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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenSat, 13 Apr 2024 01:18:46 +0000Application of Linear Inversion Theory Toward the Estimation of Seismic Source Parameters
https://resolver.caltech.edu/CaltechETD:etd-10042005-103428
Authors: {'items': [{'id': 'Alewine-Ralph-Wilson-III', 'name': {'family': 'Alewine', 'given': 'Ralph Wilson, III'}, 'show_email': 'NO'}]}
Year: 1974
DOI: 10.7907/WCNC-CQ56
<p>A discussion is given concerning the development of methods for obtaining an accurate representation of the forward elastostatic problem of describing the processes which accompany faulting. A method is suggested by which a more complicated and arbitrary static dislocation function could be approximated with the formulations derived for simple dislocation sources. A stochastic inverse is used to provide optimum estimates of the source description when observed elastostatic phenomena are systematically related to the media response of the various source parameters. This method is applied to the observed static displacement data from the 1964 Alaska earthquake and the 1971 San Fernando, California, earthquake.</p>
<p>For the Alaskan event, the surface static displacements are calculated with the finite-element numerical modeling technique in which the effects of known geologic heterogeneities of the region are taken into account. The fault model used is that of a shallow angle fault underthrusting the Alaskan continental block. The calculated optimum static offset, stress drop, and strain energy density along the fault were found to be variable with a maximum offset of about 30 m. The region of maximum stress drop (218 bars) and maximum strain energy density change is found to correspond to the region of maximum compressional wave radiation. The resolution and resolvability of the calculated static fault model is discussed.</p>
<p>For the San Fernando earthquake, the static dislocation along the assumed fault plane was also found to vary considerably. The observed surface displacements are fit to a high degree of accuracy by the given model. Included in the inversion data set are changes in the local gravity field caused by the earthquake. These changes can be predicted from known changes in elevation when a Bouguer correction is applied to the gravity data.</p>
<p>The spatial and frequency distribution of path-corrected Rayleigh waves from the San Fernando earthquake are systematically related to the faulting process. The surface wave source is taken to be a depth-distributed set of double couples. A least-squares inversion is used to find the set of source parameters which optimally fit the variance-weighted data. The inversion results indicate a depth-distributed moment of 1.7 x 10<sup>26</sup> dyne-cm. The slip angles of the sources varied in such a way along the fault that the displacements became more predominantly dip slip as the dislocation propagated upward from the point of initial rupture at about 3.0 km/sec. A sophisticated error analysis is performed to estimate the uncertainties of the calculated model variables.</p>
<p>An appendix is included in which the analytical expressions are derived for the complete strain field due to a dislocation on an arbitrarily inclined fault in a homogeneous half-space. Although the expressions are lengthy, the strain values can be calculated quickly on a computer since no numerical integration is necessary.</p>https://thesis.library.caltech.edu/id/eprint/3912I. Earthquake source models, magnitudes and scaling relations. II. Amplitudes of rotationally split normal modes for the 1960 Chilean and 1964 Alaskan earthquakes
https://resolver.caltech.edu/CaltechTHESIS:09022011-110356908
Authors: {'items': [{'id': 'Geller-R-J', 'name': {'family': 'Geller', 'given': 'Robert James'}, 'show_email': 'NO'}]}
Year: 1977
DOI: 10.7907/9ABM-QM05
In Part I several fundamental concepts in seismology are examined in detail. The different teleseismic seismic magnitude scales are studied on the basis of Gutenberg and Richter's original notepads. The "revised magnitudes" presented by Richter and Duda are shown to be basically body wave magnitudes which are converted to the surface wave basis. These revised magnitudes are systemically higher (by an average of 0.22) than the magnitudes published by Gutenberg and Richter in Seismicity of the Earth, which are basically surface wave magnitudes. Use of the revised magnitudes has led to substantial over-estimates
of the moment of great earthquakes. Fault area, rather than magnitude, should be used for moment estimates when the moment is unavailable.
A dataset of 41 moderate and large earthquakes is used to derive scaling laws relating kinematic fault parameters such as magnitudes, moment and fault dimensions. If effective stress and static stress drop are equal, then, fault rise time, τ, and fault area, S, are related by τ = 16S^½ /(7π^(3/2)β), where β is shear velocity. Fault length (parallel to strike) and width (parallel to dip) are empirically related by L = 2W. Observed data agree well with the predicted scaling relations. Fault width (i.e. the two dimensionality of faults) must not be neglected. Inclusion of width leads to different average source spectra for surface waves and body waves. The m_b versus M_s relation from this study differs significantly from the Gutenberg-Richter relation, because the Gutenberg-Richter equation was derived for body waves with a predominant period of about 5 sec and thus does not apply to modern 1 sec m_b determinations. Previous investigators who assumed that the Gutenberg-Richter relation was derived from 1 sec data were in error.
In Part II, the theory necessary to calculate the amplitudes
of the earth's rotationally and elliptically split free oscillations is developed. The amplitude of each singlet is explicitly given as the product of factors for fault geometry, seismic moment, source depth, earth structure and the geographic coordinates of the source and receiver. These results are applicable for the synthesis of either spectra or time domain records for which splitting is an important factor.
The splitting of the earth's normal modes was observed for both the 1960 Chilean and 1964 Alaskan earthquakes. The theoretical results for the excitation of singlets are used to predict the relative amplitude of observed split peaks. Good agreement is obtained for thrust fault source models derived from long period surface waves. However, other mechanisms, such as a slow isotropic volume change, are also consistent with the split mode relative amplitudes, and are excluded only by additional data.
The split modes are observed for the 1960 Chilean earthquake by analysis in the time domain. One hundred fifty hours of the Isabella, California strain record are filtered to isolate individual multiplets. Synthetic seismograms with and without splitting are used to confirm the splitting of _0S_2 and _0S_3 and to demonstrate the splitting of _0S_4, _0S_5, _0T_3 and _0T_4. Different techniques for measuring the Q of split modes are studied. It is concluded that Q determinations from comparison of time domain synthetics to data give much more stability than frequency domain techniques. Uncertainties in the calibration of the instrumental absolute amplitudes rule out a direct determination of the moment of the Chilean earthquake. However, by comparing Isabella records for Chile and Alaska, the long-period moment of the Chilean earthquake is found to be 3.3 times that of the Alaskan event. By using the moment estimated for Alaska from long period surface waves, the moment of the Chilean earthquake is estimated to be 2.4 x 10^(30) dyne cm.https://thesis.library.caltech.edu/id/eprint/6647I. Application of normal mode theory to seismic source and structure problems. II. Seismic investigations of upper mantle lateral heterogeneity.
https://resolver.caltech.edu/CaltechTHESIS:08262011-121733057
Authors: {'items': [{'id': 'Okal-E-A', 'name': {'family': 'Okal', 'given': 'Emile André'}, 'show_email': 'NO'}]}
Year: 1978
DOI: 10.7907/H2Q8-X139
In Part I, the theory of the normal modes of the Earth is investigated and used to build synthetic seismograms in order to solve source and structural problems. After a study of the physical properties of spheroidal modes leading to a rational classification, two specific
problems are addressed: the observability of deep isotropic seismic sources and the investigation of the physical properties of the Earth in the neighborhood of the Core-Mantle boundary, using SH waves diffracted at the core's surface.
In Chapter 1, it is shown that five different families of spheroidal modes can be isolated on the basis of their physical properties, including group velocities, attenuation and excitation functions. Except for a few hybrid modes, these families are arranged in "pseudoovertone" branches, along which physical properties vary smoothly. The simplified model of a spherical, non-gravitating Earth is used to give a theoretical description of the properties of modes with low angular orders. Their group velocity is shown to be consistent with the physical concept of dispersion along a pseudo-overt one branch, thereby justifying the use of asymptotic expansions along them in generating synthetic seismograms. An interpretation of the existence of the various families in terms of an increase in modecoupling
with angular order is presented. A formal classification of
the spheroidal modes into the five families is made, and a new nomenclature reflecting the physical properties of the modes is proposed.
In Chapter 2, the relative excitation of body and surface waves by isotropic and deviatoric sources is studied as a function of depth and frequency. Since the fundamental Rayleigh wave excitation dies off faster as a function of frequency and depth for isotropic than for deviatoric sources, an ultra-long period record at Pasadena of
the Colombian deep shock of 1970 (for which a compressional precursor was proposed), is studied and compared to synthetic seismograms calculated for several source models. The best agreement is obtained for a pure double-couple source. Linear combinations of synthetics for deviatoric and isotropic sources are tested for a wide range of
relative amplitudes, showing the data to be little sensitive to the presence of a reasonably large isotropic component.
In Chapter 3, profiles of seismic shear waves diffracted around the core (Sd) for three deep events recorded at stations across North America and the Atlantic Ocean are used to determine the properties of the lower mantle in the vicinity of the core-mantle boundary. The S wave velocity above the surface of the core is found to be 7.22 ±
0.1 km/s, in agreement with gross Earth models, but higher than previously reported values from direct measurements of Sd. No evidence for a low- velocity zone in the lower mantle is found. Synthetic seismograms for Sd are easily generated through normal mode summation. A comparison of the present data with a synthetic profile for Earth model 1066A gives excellent agreement at periods greater
than 45 seconds. Synthetics for other models confirm the absence of a strong low-velocity zone at the base of the mantle, and are used to strongly constrain any possible rigidity of the uppermost layers of the core.
In Part II, data sets of seismic body and surface waves are used in a search for possible deep lateral heterogeneities in the mantle. In both cases, it is found that seismic data do not require structural differences between oceans and continents to extend deeper than 250 km. In general, differences between oceans and continents are found
to be on the same order of magnitude as the intrinsic lateral heterogeneity in the oceanic plate brought about by the aging of the oceanic lithosphere. A consistent similarity is inferred between stable shields and the oldest parts of the oceans.
In Chapter I, an analysis of records of multiply reflected ScS phases from ten deep focus earthquakes yields near-vertical one-way travel-time residuals ranging from -3.5 to +5.0 seconds. Continental and oceanic residuals overlap, and both indicate large lateral variations. Similar values are found for the older oceanic basins (Western Pacific, Brazil Basin) and continental shields. Most, if not all, of the variations can be attributed to differences in the
lithosphere and asthenosphere, down to a depth of 200 km, and the present results are in good agreement with local models derived by independent means. Oceanic islands are found to be anomalous with respect to the neighboring ocean floor, the mantle beneath Hawaii, Iceland and Trindade (South Atlantic) being exceptionally slow.
In Chapter 2, Rayleigh wave phase velocities at very long
periods (185 to 290 seconds) are investigated and regionalized, taking into account the lateral heterogeneities in the oceanic plates revealed by earlier studies at shorter periods. The two-station method is applied to a few 'pure-age' oceanic paths, and is shown to
be compatible with an average gross Earth model below depths of 180 km. Under this assumed oceanic model, regionalized for age above 180 km, continental velocities are derived from a set of experimental great-circle values, both new or taken from previously published studies. The results basically agree with the earlier studies by
Kanamori or Dziewonski, and it is suggested that the assumption of a uniform oceanic model may have been responsible for some scatter in Kanamori's solution. The results of the present inversion are successfully checked against a set of values derived by the two-station
method from a pure continental, tectonic, path. A recent event in Indonesia is then used as a further independent check, in what is believed to be the first experimental determination of Rayleigh wave phase velocities over a pure shield path at very long periods. The shield velocities fall within the range of variation of their oceanic
counterparts with the age of the plate, in agreement with the results of Chapter 1. This makes velocities derived theoretically from models involving deep continent vs. ocean lateral heterogeneities inconsistent with the present set of experimental data. Finally, it is shown that
Dziewonski's model S2 reconciles all experimental seismic data relative to shields without being significantly different from oceanic models below 240 km.
https://thesis.library.caltech.edu/id/eprint/6625A Numerical Boundary Integral Equation Method for Transient Motions
https://resolver.caltech.edu/CaltechTHESIS:02142024-183355928
Authors: {'items': [{'id': 'Cole-David-Martin', 'name': {'family': 'Cole', 'given': 'David Martin'}, 'show_email': 'NO'}]}
Year: 1980
<p>This thesis presents the results of a study of a numerical technique for the solution of initial-boundary value problems of linear elastodynamics. The numerical method is based on a boundary integral equation (BIE) formulation of the mechanics of bodies of arbitrary shape. These integral equations are discretized and a time stepping technique is used to so1ve the resulting system of linear algebraic equations.</p>
<p>The theoretical basis of the continuous problem and the general interpolation and discretization scheme are described in Chapter 1. The problem is then specialized to the two-dimensional case of antiplane strain and most subsequent calculations and discussions take place in this context. The performance of the numerical method depends entirely on the interpolation scheme used, and on the manner in which boundary shapes are approximated.</p>
<p>The consequences of particular interpolation schemes for boundary value problems on a half-plane are discussed in Chapter 2. The results of several numerical calculations are compared with exact, or much more accurate solutions. This chapter also presents a comparison of the performance of the numerical BIE method with the performance of other specialized numerical procedures which have been used previously for problems of this nature. The BIE method yields results which are as accurate, or more accurate than the other methods for given discretization parameters.</p>
<p>The method is applied to basic boundary value problems for
curved symmetric and nonsymmetric boundaries in Chapter 3. The solutions obtained there are again compared to more accurate or exact solutions produced by independent methods. The general dependence of errors on discretization parameters is discussed.</p>
<p>Chapter 4 gives the solution of a problem in which a Love wave propagates through a limited region of laterally varying structure.
The time stepping nature of the BIE method makes feasible certain rearrangements of the numerical equations which yield a representation of the mechanical system in which the incident, unperturbed Love wave arises as an inhomogeneous term. Solution of this localized numerical equation then yields an intermediate variable, the change in the traction boundary value of the layered space surface, which is used to evaluate the scattered displacement wave.</p>
<p>The performance characteristics and unusual properties of the time stepping BIE method are summarized in the General Summary. The appendices deal with several subjects. Appendix A gives an evaluation of singular integrals arising in the general continuous integral equation formulation. Appendix B gives a body force equivalent of nonequilibrium static initial values. Appendix C discusses the con vergence and stability of solutions obtained using a particular inter-polation scheme. Appendix D contains FORTRAN subroutines used in evaluating discrete kernels for the antiplane strain case. Appendix E gives the solution to a diffraction problem which is used to evaluate
errors in a BIE solution of the same problem which is given in Chapter 3.</p>https://thesis.library.caltech.edu/id/eprint/16292Interpretation of Near-Source Ground Motion and Implications
https://resolver.caltech.edu/CaltechETD:etd-09072006-111327
Authors: {'items': [{'id': 'Liu-Hsui-Lin', 'name': {'family': 'Liu', 'given': 'Hsui-Lin'}, 'show_email': 'NO'}]}
Year: 1983
DOI: 10.7907/5hbj-fd95
<p>This thesis presents some deterministic modeling and interpretation of various aspects of observed near-source ground motions.</p>
<p>In Chapter 1, finite source parameters determined from waveform modeling studies are presented for two California earthquakes; the 1979 Coyote Lake event and the 1966 Parkfield event. These events were recorded by strong motion arrays with similar station to fault rupture geometries. Thus it is possible to demonstrate that differences in the ground motions recorded within 30 km of the epicenter are indeed due to the differences in rupture fault length and dislocation distribution.</p>
<p>Details of the waveform modeling for the August 6, 1979 Coyote Lake earthquake are described in part 1-A. A finite fault striking N24°W and extending to a depth of 10 km is proposed to model the strong-ground motion data. The source model suggests that right-lateral faulting initiated at a depth of 8 km and ruptured towards the south with a velocity of 2.8 km/sec. This unilateral rupture can explain the large displacements recorded south and southwest of the epicenter. However, the waveform coherency observed across an array south and southwest of the epicenter suggests that the rupture length is less than 6 km. The maximum dislocation is about 120 cm in a small area near the hypocenter and the total moment is estimated to be 3.5 x 10<sup>24</sup> dyne-cm. An abrupt stopping phase, which corresponds to a cessation of right-lateral motion, can explain the high peak acceleration recorded at array station 6. The stress drop in the hypocentral area is about 140 bars; although the average stress drop over the entire rupture surface is 30 bars. This preferred finite source model can predict observed P<i><sub>ni</sub></i> waveforms as well as the beginning features of teleseismic body waves.</p>
<p>In part 1-B, a similar waveform modeling technique is used to interpret the ground motions recorded during the June 28, 1966 Parkfield earthquake. The preferred model suggests that the earthquake involved two fault segments; one is the NE branch which extends 22 km southward from epicenter and has an average slip of 45 cm, another is the SW branch which ruptured less than 10 km and has an average slip of about 22 cm. The total moment indicated by this model is 1.25 x 10<sup>25</sup> dyne-cm. The anomalous large amplitude ground displacement seen at station Cholame No. 2 is modeled as a local amplification effect rather than a source effect due to significant dislocation near this station.</p>
<p>Direct waveform comparisons between recordings of the Parkfield event and the Coyote Lake event also support the conclusion that the rupture length of the Coyote Lake earthquake is much shorter than that of the Parkfield event. The waveform modeling also emphasizes the importance of using array data to constrain source parameters. The solution derived from a single station's recording, which in many cases is the only available information, may often produce misleading results.</p>
<p>In Chapter 2, high-frequency ground motions (ground velocity and acceleration) recorded at less than 30 km epicentral distances are studied for two aftershocks of the 1979 Imperial Valley, California earthquake. In the past, little has been done to understand these high frequency waves through a deterministic modeling approach. The waveform modeling technique and the source mechanisms of these two aftershocks are described in sections 2-A and 2-B.</p>
<p>An important feature of the ground motions recorded during the October 15, 1979 Imperial Valley earthquake sequence is the strong high frequency waves observed on the vertical components. This feature is also seen in recordings of the aftershock of October 16, 23:16, 1979, which is described in section 2-A. This polarization feature is easily explained by the basin velocity structure which bends rays towards the vertical at the free surface. Short S-P times are observed at the three closest stations (epicentral distances of 3 km to 5 km) suggesting that this aftershock occurred at a very shallow depth of about 2 km. A fault plane orientation (strike = N20°E, dip = 30°SE, and rake = -80°) obtained from a first P-motion study, generates synthetic waveforms of the strong ground velocities which are similar to those observed at three closest stations. The source time duration is determined to be 1.0 second and the moment is 1.6x10<sup>23</sup> dyne-cm. Synthetics for a number of line source models are compared with the observations. These comparisons lead to two basic mechanisms that are necessary to explain the frequency content of the observed P- and S- waves. One is that the source process is characterized by irregular rupture. It is postulated that the heterogeneous stiffness in the layered medium is the basic cause of the irregular rupture. Heterogeneous rupture generates both high-frequency P- and S-waves. In order to explain the contrast in observed frequency content it is also necessary that there is a mechanism for attenuating S-waves much stronger than P-waves.</p>
<p>The aftershock that occurred about 3 minutes after the mainshock, at 23:19 October 15, 1979 is presented in section 2-B. This aftershock was located on the Imperial fault near Highway 8 and close to the zone of high frequency energy release of the main event. The impulsive seismograms for 16 array stations, ranging from 8 km to 26 km in epicentral distance, are well suited for source parameter inversion studies to obtain an optimal solution for ground velocity and acceleration. The earthquake source is approximated by a model consisting of several point dislocation sources separated in space and time and having different dislocation orientations and moments. These source parameters were deduced by trial and error modeling as well as by applying inversion procedures. The waveforms and amplitudes of horizontal ground velocities are well modeled by two predominantly strike-slip point sources; the first source (strike = N41°W, dip = 42°NE and rake = 174°) has a moment of 0.7 x 10<sup>24</sup> dyne-cm, the second source (strike = N36°W, dip = 82°SW and rake = 181°) lies about 1 km to the north of the first and has a seismic moment of about twice that of the first source. It is suggested that the higher-frequency ground motions, such as accelerations, can be derived from very irregular source processes, whereas the longer-period ground motions, such as ground displacements, can be well modeled by simpler planar source.</p>
<p>A Futterman attenuation operator with a t<sup>*</sup><sub>β</sub> of about 0.08 to 0.1 and a t<sup>*</sup><sub>α</sub> of about 0.001 in the sedimentary region produces longer period S waves and the proper amplitude ratio between P and S waves.</p>
<p>In Chapter 3, the ground motion data from the 1971 San Fernando earthquake recorded at epicentral distances of less than 100 km are presented. Three long profiles (> 50 km ) and three short profiles (< 2 km) of ground velocity and acceleration, displayed as a function of epicentral distance are analyzed.</p>
<p>Although there is considerable variation in waveforms and peak amplitudes observed along the long profiles, there are also many examples of coherent phases seen at adjacent stations. Ground velocity profiles show striking differences in amplitude and duration between stations located on hard rock sites and stations located within the sedimentary basins. The San Fernando basin, in which the source is located, seems to respond quite differently from the Los Angeles basin which is about 30 km from the earthquake source area. Ground acceleration profiles show that there is little change in the duration of high-frequency shaking along the long profiles.</p>
<p>The three short profiles, which are all located within the Los Angeles basin, demonstrate that ground velocity waveforms are nearly identical along these profiles. Although greater variation of waveforms and amplitudes are seen for ground acceleration along these short profiles, strong phase coherence is still observed.</p>
<p>The 2D acoustical finite difference method is used to compute the effects on SH-waves of irregular velocity structures believed to exist along Profile I and Profile II. Profile I extends 65 km southward from the epicenter across the San Fernando and Los Angeles basins to a station on the Palos Verdes Peninsula. Profile II extends 95 km S 40° E along the front of the San Gabriel mountains and across the San Gabriel and Los Angeles basins. These numerical models consist of low-velocity sedimentary basins (β = 2.1 km/sec) of irregular shape which are imbedded in high-velocity basement rock (β = 3.5 km/sec). Heaton's (1982) finite source model derived from modeling the five nearest stations for the San Fernando event, is also incorporated in the interpretation. The resulting simulation suggests that the smaller S! phases in both Profile I and Profile II are direct S waves from the deep source region (13 km). The shallow source region (at 1 km) dominates high amplitude later arrived phases observed along Profile I and are due to the complicated basin path along this profile. The shallower source region, however, contributes little to the ground motions along Profile II due to the lack of thick sediments near the source region along this azimuth.</p>https://thesis.library.caltech.edu/id/eprint/3374Inversion of Body-Wave Seismograms for Upper Mantle Structure
https://resolver.caltech.edu/CaltechTHESIS:10242018-091909982
Authors: {'items': [{'id': 'Given-Jeffrey-Wayne', 'name': {'family': 'Given', 'given': 'Jeffrey Wayne'}, 'show_email': 'NO'}]}
Year: 1984
DOI: 10.7907/cgdh-0e19
<p>We invert observed long- and short-period body-wave seismograms, travel times, and apparent velocity data to further constrain the compressional velocity structure in the upper mantle beneath northwestern Eurasia and the shear-wave velocity structure beneath western North America.</p>
<p>Long- and short-period WWSSN seismograms from nuclear explosions in the Union of Soviet Socialist Republics are incorporated with apparent velocity observations to derive an upper mantle model for northwestern Eurasia. The compressional waves from these explosions have several distinctive features that provide important new information about the character of the upper mantle in the region. The seismograms from 9° to 13° exhibit impulsive first arrivals, P<sub>n</sub>, implying a smooth positive velocity gradient between depths of 60 and 150 km. There is a consistent pulse arriving about 2s after P<sub>n</sub> at the distances of 13° to 17°, and at larger ranges there are distinct reflections from two major discontinuities in the mantle. Synthetic seismograms displaying these features indicate a velocity model that correlates with other models from around the world, with a distinctive lid and low-velocity zone. The arrival following P<sub>n</sub> is modeled by positioning the low-velocity zone between 150 and 200 km. The model is relatively smooth from a depth of 200 km down to 420 km, where a 5% jump in velocity produces a triplication in the travel time curve from 15° to 23°. The observations from 21° to 26° clearly show another discontinuity at a depth of 675 km with a 4% change in velocity. These results suggest that stable continental regions may have a shadow zone that extends beyond 17°. Below 250 km there is no distinguishable difference between the model proposed for northwest Eurasia and models derived for the United States.</p>
<p>A systematic inversion technique is proposed to extract the maximum amount of information from these data. We use the WKBJ method to compute approximate synthetic seismograms in a radially heterogeneous earth. Where the WKBJ method breaks down, in low-velocity zones and near discontinuities, a generalized ray expansion is used in a layered model approximation to the velocity structure to isolate the energy that has reflected from these regions. Synthetic seismograms computed using these approximations compare very well to those computed by the more accurate method of summing primary reflections in a generalized ray sum yet require 1/20 the computation time. With this efficiency it is feasible to compute the differential seismograms necessary to pose an inverse problem.</p>
<p>With a fast means of computing synthetic seismograms, an inverse problem can be posed to relate the differences between observed and synthetic seismograms to perturbations in the velocity structure. The problem is nonlinear, especially at high frequencies, but at long periods an iterative technique based on a linearized relation between perturbations in the velocity structure and the seismograms is effective if a reasonable initial model is assumed. Some simple tests of the method indicate that convergence to a satisfactory final model is possible even when starting with a model that predicts substantially different seismograms than those observed.</p>
<p>We invert long-period SH waves recorded on WWSSN seismographs at distances from 15° to 31° in the western United States and East Pacific Rise to determine the upper mantle shear velocity structure beneath these regions. A high velocity gradient near 400 km produces clear later arrivals from 15° to 17°. We interpret large later phases observed al distances from 23° to 27° as another large velocity gradient at between 600 and 720 km depth. Inversion of these seismograms suggests that the velocity gradient in the upper 200 km of the mantle is small; there is an increase in the velocity gradient around 250 km resulting in a 4% velocity increase by 360 km. The large velocity gradient near 400 km results in a velocity increase of around 8½% between 360 km and 420 km depth. The velocity gradient becomes smaller between 420 and 600 km with a cumulative increase of 5% over these depths. The total increase in velocity from 600 to 750 km is about 14%. Below 750 km the velocity gradient is assumed to be similar to those predicted by global studies of travel times.</p>
<p>There are differences in published travel time data and models that have been derived to fit the SS phases and SS-S differential times observed in this region. The discrepancies amount to about 5s in the direct S-wave travel time at distances of 15° to 18°. The discrepancy appears to be on the order of 3 s from 19° to 23° and is not resolvable beyond. These disagreements are probably the manifestation of large velocity heterogeneities in the uppermost mantle; either assumption concerning absolute travel times can be fit by models that are virtually identical below 270 km. Absolute travel times can constrain absolute velocities and, thus, are necessary to constrain the depth to discontinuities. Waveform data can constrain the structural details better. A joint waveform and travel time inversion method is a very useful tool for interpreting seismograms for earth structure.</p>
https://thesis.library.caltech.edu/id/eprint/11244Teleseismic Array Analysis of Upper Mantle Compressional Velocity Structure
https://resolver.caltech.edu/CaltechTHESIS:10092013-142945359
Authors: {'items': [{'id': 'Walck-Marianne-Carol', 'name': {'family': 'Walck', 'given': 'Marianne Carol'}, 'show_email': 'NO'}]}
Year: 1984
DOI: 10.7907/76q0-ye98
<p>Large quantities of teleseismic short-period seismograms recorded at SCARLET provide travel time, apparent velocity and waveform data for study of upper mantle compressional velocity structure. Relative array analysis of arrival times from distant (30° < Δ < 95°) earthquakes at all azimuths constrains lateral velocity variations beneath southern California. We compare dT/dΔ back azimuth and averaged arrival time estimates from the entire network for 154 events to the same parameters derived from small subsets of SCARLET. Patterns of mislocation vectors for over 100 overlapping subarrays delimit the spatial extent of an east-west striking, high-velocity anomaly beneath the Transverse Ranges. Thin lens analysis of the averaged arrival time differences, called 'net delay' data, requires the mean depth of the corresponding lens to be more than 100 km. Our results are consistent with the PKP-delay times of Hadley and Kanamori (1977), who first proposed the high-velocity feature, but we place the anomalous material at substantially greater depths than their 40-100 km estimate.</p>
<p>Detailed analysis of travel time, ray parameter and waveform data from 29 events occurring in the distance range 9° to 40° reveals the upper mantle structure beneath an oceanic ridge to depths of over 900 km. More than 1400 digital seismograms from earthquakes in Mexico and Central America yield 1753 travel times and 58 dT/dΔ measurements as well as high-quality, stable waveforms for investigation of the deep structure of the Gulf of California. The result of a travel time inversion with the tau method (Bessonova et al., 1976) is adjusted to fit the p(Δ) data, then further refined by incorporation of relative amplitude information through synthetic seismogram modeling. The application of a modified wave field continuation method (Clayton and McMechan, 1981) to the data with the final model confirms that GCA is consistent with the entire data set and also provides an estimate of the data resolution in velocity-depth space. We discover that the upper mantle under this spreading center has anomalously slow velocities to depths of 350 km, and place new constraints on the shape of the 660 km discontinuity.</p>
<p>Seismograms from 22 earthquakes along the northeast Pacific rim recorded in southern California form the data set for a comparative investigation of the upper mantle beneath the Cascade Ranges-Juan de Fuca region, an ocean-continent transit ion. These data consist of 853 seismograms (6° < Δ < 42°) which produce 1068 travel times and 40 ray parameter estimates. We use the spreading center model initially in synthetic seismogram modeling, and perturb GCA until the Cascade Ranges data are matched. Wave field continuation of both data sets with a common reference model confirms that real differences exist between the two suites of seismograms, implying lateral variation in the upper mantle. The ocean-continent transition model, CJF, features velocities from 200 and 350 km that are intermediate between GCA and T7 (Burdick and Helmberger, 1978), a model for the inland western United States. Models of continental shield regions (e.g., King and Calcagnile, 1976) have higher velocities in this depth range, but all four model types are similar below 400 km. This variation in rate of velocity increase with tectonic regime suggests an inverse relationship between velocity gradient and lithospheric age above 400 km depth.</p>
https://thesis.library.caltech.edu/id/eprint/7986Seismicity and Crustal Structure Studies of Southern California: Tectonic Implications from Improved Earthquake Locations
https://resolver.caltech.edu/CaltechTHESIS:10082018-123143470
Authors: {'items': [{'id': 'Corbett-Edward-John', 'name': {'family': 'Corbett', 'given': 'Edward John'}, 'show_email': 'NO'}]}
Year: 1984
DOI: 10.7907/h8mm-4v50
<p>This thesis consists of studies of: 1) the 1978 Santa Barbara earthquake and its aftershocks; 2) the depth distribution of seismicity in the Transverse Ranges; 3) crustal-velocity structure of the Continental Borderlands derived from explosion data; 4) the 1981 Santa Barbara Island earthquake and its aftershocks; and 5) earthquake location procedures, in particular the calibrated master-event technique.</p>
<p> The 5.1 M<sub>L</sub> Santa Barbara earthquake of 13 August 1978 occurred at 22<sup>h</sup> 54<sup>m</sup> 52.8<sup>s</sup> GMT. The epicenter was located 3 km southeast of Santa Barbara at 34° 23.9' N latitude and 119° 40.9' W longitude with a focal depth of 12.7 km. The mainshock was followed between 13 August and 30 September by 373 aftershocks that were located with the Caltech-USGS array. The aftershock zone extended 12 km west-northwest from the epicenter and was 6 km wide in the north-south direction, and it had a very clear temporal development. During the first 20 minutes of activity, all the aftershocks were located in a cluster 7 km west-northwest of the mainshock epicenter. During the next 24 hours the aftershock zone grew to 11 km in the west-northwest direction and 4 km in the north-south direction. During succeeding weeks, the zone extended to 12 by 6 km. This temporal-spatial development relative to the mainshock epicenter may indicate that the initial rupture propagated 7 km unilaterally to the west-northwest, and the initial rupture plane may have been considerably smaller than that of the eventual aftershock zone. This smaller area suggests that the stress drop may have been significantly greater than that derived from the area of the final aftershock zone.</p>
<p>In cross-section, the aftershock hypocenters outline a nearly horizontal plane (dipping 15° or less) at 13-km depth. The mainshock focal mechanism indicates north-northeast/south-southwest compression and vertical extension. The preferred fault plane strikes N 80° W and dips 26° NNE, indicating north-over-south thrusting with a component of left-lateral movement. Focal mechanisms for 40 aftershocks also indicate compression in the general north-south direction. For most of these events, the north-dipping nodal plane dips between 7° and 45°, with most dipping 25° or more, which is significantly steeper than the plane delineated by the hypocenters themselves. These observations are consistent with a tectonic model in which much of the slip during the Santa Barbara earthquake occurred on a nearly horizontal plane. The aftershocks then might represent movement on a complex series of imbricate thrust faults that flatten into the plane of primary slip. Hence, the Santa Barbara earthquake may be taken as evidence for mid-crustal horizontal shearing in the western Transverse Ranges.</p>
<p>To further test the decollement hypothesis, Caltech catalog locations were reviewed to determine the depth distribution of earthquakes in the Transverse Ranges. Only events with ERH < 1 km and ERZ < 2 km were utilized. These were scrutinized further with a numerical test of location procedures to test the reliability of the Caltech catalog quality assignments. These tests confirmed location qualities within 40 km of the east-west axis of the Transverse Ranges, but cast doubt on locations to the north and south.</p>
<p>The bottom of the seismogenic zone is clearly deepest along the southern front of the Transverse Ranges, with the deepest earthquakes occurring in the Pt. Mugu-Malibu area and under San Gorgonio Pass. Seismic activity is noticeably shallower north and east of the San Andreas fault than it is across the fault to the southwest. The seismogenic zone is thinnest in the southern Mojave Desert and at the east end of the Transverse Ranges. The seismicity of the western Transverse Ranges is typified by several north-dipping planar structures that correlate with the aftershock zones of recent earthquakes. The eastern Transverse Ranges are typified by ubiquitous seismicity extending from the surface down to the floor of the seismogenic zone. The San Bernardino Mountains are underlain by a well-defined bottom of the seismogenic zone that dips southward from 5-km depth under the Mojave Desert to 15-km depth where it intersects the San Andreas fault. South of the San Andreas fault, seismic activity deepens abruptly to as much as 22-km depth. The most intense seismicity is localized in the San Gorgonio Pass between the north and south branches of the San Andreas fault. This study falls short of the solving the decollement question, but it does add more intriguing evidence to the puzzle.</p>
<p>A large quarry explosion detonated on Catalina Island produced clear signals at stations throughout southern California. Data from near-shore and Island stations were utilized to derive velocity structure by the slope-intercept method. A 5.2-km/sec layer underlain by a 6.3-km/sec refractor was typically observed in most azimuths. A 7.8-km/sec Moho refraction was observed at ranges beyond 120 km. The interpretation is that the crustal refractor is at 5.5-km depth and the Moho is at 22-km depth. The upper crustal layer is significantly faster (5.5 km/sec) and thinner (2.5 km) under Catalina Island. An early P<sub>n</sub> arrival and possible Moho reflections observed at San Nicolas Island may constrain the Moho to be an average of 2 km shallower in the direction west from Catalina. This velocity structure was successfully used to improve the locations of the 1981 Santa Barbara Island earthquakes.</p>
<p>The Santa Barbara Island earthquake occurred at 15:50:50 GMT on September 4, 1981, at 30° 40.9' N and 119° 3.6' W, and registered 5.3 M<sub>L</sub>. Aftershocks exhibited a clear northwest-southeast alignment that coincides with the northeast-facing escarpment of the submarine Santa Cruz-Catalina ridge. This alignment also coincides with a mapped bedrock fault which is herein referred to as the Santa Cruz-Catalina fault. Focal mechanisms of the mainshock and the 3 largest aftershocks consistently show right-lateral strike slip on a northwest-trending plane, with possibly a component of dip slip. Aftershock depths show a near-vertical fault plane. The aftershock zone was initially 6 km long or less, and was concentrated southeast of the mainshock, suggesting unilateral rupture. The aftershock zone grew bilaterally to 15-km length after 24 hours to 21 km after 10 days, and to 35 km long after several months. This behavior may be Interpreted in tenns of an asperity model.</p>
<p>This seismic activity suggests strike-slip motion on the Santa Cruz-Catalina fault, with Santa Monica basin being displaced southeastward relative to points west. Structural complexities at the northwest and southeast ends of this fault suggest that the Santa Monica basin and Catalina Island are behaving as a coherent block pulling away from the Transverse Ranges, with extension at the northwest corner of the basin and compression to the south at the Catalina escarpment. Thus the Santa Monica basin may have formed as a triangular gap opening up between Peninsular Ranges blocks and the Transverse Ranges along the lines of the model of Luyendyk et al. (1980).</p>
<p>Nearly all earthquake location programs use Geiger’s (1912) method of least squares. This rigorous statistical method assumes that all the data are of equal quality and the only source of error is in measuring arrival times. This is not generally true of real earthquake data, which has led to a number of attempts at improvement. One of the most common modifications is data weighting of three types: quality weighting, distance weighting, and residual weighting. Programs that use all three must be used carefully to avoid feedback between weighting routines, with residual weighting being the worst cause of feedback. Station corrections are used to correct for systematic velocity variations and permit higher precision relative locations. The two most popular relative location methods are Joint Hypocenter Determination (JHD) and the master-event technique. The locations in Chapters 2 and 5 were performed with a modification termed the calibrated master event (CME) method. First, an intermediate-sized event is calibrated (preferably by explosion data) to achieve the best possible absolute location. Then, the residuals and hypocenter of this master event are used for establishing station delays and starting location, respectively, for relocating the seismicity of interest. Case histories of previous location attempts document the improvement attained with the CME method.</p>https://thesis.library.caltech.edu/id/eprint/11222Crustal Structure in Southern California from Array Data
https://resolver.caltech.edu/CaltechTHESIS:10092013-134453343
Authors: {'items': [{'email': 'thearn@nmsu.edu', 'id': 'Hearn-Thomas-Martin', 'name': {'family': 'Hearn', 'given': 'Thomas Martin'}, 'show_email': 'YES'}]}
Year: 1985
DOI: 10.7907/B6HA-4P68
<p>Crustal structure in Southern California is investigated using travel times from over 200 stations and thousands of local earthquakes. The data are divided into two sets of first arrivals representing a two-layer crust. The Pg arrivals have paths that refract at depths near 10 km and the Pn arrivals refract along the Moho discontinuity. These data are used to find lateral and azimuthal refractor velocity variations and to determine refractor topography.</p>
<p>In Chapter 2 the Pn raypaths are modeled using linear inverse theory. This enables statistical verification that static delays, lateral slowness variations and anisotropy are all significant parameters. However, because of the inherent size limitations of inverse theory, the full array data set could not be processed and the possible resolution was limited. The tomographic backprojection algorithm developed for Chapters 3 and 4 avoids these size problems. This algorithm allows us to process the data sequentially and to iteratively refine the solution. The variance and resolution for tomography are determined empirically using synthetic structures.</p>
<p>The Pg results spectacularly image the San Andreas Fault, the Garlock Fault and the San Jacinto Fault. The Mojave has slower velocities near 6.0 km/s while the Peninsular Ranges have higher velocities of over 6.5 km/s. The San Jacinto block has velocities only slightly above the Mojave velocities. It may have overthrust Mojave rocks. Surprisingly, the Transverse Ranges are not apparent at Pg depths. The batholiths in these mountains are possibly only surficial.</p>
<p>Pn velocities are fast in the Mojave, slow in Southern California Peninsular Ranges and slow north of the Garlock Fault. Pn anisotropy of 2% with a NWW fast direction exists in Southern California. A region of thin crust (22 km) centers around the Colorado River where the crust bas undergone basin and range type extension. Station delays see the Ventura and Los Angeles Basins but not the Salton Trough, where high velocity rocks underlie the sediments. The Transverse Ranges have a root in their eastern half but not in their western half. The Southern Coast Ranges also have a thickened crust but the Peninsular Ranges have no major root.</p>
https://thesis.library.caltech.edu/id/eprint/7982I. Applications of Double-Exposure Holography to the Measurement of In Situ Stress and the Elastic Moduli of Rock from Boreholes. II. Shock Temperature Measurements in Fused Quartz and Crystalline NaCl to 35 GPa
https://resolver.caltech.edu/CaltechTHESIS:10242023-225432851
Authors: {'items': [{'id': 'Schmitt-Douglas-Ray', 'name': {'family': 'Schmitt', 'given': 'Douglas Ray'}, 'show_email': 'NO'}]}
Year: 1987
DOI: 10.7907/vr7c-6j57
<p>Part I.</p>
<p>The application of a new borehole technique using holographic inter ferometry to measure the in situ state of stress and the modulus of elasticity of rock is discussed. The apparatus exposes two holograms which are taken both before and after micron scale displacements are induced by
(1) drilling a small stress-relieving hole in the wall of a borehole, and (2) applying a normal point force to the borehole wall. Maximum induced displacements are approximately 10 microns; the holograms are sensitive to movements on the order of 0.1 micron. Raw data take the form of a series interference holograms which have dark fringes superimposed on the three dimensional holographic borehole wall image. Synthetic fringe patterns are used to forward model the observed in the present method of data analysis. Calibrations of the normal force method of measuring the elastic moduli is carried out on metals with well defined elastic properties. Typically each test yields elastic (Young's) moduli for brass and aluminum of 100 ± 10 GPa and 70 ± 5 GPa, respectively, which are in close agreement with
standard tests. Laboratory holographic measurements of the Young's modulus on a sample of keragenaceous dolomitic marlstone (taken from the same mine as which the in situ experiments were conducted) yielded 16.8 ± 2.8 GPa in agreement with the predicted modulus of 17.2 ± 2.0 GPa based upon published density-modulus relationships. Sonic velocity determinations of the dynamic Young's modulus on cores taken from the rock sample give values consistent with the holographic measurements of 13.5 to 19.1 GPa for assumed values of Poisson's ratio of 0.35 to 0.25. The results of field tests in a horizontal borehole in a mine pillar in the Mahogany formation of Garfield County, Colorado, are presented for both experiments. The elastic modulus was found to vary with position in the borehole from 26.9 to 36.0 GPa. The farfield stresses for a borehole station 4 m from the mine pillar free surface were found from analysis of several stress-relief holograms; the determined vertical stress within the mine pillar was -10.2 MPa (compressive) close to the predicted magnitude of -11.2 MPa.</p>
<p>Part II.</p>
<p>Greybody temperatures and emittances of fused quartz under shock compression between 10 and 30 GPa are determined. Observed radiative temperatures are higher than computed continuum temperatures for shock compressed fused quartz, however; below ~26 GPa observed emittances are < 0.02. This suggests that fused quartz deforms heterogeneously in this shock pressure range, as has been observed in other minerals. Between 10 and 16 GPa, radiative temperatures decrease from 4400 K to 3200 K, above 16 GPa to 30 GPa greybody temperatures of ~3000 K with low emittances are observed. The emittances increase with pressure from 0.02 to 0.9. The pressure range from 10 to 16 GPa coincides with the permanent densification region while the 16 to 30 GPa range coincides with the mixed phase region along the fused quartz Hugoniot. The differing radiative behaviors relate to these modes of deformation. Based upon shock recovery experiments and a proposed model of heterogeneous deformation under shock compression, the temperatures associated with low emittances in the mixed phase region probably represents the melting temperature of the high pressure phase. Above 20 GPa to 30 GPa the melting temperature of stishovite would therefore be approximately 3000 K and almost independent of pressure. The effect of pressure on melting relations for the phase system SiO₂-Mg₂SiO₄ are considered together with the proposed melting curve of stishovite and suggest that maximum solidus temperatures within the mantle of ~2370 K at 12.5 GPa and ~2520 K at 20.0 GPa. Using the proposed stishovite melting temperatures (T_m) and reasonable upper mantle temperatures (T), the effective viscosity (which is a function of the homologous temperature (T_m/T)) appears to remain nearly constant from 600 to 200 km depth in the Earth.</p>
<p>Radiative color temperatures were measured in single crystal sodium chloride under shock compression parallel to [100] over a pressure range from 20 to 35 GPa. Color temperatures from 2500 to 4500 K and emittances from 0.003 to 0.3 were determined by fitting observed spectra (450 to 850 nm) to the Planck greybody radiation law. These data support a heterogeneous shock deformation model of shocked halite in this pressure range. A 2500 K temperature rise is observed over the Bl-B2 mixed phase region from 25 to 30 GPa. Assuming that shock deformation occurs via yielding in localized planar zones which become melt and the melting temperature at high pressure controls the temperature, we infer that the temperature of the B2 fusion curve from 30 to 35 GPa rises from 3200 to 3300 K. The Bl-B2-liquid triple point is predicted at a temperature of 2250 K and 23.5 GPa.</p>https://thesis.library.caltech.edu/id/eprint/16215I. Attenuation Tomography. II. Modeling Regional Love Waves: Imperial Valley to Pasadena
https://resolver.caltech.edu/CaltechTHESIS:03192013-112511014
Authors: {'items': [{'id': 'Ho-Liu-Phyllis-Hang-Yin', 'name': {'family': 'Ho-Liu', 'given': 'Phyllis Hang-Yin'}, 'show_email': 'NO'}]}
Year: 1988
DOI: 10.7907/fb8j-fs65
<p>Abstract to Part I</p>
<p>The inverse problem of seismic wave attenuation is solved by an iterative back-projection method. The seismic wave quality factor, Q, can be estimated approximately by inverting the S-to-P amplitude ratios. Effects of various uncertain ties in the method are tested and the attenuation tomography is shown to be useful in solving for the spatial variations in attenuation structure and in estimating the effective seismic quality factor of attenuating anomalies.</p>
<p>Back-projection attenuation tomography is applied to two cases in southern California: Imperial Valley and the Coso-Indian Wells region. In the Coso-Indian Wells region, a highly attenuating body (S-wave quality factor (Q<sub>β</sub> ≈ 30) coincides with a slow P-wave anomaly mapped by Walck and Clayton (1987). This coincidence suggests the presence of a magmatic or hydrothermal body 3 to 5 km deep in the Indian Wells region. In the Imperial Valley, slow P-wave travel-time anomalies and highly attenuating S-wave anomalies were found in the Brawley seismic zone at a depth of 8 to 12 km. The effective S-wave quality factor is very low (Q<sub>β</sub> ≈ 20) and the P-wave velocity is 10% slower than the surrounding areas. These results suggest either magmatic or hydrothermal intrusions, or fractures at depth, possibly related to active shear in the Brawley seismic zone.</p>
<p>No-block inversion is a generalized tomographic method utilizing the continuous form of an inverse problem. The inverse problem of attenuation can be posed in a continuous form , and the no-block inversion technique is applied to the same data set used in the back-projection tomography. A relatively small data set with little redundancy enables us to apply both techniques to a similar degree of resolution. The results obtained by the two methods are very similar. By applying the two methods to the same data set, formal errors and resolution can be directly computed for the final model, and the objectivity of the final result can be enhanced.</p>
<p>Both methods of attenuation tomography are applied to a data set of local earthquakes in Kilauea, Hawaii, to solve for the attenuation structure under Kilauea and the East Rift Zone. The shallow Kilauea magma chamber, East Rift Zone and the Mauna Loa magma chamber are delineated as attenuating anomalies. Detailed inversion reveals shallow secondary magma reservoirs at Mauna Ulu and Puu Oo, the present sites of volcanic eruptions. The Hilina Fault zone is highly attenuating, dominating the attenuating anomalies at shallow depths. The magma conduit system along the summit and the East Rift Zone of Kilauea shows up as a continuous supply channel extending down to a depth of approximately 6 km. The Southwest Rift Zone, on the other hand, is not delineated by attenuating anomalies, except at a depth of 8-12 km, where an attenuating anomaly is imaged west of Puu Kou. The Ylauna Loa chamber is seated at a deeper level (about 6-10 km) than the Kilauea magma chamber. Resolution in the Mauna Loa area is not as good as in the Kilauea area, and there is a trade-off between the depth extent of the magma chamber imaged under Mauna Loa and the error that is due to poor ray coverage. Kilauea magma chamber, on the other hand, is well resolved, according to a resolution test done at the location of the magma chamber. </p>
<p>Abstract to Part II</p>
<p>Long period seismograms recorded at Pasadena of earthquakes occurring along a profile to Imperial Valley are studied in terms of source phenomena (e.g., source mechanisms and depths) versus path effects. Some of the events have known source parameters, determined by teleseismic or near-field studies, and are used as master events in a forward modeling exercise to derive the Green's functions (SH displacements at Pasadena that are due to a pure strike-slip or dip-slip mechanism) that describe the propagation effects along the profile. Both timing and waveforms of records are matched by synthetics calculated from 2-dimensional velocity models. The best 2-dimensional section begins at Imperial Valley with a thin crust containing the basin structure and thickens towards Pasadena. The detailed nature of the transition zone at the base of the crust controls the early arriving shorter periods (strong motions), while the edge of the basin controls the scattered longer period surface waves. From the waveform characteristics alone, shallow events in the basin are easily distinguished from deep events, and the amount of strike-slip versus dip-slip motion is also easily determined. Those events rupturing the sediments, such as the 1979 Imperial Valley earthquake, can be recognized easily by a late-arriving scattered Love wave that has been delayed by the very slow path across the shallow valley structure. </p>
https://thesis.library.caltech.edu/id/eprint/7528Ray Trace Tomographic Velocity Analysis of Surface Seismic Reflection Data
https://resolver.caltech.edu/CaltechTHESIS:08232012-133835865
Authors: {'items': [{'id': 'Stork-Christof', 'name': {'family': 'Stork', 'given': 'Christof'}, 'show_email': 'NO'}]}
Year: 1988
DOI: 10.7907/73RH-5N25
<p>Recent development of two technologies allows application of a generalized formulation of travel time inversion to very large data sets, such as the surface reflection surveys collected for oil exploration. This generalized formulation uses very small cell sizes, effectively eliminating discretization effects. Inversion of an effective continuum that has no built-in <i>a priori</i> constraints is what places this technique in the category of <i>tomography</i>.</p>
<p>In reflection surveys, the generalized formulation investigated here treats the continuous velocity field independently from the reflector locations. The <i>a priori</i> assumption, common with travel time inversions in seismic exploration data, is thus not made: that the velocity field is defined as a series of layers with constant or smoothly varying velocity. This assumption restricts significant velocity variations to occur only at reflector locations. Velocity parameterized as layers is merely one of many geologic constraints that can be added optionally in tomographic inversion.</p>
<p>The technologies that enable this generalized approach to travel time inversion are: 1) a computer program capable of tracing rays through a 2-dimensional grid of points and off reflectors with structure, and 2) iterative schemes that efficiently perform damped, constrained generalized matrix inversions over a user-specified wide eigenvalue range for very large model and data sizes. An argument is presented that a variation of Richardson's iteration is preferred to the Conjugate Gradient Iterative Method for performing the matrix inversion.</p>
<p>With this generalized formulation, Ray Trace Tomography is a first approach to tomographic transmission analysis. Travel times and ray paths are a valid approximation to the wave equation for broad velocity variations. The method efficiently addresses the characteristics of more general but much more expensive transmission techniques. For example, Ray Trace Tomography demonstrates that an iterative application of a transmission velocity analysis technique, tomography, and a scattering reflector location technique, migration, do not necessarily converge to the optimal solution. To resolve the ambiguity between velocity-reflector depth, velocity and reflector locations must be coupled in one inversion technique. Ray Trace Tomography is able to couple the two. Using it to indicate the absolute resolution between velocity and reflector depth, we find that for certain geometries, reflector depths cannot be resolved where most recorded energy travels within 45° of vertical.</p>
<p>Poor resolution of the velocity-reflector depth ambiguity and other problems are inherent to reflection surveys. These problems also exist for other transmission techniques and can be solved only through use of inversion constraints. Ray Trace Tomography can test constraints for possible use in other transmission techniques efficiently.</p>
<p>Ray Trace Tomography has difficulty with non-linearities caused by some types of starting model errors, such as small-scale reflector structure. Improved performance with non-linearities is an objective we should seek in other transmission techniques.</p>
<p>Not only is Ray Trace Tomography a useful intellectual exercise as a preliminary analysis of transmission inversion, but in many cases it is a viable technique for addressing serious problems with surface seismic reflection data. It can determine an accurate two-dimensional velocity field for migration, such as in the case of gas pockets or fault blocks. In addition, it can resolve between certain velocity and reflector ambiguities such as those occuring in the permafrost region of Alaska.</p>
<p>As a comparatively efficient technique, Ray Trace Tomography can serve as a tool for interactive interpretation. The geologist can use the ray tracing to compare various geologic models with the data and then use the inversion to fine-tune the models. The inversion enables the geologist to formulate his geologic knowledge as constraints in the inversion. By analyzing the inversion results, the interpreter will develop an understanding of the validity of the various models and the resolution amoung them.</p>https://thesis.library.caltech.edu/id/eprint/7192Finite differences and a coupled analytic technique with applications to explosions and earthquakes
https://resolver.caltech.edu/CaltechTHESIS:03192015-141813901
Authors: {'items': [{'id': 'Stead-R-J', 'name': {'family': 'Stead', 'given': 'Richard J.'}, 'show_email': 'NO'}]}
Year: 1990
DOI: 10.7907/gsvf-5426
An analytic technique is developed that couples to finite difference calculations
to extend the results to arbitrary distance. Finite differences and the
analytic result, a boundary integral called two-dimensional Kirchhoff, are
applied to simple models and three seismological problems dealing with data.
The simple models include a thorough investigation of the seismologic effects
of a deep continental basin. The first problem is explosions at Yucca Flat, in
the Nevada test site. By modeling both near-field strong-motion records and
teleseismic P-waves simultaneously, it is shown that scattered surface waves
are responsible for teleseismic complexity. The second problem deals with
explosions at Amchitka Island, Alaska. The near-field seismograms are investigated
using a variety of complex structures and sources. The third problem
involves regional seismograms of Imperial Valley, California earthquakes
recorded at Pasadena, California. The data are shown to contain evidence of
deterministic structure, but lack of more direct measurements of the structure
and possible three-dimensional effects make two-dimensional modeling of
these data difficult.https://thesis.library.caltech.edu/id/eprint/8795Regional surface wave magnitude and moment determination methods applied to nuclear explosions at the Nevada test site : implications for yield estimation and seismic discrimination
https://resolver.caltech.edu/CaltechETD:etd-04212006-165925
Authors: {'items': [{'email': 'bbwoods7@hotmail.com', 'id': 'Woods-Bradley-Brett', 'name': {'family': 'Woods', 'given': 'Bradley Brett'}, 'show_email': 'NO'}]}
Year: 1994
DOI: 10.7907/P212-Q044
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
This thesis examines the use of regional surface-wave data to measure the long-period source spectrum of underground nuclear explosions for the purposes of yield determination and seismic discrimination. It is demonstrated that regional (D < 2500 km) fundamental-mode Rayleigh and Love waveforms can be modeled with considerable accuracy. The procedure for modeling regional earth structure for such seismograms by inverting surface-wave dispersion data is described. This technique is a hybrid of preexisting surface-wave analysis and inversion methods. Theoretical path corrections are determined from the Green's function for a given modeled path. A method is described to obtain consistent, stable, time-domain surface-wave magnitude ([...]) or seismic moment ([...]) measurements from poorly dispersed regional Rayleigh waves. Source parameters for 190 Nevada Test Site explosions are determined using these methods. Observations demonstrate that the measurement/detection threshold for regional surface-waves is [...] > 4.0 (Yield = 1 kt)--a significant improvement over classical teleseismic [...] measurements. The results indicate that the [...] (or log [...]) - yield scaling relationship is near unity and constant for explosions of all measurable sizes. Site effects are also investigated to determine the portability of such surfacewave measurements. Spectral-domain moment estimates also were performed on the digital portion of the data set. Besides obtaining an average scalar moment from Rayleigh wave amplitudes, the isotropic (explosive source) and deviatoric moment (double-couple source generated by tectonic release) components were determined by a joint inversion of Rayleigh and Love wave amplitude and phase data. Although in the most general case the inversion solution is non-unique, constraining the depth of the deviatoric source to be equal to that of the explosion and assuming a vertical strike-slip orientation yields a unique linear inversion solution. The spectral moment estimates are similar to the time-domain values, although the spectral-domain moment variances are appreciably smaller than the time-domain ones. A regional short-period vs. long-period seismic discriminant is developed using the ratio of the seismic moment to local magnitude ([...]). This discriminant successfully separates the explosion and earthquake populations at all measurable source sizes, so that for a given seismic moment source level, an explosion has an [...] 0.5 magnitude units larger than a comparable-sized earthquake.
https://thesis.library.caltech.edu/id/eprint/1440