.14 the dimensions of the source introduces the factor sia X /X and the existence of a rise tim e factor (1 — itur)"1. The spectral amplitudes have the following form: For low frequencies, as w tends to zero, the spectral amplitudes tend to a constant value; for values of u; larger than a certain value u > c, the spectral amplitudes decreases as w-2 . The properties of the spectral am plitudes and phases for body and surface waves radiated from a source are the basis for the determ ination of the parameters which define the dimensions of the source. These models introduce the following parameters: L, the fault length; W, the fault width; u, the rupture velocity; Au, the perm anent slip; and r , the rise time. The complete process of fracture propagation from a kinematical point of view must include the description of its nucleation, spreading and stopping [88] [86] [69]. The theory of propagating dislocations has also been applied to the study of the near field displacements by Aki [4], Haskell [45] and others using numerical integrations. Another approach to the problem of fracture over an extended fault was presented by Brune [21], He modeled the earthquake dislocation as a tangential stress-pulse applied to the interior of a dislocation surface. The pulse is applied instantaneously over the whole fault surface, neglecting fault propagation effects. He described the 11 near and far field displacements in the time and frequency domain. The spectrum has a flat part for low frequencies and decays as w~2 for frequencies larger than a particular value u c or f c called the corner frequency. The corner frequency is proportional to the dimensions of the source. The radius of the circular fracture is related to the corner frequency of the S waves by 2-3^ r o m = 2WT ( ’ 2.5 Scaling relations. As we saw before the far-field displacement spectrum is flat at low frequencies and decay with increasing frequency above the corner frequency. The corner period, the reciprocal of the corner frequency, is proportional to the source dimension. A source scaling relation describes the manner in which the source dimension increases with increasing seismic moment. For a given seismic moment smaller source dimensions would give rise to a shorter source duration and a higher corner frequency. This in turn would mean an increase in stress drop. Aki [3], based on the assumption that large and small earthquakes are similar phenomena, proposed the w2 scaling law. His assumption implies the same geometry, a constant stress drop and constant rupture and slip velocities independent of fault length. The earthquakes share the same spectral shape, which decays inversely proportional to the square of frequency beyond the corner frequency. In studies of large earthquakes it has been found that stress drop is roughly independent of the seismic moment [58] and that the seismic moment is proportional to r 3, where r is the source radius, confirming the existence of the to2 scaling law for large earthquakes. Shimazaki [94] confirmed that the seismic moment is proportional to £ 3, where L is the fault length, for earthquakes with seismic moment smaller than 7.5 x 102 5 dyne cm but he observed that it is proportional to L2 for larger earthquakes. He explained this difference by the fault width constrained by the brittle zone for the large ones while the smaller ones do not rupture the all seismogenic zone and thus they follow the self-similarity. The scaling law was reported to hold also for small earthquakes. Del Pezzo et al [79] studied the seismic activity at the Phelegraean Fields volcanic area. Inverting 12 individual displacement spectrum, they found constant stress drop for earthquakes with seismic moment between 0.5 x 101 8 dyne cm and 0.13 x 102 1 dyne cm. Constant stress drop for micro earthquakes was shown also by Frankel et al [32]. They used earthquakes with seismic moments down to 101 8 dyne-cm, from the Anza seismic network. Taking the spectral ratio of earthquakes from the area (Empirical Green’s Function) they found that the observed corner frequencies are substantially lower than the source corner frequencies, which follow an u> 2 scaling taw. Hanks [38] combined results from various works and claimed that the stress drop is independent of the moment in the range 101 8 < M 0 < 1028. Iio [54] studied microearthquakes with S-P tim e less than 0.6 sec, recorded on a hard rock site. Using the first cycle of the P-wave he observed that the corner frequency of earthquakes with seismic moment down to 101 '1 dyne-cm is up to 176 Hz with a spectral fall off higher than two. Glassmoyer et al [36] used the after shocks of the 1986 Northeastern Ohio earthquake to obtain the source param eters of earthquakes with seismic moment as small as 9 x 101 G dyne-cm. Their data show no evidence for an upper limit in the corner frequency but show a decrease in stress drop with decreasing seismic moment. Probably the most convincing results for the existence of the scaling law for small earthquakes come from borehole instrum ents. Malin et al [66], Hauksson et al [47] found th at apparent corner frequencies of microearthquakes are significantly higher for borehole recordings than for seismometers located on the surface. Abercrombie et al [2] and Abercrombie [1] using borehole data from a depth of 2.5 km at Cajon Pass did not observe any breakdown from the scaling law for earthquakes with m agnitude M i — — 1 to 5.0. Also the constancy of stress drop has been found for seismic events in gold mines in South Africa [35] and in coal mine in Poland [34]. Gibowicz [33] combined seismic events from mines in South Africa, Canada, Poland and Germany. He found that in most of the cases a constant stress drop is observed but that the seismic moment, referred to the same range of corner frequencies* is higher in hard rock gold mines than in coal mines inside fractured sandstones. In contrast to these results there are evidence of a breakdown in self sim ilarity between large and small earthquakes. Chouet et al [24] analyzed earthquakes from California, Japan, and Hawaii using the coda waves from small earthquakes. The 13 advantage of the coda method is that it does not require the close proximity between a pair of events because of the naturally averaging process of randomly back scat tering coda, allowing the use of a simple statistical technique for isolating the source effect from the effects of scattering and attenuation. After isolated the source factor they constructed the scaling laws th at describe the earthquakes in each region. In figure 25 of their paper we can see th at the corner frequencies of the earthquakes from each area follow a different scaling law. In most of the areas the scaling law is consisting from two parts. There is a section with the larger earthquakes following self similarity and a section where the earthquakes have constant corner frequency, resulting in a stress drop increase with increasing seismic moment. Rautian et al [81], [82] examined over 1000 earthquakes in the Garm region using the coda method. They observed (figures 10-12 of their paper [82]) that stress drop increases linearly with seismic moment, in a logarithmic scale, for earthquakes with seismic moment M < 102° dyne cm, while it is constant for earthquakes with larger seismic moment. Earthquakes from different regions shown to follow different scaling laws, with earthquakes from Paleozoic basement having higher stress drop than earthquakes from areas with Mesozoic and Cenozoic sediments. Comparing the results of Chouet [24] and Rautian [82] with those of Hanks [38] and Abercrombie [2], [1] it is noticeable that the results with the coda m ethod have less scattering than the others. For example on figure 2.2 from Abercrombie [2] we notice that the stress drop varies from O.lbars to 100 bars. One reason for this is the natural process that creates the coda waves [24]. A constant corner frequency was also observed in other cases. A rchuletta et al [14] determined spectral source parameters for a wide magnitude range of events of the 1980 M ammoth Lakes earthquake sequence. They found th at for events with seismic moment greater than about 102 1 dyne cm the stress drop is nearly constant at around 50 bars, while for smaller events the stress drop decreases with seismic moment with an upper limit in the corner frequency of 15-20 Hz. They argue that their observation can not be a result of attenuation and conclude th at the r 3 law does not hold for small earthquakes. Fletcher et al [29] calculated the source radius of earthquakes from the Anza seismic network. After correcting them for attenuation they found th at the source radii is roughly constant over four orders in magnitude in seismic moment. Oncescu 14 S eism ic M om ent (N m ) ACajon Pass Borehole (Model 2) • Various Combined Studies 10" Unes of constant stress drop (MPa) 10® Source Dimension (m) Figure 2.2: Seismic moment with source dimensions, including borehole data [1] 15 et al [73] using a joint source-site inversion calculated the source spectra of the 1992 Roermond earthquake in Belgium. They found a violation of the scaling law for earthquakes with m agnitude smaller than 3.4. Stress drop decreasing with seismic m oment has been observed also for induced seismicity in mines. In South Africa mines Bicknell et al[19] exam ined over 100 trem ors w ith m agnitude from 0 to 3, which were recorded on th e surface and at depths of 1768 m and 3048 m within the Western Deep Levels gold mine. It was found th at the breakdown in self sim ilarity persists with the underground d ata recorded within a few hundred meters of the source. The nonsimilar behavior of small earthquakes has been interpreted as a source effect. Aki [5], [6], [7], [8] has proposed th at it represents a m inim um source dim en sion. There is some theoretical basis for the existence of a m inimum earthquake. As we saw from the dynamical models the crack diam eter can not be sm aller than a value L c for unstable rupture to initiate. Accordingly from rock mechanic experi ments [25] it was observed th at dynamic instability occurs only when a circular fault patch exceeds a critical radius. The fault zone width was proposed as the m ain phys ical param eter that controls the size of the characteristic earthquake. Observations on the fault zone of the Landers earthquake using trapped modes [63] give a value of 200 m for the fault width. The fault zone coincides with the breakdown zone in the crack tip. Inelastic processes inside it, like enhanced or retarded pore fluid flow, plastic deformation of fault gouge and so forth obstruct the initiation of rupture. Coupled with the idea of the minimum earthquake is /„,„*• Papageorgiou and Aki [75], [76] observed th at the acceleration power spectrum of m ajor earthquakes in California depart from the flatness expected from the o> " 2 model and decay beyond a cut ofF frequency, which is called f max. They considered th at is a source effect and th at it represents a smoothing factor of the seismic radiation. They related the constant v / / max, where v is the rupture velocity, with the size of the breakdown zone. The size of the breakdown zone, as it is calculated from the f max of earthquakes in California, is of the order of several hundred m eters. Applying the specific barrier model Aki [7] found a decrease of the barrier interval with decreasing m agnitude. This is because the decrease in m agnitude is prim ary due to the decrease in fault slip, so th at the barrier interval has also to decrease, in order to keep the local stress drop constant (Fig.2 in [7]). So the subevent crack diam eter equals the breakdown 16 zone at about M =5.0, for California earthquakes, and the size of it is comparable with the size of the fault zone width as it was calculated from trapped mode studies and the results from f max- On the other hand the change in spectra scaling can also be explained by a t tenuation effects. Frankel [30} found th a t the apparent corner frequencies of m i croearthquakes recorded at hard rock site in the Virgin Islands were correlated with the receiver site and proposed th at these corner frequencies were produced by severe attenuation under the receiver sites. He suggested th at the apparent breakdown in the scaling law of small events could be a consequence of the attenuation beneath the receiver sites. Hanks [39] observed th at the f max from an aftershock of the Oroville earthquake depended on the site surface geology, thus concluded th at it is an atten uation effect. Anderson et al [11] noted th at the f max of large earthquakes can be explained by severe attenuation from a frequency independent Q, inside a surface layer, called the k effect. They assumed an u> -2 fall off in the source spectrum and inferred a low Q in the near surface m aterial in the Imperial valley. Anderson [10] showed th at an exponential function with a frequency independent Q could alter the apparent scaling of corner frequency with seismic m om ent and it can explain an apparent constant corner frequency for small earthquakes and the appearance of fm ax on the acceleration spectrum . Another interesting observation comes from the scaling of the seismic energy with the seismic m om ent. If small earthquakes are sim ilar to large earthquakes then the relationship between seismic moment and seismic energy should be the same as the relationship between seismic moment source dimensions. Recent calculations of the seismic energy [1], [97] shown th at even in the case th at the loci of the corner frequencies do not deviate from self sim ilarity the seismic energy does. A decrease of the seismic energy with seismic m oment is clear, even in borehole d ata [1], and atten uation can not be consider responsible for it. Since the seismic energy is proportional to the square of the velocity spectrum , depends on the higher frequencies more than the stress drop, which is calculated from the corner frequency, and probably is more suitable to record the complexity of the earthquake source. 17 The other fundamental earthquake scaling relationship is expressed in their size frequency distribution. In any region it is found th at the num ber of earthquakes N (M 0) with seismic moment > M0 is given by N (M 0) = aM? (2.17) where a is a space tim e variable. This is known as the Gutenberg-Richter or Ishimoto- lida relation. This type of power law size distribution is typical of fractal sets and it comes from the self-similarity of earthquakes. The exponent B is related to the fractal self similarity dimension D. Because fracture is also a fractal process the sizes of faults and joints also obey power law distributions. Any deviation from the self similarity for earthquakes should be reflected in the power laws th at govern fault distribution and in equation 2.17. Aki [6] studied the frequency m agnitude relationship for earthquakes with mag nitude range — 1/3 to 4 recorded at a borehole station in the Newport-Inglewood fault. He found a clear departure of the observed frequency-magnitude relation for earthquakes with M < 3 from the linear relation (on logarithmic scale) extrapolated from the data with M > 3. The observed number of earthquakes with M =0.5 was almost 10 times smaller than that expected from the extrapolation of empirical re lation for earthquakes with magnitude larger than 3. Rydelek and Sacks [84] after checking the earthquake catalogue for completeness found the same departure for earthquakes, in southeast Hokkaido, with magnitude less than 2.0. Pacheco et al [74] observed a different size distribution between earthquakes with m agnitude smaller and larger than 7.0 for shallow earthquakes, using worldwide data. The reason for this is the finite length of the brittle zone as in the case of the deviation from self similarity that was found by Shimazaki [94], 18 C hapter 3 Sim ultaneous Inversion o f Source and P ath Effects 3.1 Introduction This chapter presents the results for the determination of site amplification and source factor by an inversion method. In this method we decompose the S wave spectrum into source, path, and site terms. The decomposition method using inversion technique was first proposed by An drews [13] to separate the source and site spectra from strong ground motion. As he indicated there is a non unique trade off problem in the formulation of the inver sion because neither the source nor the site spectra have explicit formulation. One constraint, at least should be used to avoid this trade off. Hartzell [41] classified the methodologies into two types, according to the constrain that they use. The site response of at least one station [13],[41],[96],[61] can be used as a constraint, or the shape of the source spectrum [20], [28], [93]. In the first case the formulation is linear while when the source spectrum is constrained an iterative method between a linear and a non linear inversion is used. The advantages of this method are that no a priori knowledge of the velocity structure or the source process is needed and that a simultaneous estim ation of source and site effects is possible. The main disadvantage, in the case th at a reference station is used, is that [60] the constraint is unreliable in high frequencies, because the factor of site amplification can be different than 2 due to effects of anelastic attenuation within the surface layers [60], [56]. 19 3.2 Form ulation of the Inversion The observed S wave spectrum can be written as 0 « ( /) = (3.1) where OtJ - is the observed spectrum from the i earthquake recorded at the j station, Si is the source spectrum , Gj is the site response spectrum , Rij is the hypocentral distance, u is the geometrical spreading factor, Qs is the quality factor and va is the S wave velocity. By taking the logarithm of both terms in equation 3.1 we construct the following system of linear equations 0 ^ { f) = log <$(/) + log Gj(f) (3.2) where Oij(f) = Iog(0tj/?£) — ( ^ ^ j ) l o g ( e ) , is the logarithm of the observed spec trum , corrected for attenuation and geometrical spreading factor which assumes the value v — 1. Equations 3,2 can be written in m atrix form d = G m (3.3) where m is the solution vector, d is a data vector, and G is the m atrix which relates m to d. The construction of these matrixes can been seen in figure 3.1. As a constraint we used the site amplification factor of one station (AQUA). The reasons th at we used AQUA was because it was installed on a granitic outcrop, with small weathering zone [27] and it was in operation for the largest tim e period than the other stations. We choosed to use as a constraint a reference station instead of the source spectrum because this allows the inversion to be linear. Besides that we did not want to constrain the source spectrum , since it is the object of the inversion. Another reason is that we could not obtain the instrum ent responses of the stations. So we assume that they are included in the station responses. The equality constraint is expressed as C m = h (3.4) 20 Source Site G = (1 0 - ■■ 0 1 0 • • ■ 0 \ 1 0 • ■■ 0 0 1 • 0 1 0 * * 0 0 0 • • . 1 0 1 • * 0 1 0 • • • 0 0 1 • • i 0 0 1 • • • 0 * 0 1 . • 0 0 0 • 1 0 0 ■ ■ • 1 1 0 • • • 0 0 0 • >■ 1 0 * 1 • • • 0 ^0 0 • * * * • 1 * 0 • * 0 • • : d m = ( 52 91 92 * V 9i ) , d = ( o n \ 012 021 022 °2j O il °i2 \ oTj / Model parameters D ata Figure 3.1: Detail of m atrix equation 3.3 Source Site C = ( 0 0 0 | 1 0 ••• 0 ) Constraint m atrix m = / s, \ S2 * * Si m \ 9j 7 Model parameters Figure 3.2: Detail of m atrix equation 3.4. The only non zero element in the con straint m atrix corresponds to the reference station. where h is the vector containing elements of constrained values and C is a coef ficient m atrix which relates m to h. Figure 3.2 illustrates m atrix equation 3.4 We solve the system of equations 3.3 in a least square manner with equality constraints, using the singular value decomposition method [62]. First we find the singular value decomposition of the constraint m atrix C C = U cA cV<r (3.5) where V , U are orthogonal matrixes and A is a diagonal m atrix with the eigenvalues of the eigenvectors that construct the two orthogonal matrixes. Then the general solution of equation 3.4 is m = V cA ^ U jh + Voa (3.6) where a is an arbitrary vector and V 0 contains the eigenvectors with zero eigenvalues, representing the portion of the model space that is not illuminated by the operator 22 C, The vector o can be determ inated by substituting 3.6 in equation 3.3. Then we have Ga = d (3.7) where d = d — GCgM i, C "1 being the generalized inverse of C and G = G V n. This system can be solved as an unconstrained least square problem o = G ^ d (3.8) Substituting equation 3.8 in equation 3.6 we get the model vector m = C " 1h + V 0G ; 1a (3.9) The covariance m atrix T is defined by T = < (ni0 — m )(m 0 - m )T > where is the true model vector. Substituting equation 3.9 we get r = VoGg1 < A d A d T > G"1 TV^ where Ad Ad? is a diagonal m atrix with elements - _ r ( ® 5 ~ 0 ° g 5.c + l°g f f J C ) ) 2 i o . 5 / > _ ( . / + / _ i) 1 where log$,c,log<7 je are the calculated source and site spectrum and P — (J + I — 1) represent the number of observations P, minus the degrees of free dom lost. 3.3 D ata A nalysis Our data set is consisted of earthquakes that were recorded from a temporal net work in the area of Joshua Tree, which was deployed from the Southern California Earthquake Center (SCEC) for a period starting April 22 1992 and ending June 5 1992. The main advantage of this data set is the short epicentral distances between 23 earthquakes and stations, which allows for recording of small earthquakes down to m agnitude 1.0 with high signal to noise ratio and reduction of path effects. Another advantage is th at the site effects are expected to be minimal because most of the stations were located on granite outcrops. This network was build up using L22 velocity sensors and FBA23 accelerometers connected to REFTEK. We retrieved the seismograms in SAC format from the SCEC database at C.I.T. After visually inspected records from all the stations we select four of them to be used in the inversion. These stations recorded most of the events and they provide data of very good quality with low noise levels. The sampling rate was 250 sps for AQUA, SDCE and 100 sps for COVF and KEYV. They also have a wide azimuthal distribution, minimizing any azimuthal dependence of the source spectrum. We selected events which were recorded from at least three stations, with signal to noise ratio more than two, up to 40 Hz. In total we used 268 events (Table 3.1). Figure 3.3 shows the locations of the earthquakes and the stations. For the calculation of the earthquake spectrum we used a three seconds window, starting from the arrival of the S waves. To avoid spectral leakage the adaptive multi taper spectral estimation method [77] was used. The spectrum of the earth quakes was used from 1 Hz up to 40 Hz. Examples of our data can been seen in figures 3.4, 3.5. Using a moving point average window we smoothed the spectrum and we run our inversion for 53 frequencies. After calculating the source spectrum we fit it with the Levenberg-Marquart non-linear inversion method [80] using the following model SU) = ^ (3.10) where S(f) is the observed spectrum, Aa is the flat part of the spectrum ,f c is the corner frequency and 7 is the high frequency fall off. The seismic moment was determ inated from the magnitude using the following formulas log(Af0) = 1.5m, + 16 (3.11) log(A/ 0 = 1.1m/ + 11 (3.12) 24 Equation 3.11 is used for m; > 2.5 while equation 3.12 was used for smaller mag nitudes. These equation were derived from Bakun [15] for Californian earthquakes. 25 -J — I— 1 — I— 1 — I— I— I— I— I— I— I— 1 I 1- ■ . I I I . . a i 5 ? rn n . , COVF "9 S D C E .^A <5bA c V ° % o oo 5 Km © .. ^ KHYV 1 1 1 I I I I I I I I I I— I — I— ]— I — I— I— I — I— *30' 116*25* iia *wi* lit* is - m i'irt' l— i — r 116*30' 116*20 116*15' U 8 116* 10' 0.0 £ M < 1.0 1.0 £ M < 2.0 2.0 £ M < 3.0 3.0 £ M < 4.0 Figure 3.3: Locations of earthquakes and stations that were used in the inversion 26 I f -20 -4 0 - 40, 10* Frequency Hz -1 0 - 20. Time te c 1 0 ' 10* i > 10' 1 0 ’ 10' Figure 3.4: Seismograms (displacement) of an earthquake m agnitude 1.60 and the S-wave spectrum . The noise level (dash line) was calculated from a three seconds window before the P arrival. 27 2049999AOUA.O.EKN.SAC 2049999 .AOUA.D.EHE.SAC 300 200 200 100 100 -100 20 1 0 to* to 1 10* 10' Frequency Hi 2049999JUXJA.0 EHZ.SAC 150 100 50 1 0 0 ■ iso. Frequency Hi Figure 3.5: An earthquake m agnitude 2.5 28 3.4 R esults and D iscussion Since we do not invert for path attenuation we tried to estim ate its effect in our results. Ouyang (personal communication) with the same dataset estim ated the Q value using coda waves and a single scattering model. She found th at the Q value varies from 200 to 300 for frequencies between 1.5 Hz - 12.0 Hz. Using a subset of 150 events we run the inversion with Q ranging from 100 to 400 and we calculated the corner frequencies after each inversion. Figure 3.6 shows the corner frequencies with Q=150 and Q=300. In general the corner frequencies did not vary more than 10% while the maximum change was around 20%. The corner frequencies of the larger events varies significantly less than the corner frequencies of the smaller ones, were the larger variations were observed. Finally we choosed to use Q=200. Another of our concerns was the existence of a well know trade off between f c and the high frequency fall off. An individual spectrum can be fit either with a low f c and a high frequency fall off or a high f c and a low high frequency fall off. We plotted the high frequency fall off 7 with f c (figure 3.15).We did not observe any dependence of 7 with the calculated f c. So we do not think th at our results suffer from any serious bias. The values of 7 vary from 2.0 up to 4.5. Iio [54] studying aftershocks of the West Nagano prefecture earthquake found that the high frequency fall off was from 2.2 up to 8.4. He argued that these high values were not a attenuation effect but a real source property with the small earthquakes having a slower source process than the large earthquakes. Brune [22] observed a fall ofT of 3.5 for high stress earthquakes and 2.32 for low stress earthquakes from Anza. Abercrombie [1] found values ranging from 1.0 up to 4.0. This high frequency fall off could be a source effect. If we view the fault rupture from a kinematic way of view there are some effects which lead to a higher spectral fall off than 2.0. If we make the slip on the fault build up gradually and the rupture front begin at a point and spread out, then a plausible kinematic representation will have the far field radiation build up as a quadratic in the tim e domain and fall off as uj-3 at high frequencies in the spectral domain [89], [90]. Madariaga [65] found from his numerical model that the high frequency fall off can have an azimuthal dependence . The high frequency fall offs that we observe can not be of an azim uthal de pendence, since we are using a m ultistation inversion. Plotting the fall off with 29 Seism ic M o m e n t (dyne c m ) J o s h u a T r e e A f t e r s h o c k s f c N - S -4 -0 J o s h u a T r e o A f t e r s h o c k s f c E - W -0 J o s h u a T r e e A f t e r s h o c k s f c Z §1 0 s -4 -3 , - 2 : i -0 Figure 3.6: Corner frequencies with Q=150 •, and Q=300 -f- 30 M a g n i tu d e m agnitude (Figure 3.16) we do not observe any difference between small and large earthquakes. We believe that site effects play are mainly responsibly for these high values of fall off. Our flat amplification factor assumption probably does not hold for the high frequencies, altering the high frequency fall off. Figures 3.7, 3.8, 3.9 presents some of our our calculated spectrum with the fitting curve. In figures 3.10, 3.11, 3.12 we can see the site effects for the three stations. These stations were installed in granitic outcrops with weathering zones of varying thickness [27] .The vertical components in all of them have the less site effects. Station COVF shows a strong amplification in the low frequencies ((6-8 HZ). SDCE shows the highest amplification around 10-15 Hz. Generally there are no significant differences in the amplification factor of the two horizontal components. In figure 3.13 we show the calculated corner frequencies with seismic moment. We observe that the corner frequencies increase with m agnitude for earthquakes in the m agnitude range 2.0 < M < 3.5. Below m agnitude 2.0 the corner frequency remains roughly constant with an upper limit around 25Hz - 30Hz This observation agrees with previous works that observed a constant corner frequency for small earthquakes. The value of 30 Hz is higher than the limit of 10 Hz - 20 Hz th at it was found from Chouet [24] and Archuletta [14]. We can not compare our results with those of Raustian et al because of their different method of definining the corner frequency at their spectrum . Because of the constant fc the stress drops decreases with decreasing seismic moment (figure 3.14). While it is of the order of 100 bars, for the large aftershocks it decreases down to 0.1 bars for the small ones. Another observation is that for the same m agnitude the values of f c shows a range of 10 Hz. Trying to explain this we notice a clear dependence of the f c with depth. Plotting f c with depth (figures 3.18, 3.19, 3.20) for different m agnitude ranges we observe a clear increase of f c with depth. This can be either a real source property or an effect of depth dependent attenuation. In the second case a decrease of attenuation with depth would have as a result the overestimation of the f c for deep earthquakes. An overestimation of the attenuation for the deep earthquakes would also result to a decrease of the high frequency fall off with depth. Since we do not observe a dependence of the the high frequency fall off with depth(Figure 3.17) we believe that depth dependent attenuation is not responsible for our results. Also 31 • V 1 9 * 1 0 * ( 0 * vf Figure 3.7: Examples of source spectrum , vertical component any errors in the calculation of the corner frequency from our constraint would have affect all of our earthquakes and not some of them. We believe that the depth dependence is a real source property. 32 v f (o' (O ' w * 1 1 * Figure 3.8: Examples of source spectrum , E-W component 33 Figure 3.9: examples of source spectrum , N-S component 34 Amplification factor Amplification factor COVF N-S 10 .0 10' ,o 101 10' COVFZ Frequency Hz 10 .0 10' .2 .1 10 10‘ 10 10° .2 10 Frequency Hz Frequency Hz Figure 3.10: Am plification factor at station COVF Amplification factor Amplification factor SDCE N-S 10' ,1 Frequency Hz SDCE E-W 10' 101 10° .2 Frequency Hz SDCE Z a > T 3 CL E < Frequency Hz Figure 3.11: Am plification factor at station SDC E Amplification factor Amplification factor KEYV N-S 10 .2 10‘ KEYV Z Frequency Hz 10 A 10' o o j c o 's s ■ q. E < 10 A 10 " .2 10* 10' Frequency Hz Frequency Hz Figure 3.12: Am plification factor at station K EY V Seism ic M om e n t (dyne c m ) J o s h u a T r e e A f te r s h o c k s Ic N - S J o s h u a T r e e A f te r s h o c k s I c E - W -a Bur 1 0 1 1 0 J o s h u a T r o o A f te r s h o c k s fc Z 10' 10 F r e q u e n c y (H Z ) F r e q u e n c y (H Z ) I 1 0 1 F r e q u e n c y (H Z ) Figure 3.13: Corner frequencies with seismic moment 38 M a g n itu d e Seismic moment dyn'cm Joshua Tree aftershocks E-W Joshua Treo aftershocks N-S Source radious m Source radious m Joshua Tree aftershocks 2 Source radious m Figure 3.14: Seism ic m om ent and source dim ension 39 10 15 20 25 Comer Frequency (Hz) E-W 30 35 40 15 20 25 Comer Frequency (Hz) Z v 10 15 20 25 Comor Frequency (Hz) 30 35 40 Figure 3.15: High frequency fall off with corner frequency m c "i re CO I — * C l i-t re si e re a *< a 1 3 a cn a_ et- c ta re High Frequency fall off u < n *K U Ol o in u b i M a g n i t u d e High Frequency fall off I O C J A ( D High Frequency fail off ro u tn e > e > m t K M m m xmm K K M K KM X X X X Ol (n tn High frequency fall off High frequency fan off High frequency fall off t-O N-S N-S2.0«M<2.5 N-S 1.5<* M<2.0 SO I --------------------- 1 --------------------- 1 --------------------- r 4 0 - I ^30- 4) O 1 --------------1 --------------1 --------------1 --------------1 -------------- 0 5 10 15 20 25 Depth (km) N -S M<1.5 5 0 d o 2 0 to 0, 0 5 10 15 2 0 25 Depth (km) Figure 3.18: Corner frequency with depth for different m agnitude ranges, N-S com ponent 43 E-W 2,0<« M<2.5 o c o Depth (km) E-W 1.5<- M<2.0 < b °o ° o Depth (km) E-W M<1.5 50 20 i s ( D 10 0, 10 25 0 5 15 20 Depth (km) Figure 3.19: Corner frequency with depth for different m agnitude ranges, E-W com ponent 44 Z 2.0<-M<2.5 oo o 50 4 0 1 loo r 20 < u E 3 10 10 15 Depth (km) Z M<1.5 Depth (km) 20 1 ,m i— — r----------------------1 ----------------------1 ---------------- i ------- o * o ■ < £ 3 < b o ° ° fl ° o ° oo ■ ______________t______________ i ___________ j ------------- 25 Figure 3.20: Corner frequency with depth for different m agnitude ranges, vertical component 45 _ l 1 I I I 1 I J L. _ t 1 _____ L _ _ L - - i 1 -------- 1_____ r irt in n r - > .COVF S 1 ?? o’ A Q U A 0 ° o o 5 Km .KEYV "i------1 ------1 ----- 1 ----- ]-------1 --- 1 ------ 1 ----- 1 ----- 1 ----- 1 ----- 1 ----- 1 ------r 116*30" 116*25* 116*20* 1 r 116* IS* i — I---- 1 ---- 1 ---- 1 ---- r 116*10* • 04 s M < 1.0 • 14 S M < 2.0 « 2J) S M < 3.0 34 S M < 4.0 Figure 3.21: Location of the earthquakes with depth more than 7 km and corner frequencies higher than 18 Hz (solid circles) and those with depth less than 6 km and corner frequencies less than 16 km 46 Date Time Latitude Longitude Depth M agnitude Event ID 92 4 30 0 58 6.55 34 00.46 -116 19.73 8.93 1.20 2049712 92 4 30 1 18 27.75 33 57.45 -116 20.16 6.86 1.70 2049715 92 4 30 2 1 44.98 33 56.67 -116 21.66 5.98 1.60 2049722 92 4 30 2 5 23.70 33 57.91 -116 19.23 10.62 1.60 2049723 92 4 30 2 39 57.81 33 58.53 -116 19.43 11.40 1.30 2049725 92 4 30 3 2 8.72 33 58.54 -116 19.42 6.85 1.70 2049729 92 4 30 3 15 35.67 33 57.69 -116 21.43 3.87 1.40 2049733 92 4 30 4 20 43.12 33 56.79 -116 16.66 5.87 1.50 2049743 92 4 30 4 47 53.58 33 57.71 -116 19.02 9.95 1.70 2049749 92 4 30 4 52 9.56 33 56.22 -116 19.04 4.70 1.80 2049750 92 4 30 5 1 44.59 33 55.93 -116 19.18 4.72 1.20 2049751 92 4 30 5 25 46.02 33 57.10 -116 18.88 8.45 2.00 2049754 92 4 30 5 43 14.48 34 1.28 -116 19.42 7.31 2.20 2049755 92 4 30 6 25 15.43 33 57.59 -116 20.18 3.57 1.60 2049761 92 4 30 6 36 11.08 33 58.62 -116 19.01 8.75 1.40 2049762 92 4 30 6 44 12.93 33 56.76 -116 20.03 5.07 1.90 2049764 92 4 30 7 11 55.97 34 2.16 -116 18.44 4.98 1.70 2049770 92 4 30 8 11 39.91 33 53.75 -116 18.35 4.67 1.80 2049780 92 4 30 8 32 19.07 34 1.63 -116 19.38 6.62 1.60 2049784 92 4 30 9 0 20.90 34 2.95 -116 19.86 4.22 1.60 2049788 92 4 30 9 44 45.31 34 3.44 -116 20.47 4.34 1.50 2049795 92 4 30 10 0 35.12 34 1.19 -116 19.32 10.84 1.30 2049798 92 4 30 10 7 53.65 33 57.70 -116 20.14 6.85 1.30 2049799 92 4 30 10 32 37.39 33 57.04 -116 18.62 8.75 1.10 2049803 92 4 30 10 43 33.95 33 58.12 -116 17.14 3.72 2.60 2049804 92 4 30 10 53 25.38 33 57.70 -116 20.74 3.97 1.60 2049806 92 4 30 11 16 41.37 33 57.64 -116 21.99 4.18 1.90 2049813 92 4 30 11 47 56.71 33 59.89 -116 16.88 3.64 1.90 2049816 92 4 30 12 17 30.19 33 53.86 -116 15.48 4.41 1.30 2049818 92 4 30 12 23 43.64 33 57.58 -116 19.64 4.97 1.40 2049819 92 4 30 12 51 36.38 34 2.09 -116 18.35 3.21 1.80 2049825 92 4 30 12 56 11.80 33 58.96 -116 15.79 5.66 1.90 2049827 92 4 30 13 18 10.03 34 0.36 -116 19.40 11.77 1.50 2049829 92 4 30 13 43 3.25 33 57.18 -116 18.89 4.88 1.70 2049832 continue Table 3.1: Date, time, location, and magnitude of the earthquakes th at were used in the inversion 47 continue Date Time Latitude Longitude Depth Magnitude Event ID 92 4 30 13 52 18.98 34 0.05 -116 19.06 4.74 1.90 2049834 92 4 30 14 26 49.62 33 57.48 -116 18.97 6.06 1.50 2049841 92 4 30 14 47 17.38 34 1.37 -116 19.39 3.44 1.90 2049845 92 4 30 15 8 50.09 33 59.62 -116 15.05 3.30 1.90 2049850 92 4 30 15 18 35.91 34 2.72 -116 19.31 6.21 1.90 2049852 92 4 30 15 58 29.93 33 59.85 -116 15.05 4.93 1.70 2049858 92 4 30 17 33 40.92 33 53.98 -116 16.41 4.74 1.30 2049871 92 4 30 17 54 29.46 34 0.43 -116 19.41 7.45 2.10 2049874 92 4 30 20 15 51.12 33 59.54 -116 16.84 5.22 2.60 2049896 92 4 30 20 27 57.63 34 1.91 -116 19.13 9.12 2.40 2049897 92 4 30 20 43 26.19 33 56.68 -116 18.74 4.79 1.70 2049900 92 4 30 21 7 30.38 33 57.58 -116 21.49 3.73 1.50 2049901 92 4 30 22 11 38.11 33 57.63 -116 19.08 5.13 2.00 3024175 92 4 30 22 46 18.23 33 56.30 -116 21.67 6.76 1.50 2049923 92 5 1 0 41 58.92 34 0.83 -116 17.49 14.67 1.20 2049934 92 5 1 1 27 16.90 33 54.01 -116 17.50 5.09 2.10 2049943 92 5 1 2 57 17.85 33 59.68 -116 15.44 3.10 1.90 2049956 92 5 1 3 0 57.26 33 57.41 -116 21.87 4.30 1.50 2049958 92 5 1 3 4 29.65 34 2.13 -116 19.64 8.66 1.90 2049959 92 5 1 3 15 31.20 33 57.07 -116 21.51 4.75 1.30 2049962 92 5 1 3 29 0.53 33 59.95 -116 19.15 10.20 2.10 3021108 92 5 1 4 10 50.79 33 56.76 -116 20.87 4.83 2.10 2049968 92 5 1 4 20 13.10 33 57.20 -116 22.04 4.89 1.80 2049971 92 5 1 4 46 39.24 33 54.06 -116 17.77 6.60 1.20 2049977 92 5 1 5 23 50.19 33 57.15 -116 19.15 8.28 1.40 2049982 92 5 1 6 3 27.42 34 2.11 -116 19.28 5.50 3.40 2049987 92 5 1 7 6 39.35 34 2.16 -116 18.54 3.47 2.50 2049992 92 5 1 7 13 53.23 33 58.44 -116 21.48 4.91 2.30 2049994 92 5 1 7 30 41.95 34 2.29 -116 20.25 4.17 1.90 2049996 92 5 1 8 0 24.31 33 57.28 -116 21.39 5.53 2.50 2049999 92 5 1 8 11 45.90 34 1.67 -116 19.56 7.20 2.40 2050000 92 5 1 8 49 15.83 33 56.13 -116 19.35 4.50 1.80 2050003 92 5 1 8 53 5.74 33 57.41 -116 19.11 6.34 1.70 2050004 92 5 1 9 3 40.96 33 59.61 -116 15.66 3.50 1.90 2050005 continue 48 continue Date Time Latitude Longitude Depth Magnitude Event ID 92 5 1 12 15 34.07 33 57.00 -116 18.91 5.77 2.00 2050028 92 5 1 14 48 23.65 33 54.55 -116 17.97 4.61 1.50 2050043 92 5 1 15 2 37.61 33 58.67 -116 21.48 5.76 1.60 2050045 92 5 1 15 32 0.27 33 57.39 -116 21.85 5.02 1.70 2050048 92 5 1 16 2 16.51 33 56.51 -116 18.78 4.91 1.50 2050054 92 5 1 16 3 17.54 34 1.49 -116 19.12 11.06 1.70 2050055 92 5 1 16 11 15.04 33 56.92 -116 20.52 4.96 1.80 2050056 92 5 1 16 42 27.84 33 56.61 -116 18.88 4.87 1.60 2050059 92 5 1 19 11 46.43 34 0.35 -116 19.39 9.41 1.80 2050080 92 5 1 19 47 18.00 33 57.68 -116 21.51 4.59 1.80 2050086 92 5 1 20 52 36.05 33 56.41 -116 18.91 5.16 1.70 2050095 92 5 1 20 59 47.37 33 56.31 -116 18.89 4.97 1.80 2050098 92 5 1 22 48 32.84 33 57.05 -116 21.27 4.35 1.40 2050114 92 5 1 22 58 14.28 33 57.81 -116 19.54 4.09 1.60 2050117 92 5 1 23 10 11.78 33 57.61 -116 19.06 7.76 1.90 2050121 92 5 1 23 16 7.66 33 59.56 -116 18.74 4.64 1.70 2050122 92 5 2 1 26 55.88 33 57.82 -116 19.21 4.02 2.10 2050142 92 5 2 3 12 53.70 33 56.62 -116 18.89 6.00 1.30 2050155 92 5 2 5 10 31.50 34 1.80 -116 19.22 3.48 2.10 2050176 92 5 2 5 27 49.90 33 57.69 -116 20.23 5.00 2.20 2050179 92 5 2 5 56 51.52 33 57.63 -116 19.99 5.02 2.30 2050186 92 5 2 6 57 54.40 33 56.59 -116 20.82 5.28 1.40 2050193 92 5 2 7 21 57.93 34 0.59 -116 19.14 8.83 2.00 2050198 92 5 2 7 40 9.29 33 59.41 -116 16.95 5.50 2.30 2050199 92 5 2 8 9 55.62 33 58.41 -116 18.78 12.64 1.50 2050206 92 5 2 8 17 4.65 33 59.82 -116 18.99 9.51 1.50 2050208 92 5 2 8 52 12.88 34 2.22 -116 19.68 4.83 1.10 2050215 92 5 2 9 42 4.17 33 57.27 -116 20.47 4.80 2.90 2050221 92 5 2 10 45 10.73 33 57.96 -116 20.36 4.16 1.80 2050227 92 5 2 11 38 33.35 33 59.70 -116 15.08 3.57 1.90 2050233 92 5 2 12 7 19.13 33 57.57 -116 20.42 4.85 2.30 2050235 92 5 2 12 50 19.98 33 59.69 -116 16.96 5.24 2.00 2050244 92 5 2 13 1 44.17 34 2.18 -116 18.75 5.10 2.00 2050245 92 5 2 13 29 54.50 33 59.71 -116 16.98 3.54 3.20 2050247 continue 49 continue D ate Time Latitude Longitude Depth Magnitude Event ID 92 5 2 13 41 59.37 33 59.68 -116 16.77 4.95 3.30 2050248 92 5 2 14 11 46.88 33 53.55 -116 17.17 4.95 1.90 2050251 92 5 2 18 50 18.25 34 2.10 -116 19.12 8.70 1.30 2050289 92 5 4 12 45 0.87 33 58.28 -116 19.02 9.69 1.00 2050624 92 5 5 9 19 53.85 33 57.88 -116 18.90 6.00 0.90 2050781 92 5 6 9 10 20.07 33 57.78 -116 18.76 4.73 0.90 2050983 92 5 6 9 52 40.28 33 57.00 -116 18.71 4.59 1.10 2050989 92 5 7 5 10 2.34 33 56.66 -116 18.12 11.93 1.10 2051122 92 5 7 8 6 16.76 34 1.48 -116 19.40 5.54 1.10 2051138 92 5 8 9 27 22.07 33 57.62 -116 18.76 5.35 1.10 2051313 92 5 10 7 10 22.00 34 1.77 -116 19.03 4.76 1.00 2051586 92 5 10 10 24 47.22 33 56.54 -116 18.89 5.39 1.00 2051605 92 5 11 4 51 52.61 33 56.77 -116 21.57 4.90 1.10 2051726 92 5 11 7 22 26.48 34 2.31 -116 22.17 4.11 1.10 2051742 92 5 11 10 46 0.78 33 58.12 -116 19.08 4.14 1.10 2205175 92 5 11 22 31 32.52 33 58.17 -116 21.43 6.43 1.00 2051843 92 5 12 1 59 0.28 34 0.91 -116 19.23 10.10 1.10 2051861 92 5 12 7 39 2.03 33 59.25 -116 15.77 8.30 1.10 2051898 92 5 12 19 54 26.36 34 1.13 -116 19.16 8.30 1.10 2051992 92 5 15 0 5 2.62 33 59.82 -116 17.07 5.87 2.80 2052303 92 5 15 3 27 16.84 34 0.16 -116 19.16 9.69 1.60 2052314 92 5 15 3 35 39.91 34 2.10 -116 18.93 10.91 1.90 2052315 92 5 15 4 50 28.72 33 58.38 -116 20.96 5.70 1.30 2052320 92 5 15 4 56 27.48 34 2.15 -116 18.71 7.09 1.60 2052322 92 5 15 5 15 29.46 33 59.55 -116 16.93 5.81 3.10 2052324 92 5 15 5 49 31.59 33 59.53 -116 16.95 5.78 2.30 2052327 92 5 15 5 52 42.94 33 59.51 -116 16.91 5.84 1.60 2052328 92 5 15 6 56 9.94 34 2.06 -116 15.38 5.53 1.80 2052333 92 5 15 8 21 21.95 34 2.09 -116 15.55 6.31 1.40 2052338 92 5 15 9 24 3.66 33 59.54 -116 17.00 5.78 3.00 2052340 92 5 15 10 13 3,79 33 58.32 -116 18.83 5.29 1.40 2052343 92 5 15 10 19 45.46 33 59.13 -116 15.77 7.75 1.80 2052344 92 5 15 11 41 16.62 33 59.82 -116 15.04 3.92 1.70 2052349 92 5 15 12 18 51.28 33 57.05 -116 18.29 5.05 1.20 2052352 92 5 15 12 27 2.43 34 1.16 -116 22.47 5.02 1.20 2052354 continue 50 continue Date Time Latitude Longitude Depth Magnitude Event ID 92 5 15 12 38 27.74 33 59.23 -116 15.43 6.61 1.80 2052355 92 5 15 14 21 38.07 33 59.56 -116 16.96 5.60 1.90 2052363 92 5 15 15 57 56.73 33 58.50 -116 21.89 4.73 1.10 2052365 92 5 15 18 0 7.98 34 1.16 -116 18.93 5.42 1.50 2052388 92 5 15 19 44 58.45 33 59.69 -116 16.74 4.88 1.30 2052397 92 5 15 19 55 56.79 34 2.07 -116 15.41 5.90 1.60 2052398 92 5 15 22 27 14.93 33 59.05 -116 18.53 10.22 1.00 2052408 92 5 15 22 42 20.52 33 57.05 -116 17.80 4.26 1.40 2052410 92 5 16 1 37 1.54 34 2.00 -116 19.39 6.20 1.40 2052431 92 5 16 1 45 5.10 34 2.16 -116 15.48 5.23 1.90 2052433 92 5 16 2 14 44.26 34 2.52 -116 21.08 3.53 1.90 2052436 92 5 16 2 16 40.16 33 57.94 -116 20.04 6.60 1.40 2052437 92 5 16 2 20 56.95 33 58.86 -116 19.17 8.64 1.30 2052438 92 5 16 3 32 38.47 34 2.21 -116 18.70 6.45 1.60 2052441 92 5 16 5 52 7.79 33 59.09 -116 15.87 5.08 1.40 2052454 92 5 16 6 16 31.10 33 57.01 -116 21.85 6.52 1.80 2052456 92 5 16 7 11 24.23 33 54.08 -116 15.64 6.04 1.10 2052460 92 5 16 7 33 4.85 33 53.57 -116 16.66 8.79 1.50 2052462 92 5 16 8 2 11.17 33 57.42 -116 19.59 6.07 0.90 2052466 92 5 16 8 38 8.93 34 2.42 -116 19.65 4.81 1.20 2052468 92 5 16 9 35 59.70 33 54.22 -116 17.06 5.61 1.30 2052472 92 5 16 10 6 50.08 33 59.51 -116 15.55 6.67 1.70 2052474 92 5 16 10 32 39.29 33 58.85 -116 16.75 3.78 2.00 2052477 92 5 16 12 5 20.26 33 57.35 -116 21.50 4.59 1.30 2052481 92 5 16 13 12 21.78 33 59.22 -116 15.98 8.21 1.80 2052487 92 5 16 14 7 12.78 34 3.10 -116 19.24 6.62 1.50 2052490 92 5 16 16 25 46.41 33 58.28 -116 19.81 5.86 1.40 2052502 92 5 16 18 38 46.46 34 3.84 -116 22.86 9.19 1.10 2052516 92 5 16 19 3 20.62 34 2.52 -116 22.28 3.66 1.40 3026182 92 5 16 22 45 39.07 34 1.71 -116 19.16 7.65 1.30 2052541 92 5 17 0 45 15.58 34 0.94 -116 19.00 6.45 1.60 2052547 92 5 17 1 39 28.44 33 58.74 -116 15.47 7.66 1.70 2052553 92 5 17 4 3 55.56 33 58.24 -116 19.29 5.57 1.40 2052561 92 5 17 8 32 5.46 34 2.06 -116 19.09 4.90 1.90 2052579 92 5 17 8 48 23.44 33 58.72 -116 15.31 7.89 1.70 2052580 continue 51 continue Date Time Latitude Longitude Depth Magnitude Event ID 92 5 17 8 57 4.09 33 57.25 -116 21.15 7.71 1.00 2052583 92 5 17 9 6 52.18 33 53.42 -116 18.62 7.66 1.00 2052585 92 5 17 9 15 10.73 33 58.80 -116 15.49 8.02 1.50 2052586 92 5 17 9 50 57.32 34 2.06 -116 15.42 4.80 1.30 2052588 92 5 17 10 3 39.45 33 59.58 -116 15.57 3.61 1.40 2052591 92 5 17 13 19 53.96 34 3.32 -116 20.99 5.81 1.40 2052614 92 5 17 13 52 11.35 33 58.82 -116 15.65 6.36 1.50 2052617 92 5 17 16 8 21.01 33 57.24 -116 18.41 5.61 1.70 2052631 92 5 17 18 25 49.49 34 0.02 -116 16.87 5.67 1.40 2052639 92 5 17 18 33 17.95 34 0.04 -116 19.33 7.67 1.50 2052640 92 5 17 18 36 20.72 34 0.04 -116 17.67 5.86 1.60 2052641 92 5 17 18 48 57.92 33 57.78 -116 19.98 6.56 1.40 2052644 92 5 17 19 13 30.54 33 57.42 -116 20.80 7.19 1.10 2052645 92 5 17 19 51 0.55 33 58.98 -116 17.15 6.10 1.50 2052649 92 5 17 19 59 13.11 33 57.72 -116 20.05 6.48 1.50 2052650 92 5 17 22 29 58.67 33 57.27 -116 22.02 7.34 1.50 2052657 92 5 17 22 32 57.70 33 58.02 -116 18.84 6.57 1.40 2052658 92 5 17 23 56 21.65 33 58.00 -116 19.94 6.84 1.60 2052661 92 5 18 1 44 39.14 34 0.02 -116 16.91 5.45 1.80 2052669 92 5 18 2 10 39.15 34 1.48 -116 19.31 10.11 2.30 2052674 92 5 18 4 44 7.04 33 57.26 -116 18.29 5.71 2.60 2052679 92 5 18 6 52 39.35 33 57.33 -116 21.19 8.00 1.80 2052687 92 5 18 8 27 55.25 34 2.05 -116 15.68 5.30 1.40 2052694 92 5 18 9 23 49.55 33 56.51 -116 20.60 7.33 1.40 2052701 92 5 18 11 42 43.82 34 1.14 -116 18.99 5.19 1.30 2052711 92 5 18 11 49 12.13 34 0.62 -116 19.19 7.39 1.40 2052712 92 5 18 12 24 8.02 34 2.14 -116 15.47 5.46 1.40 2052715 92 5 18 13 31 12.86 33 57.24 -116 21.20 6.51 1.20 2052720 92 5 18 13 43 28.86 33 59.99 -116 17.05 6.10 1.60 2052722 92 5 18 14 0 28.78 34 2.34 -116 7.73 7.10 2.10 2052723 92 5 18 15 17 18.92 34 1.86 -116 19.03 8.95 1.40 2052726 92 5 18 16 5 42.41 33 57.87 -116 20.13 7.44 1.90 2052732 92 5 18 16 10 38.92 33 57.35 -116 19.08 4.84 2.50 2052733 92 5 18 16 18 26.22 33 57.25 -116 19.85 6.39 2.50 2052734 continue 52 continue Date Time Latitude Longitude Depth Magnitude Event ID 92 5 18 16 33 10.44 33 58.15 -116 20.37 6.49 2.60 2052736 92 5 18 16 43 20.39 33 57.40 -116 20.35 6.58 1.90 2052737 92 5 18 16 48 25.55 33 57.26 -116 19.89 6.34 1.60 2052739 92 5 18 17 0 19.14 33 57.61 -116 19.23 5.12 2.10 2052743 92 5 18 17 25 39.11 33 57.38 -116 19.91 7.02 0.80 2052748 92 5 18 17 36 45.84 34 2.46 -116 18.99 9.22 1.90 2052749 92 5 18 19 46 47.71 33 57.22 -116 18.86 3.91 1.40 2052760 92 5 18 20 12 38.46 33 57.56 -116 19.93 7.14 1.70 2052763 92 5 18 20 14 45.15 33 57.21 -116 19.74 5.79 1.30 2052764 92 5 19 0 14 15.26 33 57.93 -116 20.28 7.47 3.20 2052794 92 5 19 0 49 23.73 33 57.19 -116 19.86 6.60 2.10 2052798 92 5 19 1 7 16.48 33 57.09 -116 19.83 6.25 1.70 2052801 92 5 19 1 18 13.27 33 57.15 -116 20.45 4.58 1.80 2052802 92 5 19 1 19 22.66 33 57.24 -116 19.84 6.73 1.40 2052803 92 5 19 1 31 6.75 33 57.18 -116 19.96 5.85 1.70 2052807 92 5 19 1 33 11.06 33 57.13 -116 19.85 6.34 1.50 2052808 92 5 19 2 43 12.72 33 57.20 -116 20.40 4.48 1.90 2052815 92 5 19 3 2 50.81 34 6.33 -116 23.30 7.68 1.90 2052817 92 5 19 4 31 36.98 34 1.95 -116 19.45 8.59 1.60 2052823 92 5 19 4 33 47.31 33 57.36 -116 19.90 7.08 2.20 2052824 92 5 19 5 25 25.80 33 57.65 -116 18.61 6.29 1.20 2052825 92 5 19 6 11 42.48 33 57.35 -116 18.46 9.25 1.90 2052829 92 5 19 7 26 47.73 33 57.35 -116 19.75 6.56 1.60 2052836 92 5 19 7 52 33.34 33 56.49 -116 18.43 3.19 1.50 2052838 53 Event Z N -S E -W f c Hz 7 R m Sc Hz 7 R m f c Hz 7 R in 2049712 23.40 2.98 55.69 20.53 2.22 63.47 19.58 2.37 66.54 2049715 15.86 3.27 82.16 14.62 3.16 89.13 16.14 3.46 80.75 2049722 11.84 2.98 110.03 10.32 2.60 126.21 11.00 2.67 118.40 2049723 23.37 3.41 55.77 20.48 2.81 63.62 23.13 3.53 56.34 2049725 28.67 3.31 45.45 25.79 2.24 50.52 27.84 2.89 46.81 2049729 16.51 2.72 78.95 15.23 2.73 85.54 17.28 3.08 75.41 2049733 12.60 3.22 103.40 11.76 2.97 110.75 14.21 3.25 91.70 2049743 14.03 2.84 93.08 10.08 2.09 129.28 15.04 2.78 86.62 2049749 20.72 2.66 62.90 17.26 2.28 75.50 21.72 2.75 60.00 2049750 13.11 3.16 99.35 11.51 2.78 113.23 12.98 2.80 100.36 2049751 14.53 2.98 89.64 11.64 2.53 111.95 16.25 3.04 80.18 2049754 20.38 3.87 63.93 17.23 3.16 75.62 19.65 3.59 66.31 2049755 16.06 3.21 81.15 16.30 3.20 79.95 17.32 3.59 75.25 2049761 12.16 3.18 107.15 11.64 3.09 111.89 10.72 2.96 121.59 2049762 19.04 3.05 68.42 15.47 2.36 84.24 16.18 2.36 80.54 2049764 12.30 3.02 105.94 9.05 2.82 143.95 11.38 3.12 114.45 2049770 12.50 3.15 104.21 11.56 3.41 112.70 12.93 3.71 100.74 2049780 14.48 3.79 89.99 13.22 3.51 98.55 14.78 3.83 88.14 2049784 17.65 2.75 73.84 17.33 2.91 75.18 14.57 2.34 89.45 2049788 14.09 3.73 92.47 11.72 3.36 111.17 13.17 3.49 98.97 2049795 13.08 3.89 99.64 12.05 3.64 108.09 12.81 3.94 101.75 2049798 25.34 3.00 51.42 23.72 2.17 54.95 22.57 2.58 57.73 2049799 18.49 3.11 70.46 15.68 2.66 83.12 19.49 3.28 66.85 2049803 21.45 2.64 60.76 17.48 1.95 74.53 24.10 3.05 54.06 2049804 10.47 3.53 124.43 7.78 3.07 167.47 9.61 3.45 135.54 2049806 15.54 3.94 83.82 13.94 3.29 93.46 15.70 3.76 83.02 2049813 14.65 3.49 88.96 14.51 3.23 89.80 14.15 3.14 92.10 2049816 11.96 3.16 108.95 12.44 3.27 104.76 12.34 3.26 105.58 2049818 12.35 3.77 105.47 12.89 3.77 101.11 11.36 3.39 114.64 2049819 13.48 3.20 96.67 12.67 3.07 102.84 13.35 3.50 97.60 2049825 13.69 3.43 95.15 12.65 3.34 102.98 11.92 3.19 109.30 2049827 14.04 3.49 92.79 13.42 3.37 97.08 15.59 3.64 83.58 2049829 18.22 3.17 71.53 16.45 2.80 79.20 19.77 3.32 65.91 2049832 11.65 3.42 111.88 10.53 3.05 123.67 12.24 3.44 106.45 2049834 13.70 3.344 95.09 12.63 3.14 103.14 15.10 3.74 86.29 continue Table 3.2: Corner frequencies / « high frequency fall off 7 and source dimension R from the inversion 54 continue Event Z N -S E -W fc Hz 7 R m fc Hz 7 R m fc Hz 7 R m 2049841 13.30 2.43 97.93 11.57 2.46 112.63 13.67 2.74 95.32 2049845 15.39 3.72 84.66 13.88 3.41 93.84 16.31 3.98 79.87 2049852 16.45 3.25 79.22 15.57 3.08 83.68 14.94 3.06 87.20 2049858 10.59 2.86 123.05 11.22 3.00 116.15 9.39 2.81 138.76 2049871 13.08 3.18 99.60 12.02 2.80 108.38 12.99 3.04 100.27 2049874 13.90 3.13 93.76 11.70 2.92 111.34 11.14 2.66 116.98 2049896 8.63 3.05 151.03 7.60 2.93 171.46 9.81 3.29 132.80 2049897 21.22 4.00 61.42 18.97 3.44 68.67 19.76 3.83 65.93 2049900 12.58 3.24 103.56 12.12 3.13 107.48 13.10 3.44 99.42 2049901 8.61 3.13 151.37 6.88 2.82 189.24 7.76 2.98 167.86 3024175 7.94 2.73 164.05 6.83 2.66 190.65 7.93 2.74 164.29 2049923 12.77 2.89 102.03 11.08 2.41 117.55 14.08 2.87 92.57 2049934 25.06 3.07 52.00 20.45 2.22 63.71 23.83 2.45 54.69 2049943 13.30 3.81 97.97 12.53 3.50 104.01 13.51 3.73 96.44 2049956 10.69 3.29 121.87 11.15 3.44 116.83 11.59 3.53 112.38 2049958 13.25 3.60 98.34 10.06 2.74 129.52 11.54 3.00 112.94 2049959 19.01 3.30 68.54 15.78 2.70 82.58 19.47 3.28 66.91 2049962 15.12 3.35 86.16 11.24 2.58 115.87 12.85 2.68 101.40 3021108 23.58 3.24 55.27 18.75 2.68 69.49 18.53 2.52 70.33 2049968 11.36 3.55 114.69 10.42 3.29 125.06 9.86 3.19 132.08 2049971 15.57 3.87 83.68 14.43 3.56 90.32 13.34 3.26 97.69 2049977 12.56 1.90 103.77 11.58 3.00 112.48 13.35 3.26 97.59 2049982 21.91 3.32 59.49 20.17 2.62 64.60 21.40 2.82 60.88 2049987 7.67 3.27 169.94 6.68 3.11 195.06 7.87 3.37 165.41 2049992 13.31 3.69 97.91 12.72 3.62 102.46 14.07 3.91 92.64 2049994 11.08 3.71 117.54 10.95 3.73 118.94 10.51 3.57 124.01 2049996 14.66 3.53 88.86 12.44 3.09 104.73 14.61 3.56 S9.17 2049999 13.17 3.90 98.92 13.22 4.09 98.56 15.31 4.37 85.10 2050000 16.40 3.88 79.46 15.40 3.77 84.59 17.46 4.07 74.62 2050003 12.81 3.25 101.68 13.23 3.38 98.49 12.97 3.41 100.44 2050004 15.54 3.84 83.87 13.96 3.19 93.35 15.24 3.51 85.48 2050005 13.22 3.29 141.23 7.10 2.82 183.36 10.06 3.32 129.51 2050008 10.84 3.09 120.16 9.58 2.85 136.00 11.20 3.09 116.27 2050028 15.86 3.91 82.16 15.45 3.49 84.31 15.31 3.53 85.13 continue 55 continue Event Z N -S E -W f c Hz 7 R m f c Hz 7 R m f c Hz 7 R m 2050043 15.76 3.54 82.69 15.57 3.31 83.71 14.04 3.01 92.77 2050045 12.91 3.66 100.90 11.17 3.28 116.59 11.87 3.24 109.80 2050048 13.45 2.79 96.88 15.37 3.27 84.78 13.77 2.75 94.65 2050054 11.78 2.91 110.64 11.36 2.54 114.71 13.51 2.91 96.45 2050055 23.41 2.65 55.66 25.44 3.18 51.21 21.97 2.44 59.31 2050056 13.27 3.30 98.18 11.43 3.12 113.98 13.65 3.66 95.46 2050059 13.01 3.32 100.17 14.07 3.44 92.62 14.07 3.53 92.58 2050080 18.67 3.08 69.79 17.28 2.65 75.41 17.83 3.10 73.07 2050086 13.58 3.22 135.98 10.18 3.24 127.95 11.08 3.52 117.57 2050095 13.79 3.26 94.52 12.13 2.83 107.42 13.60 3.21 95.78 2050098 11.20 2.79 141.56 8.94 2.72 145.72 9.98 2.89 130.51 2050114 16.43 3.67 79.28 10.79 2.57 120.72 14.11 3.09 92.31 2050117 13.04 3.29 99.88 11.03 2.94 118.08 12.17 3.24 107.05 2050121 19.47 3.04 66.93 12.90 2.12 101.00 18.96 3.05 68.73 2050122 14.64 3.08 88.99 14.06 2.95 92.66 16.38 3.56 79.53 2050142 9.49 3.24 137.22 7.26 2.92 179.32 7.88 3.01 165.36 2050155 13.94 3.20 93.48 9.53 2.50 136.70 13.67 2.97 95.31 2050176 12.93 3.33 100.73 15.39 3.61 84.66 12.32 3.17 105.75 2050179 14.45 3.37 90.19 12.24 3.00 106.48 16.75 3.70 77.77 2050186 7.86 2.81 165.66 6.75 2.58 193.05 7.59 2.66 171.63 2050193 11.94 2.85 109.13 6.32 2.14 205.96 10.30 2.59 126.49 2050198 20.19 2.92 64.54 19.29 2.88 68.07 19.66 3.49 65.35 2050199 12.08 3.44 107.82 12.50 3.40 104.21 15.15 4.00 86.01 2050206 12.82 2.93 101.64 11.67 2.41 111.62 12.24 2.67 106.40 2050208 21.09 2.89 61,78 21.44 3.02 60.77 20.44 2.81 63.74 2050215 16.89 3.34 77.13 13.80 2.84 94.44 15.71 3.08 82.96 2050221 12.54 3.59 103.90 10.89 3.61 119.66 12.02 3.74 108.41 2050227 13.19 3.54 98.75 12.21 3.28 106.70 12.68 3.23 102.76 2050233 10.36 3.35 125.69 7.30 3.00 178.46 9.95 3.29 130.97 2050235 16.26 4.11 80.15 14.78 3.77 88.14 16.26 4.01 80.14 2050244 14.44 3.25 90.21 12.15 3.03 107.24 14.18 3.24 91.86 2050245 15.41 3.26 84.53 13.68 3.12 92.79 15.33 3.32 86.74 2050247 9.60 3.78 135.67 8.11 3.49 160.71 10.02 3.72 129.98 2050248 10.19 3.G6 127.80 9.21 3.58 141.45 11.12 3.80 116.15 2050251 12.00 3.84 108.55 10.17 3.49 128.15 12.20 3.83 106.76 continue .. . 56 continue Event Z N -S E -W f c Hz 7 R m f c Hz 7 R m f c Hz 7 R m 2050289 22.80 2.94 57.00 19.56 2.10 66.61 22.82 3.34 57.10 2050624 25.96 2.78 50.19 25.34 2.46 51.42 24.12 2.17 54.03 2050781 11.41 2.66 125.13 5.55 3.56 234.87 13.68 3.06 95.75 2050983 11.84 2.41 132.37 13.06 2.64 99.73 17.92 4.43 72.70 2050989 11.67 2.59 111.68 11.88 2.49 109.63 17.13 3.94 76.05 2051122 22.40 3.27 58.16 30.51 3.49 51.21 18.87 2.86 69.06 2051138 16.31 3.00 79.87 12.23 2.53 106.56 15.43 3.03 84.46 2051313 11.33 2.17 115.03 8.01 1.76 162.54 16.98 2.82 76.73 2051586 16.73 2.81 77.90 13.48 2.52 96.69 17.20 3.51 75.76 2051605 12.89 3.34 101.10 10.42 2.91 124.99 16.98 4.73 76.74 2051726 17.81 3.17 73.17 13.92 2.57 93.58 16.66 3.16 78.20 2051742 14.88 3.46 87.57 13.68 3.35 95.25 11.60 3.08 112.34 2205175 16.40 3.26 105.11 11.16 2.80 116.76 13.64 3.42 95.54 2051843 15.28 3.11 85.28 10.11 2.28 128.90 21.41 2.94 60.87 2051861 24.70 3.25 52.76 18.10 2.36 72.00 21.41 3.33 60.87 2051898 14.58 2.37 89.35 10.28 2.03 126.77 21.73 2.95 59.97 2051992 21.25 2.75 61.33 17.55 2.22 68.71 22.06 3.37 57.10 2052303 8.98 3.01 145.00 7.96 2.76 163.58 10.84 3.59 120.18 2052314 14.78 2.81 88.14 12.20 2.78 106.80 19.30 2.87 67.50 2052315 37.76 3.17 34.51 35.26 2.69 36.96 31.28 4.49 41.66 2052320 17.50 3.57 74.46 18.23 3.20 71.47 19.33 3.90 67.40 2052322 16.46 3.25 79.17 17.56 2.96 74.22 19.58 4.08 66.56 2052324 9.83 3.34 132.51 8.69 3.17 149.86 12.51 4.26 104.16 2052327 13.47 3.46 96.75 13.07 3.08 99.70 15.40 3.98 84.63 2052328 14.97 3.68 87.01 16.54 3.35 78.77 17.93 4.14 72.68 2052333 12.01 4.03 108.47 12.25 3.82 106.37 12.69 4.24 102.68 2052338 12.86 3.95 101.30 13.30 3.78 97.97 13.79 4.28 94.51 2052340 8.54 3.17 152.54 7.12 3.31 182.89 9.33 3.65 139.65 2052343 14.79 3.85 88.07 14.02 3.26 92.92 16.35 4.02 79.69 2052344 13.62 2.84 95.64 11.88 2.59 109.65 15.35 3.34 84.86 2052349 13.52 3.59 96.40 12.20 3.27 106.80 14.50 3.83 89.88 2052352 13.58 3.75 95.97 12.37 2.87 105.29 15.18 3.77 85.83 2052354 14.60 4.12 89.24 15.44 3.72 84.41 16.46 4.26 79.17 2052355 16.40 3.52 79.46 13.62 2.81 95.65 18.42 4.28 70.76 2052363 13.11 3.59 99.41 10.97 2.71 118.72 14.83 3.71 87.86 continue 57 continue Event Z N -S E -W f c Hz 7 R m f c Hz 7 R m f c Hz 7 R m 2052365 15.68 3.29 83.12 14.27 3.03 91.32 15.65 3.53 83.27 2052388 14.37 3.70 90.66 14.86 3.45 87.67 16.44 3.82 79.27 2052397 12.50 3.01 104.23 11.27 2.68 115.56 15.26 3.48 85.37 2052398 10.75 3.59 121.24 11.02 3.54 118.25 10.77 3.58 121.02 2052408 35.76 3.63 36.44 38.46 1.67 33.89 30.88 4.09 42.20 2052410 13.71 2.98 95.01 11.74 2.54 110.96 16.28 3.78 80.04 2052431 15.15 3.42 86.01 15.23 3.15 85.55 15.65 3.77 83.27 2052433 14.03 4.23 92.89 14.82 3.98 87.91 15.46 4.51 84.29 2052436 10.90 3.13 119.57 10.68 2.97 122.03 12.04 3.35 108.25 2052437 18.51 2.85 70.38 13.64 2.41 95.54 17.93 3.44 72.68 2052438 20.46 3.38 63.68 22.90 3.26 56.90 20.07 3.51 64.92 2052441 15.43 3.45 84.46 14.38 3.27 90.59 15.60 3.55 83.53 2052454 8.49 2.89 153.39 14.38 2.45 90.59 10.33 3.25 126.17 2052456 13.10 2.56 99.49 11.08 2.80 117.55 14.53 3.79 89.65 2052460 14.75 3.46 88.33 16.40 2.84 79.46 19.07 3.89 6S.33 2052462 15.65 3.29 83.25 17.09 2.47 76.25 22.11 3.72 58.93 2052466 18.13 2.83 71.87 12.73 2.00 102.36 18.48 3.19 70.51 2052468 19.04 3.45 68.42 14.75 2.57 88.32 19.60 4.24 66.47 2052472 15.75 3.98 82.74 14.30 3.48 91.12 16.49 4.19 79.02 2052474 14.91 3.23 87.38 12.98 2.7 100.39 15.82 3.45 82.39 2052477 10.93 3.77 119.21 10.84 3.76 120.24 13.05 4.44 99.87 2052481 12.08 3.42 107.86 11.41 2.96 114.18 12.85 3.62 101.42 2052487 11.34 2.57 114.85 9.94 2.39 131.07 13.39 3.18 97.28 2052490 18.07 3.57 72.11 16.34 3.10 79.74 17.95 3.89 72.61 2052502 14.86 3.03 87.70 14.24 2.31 91.48 17.64 3.79 73.87 2052516 13.79 2.97 94.51 14.38 2.84 90.61 13.11 3.02 99.35 3026182 14.88 3.63 87.56 15.87 3.53 82.11 16.35 3.73 79.68 2052541 17.36 3.87 75.05 17.75 3.45 73.42 20.44 4.42 63.76 2052547 16.57 3.39 78.65 16.40 3.09 79.47 17.28 3.53 75.42 2052553 15.41 3.00 84.53 11.10 2.35 117.40 17.38 3.75 74.96 2052561 15.29 3.03 85.21 14.61 2.78 89.20 16.56 3.56 78.70 2052579 9.01 2.45 144.55 9.09 2.66 143.35 9.98 2.94 130.56 2052583 26.79 3.55 48.65 30.15 3.34 43.22 27.86 4.98 46.77 2052585 27.83 3.13 46.82 27.35 2.36 47.64 32.06 3.22 40.64 continue 58 continue Event Z N -S E -W fc Hz 7 R m fc Hz 7 R m fc Hz 7 R m 2052586 20.25 3.17 64.36 18.15 2.79 71.81 19,63 3.60 66.39 2052588 17.07 3.06 76.33 15.55 3.32 83.78 16.86 4.10 77.29 2052591 11.63 3.52 112.01 11.62 3.20 112.09 12.23 3.70 106.55 2052614 15.26 3.31 85.41 17.70 3.41 73.63 17.79 4.09 73.24 2052617 16.48 3.57 79.08 12.14 2.36 107.30 18.35 3.82 71.02 2052631 13.51 3.11 96.43 11.62 3.04 112.07 13.77 3.68 94.61 2052639 14.32 2.68 90.97 13.73 2.68 94.87 14.82 3.29 87.90 2052640 21.67 3.43 60.14 21.40 2.96 60.89 21.66 3.32 60.15 2052641 16.15 3.53 80.68 15.47 3.10 84.23 16.26 3.75 80.14 2052644 16.42 3.13 79.37 18.36 2.81 70.99 17.72 3.49 73.54 2052645 22.23 3.13 58.61 12.81 1.73 101.74 23.33 3.72 55.84 2052649 17.72 3.56 73.53 16.27 2.94 80.06 20.65 4.00 63.09 2052650 18.48 3.74 70.50 17.70 3.20 73.64 18.04 4.09 72.25 2052657 21.73 3.62 59.96 19.84 3.51 65.66 19.37 3.90 67.28 2052658 13.79 2.89 94.51 14.64 2.46 88.99 16.42 3.04 79.35 2052661 18.46 3.21 70.60 12.83 2.32 101.53 20.16 4.24 64.63 2052669 12.13 3.00 107.38 9.66 3.03 134.85 13.94 4.23 93.47 2052674 23.15 3.84 56.30 19.39 2.67 67.21 23.06 4.30 56.51 2052679 13.25 3.11 98.33 11.48 3.21 113.49 14.00 4.05 93.05 2052687 21.80 3.65 59.79 19.05 3.15 68.42 22.55 4.38 57.80 2052694 12.92 3.53 100.85 13.43 3.37 97.04 13.94 3.71 93.49 2052701 19.09 2.48 68.27 18.25 2.25 71.38 23.13 3.87 56.34 2052711 12.14 3.42 107.29 13.02 2.73 100.04 17.04 3.85 76.46 2052712 23.21 3.18 56.14 20.38 2.43 63.93 24.64 4.21 52.88 2052715 14.71 3.29 88.57 16.48 3.34 79.08 15.14 3.40 86.08 2052720 17.13 3.45 76.05 18.57 2.91 70.18 20.60 3.68 63.25 2052722 12.29 3.18 106.02 11.75 2.64 110.87 16.57 3.90 78.62 2052723 15.41 3.54 84.56 11.23 2.92 115.98 19.93 4.87 65.39 2052726 23.48 3.11 55.51 21.66 2.48 60.16 24.53 3.91 53.12 2052732 18.95 3.86 68.78 19.51 3.18 66.79 19.77 3.73 65.90 2052734 12.68 3.20 102.71 7.72 2.51 168.81 12.88 3.20 101.17 2052736 9.98 3.43 130.57 9.75 2.59 133.66 11.98 3.14 108.79 2052737 17.15 3.67 75.99 13.58 2.83 95.97 18.67 4.33 69.79 continue 59 continue Event Z N -S E -W f c Hz 7 R m f c Hz 7 R m f c Hz 7 R in 2052739 14.00 3.48 93.06 11.76 2.66 110.76 14.35 3.63 90.79 2052743 13.74 3.71 94.82 12.84 3.33 101.49 14.70 4.06 88.66 2052748 16.10 2.46 80.91 15.52 3.09 83.98 18.92 4.40 68.87 2052749 17.00 4.00 76.66 13.32 2.45 97.83 17.06 3.33 76.38 2052751 15.69 4.23 83.05 14.04 3.37 92.81 17.43 4.66 74.77 2052760 13.22 3.42 98.58 11.95 2.88 108.99 16.00 3.85 81.42 2052763 17.94 4.11 72.62 16.12 3.41 80.82 19.42 4.69 67.10 2052764 14.55 2.97 89.58 12.56 2.74 103.77 14.35 3.52 90.78 2052794 7.95 2.64 163.88 5.910 2.47 220.55 9.86 3.24 132.15 2052798 15.45 3.87 84.36 13.07 3.21 99.69 17.34 4.54 75.16 2052801 11.99 2.32 108.64 9.18 2.26 141.99 11.85 2.86 109.98 2052802 14.40 3.73 90.49 12.46 3.40 104.54 12.57 3.65 103.65 2052803 16.78 3.00 77.67 14.38 3.20 90.58 17.60 4.30 74.05 2052807 12.74 3.29 102.27 13.76 3.13 94.67 13.29 3.45 98.02 2052808 17.14 3.33 76.01 11.81 2.37 110.29 19.56 4.34 66.61 2052815 11.69 2.53 111.42 10.68 2.13 122.02 12.23 3.90 106.51 2052817 14.14 3.21 92.13 13.71 3.29 95.04 14.11 3.70 92.31 2052823 25.33 3.58 51.45 22.51 2.47 57.88 22.90 3.48 56.90 2052824 13.35 2.32 97.57 12.86 2.60 101.34 17.63 3.96 73.93 2052825 18.66 3.45 69.82 13.03 2.45 99.96 17.05 3.11 76.40 2052829 22.02 3.45 59.17 19.05 2.64 68.41 23.82 4.61 54.71 2052836 10.49 2.58 124.22 7.42 2.55 175.49 11.50 3.52 113.28 2052838 10.56 3.35 123.42 9.66 3.21 134.80 12.17 3.85 107.10 60 C hapter 4 E m pirical G reen’s Function 4.1 Introduction A m ethod for removing site and path effects from a seismogram is the Empirical Green’s Function (EGF). Since the pioneering work of Hartzell [40], the use of small earthquakes as empirical Green’s functions has gained considerable popularity, both in the synthesis of ground motion, as well as in the estim ation of source tim e functions of large earthquakes [55], [57], [59], [71], [30], [31], [70], [51], [50]. The advantages of this approach to the inversion procedure described in chapter 3 are two fold. The EGF is precise, regardless of the structure complexity while no information is necessary about the earth structure or the source process, and is faster.The main assumption of it is that the site and path effects are linear, over the magnitude range considered. One way of using the EGF method is to synthetise the ground motion from an earthquake using the recordings of smaller events, [40], [55]. The fault plane of a large earthquake is divided into a number of elements. Each element size is taken to m atch the fault size of a small earthquake, with the same location, which is used as a subevent. Then the ground motion for the large earthquake is approximated by the weighted and phase delayed summation of the ground motion from the small earthquakes. Another way of using the EGF is in the estim ation of source tim e function of the large shock by deconvolution with the record of a small earthquake [71],[30],[70],[51], [50] .The deconvolution is usually on the frequency domain and is achieved by spec tral division. Then for frequencies less than the corner frequency of the G reen’s 61 function (where the delta-function assum ption holds) the result represents the source tim e function of the large earthquake. Unlike the coda m ethod where the pair of the earthquakes does not have to have the same hypocenters, the proximity of the two events is very crucial when direct body waves are used. Mori [70] showed th at if the hypocenters of the two events differ some hundreds of m eters then the source param eter estim ation becomes unreliable. 4.2 M eth od o f analysis First we selected areas were clusters of aftershocks, with varying depth, had occurred. We retrieved the waveforms of earthquakes, from the SCEC database, as they were recorded at AQUA. After plotting the waveforms we separated the earthquakes in groups, first according to their location and depth and afterwards according to their P and S wave polarities. Then we tried to find events with sim ilar body waveforms. A band pass Chebychev type I filter with corner frequencies at 2 Hz and 10 Hz, was applied so th at we’d filter out the high frequencies. Based the sim ilarity of the waveforms we selected pairs of earthquakes th at were used in the deconvolution. As a last step we retrieved the recordings of the selected events from the rest of the stations. Finally we used 41 events with m agnitude ranging from 0.9 up to 3.6 (Figure 4.1 and Table 4.1). Examples of earthquake pairs can be seen in figures 4.2, 4.3, 4.4, 4.5. The seismograms were integrated to give displacement and high pass filtered at 0.8 Hz. We used a three seconds window, starting from the arrival of the S waves. The spectrum was calculated using the m ultitaper spectral estim ation m ethod [77]. As it is well know from earlier studies, the deconvolution is an unstable process; zeroes in the denom inator dom inate the quotient spectrum . In micro earthquakes this instability is typical at high frequencies where the signal to noise ratio is small. The spectral division generally m ust be adjusted to obtain a useful result. Usually a high cut filter is applied to the num erator spectrum to reduce the high frequency instability. H elm bergeret al [48] suggested the waterlevel correction in which squared spectral am plitudes of the denom inator are not allowed to fall below a fraction of the peak squared spectral am plitude. In our case we smoothed th e spectrum using a three point running average window before the ratio of the spectrum am plitudes. 62 In every case the lower limit of the ratio was at 1.5 Hz while the higher limit was determ inated manually so that the signal to noise ratio would be more than 1.5. The am plitude ratio was fit using the following model O(f) = — 1 + (4.1) ! + ( £ ) ’ 1 ' where is 0(f) is the ratio, Hi, f)2 is the flat part of the spectrum for the large and small earthquake and f c\ ,/ C 2 their corner frequencies. For the fitting we used a grid search algorithm. We fit the ratio for pairs of corner frequencies from 3.0 Hz up to 80 Hz. The pair with the smallest residuals was choosed as the optim um one. We calculated the pairs of the corner frequencies for the same events using their waveforms from all the available stations and their average values were considered to be the corner frequencies of the earthquakes. 4.3 R esults and D iscussion Examples of spectral ratios can been seen in figures 4.6, 4.7. To estim ate the reli ability of the corner frequency we present the misfit between the modeled and the observed ratio for all the pairs of corner frequencies. We observe that the corner frequency of the larger earthquake is better constrained than the corner frequency of the smaller one. Assuming that pairs of corner frequencies with misfit within the 25% of the optimum one are acceptable, then the variation in the estim ation of f e is less than 5 Hz for the large events, equation Another way of estim ating the uncertainties is from the consistency of the values th at we obtained using different stations for the same pair of earthquakes or using the same earthquake in different pairs. Calculating the standard deviation of these values we found that it is up to 4-5 Hz for the large events and up to 10 Hz for the small events. Figure 4.8 presents the corner frequencies that we calculated with the EGF m ethod. Table 4.2 includes also these results. We observe that f c increases with decreasing seismic moment without any obvious upper limit in the corner frequency to be present. The corner frequency of earthquakes with magnitude around 1.0 varies from 15IIz up to 60Hz. The stress drop that we calculated using Brune’s model (equation 2.16) with /? = 3.4A:m/secis shown in figure 4.9. We must point 63 33*50' 33*55' 3 - 1 * 0 0 ' 3 4 " U 5 5 K m 116*30’ i | i 116* 25' 1 |,_T 116*20* 116*15' 0 O 8 116* 10' 0.0 & M < 1.0 1.0 £ M < 2.0 2.0 £ M < 3.0 3.0 £ M < 4.0 Figure 4.1: The earthquakes that we used with the EGF m ethod 204M50.AOUA.D.EHM.5AC-20S204J.AOUA.D.EHN.SAC 204WMAQU A.0.EHE.SAC-2052041 AQUK D EHE. SAC 100 0 -100. — , !----- 1 " 1 0 0 5 1 1.5 2 2 5 3 3 5 4 45 to o 0 0 5 1 15 2 2.5 3 3.5 4 4 5 -100 0 0.5 1 15 2 2 5 3 3 5 4 4 5 S i -------- .-------- 1 ---------1 -------- 1 -5, t -1 — r — /\Jjw vw w -v7yv\/w vA w ^^W v N -^r ^ ^ 0 0.5 1 15 2 2 5 3 3 5 4 4 5 T lm euc 500 200 2 5 3 5 45 05 15 2.5 4 5 15 3 5 2 5 4.5 -500. - 200. 3 5 0 5 15 2 5 1 5 2 5 3 5 4 5 -to, 05 05 2 5 2 5 3 5 4.5 Figure 4*2: Pair of earthquakes that was used with the EGF method. For every component the first window is the seismogram of the large earthquake (displace m ent), and the second window is the waveform of the small earthquake. The third and fourth windows are the same events after being band passed. All windows start from the P wave arrival 65 2 0 0 2040403 A O U A D .EH N .SA C -2049367.A O U A D E H N 5A C 2049403 A O U A O E H E .S A C -2O 40367JU aU A D E H E .S A C - 200, 2 0 0 0.5 -*( 1 0 0 1.5 2 2-5 3 3 5 — r " - » t F < -1 0 0 . 45 0 0-5 1 1-5 2 2.5 3 35 4 45 20 1--------------- r 0 0 5 “I”. 1 0 0 05 - 10, ‘ ‘ - 1.5 2 2.5 3 35 - 20, 45 0 OS 1 1.5 2 25 3 3 5 4 45 100r 1.5 2 25 3 3.5 - 1 0 0 , - t-------- r ~ I l 45 0 05 1 1.5 2 25 3 3 5 4 4.5 201 ---------. -------- r - 20, r 1 - " ■ ■ » 0 0.5 1 1.5 2 25 3 35 4 4.5 Q 05 1 1.5 2 25 3 35 4 4.5 T k n a t t c U m a t o c 50 2049403.AQUA.OEKZ.SAC-2O49367J1QUAO.EHZ.SAC -5 0 , ■ 1 ■ 10 0 05 1 1.5 2 2.5 3 3.5 4 4.5 “10. —i— '— > ----------------1----------------- -r------------—i----------— r ~ 1 ■ * 50 0 0.5 1 15 2 25 3 35 4 45 i i r i i < i i -5 0 , 0 0.5 1 1.5 2 25 3 3 5 4 4.5 ■ i —■ 11 i i . i i » i i - 5. 0 0.5 1 15 2 25 3 3 5 4 45 T I itwmc Figure 4.3: Example of an earthquake pair, as in figure 4.2 66 2052572.A Q U M ) EHN SA C -2051775A O U A .D EHN SAC 20 5 2572A O U A .O .eH 6.S A C *2051775A Q U A O £H E .S A C 2000 1000 ► 2000, - 1000, 05 1.5 2.5 3.5 4 5 1.5 35 0.5 1.5 35 1000 - 1000, 2.5 3.5 1.5 25 -50, -50, 0.5 1.5 4 5 35 1 0 0 0 • 1 0 0 0 , 0.5 1.5 3.5 0.5 2.5 1000 - 1000, 0 5 1.5 - 20, 0.5 1.5 \/s" 1 -- Tlmatgc Figure 4.4: Example of an earthquake pair, as in figure 4.2 67 1000 - 1000, 2052311 AOUA.D.EHN.SAC-2049754.AQIM.D.EHNSAC i f i , - . T .. . — T — . — — i------« ---- —' ~ ^ y \ y V / w s y \ / \ / v v > ^ . <000 205ail-MXIA-DEHE.SAC-2049754AOUA.DEHe.SAC - 1 0 0 0 . I I ---------I ----* ----I ---------r ~ 0 0.5 1 15 2 25 3 35 4 45 S 0 05 1 1.5 2 25 3 3.5 4 45 5 -5 0 . 50 50, ‘ * 1 1 1 1 J 1 1 1000 0 0.5 1 1.5 2 2.5 3 05 4 4 5 5 0 05 1 1.5 2 2-5 3 35 4 4.5 5 - 1000( 50 1000 - 1000, 0 05 1 1.5 2 25 3 35 4 45 5 0 05 1 15 2 2.5 3 35 4 4.5 S -50, j ■ ■ ■ 50 -50, 0 0.5 1 1.5 2 25 3 35 4 45 3 0 0 5 1 1.5 2 2.5 3 35 4 45 5 Tima toe Tkntitc 500 2052311 AQUA-D EHZ.SAC-2049754 AOUA.D.EHZ.$AC -500, 20 0 05 1 15 2 2 5 3 3 5 4 45 5 i i r i i — f t i t - 20, 200 0 05 1 15 2 2 5 3 3.5 4 45 5 - 200, i i i i to 0 05 1 t s 2 25 3 3 5 4 45 5 - 10. ■ * ■ . I . j i i . 0 05 1 15 2 25 3 35 4 45 5 Tknauc Figure 4.5: Example of an earthquake pair, as in figure 4.2 68 out th a t the uncertainties in the stress drop values are larger than the uncertainties associated with th e corner frequency since the stress drop depends on the f c and S waves velocity in th e third power. We do not observe a m inimum size for the small earthquakes, but a slight dependence of the stress drop with the seismic m oment exists. The larger aftershocks have stress drops in the range of 1000 bars to 100 bars, while the smallest events are concentrated around 10 bars. Hough et al [50] and Lindley [64] have calculated the corner frequencies and stress drop for some of the Joshua Tree aftershocks, using the EG F m ethod. Hough exam ined 122 aftershocks with m agnitude ranging from 1.8 to 4.9. T he corner frequencies th at he calculated are up to 60 Hz , in the sam e order as our results. Lindley using TERRAscope data found th at the stress drop for 12 large aftershocks, with seismic m oment between 2 x 102 1 dyne cm and 2 x 102 5 dyne cm is between 4.2 and 41 bars. Finally we tried to verify the depth dependence of the corner frequency. Plotting f c w ith depth (figures 4.10, 4.11, 4.12) for different m agnitude ranges we observe th a t the corner frequency increases with depth. For these figures we used events th at were used as “large “ events in the spectral division or small earthquakes th at were used in more than one division. T he depth dependence is more clear and for the larger of the aftershocks, since these are the ones th at were used as “large events” in the pairs. 69 s« :! iliiiiii* I (Mil 1 0 * F cl Figure 4.6: Examples of spectral ratios with the best fit curve. On the right of each example the distribution of the residuals is shown for all the calculated pairs of corner frequencies. The optimum pair of corner frequencies is shown with an asterisk. Pairs with residuals within 25% of the optimum are shown with crosses. Circles represent pairs with residuals between 25% and 50% of the optim um . Pairs with larger residuals are represented with dots 70 2052974 AQUAtt049723AQUA 2052974AQUA/2049723 AQUA Fcl- 7Fc2- 13 1 0 * F req u en cy {H z ) Fcl 2052769AQlTA/2052779AQUA 2052769 AQUA / 2052779AQUA Fcl -10 Fc2* 19 1 Fcl Figure 4.7: Examples of spectral ratios 71 .Inchua Tree Aftershocks fc N Joshua Tree Aftershocks fo E -S s -4 -3 o & m 1 -0 0 10" Joshua Tree Aftershocks fc Z -S glO ' -4 -3 00 -0 Frequency (Hz) -2? Figure 4.8: Corner frequencies with seismic moment, as they were calculated with the EG F method 72 Seismic moment (dyne cm) Joshua Tree aftershocks E Joshua Tree aftershocks N < 3 0 Source radioes (m) Source radious (m) Joshua Tree aftershocks Z o o . |to : Source radious (m) Figure 4.9: Seism ic m om ent with source dim ension 73 N2.0<-M<2.5 a. Depth (km) N 1.5<*M<2.0 5 30 Depth (km) N M<1.5 Depth (km) Figure 4.10: Corner frequencies with depth, N-S com ponent 74 C R C < 1 n > Q o * - » a re •-j a ra a n m * a CD o- o ■ a (T j a o 3 a o a ra a Comer Frequency (Hz) o a -3 a > o O r D epth (Km) E M<1.5 Comer Frequency (Hz) » hi u n. Comer Frequency (Hz) I — & let (fcoGfH (n o o o m o C D Comer Frequency (H z) Comer Frequency (H z) Comer Frequency (Hz) Z2.0<-M<2.5 Depth (km) Z1.5<-M<2.0 Depth (km) 10 0, Depth (km) Figure 4.12: Corner frequencies with depth, vertical com ponent Date Time Latitude Longitude Depth Magnitude Event ID 92 04 26 00 53 19.6 34 2.01 -116 18.74 7.01 1.80 3018769 92 04 26 02 20 35.5 33 57.99 -116 20.07 7.28 2.50 2048658 92 04 26 03 07 58.2 34 0.18 -116 19.57 9.76 3.60 3018817 92 04 26 08 17 30.9 34 2.78 -116 18.79 7.70 2.50 2048716 92 04 27 09 59 28.2 33 58.29 -116 19.16 10.43 1.40 3019018 92 04 27 22 59 40.7 34 2.88 -116 18.69 10.01 1.90 2049164 92 04 28 03 18 28.3 33 57.31 -116 20.38 4.46 2.70 2049220 92 04 28 04 14 42.0 33 57.08 -116 20.93 5.46 1.70 2049229 92 04 28 12 09 01.1 34 2.21 -116 19.10 7.45 2.10 2049299 92 04 28 17 42 47.7 33 57.45 -116 18.65 6.41 1.40 2049367 92 04 28 18 59 34.1 33 57.50 -116 18.66 6.23 1.30 3072264 92 04 28 20 41 12.9 33 57.48 -116 18.63 4.60 2.20 2049403 92 04 30 02 05 23.7 33 58.32 -116 19.04 10.51 1.60 2049723 92 04 30 05 25 46.0 33 57.51 -116 18.62 9.38 2.00 2049754 92 04 30 20 27 57.6 34 2.31 -116 18.84 10.58 2.40 2049897 92 05 01 04 31 14.1 33 57.12 -116 20.75 5.53 1.50 3020982 92 05 03 05 30 10.0 33 57.42 -116 18.72 5.85 1.70 2050382 92 05 04 23 49 30.6 33 57.87 -116 18.73 8.67 1.30 2050714 92 05 05 17 28 41.3 33 57.06 -116 20.08 6.30 1.90 2050834 92 05 06 03 18 42.8 33 57.17 -116 18.62 7.00 1.30 3024328 continue Table 4.1: Date, time, location and magnitude of the earrtliquakes th at we used with the EG F method 77 continue Date Time Latitude Longitude Depth Magnitude Event ID 92 05 06 05 10 43.9 33 57.01 -116 18.70 6.40 3.60 2050956 92 05 10 16 54 11.1 33 57.26 -116 18.26 7.50 2.60 2051652 92 05 10 23 26 14.0 34 1.87 -116 18.72 4.90 1.50 2051692 92 05 11 02 32 13.9 34 0.34 -116 19.02 9.63 1.90 2051714 92 05 11 13 34 54.1 33 57.89 -116 18.77 8.99 2.10 2051775 92 05 11 22 04 43.9 33 57.65 -116 18.66 9.02 1.30 2051839 92 05 13 03 27 26.1 33 57.96 -116 19.90 7.18 1.30 2052041 92 05 15 01 36 50.4 33 57.53 -116 18.71 9.75 3.40 2052311 92 05 15 03 27 17.1 34 0.16 -116 19.16 9.69 1.60 205214 92 05 17 06 21 31.5 33 57.84 -116 18.84 9.26 3.70 2052572 92 05 18 04 44 07.3 33 57.26 -116 18.29 5.71 2.60 2052679 92 05 18 20 21 11.4 33 57.54 -116 19.35 6.50 1.70 2052765 92 05 18 20 33 08.6 33 57.85 -116 20.14 7.11 1.90 2052767 92 05 18 20 36 56.7 33 57.39 -116 19.94 5.67 2.60 2052768 92 05 18 20 48 48.0 33 57.07 -116 19.79 6.08 2.20 2052771 92 05 18 22 05 18.0 33 57.28 -116 19.91 5.66 1.50 2052779 92 05 19 01 31 07.1 33 57.18 -116 19.96 5.85 1.70 2052807 92 05 19 10 04 01.0 33 57.22 -116 19.81 5.43 1.90 2052852 92 05 20 07 24 00.1 33 58.10 -116 18.87 10.53 3.00 2052974 92 05 21 10 58 35.2 33 57.32 -116 20.81 7.33 0.90 2053109 92 05 21 16 32 08.3 33 57.23 -116 20.82 6.3 2.00 2053135 78 Event Z N -S E -W f c Hz C T d R m f c Hz crj R m f c Hz <?d R m 2048658 14.0 1.7 90.44 14.0 2.1 90.44 17.0 2.9 74.48 2048716 11.0 1.4 115.11 12.6 4.6 100.49 11.8 3.3 107.30 2049164 23.0 5.1 55.05 21.0 4.2 60.29 22.0 3.4 57.55 2049220 7.0 1.6 180.89 11.5 5.2 110.10 7.0 3.0 180.89 2049229 16.0 79.13 23.5 8.4 53.88 16.0 9.8 79.13 2049299 18.0 0.5 70.34 19.0 66.64 18.5 68.44 2049367 17.3 5.5 73.19 14.6 4.5 86.72 12.0 6.0 105.51 2049403 10.5 5.2 120.59 11.0 4.8 115.11 14.5 4.6 87.32 2049723 22.0 2.0 57.55 25.0 2.9 50.64 23.0 3.5 55.08 2049754 34.0 2.6 37.24 36.0 6.0 35.17 38.0 8.5 33.32 2049S97 29.0 2.8 43.66 25.0 2.8 50.64 27.0 2.8 46.89 2050382 19.5 4.9 64.93 19.0 4.2 66.64 23.0 55.05 2050714 24.0 3.0 52.75 26.0 4.5 48.70 20.0 4.0 63.31 2050834 12.5 3.7 101.29 16.5 5.7 76.74 16.5 4.7 76.74 2050956 8.0 2.5 158.27 5.8 1.0 218.31 8.3 5.5 152.55 2051652 19.2 7.5 65.94 21.4 4.4 59.16 20.3 5.03 62.37 2051692 16.0 7.0 79.13 15.0 5.4 84.41 18.0 6.0 70.34 2051714 29.0 3.8 43.66 30.0 3.2 42.20 24.0 4.2 52.75 2051775 22.5 7.2 56.27 26.0 10.5 48.70 26.3 5.1 48.14 2051839 33.0 5.6 38.37 40.0 6.3 31.65 40.5 7.3 31.26 2052041 21.0 5.3 60.29 22.0 8.3 57.55 26.0 7.0 48.70 continue Table 4.2: Corner frequencies and source dimensions of the earthquakes that we used with the EG F method 79 continue Event Z N -S E -W fc Hz < ? d R m h Hz O d R m fc Hz < * d R m 2052311 14.7 2.5 86.13 14.0 6.1 90.44 14.0 8.7 90.44 2052572 11.1 4.8 114.07 10.0 2.4 126.62 10.4 2.4 121.75 2052765 16.0 5.0 79.13 14.0 5.3 90.44 15.0 1.0 84.41 2052767 30.0 42.20 28.0 45.22 32.0 39.56 2052768 8.4 2.2 150.74 8.6 2.3 147.23 10.2 3.3 124.14 2052771 17.2 3.1 73.61 11.6 1.1 109.15 16.6 4.9 76.27 2052779 20.7 5.5 61.17 21.6 3.5 58.62 20.0 6.5 57.55 2052807 15.6 1.5 81.16 18.4 7.2 68.81 19.0 5.4 66.64 2052852 20.3 1.1 62.37 17.0 1.7 74.48 17.3 7.5 73.19 2052974 11.0 3.6 115.11 9.3 1.2 136.15 15.6 3.5 81.16 2053109 69.0 10.5 18.35 48.0 8.5 26.37 56.0 11.5 22.61 2053135 19.0 4.2 66.64 18.5 1.7 68.44 21.0 1.0 60.29 205214 23.0 8.3 55.05 23.0 10.0 55.05 28.0 9.0 45.22 3018769 19.5 4.9 64.93 27.0 2.8 46.89 23.2 5.4 54.57 3018817 7.0 0.2 180.89 9.6 1.1 131.89 9.0 2.8 140.69 3019018 32.0 6.0 39.56 28.0 6.4 45.31 30.0 7.3 42.20 3020982 21.0 3.5 60.29 21.5 3.5 58.89 25.0 3.5 50.64 3024328 21.2 5.4 59.72 16.2 4.1 78.16 21.5 3.5 58.89 3072264 16.0 4.2 79.13 20.0 5.4 63.31 23.5 6.1 53.88 80 C hapter 5 C onclusions We calculated the corner frequency of earthquakes from the Joshua Tree aftershock sequence using a simultaneous inversion of source and site effects and the EG F m ethod. W hile for the larger of the earthquakes, th at we used, both of the m ethods give similar results, there is discrepancy in our results for the smaller earthquakes. Our results from the inversion show that the corner frequency of the small earthquakes is up to 30 Hz, while from the EGF method they reach up to 60 Hz. Even if the results from the EGF m ethod are not well constrain for the small earthquakes, th at were used as Green’s function, we believe th at the EG F gives more reliable results than the inversion. This is because for the inversion we assume a flat response for one of the stations and this assumption m ight be erroneous for the high frequencies. Also the EG F is more successful in removing the path effects because we were very strict in the selection of our data, restricting ourselves only in pairs with very sim ilar waveforms and m ost of the times we were able to calculate the corner frequency of an earthquake using more than one station or using the earthquake in different pairs. Our data do not support the existence of an upper limit in the range of 10Hz- 20Hz in the corner frequency, as it was found by previous researchers. Also we do not observe any differences between earthquakes inside the m ajor fault zone of the Joshua Tree earthquake and outside it. The high frequency fall ofT, as it was calculated from the inversion,takes values between 2.0 and 4.5. Again we believe th at this is mainly from the site effects, but we can not exclude a source origin for these high values. 81 The stress drop estim ates are less reliable than the estimates of the corner fre quency, since the stress drop depends on the third power of the corner frequency and the S wave velocity. We estim ate that the variance in the stress drop values from the EG F method is up to 30 Hz. We observe a decrease of the stress drop with decreasing seismic moment. The large earthquakes have stress drop with values around 1000 bars while the stress drop of the small earthquakes is around 10 bars. This decrease in the stress drop with decreasing seismic moment was found from numerous researchers before. Glassmoyer et al. [36] observed a decrease in the stress drop, with decreasing moment for small earthquakes, without finding a minimum source radius. Also Haar et al [37] observed the same phenomenon for earthquakes in the Eastern United States. These observations suggest that the source process of the small earthquakes is different from the source process of the large earthquakes and self similarity does not hold. Both of the methods shown that the deep earthquakes have higher corner fre quencies than the shallow ones, without this being an artifact of attenuation, but a source property. There are several possible explanations for these high stress drop events. Rock mechanics experiments have shown that stress drop increases with confining pressure and applied stress [78]. The increase of the confining pressure with depth could result in an increase of the stress drop. Even if this increase was never observed before [92] certain ground motion parameters such are peak acceleration and velocity, which are proportional to dynamic stress drop, show a depth dependence [68]. Studies of aftershocks usually show that aftershocks with high stress drop are concentrated in areas which had not slip during the mainshock. Smith et al. [95] studied the aftershocks of the 1984 Round Valley earthquake. They found that after shocks with high stress drop were concentrated below and above the ruptured area and in a conjugate fault, while low stress aftershocks had occurred in the ruptured area. Mori [70] observed the same pattern with high stress aftershocks concentrated in areas with little or no slip from the main event. Residual high stress around the ruptured area of the mainshock is held for these high stress drop aftershocks. Since we observe our high stress events in the area of the mainshock rupture area, we do not believe that residual high stress is responsible for our observation. 82 Another explanation is that this difference can be due to m aterial inhomo geneities. Zhao et al [98] constructed a detailed P wave tomographic image of the Joshua Tree, Landers and Big Bear earthquakes area. In the Joshua Tree area they found a large high velocity area beginning at a depth of 10 km. Although it is not clear how seismic velocity is related to earthquake rupture zones, higher velocity ar eas are generally considered to be associated with more brittle and com petent parts of the crust which can sustain high stress, while lower velocity areas may represent regions with high degree of fracture. So the high stress drop earthquakes may be reflect the existence of a high stress area. This depth dependence affects the scaling of corner frequency and hence the relation between stress drop and seismic moment. In figure 5.1 we present the corner frequencies of earthquakes with depth less than 7 km with circles and those with depth larger than 7 km with crosses. We observe th at they follow different scaling laws. It seems that the scattering that is present in the data of Hanks or Abercrombie is because that they include earthquakes from different areas, where different scaling laws hold. 83 Joshua Tioo Aftershocks fc £ Joshua Tioo Aftershocks Ic N -5 *4 glO ! -4 -3 -3 + o -2 -2 05 t 0 Froquoncy (Hi) Frequoncy (H z) Joshua Tree Aftershocks tc Z -5 -4 -o -3 +0 -2 -0 to" Figure 5.1: Corner frequencies of earthquakes with depth less than 7 km (o) and depth larger than 7 km (+ ) 84 R eference List [1] R. Abercrombie. Earthquake source scaling relationships from -1 to 5 m t us ing seismograms recorded at 2.5 km depth. Journal of Geophysical Research, 100:24015-24036, 1995. [2] R. Abercrombie and P. Leary. Source param eters of small earthquakes recorded at 2.5km depth, Cajon Pass, Southern California; implications for earthquake. Geophysical Research Letters, 20:1511-1514, 1993. [3] K, Aki. Scaling law of seismic spectrum. Journal o f Geophysical Research, 72:1231-1271, 1967. [4] K. Aki. 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Creator Beltas, Periklis (author)

Core Title Source Parameters Of The Joshua Tree Aftershock Sequence

Degree Master of Science

Degree Program Earth Sciences

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

Tag geophysics,OAI-PMH Harvest

Language English

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Advisor Aki, Keiiti (committee chair), Lund, Steve P. (committee member), Sammis, Charles G. (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c18-12458

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