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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenThu, 30 Nov 2023 19:54:56 +0000Exact Transient Solution of Some Problems of Elastic Wave Propagation
https://resolver.caltech.edu/CaltechETD:etd-02212006-132324
Authors: Flinn, Edward Ambrose
Year: 1960
DOI: 10.7907/QRYY-CD29
Exact solutions are obtained for three problems of progressive elastic wave propagation in bounded media: (1) SH wave propagation from an impulsive point source in an infinite plate; (2) torsional waves in a solid cylinder; (3) radiation from an impulsive source of compressional and of shear waves in an infinite solid plate held between smooth rigid surfaces. The Laplace transform method is used.
Problems (1) and (3) are shown to be closely related. For these problems the solution is expressed both as an infinite series of normal modes and an infinite series of multiple reflections, and it is shown that the two representations of the solution are related by Poisson's summation formula. Solutions are obtained for both a delta-function and a unit function input.
Problem (2) is solved as an infinite series of normal modes for an impulsive shear stress source distributed over a normal section of the cylinder. The case of a point source on the axis of the cylinder is examined in detail.
Problem (3) involves mixed boundary conditions. A relation between the solution of this problem and wave propagation in a free plate is discussed.https://thesis.library.caltech.edu/id/eprint/693Geophysical Studies of the Basin Structures along the Eastern Front of the Sierra Nevada
https://resolver.caltech.edu/CaltechETD:etd-01312006-152504
Authors: Healy, John Helding
Year: 1961
DOI: 10.7907/403B-RW91
<p>Eighteen seismic refraction profiles were shot and about 1200 gravity stations were occupied in the basins bordering the eastern Sierra Nevada between Owens Lake and the Garlock Fault. The results of these data show that basin structures with maximum depths averaging between 4000 to 6000 feet follow the front of the Sierra for this entire distance except for about ten miles near Little Lake.</p>
<p>These basins are usually narrow, fault-bounded structures with their deepest parts close to the front of the Sierras.</p>
<p>Analysis of the regional gradients indicates that the Mohorovicic discontinuity can play only a minor role in the isostatic support of the Sierra Nevada.</p>
https://thesis.library.caltech.edu/id/eprint/419An Investigation of the Earth's Free OsciIIations
https://resolver.caltech.edu/CaltechTHESIS:04132011-081816354
Authors: Smith, Stewart Wilson
Year: 1961
DOI: 10.7907/S9RW-R653
The free oscillations of the earth excited by the Chilean earthquake of 1960 have been measured by power spectral analysis of strain and pendulum seismographs. A revised and more precise table of free oscillation periods is presented. The period of the fundamental spheroidal mod _0S^0_2 is 53.82 minutes.
Fine structure analysis has shown that for the first three spheroidal modes there is good agreement between the observed splitting and that calculated for a rotating earth. Results for the toroidal modes are uncertain.
A theory is presented that allows recovery of some of the source properties from observations of phase differences for spheroidal modes. A comparison of theory with observation confirms original estimates of a fault length of 1000 km and a rupture velocity of between 3 and 4 km/sec. The effect of a moving source that decays exponentially with distance changes the pattern of phase shifts slightly but does not change estimates of the fault parameters. An alternative interpretation of the source properties in terms of the relative amplitudes of 2n + 1 split lines for each mode is presented but no calculations are performed.
Preliminary data on the effects of geomagnetic storms on the oscillations of the earth place an upper limit of about 5 x 10^(16) ergs/cph for the energy density associated with the elastic coupling of several magnetic storms.
https://thesis.library.caltech.edu/id/eprint/6319Propagation of Leaking Modes in a Plane Seismic Waveguide. Propagation of Leaking Interface Waves
https://resolver.caltech.edu/CaltechTHESIS:04122011-145755371
Authors: Phinney, Robert Alden
Year: 1961
DOI: 10.7907/5TG9-XN02
<p>The work of Rosenbaum describing propagation or imperfectly trapped (leaking) modes in an acoustic waveguide is extended to two problems of geophysical importance. The problem of a liquid layer coupled to an elastic halfspace is considered first, in a paper entitled: Propagation of Leaking Modes in the Crustal Waveguide: The Oceanic PL wave. Theoretical results obtained in this first paper may be applied, after slight generalization, to the most general type of plane seismic waveguide. In a second paper, entitled: Propagation of Leaking Interface Waves, we discuss these generalizations and apply them to the fundamental problem of pulse propagation along a plane interface. The most important result of both papers is the description of the earliest-arriving signal traveling in the waveguide as a result of a transient point excitation.</p>
<p>Numerical results for both problems were obtained by solving the complex period equation on the Burroughs 220 computer. The programming framework and the numerical methods used are discussed in a third section of this thesis.</p>
https://thesis.library.caltech.edu/id/eprint/6311Radiation of Seismic Surface-Waves from Finite Moving Sources
https://resolver.caltech.edu/CaltechETD:etd-03172006-103207
Authors: Ben-Menahem, Ari
Year: 1961
DOI: 10.7907/14NZ-KT62
A theory is proposed for the propagation of seismic surface-waves from finite moving sources. The method consists of obtaining, in the first place, basic solutions for surface displacements from directional sources. These solutions are integrated to obtain the effect of a moving fault with arbitrary dip angle. Displacements are evaluated for Rayleigh and Love-waves, at long ranges. It is shown that the dimensions of the source and the speed of rupture play an important role in the wave-pattern and cannot be ignored whenever the dimensions of the source are of the order of the radiation's dominant-wave-length. It is demonstrated how this theory may lead to a derivation of the velocity of rupture and the fault-length from seismic records of a single station. Evidence is furnished both from two-dimensional model experiments and the Chilean Earthquake of May 1960.https://thesis.library.caltech.edu/id/eprint/982Geophysical Investigations in the Colorado Delta Region
https://resolver.caltech.edu/CaltechTHESIS:12072009-142350784
Authors: Kovach, Robert Louis
Year: 1962
DOI: 10.7907/B362-3G65
The combined approach of gravity and seismic re-fraction exploration was used to determine depths of the Cenozoic section and to study the fault pattern in the Colorado Delta region. Basement depths measured varied from about 2200 feet to a minimum depth of 15,400 feet along the international border, east of Calexico. A study of the seismicity of the region shows that the greatest seismic activity over the past 60 years has been along the San Jacinto fault system. Continuity of specific major faults is difficult to establish using gravity methods alone because of the lack of indicated vertical throw on the faults. No conclusive evidence is presented for establishing the continuity of the Mission Creek-Banning fault southward into the present area of investigation, although geophysical evidence is presented for a fault present beneath the Sand hills (Algodones Dunes).https://thesis.library.caltech.edu/id/eprint/5426Surface Wave Propagation in Layered Anistropic Media
https://resolver.caltech.edu/CaltechETD:etd-10142002-091205
Authors: Anderson, Don Lynn
Year: 1962
DOI: 10.7907/ADTM-DX51
An analysis is made of the dispersive properties of layered anisotropic media, emphasis being placed on the geophysically important case of transverse isotropy. Period equations are derived for Rayleigh, Stoneley and Love type waves. A correspondence is established, in certain cases, with ray theoretical and plane stress solutions.
The general anisotropic problem (orthorhombic symmetry) is considered briefly for certain propagation directions and is used to derive the two-dimensional theory of seismic modeling.
The single layer solutions are generalized to the n-layer problem by use of Thomson-Haskell matrices. The results are used to interpret long period surface wave data. It is found that an anisotropy of approximately 8% in the low velocity zone removes the discrepency between Love and Rayleigh waves.https://thesis.library.caltech.edu/id/eprint/4076Surface Wave Propagation in the Western United States: I. Crustal Structure in the Western United States from Multi-mode Surface Wave Dispersion. II. The Effects of the Continental Margin in Southern California on Rayleigh Wave Propagation
https://resolver.caltech.edu/CaltechTHESIS:05162012-110631966
Authors: Alexander, Shelton Setzer
Year: 1963
DOI: 10.7907/GDQP-PB52
<p>Part I</p>
<p>Multi-mode group velocity dispersion of both Rayleigh and Love waves was measured for a number of paths in the Western United States by means of a technique developed for separating the modes. Results for each region studied are interpreted in terms of a crustal structure which produces simultaneous agreement with all the modes observed, as well as available body wave data. Certain diagnostic features
of group velocity dispersion curves were noted and used to advantage in this study.</p>
<p>The analysis techniques developed have rather broad geophysical applications, for example in studies of source properties, interference phenomena, and noise properties.</p>
<p>Part II</p>
<p>The effects of the transition zone at the continental margin of Southern California on Rayleigh wave propagation have been investigated. Among the anomalous effects discovered are a minimum in phase velocity between 20 and 35 seconds period, different phase velocities on reversed paths across the same array, and systematic lateral re-fraction at the continental boundary. These anomalous effects can be attributed largely to the slope and curvature of the Mohorovičić discontinuity across this region.
An ultrasonic model was constructed to aid in interpreting these results.</p>
<p>Interpretation of the dispersion for periods below 20 seconds indicates that the crust thickens toward the continent with a slope of about 5° attaining a thickness of approximately 35 km under Southern California.</p>
https://thesis.library.caltech.edu/id/eprint/7036Part I. Propagation of acoustical gravity waves from an explosive source in the atmosphere. Part II. Rayleigh and Love waves from sources in a multilayered elastic half-space
https://resolver.caltech.edu/CaltechETD:etd-02252004-140415
Authors: Harkrider, David Garrison
Year: 1963
DOI: 10.7907/QEDG-NT74
<p>Part I:</p>
<p>A matrix formulation is used to derive the pressure variation for acoustic gravity waves from an explosive source in an atmosphere modelled by a large number of isothermal layers. Comparison of theoretical and experimental barograms from large thermonuclear explosions leads to the following conclusions: (1) The major features on the barogram can be explained by the super-position of four modes, (2) Different portions of the vertical temperature structure of the atmosphere control the relative excitation of these modes, (3) A normalized point source is sufficient to model thermonuclear explosions, (4) The observed shift in dominance of certain frequencies with yield and altitude can be explained using the empirical scaling laws derived from the direct wave near the explosion.</p>
<p>Part II:</p>
<p>A matrix formulation is used to derive integral expressions for the time transformed displacement fields produced by simple sources at depth in a multilayered elastic isotropic halfspace. The integrals are evaluated for their residue contribution to obtain surface wave displacements in the frequency domain. The theory includes the effect of layering and source depth for the following: (1) Rayleigh waves from an explosive source, (2) Rayleigh waves from a vertical point source, (3) Rayleigh and Love waves from a vertical strike slip fault model. The latter source also includes the effect of fault dimensions and rupture velocity. The theory presented here is the ground work for the numerical computation of theoretical seismograms for use in a later paper in which a comparison will be made between observations and theory in both the time and frequency domain. A discussion is included on how these comparisons might be used in the frequency domain to estimate source depth.</p>https://thesis.library.caltech.edu/id/eprint/753Velocities of long period surface waves and microseisms and their use in structural studies. I. Mantle Love and mantle Rayleigh waves and the structure of the earth's upper mantle. II. Microseisms and their application to seismic exploration
https://resolver.caltech.edu/CaltechTHESIS:11132012-094305927
Authors: Toksoz, M. Nafi
Year: 1963
DOI: 10.7907/1X99-MR13
<p>Part I:</p>
<p>Phase velocities of Love waves from five major earthquakes are measured over six great circle paths in the period range of 50 to 400 seconds. For two of the great circle paths the phase velocities of Rayleigh waves are also obtained. The digitized seismograph traces are Fourier
analyzed, and the phase spectra are used in determining
the phase velocities. Where the great circle paths are
close, the phase velocities over these paths are found to
be in very good agreement with each other indicating that
the measured velocities are accurate and reliable. Phase
velocities of Love waves over paths that 1ie far from each
other are different, and this difference is consistent and
much greater than the experimental error. From this it is
concluded that there are lateral variations in the structure
of the earth's mantle.</p>
<p> The phase velocity data are compared with theoretical dispersion curves of seven different earth models. None of
these models fit the data. Two new upper mantle models,
one to fit the data over an almost completely oceanic path
and the other over a mixed oceanic and continental path,
are designed. The significant features of these models
are correlated with the body wave observations and with the
hypothesized thermal model and the mineralogical structure
in the mantle.</p>
<p>Part II:</p>
<p>A study of microseisms is made to determine some
of their statistical properties and to investigate the
feasibility of their use in determining the shallow
structures of the earth's crust by the phase velocity
method. It is found that the microseisms in the period
range of to 6 seconds arrive from several directions with
comparable strength and at the same time. There are occasional
short intervals of 10 - 40 seconds during which microseisms
are mostly unidirectional. It is also found that
these relatively short period microseisms are not stationary
in the wide sense over time intervals longer than 5 or 10
minutes.</p>
<p>The phase velocities of microseisms recorded with an
array of 8 instruments are measured In four different
locations. The velocities, although scattered, are found
to be in agreement with the theoretical dispersion curve
for the fundamental Rayleigh mode, computed using the
available seismic velocity information. An error analysis
is made and the confidence limits are placed within ±20
percent of the measured velocities.</p>https://thesis.library.caltech.edu/id/eprint/7269A Geophysical Study of the Salton Trough of Southern California
https://resolver.caltech.edu/CaltechETD:etd-10142002-105706
Authors: Biehler, Shawn
Year: 1964
DOI: 10.7907/ZZ33-6E45
<p>More than 2300 gravity observations were made in the northern end of the Salton trough, including an underwater gravity survey of the Salton Sea. 400 gravity observations by Kovach are used to extend the gravity map southward and 700 gravity observations from oil companies and Woollard are used for part of the regional control. A complete Bouguer anomaly map of the California portion of the Salton trough area shows that the general trend of the isogal contours is parallel to the over-all northwest trend of the tectonic pattern. The contours northeast of the Coachella Valley trend east parallel to the Transverse Range structure. The Coachella Valley and Borrego sink are associated with gravity lows, the Salton volcanic domes with a gravity maximum, and the Peninsular Ranges with a gravity minimum. The anomalous mass of the Salton volcanic domes is 6 to 7 km deep with a radius of 3.5 to 4.5 km based on the "half-width" interpretation of a sphere. Due to uncertainties arising from contemporaneous metamorphism of the sediments and the ambiguity in the regional gravity field a detailed interpretation was not attempted.</p>
<p>All of the major fault zones are associated with small gravity lows. A series of these small lows southeast along the projected trace of the Banning-Mission Creek fault may indicate continuation of faulting toward Yuma, Arizona. The steep gravity gradient across this fault in the Coachella Valley can be explained by a steep contact between crystalline rock and sediments which exceed 4 km thickness in the Indio-Mecca area.</p>
<p>Seismic refraction profiles were established at Thousand Palms, Truckhaven, Frink, and Westmorland. These give depths to basement of 4350, 5540, 7340, and 18,300 ft respectively. The Westmorland profile establishes the depth to basement near the center of the trough.</p>
<p>Regional gravity studies indicate that much of the gravity low over the Peninsular Ranges can be explained by a thickening of the crust from 29 to 33 km. The Imperial Valley, with over 5.5 km of sediments, is anomalously associated with a broad gravity high. This is interpreted in terms of a thinning crust under the valley possibly to a depth of 21 km, relative to 29 km at San Diego. The crustal structure of the Imperial Valley is probably the northward continuation of the structure of the Gulf of California and may represent the initial stages of an alteration from continental to oceanic type section by rifting and northwest movement of the Baja California peninsula and western California relative to the stable area northeast of the San Andreas fault system.</p>
https://thesis.library.caltech.edu/id/eprint/4077Part I - The radiation of elastic waves from a spherical cavity in a half space. Part II - Precision determination of focal depths and epicenters of earthquakes.
https://resolver.caltech.edu/CaltechTHESIS:03202015-145559091
Authors: Cisternas, Armando
Year: 1965
DOI: 10.7907/K750-5J16
<p>Part I: The dynamic response of an elastic half space to an explosion in a buried spherical cavity is investigated by two methods. The first is implicit, and the final expressions for the displacements at the free surface are given as a series of spherical wave functions whose coefficients are solutions of an infinite set of linear equations. The second method is based on Schwarz's technique to solve boundary value problems, and leads to an iterative solution, starting with the known expression for the point source in a half space as first term. The iterative series is transformed into a system of two integral equations, and into an equivalent set of linear equations. In this way, a dual interpretation of the physical phenomena is achieved. The systems are treated numerically and the Rayleigh wave part of the displacements is given in the frequency domain. Several comparisons with simpler cases are analyzed to show the effect of the cavity radius-depth ratio on the spectra of the displacements.</p>
<p>Part II: A high speed, large capacity, hypocenter location program has been written for an IBM 7094 computer. Important modifications to the standard method of least squares have been incorporated in it. Among them are a new way to obtain the depth of shocks from the normal equations, and the computation of variable travel times for the local shocks in order to account automatically for crustal variations. The multiregional travel times, largely based upon the investigations of the United States Geological
Survey, are confronted with actual traverses to test their validity.</p>
<p>It is shown that several crustal phases provide control enough to obtain good solutions in depth for nuclear explosions, though not all the recording stations are in the region where crustal corrections are considered. The use of the European travel times, to locate the French nuclear explosion of May 1962 in the Sahara, proved to be more adequate than previous work.</p>
<p>A simpler program, with manual crustal corrections, is used to process the Kern County series of aftershocks, and a clearer picture of tectonic mechanism of the White Wolf fault is obtained.</p>
<p>Shocks in the California region are processed automatically and statistical frequency-depth and energy depth curves are discussed in relation to the tectonics of the area.</p>
https://thesis.library.caltech.edu/id/eprint/8799Elastodynamic source theory
https://resolver.caltech.edu/CaltechETD:etd-01102003-112222
Authors: Archambeau, Charles B.
Year: 1965
DOI: 10.7907/A3XS-PS89
The mathematical formulation and evaluation of the radiation field for general elastodynamic sources is given and applications of the theory to the description of source fields of geophysical interest are treated. The study was primarily undertaken to provide a theoretical basis for estimating the properties of the tectonic stress field and parameters of rupture phenomenon in the earth through observations of the radiation field from earthquakes and other tectonic sources.
Thus the description of the tectonic source is particularly emphasized, both as to its physical origins and with respect to the radiation field to be expected from it. The mathematical description of the tectonic source field is achieved in terms of an elastic relaxation theory of radiation which corresponds to a generalized initial value problem involving the initial prestress field. As a consequence, the radiation field is obtained in terms of the rupture expansion rate (velocity of rupture), the rupture dimensions and orientation and the magnitude and orientation of the initial stress field. Inertial conditions are inherent in the relaxation theory so that the time dependence of the field is automatically specified. Careful attention is given to causality relationships so that the resulting field expressions contain the complicated space-time relationships associated with a tectonic source field. Energy and equilibrium relations are considered and expressions are obtained for the estimated energy release and the final static field in terms of the source parameters.
Detailed properties of the radiation field are given in the form of source field amplitude and phase spectra. Spatial radiation patterns are obtained showing the direction properties as functions of frequency, prestress and other source parameters. Similar results are given for shock induced rupture under prestress conditions, along with estimates of tectonic energy release.
It is concluded that the theoretical predictions for the properties of the radiation field from a spontaneous rupture source are in general agreement with the actual observations of the field from such a source, but that accurate estimates of the prestress and rupture parameters require a more complete coverage and analysis of the field than is usually the case. It is concluded from a preliminary analysis of the Ranier nuclear explosion that tectonic energy release did occur and that the anomalous radiation observed would correspond to a prestress shear field of the order of 20 bars.
The most likely mechanism of rupture at depth in the earth is considered to be unstable creep phenomenon resulting in phase change (melting) and the rupture source models adopted are not inconsistent with this hypothesis.
https://thesis.library.caltech.edu/id/eprint/98Body-Wave and Earthquake Source Studies
https://resolver.caltech.edu/CaltechTHESIS:09282017-160405428
Authors: Teng, Ta-Liang
Year: 1966
DOI: 10.7907/9VPH-AN84
<p>The present work concerns a study on the radiation and propagation
of seismic body waves. Based on a reformulated seismic ray
theory and supplemented by the results of several associated
boundary value problems, a method of body wave equalization is
described which enables the extrapolation of body-wave fields from
one point to another.</p>
<p>Applications of the above method to studies of earthquake
source mechanism and earth's structure, specifically its anelasticity,
are presented. The findings for two deep-focus earthquakes can be
summarized by: (1) a displacement dislocation source, or an
equivalent double couple, can generally explain the observed radiation
fields, (2) the source time functions can be explained by a
build-up step (1 - e <sup>-t/τ</sup>)H(t), and τ appears to be longer for larger
earthquakes, (3) the total energy calculated from equalized spectrums
is: for the Banda Sea earthquake (M = 6-1/4 - 6-3/4), E = 1.01x10<sup>22</sup>
ergs; and for the Brazil earthquake (M = 6-3/4 - 7), E = 2.56x10<sup>23</sup>
ergs.</p>
<p>From the spectral ratios pP/P and P/P, it is found (1) that
the upper 430 km of the mantle has an average Q<sub>ɑ</sub> = 105, (2) that Q<sub>ɑ</sub>
increases very slowly until depth of about 1000 km, and (3) that
Q<sub>ɑ</sub> rises rapidly beyond a depth of 1000 km, remains a high value
in the lower mantle and drops sharply toward the core-mantle
boundary.</p>https://thesis.library.caltech.edu/id/eprint/10467