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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenSat, 13 Apr 2024 00:50:36 +0000Body-Wave and Earthquake Source Studies
https://resolver.caltech.edu/CaltechTHESIS:09282017-160405428
Authors: {'items': [{'id': 'Teng-Ta-Liang', 'name': {'family': 'Teng', 'given': 'Ta-Liang'}, 'show_email': 'NO'}]}
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/10467Part I. Lower Limit of the Total Energy of Earthquakes and Partitioning of Energy Among Seismic Waves. Part II. Reflected Waves and Crustal Structures
https://resolver.caltech.edu/CaltechTHESIS:11042016-160516864
Authors: {'items': [{'id': 'Wu-Francis-Taming', 'name': {'family': 'Wu', 'given': 'Francis Taming'}}]}
Year: 1966
DOI: 10.7907/4VK8-6245
<p>Part I:</p>
<p>The basic formulae for estimating the energy in the seismic waves are derived. The formulae take into account the radiation pattern of the source, the compensation for the non-elastic absorption of the waves, the velocity-density structure of the earth, the effects of the crustal structure under the receiver and the response of the recording instruments. Operations are performed in the frequency domain.</p>
<p>Estimation of the seismic energy of an earthquake is closely related to the determination of the source mechanism and the radiation pattern of the source. We have determined the surface wave radiation pattern of a shallow shock and the P wave radiation pattern of an intermediate shock to show the correspondence between the fault-plane solutions and the fault mechanisms derived from radiation pattern.</p>
<p>We have obtained the energies of the two earthquakes mentioned above as well as 7 other earthquakes with known fault-plane solutions and/or radiation patterns. The "total" seismic energies for these earthquakes (magnitudes between 6 1/2 and 7 1/2) using the present procedures are at least an order of magnitude higher than those arrived at from the current magnitude-energy formula. The S wave energies are approximately an order higher than that of the P waves.
The surface wave energies for the shallow shocks are three orders of magnitude less than the body wave energies. Thus, the S wave seems to be the main seismic wave energy carrier.</p>
<p>Energies in the lower order spheroidal oscillations (ℓ = 2, 15) for the 1964 Alaskan earthquake have been calculated from Isabella strain data and Berkeley ultra-long period pendulum seismometer data. The sum of the energies is 10<sup>23</sup> ergs.</p>
<p>Part II:</p>
<p>Haskell's formulation for reflection of the body waves at the
base of a solid crust is extended to include overlying liquid layers.
Normalized displacement and the phase shift at the base of the crust
as a function of angle of incidence and frequency are calculated for
two continental models and an oceanic model. Complex reflection
coefficients are inverse-Fourier transformed numerically to the
time domain to show the change of pulse shape upon reflection. These
time traces show that the water layer of the oceanic model causes
the main difference between continental and oceanic reflections.
Sample seismograms from a deep shock were compared to the theoretical
records; they are found to be consistent. PP waves from a deep
earthquake recorded at Tonto Forest Seismic Array were processed to
display the details of an oceanic PP wave.</p>
https://thesis.library.caltech.edu/id/eprint/9976Measurements of Mantle Velocities of P Waves with a Large Array
https://resolver.caltech.edu/CaltechTHESIS:03252016-135744669
Authors: {'items': [{'id': 'Johnson-Lane-Richard', 'name': {'family': 'Johnson', 'given': 'Lane Richard'}, 'show_email': 'NO'}]}
Year: 1966
DOI: 10.7907/D44Y-6K65
A large array has been used to investigate the P-wave
velocity structure of the lower mantle. Linear array processing
methods are reviewed and a method of nonlinear processing is
presented. Phase velocities, travel times, and relative amplitudes
of P waves have been measured with the large array at the Tonto
Forest Seismological Observatory in Arizona for 125 earthquakes
in the distance range of 30 to 100 degrees. Various models are
assumed for the upper 771 km of the mantle and the Wiechert-Herglotz
method applied to the phase velocity data to obtain a velocity
depth structure for the lower mantle. The phase velocity data
indicates the presence of a second-order discontinuity at a depth of
840 km, another at 1150 km, and less pronounced discontinuities at
1320, 1700 and 1950 km. Phase velocities beyond 85 degrees are
interpreted in terms of a triplication of the phase velocity curve, and
this results in a zone of almost constant velocity between depths of
2670 and 2800 km. Because of the uncertainty in the upper mantle
assumptions, a final model cannot be proposed, but it appears that
the lower mantle is more complicated than the standard models and
there is good evidence for second-order discontinuities below a depth
of 1000 km. A tentative lower bound of 2881 km can be placed on the
depth to the core. The importance of checking the calculated velocity
structure against independently measured travel times is pointed out.
Comparisons are also made with observed PcP times and the agreement
is good. The method of using measured values of the rate of
change of amplitude with distances shows promising results.https://thesis.library.caltech.edu/id/eprint/9634A Comparison of Observed Permanent Tilts and Strains Due to Earthquakes with those Calculated from Displaced Dislocations in Elastic Earth Models
https://resolver.caltech.edu/CaltechTHESIS:12142017-084449592
Authors: {'items': [{'id': 'McGinley-John-Robert-Jr.', 'name': {'family': 'McGinley', 'given': 'John Robert, Jr.'}}]}
Year: 1969
DOI: 10.7907/38KM-RT32
<p>Theoretical solutions are derived for a model of faulting in
elastic media and for the effect of lateral inhomogeneities on the
earth's free oscillations. The solutions are used in a study of
permanent tilts and strains observed a few hundred kilometers from
earthquakes.</p>
<p>It is shown that the static deformational field due to a
suitably chosen dislocation fault model is the same as that due
to introduction of a stress free surface into a prestressed medium.
Formal mathematical solutions are derived for the static deformational
fields due to dislocation fault models in a homogeneous elastic
sphere and a layered elastic half-space. For the layered half-space
explicit solutions are given in terms of integral transforms for the
surface displacements, tilts, and strains due to a slip fault
and a dilatational source. A perturbation procedure is developed
for calculating the effects of lateral changes in elastic constants
on the earth's free oscillations. The procedure is applied to obtain
expressions for the effect of some simple inhomogeneity geometries
on the torsional free oscillations.</p>
<p>Numerical evaluation of the static, elastic, dislocation
solutions shows that the observed tilts and strains are large compared
with theoretical predictions and sometimes show the opposite sign.
The hypothesis that a weak layer in the lower crust or upper mantle
can explain the observations is investigated. It is found that a
very weak layer, approaching a liquid-like behavior, does help to
explain the observations. The compatibility of a very weak layer
with observed surface wave dispersion is tested using the results
of the perturbation calculations for the torsional free oscillations.
A very weak layer is determined as compatible with observed surface
wave dispersion only if very thin and with some frequency dependence
in its elastic properties. It is concluded that although a regional
weak layer in the lower crust or upper mantle can help to explain
the observed tilts and strains, other regional or local structural
effects or source complications must also be important.</p>
https://thesis.library.caltech.edu/id/eprint/10609Part I. The Effect of Temperature and Partial Melting on Velocity and Attenuation in a Simple Binary System. Part II. Effect of Temperature and Pressure on Elastic Properties of Polycrystalline and Single Crystal MgO
https://resolver.caltech.edu/CaltechTHESIS:04022018-124017475
Authors: {'items': [{'id': 'Spetzler-Hartmut-A-W', 'name': {'family': 'Spetzler', 'given': 'Hartmut A. W.'}, 'show_email': 'NO'}]}
Year: 1969
DOI: 10.7907/CZFN-2N63
<p>A possible explanation of the low-velocity, low-Q zone in the upper mantle is partial melting, but laboratory data has not been available to test this conjecture. As a first step in obtaining an idea of the role that partial melting plays in affecting seismic variables, the longitudinal and shear velocities and attenuations were measured in a simple binary system that is completely solid at low temperatures and involves 17% melt at the highest experimental
temperature. The system investigated was NaCl•H<sub>2</sub>O. At temperatures below the eutectic the material is a solid mixture of H<sub>2</sub>O (ice)
and NaCl•H<sub>2</sub>O. At higher temperatures the system is a mixture of ice and NaCl brine. In the completely solid regime the velocities and Q change slowly with temperature. There is a marked drop in the velocities and Q at the onset of melting. For ice containing 1% NaCl, the longitudinal and shear velocities change discontinuously at this temperature by 9.5 and 13.5%, respectively. The corresponding Q's drop by 48 and 37%. The melt content of the mixture at temperatures on the warm side of the eutectic for this composition is about 3.3%. The abrupt drop in velocities at the onset of partial melting is about three times as much for the ice containing 2% NaCl;
for this composition, the longitudinal and shear Q's drop at the eutectic temperature by 71 and 73%, respectively. If these results can be used as a guide in understanding the effect of melting on seismic properties in the mantle, we should expect sharp discontinuities in velocity and Q where the geotherm crosses the solidus. The phenomena associated with the onset of melting are more dramatic than those associated with further melting.</p>
<p> The theory for randomly oriented fluid-filled penny-shaped cracks satisfactorily explains the velocity data. The anomalous behavior on the warm side of the eutectic temperature is attributed to thermochemical effects associated with interaction of the sound wave with the phase equilibria. This phenomenon is not observed
when supercooling is possible.</p>
<p>A laboratory has been constructed to measure the elastic
properties of solids to 12 kbar and 1200°K by ultrasonic interferometry techniques. The elastic constants and their temperature and pressure derivatives have been measured to high temperature and pressure for both single crystal and polycrystalline MgO. A pseudoresonance technique involving pulse superposition and a lapped buffer rod without bond were used in order to obtain the necessary precision.
The results for the single crystal are tabulated below.</p>
https://thesis.library.caltech.edu/id/eprint/10785A Comparision of Observed Permanent Titles and Strains Due to Earthquakes with Those Calculated from Displaced Dislocations in Elastic Earth Models
http://resolver.caltech.edu/CaltechTHESIS:03242017-153808607
Authors: {'items': [{'id': 'McGinley-John-Robert', 'name': {'family': 'McGinley', 'given': 'John Robert'}, 'show_email': 'NO'}]}
Year: 1969
DOI: 10.7907/9h53-jq64
<p>Theoretical solutions are derived for a model of faulting in
elastic media and for the effect of lateral inhomogeneities on the
earth's free oscillations. The solutions are used in a study of
permanent tilts and strains observed a few hundred kilometers from
earthquakes.</p>
<p>It is shown that the static deformational field due to a
suitably chosen dislocation fault model is the same as that due
to introduction of a stress free surface into a prestressed medium.
Formal mathematical solutions are derived for the static deformational
fields due to dislocation fault models in a homogeneous elastic
sphere and a layered elastic half-space. For the layered half-space
explicit solutions are given in terms of integral transforms for the
surface displacements, tilts, and strains due to a slip fault
and a dilatational source. A perturbation procedure is developed
for calculating the effects of lateral changes in elastic constants
on the earth's free oscillations. The procedure is applied to obtain
expressions for the effect of some simple inhomogeneity geometries
on the torsional free oscillations.</p>
<p>Numerical evaluation of the static, elastic, dislocation
solutions shows that the observed tilts and strains are large compared
with theoretical predictions and sometimes show the opposite sign.
The hypothesis that a weak layer in the lower crust or upper mantle
can explain the observations is investigated. It is found that a
very weak layer, approaching a liquid-like behavior, does help to
explain the observations. The compatibility of a very weak layer
with observed surface wave dispersion is tested using the results
of the perturbation calculations for the torsional free oscillations.
A very weak layer is determined as compatible with observed surface
wave dispersion only if very thin and with some frequency dependence
in its elastic properties. It is concluded that although a regional
weak layer in the lower crust or upper mantle can help to explain
the observed tilts and strains, other regional or local structural
effects or source complications must also be important.</p>
https://thesis.library.caltech.edu/id/eprint/10106Part 1. Dynamic Response of Phase Boundaries in the Earth to Surface Loading. Part 2. Pleistocene Glaciation and the Viscosity of the Lower Mantle
https://resolver.caltech.edu/CaltechTHESIS:04052018-084913740
Authors: {'items': [{'id': "O'Connell-Richard-John", 'name': {'family': "O'Connell", 'given': 'Richard John'}, 'show_email': 'NO'}]}
Year: 1969
DOI: 10.7907/3JGM-5Q68
<p>Part 1. Analytic approximate solutions have been found for the response of a phase change to pressure loading. These solutions allow the behavior of the system to be analyzed in terms of simple parameters of the system. Different characteristic types of behavior are shown to obtain for short times and long times, and criteria for defining these characteristic time scales are given in
terms of known parameters. The distribution of heat sources and convective heat transport are shown to generally have only minor influence on the solution, and may be neglected in many cases. The important parameters are the latent heat of the phase change, and the difference between the Clapeyron slope and the temperature gradient at the phase boundary; in addition the long term behavior is governed by the boundary conditions at the surface and at depth,
and the relative positions of the surface, the phase boundary, and the lower boundary. The effect of thermal blanketing from sediments is included in the solution, and it depends primarily on the depth of the phase boundary and the average temperature gradient in the sediments. The effect of isostasy in conjunction with a phase change is shown to be of major importance; the existence of instabilities where the water depth increases with sedimentation are demonstrated. These solutions allow the history of a sedimentary basin to be calculated, and characterized in terms of certain types of behavior. The existence of oscillatory behavior is demonstrated, where repeated cycles of sedimentation and erosion take place.
These oscillations can either decay or grow in amplitude, and expressions are given for their frequency and damping or growth constants. A phase change mechanism can account for thicknesses of sediments which exceed the depth of the basin in which they were deposited by a factor of twenty or more. These solutions allow the discussion of the geological implications of phase changes in a quantitative manner. The consequences of a phase change can be
accurately calculated. This will allow the more complete investigation of the role of phase changes in geologic processes.</p>
<p>Part 2. The non-tidal acceleration of the earth, revealed by astronomical observations and records of eclipses in antiquity, is attributed to the change in the earth's moment of inertia resulting from isostatic response to the most recent deglaciation and rise in sea level. The isostatic response time for a spherical harmonic deformation
of degree two is calculated on this basis to be either ~2000
years or ~100,000 years. A correlation of the geopotential with the potential that would have existed following de glaciation indicates that any large scale anomalies resulting from deglaciation have already decayed. This rules out the 100,000 relaxation time; thus the relaxation time of the earth is ~2000 years for degree two. Calculations of the relaxation time spectrum of a layered, gravitating spherical viscous earth model indicates that a model with a uniform mantle viscosity of ~10^(22) poise, except for fine structure in the upper few hundred kilometers, can satisfy the relaxation time of 3000 years for degree two as well as the relaxation time of ~4000
years for degree twenty which results from studies of uplift in Fennoscandia. A zone of high viscosity in the lower 800 km. of the mantle has a significant effect on the degree two relaxation time. This rules out any substantial increase in viscosity in the lower mantle. The calculated viscosity permits rapid polar wandering and convection in the lower mantle.</p>
https://thesis.library.caltech.edu/id/eprint/10792Regional Variations in Upper Mantle Structure Beneath North America
https://resolver.caltech.edu/CaltechTHESIS:09242015-115554328
Authors: {'items': [{'id': 'Julian-Bruce-Rene', 'name': {'family': 'Julian', 'given': 'Bruce Rene'}, 'show_email': 'NO'}]}
Year: 1970
DOI: 10.7907/PT11-B635
<p>Several types of seismological data, including surface wave
group and phase velocities, travel times from large explosions, and
teleseismic travel time anomalies, have indicated that there are
significant regional variations in the upper few hundred kilometers
of the mantle beneath continental areas. Body wave travel times and
amplitudes from large chemical and nuclear explosions are used in
this study to delineate the details of these variations beneath
North America.</p>
<p>As a preliminary step in this study, theoretical P wave travel
times, apparent velocities, and amplitudes have been calculated
for a number of proposed upper mantle models, those of Gutenberg,
Jeffreys, Lehman, and Lukk and Nersesov. These quantities have been
calculated for both P and S waves for model CIT11GB, which is derived
from surface wave dispersion data. First arrival times for all the
models except that of Lukk and Nersesov are in close agreement,
but the travel time curves for later arrivals are both qualitatively
and quantitatively very different. For model CIT11GB, there are two
large, overlapping regions of triplication of the travel time curve,
produced by regions of rapid velocity increase near depths of 400 and
600 km. Throughout the distance range from 10 to 40 degrees, the
later arrivals produced by these discontinuities have larger
amplitudes than the first arrivals. The amplitudes of body waves,
in fact, are extremely sensitive to small variations in the velocity
structure, and provide a powerful tool for studying structural
details.</p>
<p>Most of eastern North America, including the Canadian Shield
has a Pn velocity of about 8.1 km/sec, with a nearly abrupt increase
in compressional velocity by ~ 0.3 km/sec near at a depth varying
regionally between 60 and 90 km. Variations in the structure of
this part of the mantle are significant even within the Canadian
Shield. The low-velocity zone is a minor feature in eastern
North America and is subject to pronounced regional variations.
It is 30 to 50 km thick, and occurs somewhere in the depth range
from 80 to 160 km. The velocity decrease is less than 0.2 km/sec.</p>
<p>Consideration of the absolute amplitudes indicates that the
attenuation due to anelasticity is negligible for 2 hz waves in the
upper 200 km along the southeastern and southwestern margins of
the Canadian Shield. For compressional waves the average Q for
this region is > 3000. The amplitudes also indicate that the
velocity gradient is at least 2 x 10<sup>-3</sup> both above and below the
low-velocity zone, implying that the temperature gradient is < 4.8°C/km
if the regions are chemically homogeneous.</p>
<p>In western North America, the low-velocity zone is a pronounced
feature, extending to the base of the crust and having minimum
velocities of 7.7 to 7.8 km/sec. Beneath the Colorado Plateau and
Southern Rocky Mountains provinces, there is a rapid velocity increase
of about 0.3 km/sec, similar to that observed in eastern North
America, but near a depth of 100 km.</p>
<p>Complicated travel time curves observed on profiles with
stations in both eastern and western North America can be explained
in detail by a model taking into account the lateral variations in
the structure of the low-velocity zone. These variations involve
primarily the velocity within the zone and the depth to the top
of the zone; the depth to the bottom is, for both regions, between
140 and 160 km.</p>
<p>The depth to the transition zone near 400 km also varies
regionally, by about 30-40 km. These differences imply variations
of 250 °C in the temperature or 6 % in the iron content of the
mantle, if the phase transformation of olivine to the spinel
structure is assumed responsible. The structural variations at
this depth are not correlated with those at shallower depths, and
follow no obvious simple pattern.</p>
<p>The computer programs used in this study are described in
the Appendices. The program TTINV (Appendix IV) fits spherically
symmetric earth models to observed travel time data. The method,
described in Appendix III, resembles conventional least-square
fitting, using partial derivatives of the travel time with respect
to the model parameters to perturb an initial model. The usual
ill-conditioned nature of least-squares techniques is avoided by
a technique which minimizes both the travel time residuals and the
model perturbations.</p>
<p>Spherically symmetric earth models, however, have been found
inadequate to explain most of the observed travel times in this
study. TVT4, a computer program that performs ray theory calculations
for a laterally inhomogeneous earth model, is described in Appendix II.
Appendix I gives a derivation of seismic ray theory for an arbitrarily
inhomogeneous earth model.</p>
https://thesis.library.caltech.edu/id/eprint/9173Seismological applications of lattice theory
https://resolver.caltech.edu/CaltechTHESIS:12192012-162926776
Authors: {'items': [{'id': 'Sammis-C-G', 'name': {'family': 'Sammis', 'given': 'Charles George'}, 'show_email': 'NO'}]}
Year: 1971
DOI: 10.7907/S6B1-6N30
<p>Lattice models based upon empirical two-body potential functions
are used to predict the elastic constants of “mantle-candidate” minerals
at high pressures for direct comparison with seismic velocity profiles.
The method of long waves, originally formulate d by Born and his coworkers,
has been applied to solids in the rock salt, spinel, and rutile
structures. Calculations for NaCl (rock salt), MgO (rock salt), Al_2MgO_4
(spinel), and TiO_2 (rutile) are compared with recent high-precision
ultrasonic data. The effect of van der Waals forces and second-neighbor
anion-anion interactions is shown to be small. The NaCl and MgO data
are best fit with an exponential cation-anion repulsive potential. The
elastic constants of MgO cannot be well fit unless the ionicity (valence
product) is lowered to 0.7 of its full ionic value. For NaCl this is not
required. The shear instability (C_(44) = 0) is predicted for both NaCl and
MgO, but the exact pressure is sensitive to the details of the potential.</p>
<p>Using the Mg-O two-body potential found for periclase, Al_2MgO_4
spinel was investigated using only two pieces of input datum, K and ρ.
Although the predicted elastic constants were in good agreement with the
data, the pressure derivatives were not. The discrepancy is caused by
a large contribution from the internal deformations which occur in all
non-centro symmetric structures. The same result was found for TiO_2. A
relaxation of the rigid-ion and central-force approximations may correct
this discrepancy.</p>
<p>Using the Mg-O bond parameters found for periclase and the
Si-Q bond parameters found from K and ρ of stishovite, the elastic
properties of the high-pressure polymorph δ–Mg_2SiO_4 spinel were
predicted. The predicted equilibrium density was in agreement with
previous experimental extrapolations; the predicted μ parameter was
in agreement with prior estimates based on bond-length arguments, and
the predicted bulk modulus was in agreement with prior systematics
estimates. However, the internal deformation contribution again
dominated the pressure derivatives and caused both the predicted V_p
and V_s to be lower than the corresponding seismic velocities in the
"spinel region" of the mantle. A comparison of MgO (rock salt) and
SiO_2 (stishovite) with the seismic profiles for the "post-spinel" lower
mantle shows a discrepancy in both absolute value and gradient. Unlike
the silicate spinel, this is not obviously caused by the internal deformations.
The lattice models predict that both TiO_2 and stishovite will
become unstable in shear (1/2 (C_(11) – C_(12) = 0) at high pressure.</p>
<p>Other methods of using laboratory data to interpret seismic
profiles are reviewed. Birch's formulation of isotropic finite strain
theory is corrected and used to test the homogeneity and adiabaticity
of the lower mantle of recent earth-inversion models. Systematics are
shown to be insufficient to treat the shear properties. Although lattice
models are limited by empirical approximations to the complex bonding
forces, the empiricism is on a more basic level than that of velocity
density systematics previously used to interpret seismic profiles. By
using lattice models, one gains the natural dependence of both the compressional
and shear properties on the crystal structure.</p>
https://thesis.library.caltech.edu/id/eprint/7349Estimation of the radial variation of seismic velocities and density in the earth
https://resolver.caltech.edu/CaltechTHESIS:08292011-141658832
Authors: {'items': [{'id': 'Jordan-T-H', 'name': {'family': 'Jordan', 'given': 'Thomas Hillman'}, 'show_email': 'NO'}]}
Year: 1973
DOI: 10.7907/K0B1-PW97
An inversion procedure is developed to estimate the radial
variations of compressional velocity, shear velocity, and density in the Earth. The radial distributions are defined as spherically symmetric averages of the actual distributions in the laterally heterogeneous Earth, and the nature of the averaging implied by averaging
certain sets of eigenperiod and travel-time data is examined. For travel-time data, the spherical averaging yields the Terrestrial Monopole if the data sample a distribution derived from a uniform distribution of sources and receivers. Since this is difficult to obtain for absolute times, differential travel times are used to
constrain the velocities. It is shown that the bias inherent in available sets of differential travel-time data is considerably less than that in equivalent sets of absolute travel-time data, if the phase combination is suitably chosen. Observations are presented for
the phase combinations PcP-P, ScS-S, P'(AB)-P'(DF), and P'(BC)-P'(DF).
The inversion algorithm developed is based on a linear approximation to the perturbation equations and is shown to provide a stable method for estimating the radial distributions of velocities and density from a finite number of inaccurate data. The linear inversion
theory presented is complete; it allows one to estimate the resolving power of the data and the resolvability of specified features in the model.
Three estimates of the radial distributions are derived using an extensive set of eigenperiod and travel-time data. One model, designated model B1, fits 127 of the 177 eigenperiods of the Dziewonski-Gilbert set within their formal 95% confidence intervals. This model satisfies extensive sets of auxillary data as well.
It is shown from resolving power calculations that little information is lost by using differential travel times in lieu of absolute times. It is demonstrated that the nature of the averaging in the estimation procedure for given sets of gross Earth data can be improved by judicious specification of the norm on the space of models.
https://thesis.library.caltech.edu/id/eprint/6629Part I. A study of the velocity structure of the earth by the use of core phases. Part II. The 1971 San Fernando earthquake series focal mechanisms and tectonics
https://resolver.caltech.edu/CaltechTHESIS:02202014-135247734
Authors: {'items': [{'id': 'Whitcomb-J-H', 'name': {'family': 'Whitcomb', 'given': 'James Hall'}}]}
Year: 1973
DOI: 10.7907/JDKQ-2Z91
<p>The initial objective of Part I was to determine the nature of
upper mantle discontinuities, the average velocities through the
mantle, and differences between mantle structure under continents
and oceans by the use of P'dP', the seismic core phase P'P' (PKPPKP)
that reflects at depth d in the mantle. In order to accomplish this,
it was found necessary to also investigate core phases themselves
and their inferences on core structure. P'dP' at both single stations
and at the LASA array in Montana indicates that the following zones
are candidates for discontinuities with varying degrees of confidence:
800-950 km, weak; 630-670 km, strongest; 500-600 km, strong but
interpretation in doubt; 350-415 km, fair; 280-300 km, strong, varying
in depth; 100-200 km, strong, varying in depth, may be the bottom of
the low-velocity zone. It is estimated that a single station cannot
easily discriminate between asymmetric P'P' and P'dP' for lead times
of about 30 sec from the main P'P' phase, but the LASA array reduces
this uncertainty range to less than 10 sec. The problems of scatter
of P'P' main-phase times, mainly due to asymmetric P'P', incorrect
identification of the branch, and lack of the proper velocity
structure at the velocity point, are avoided and the analysis shows
that one-way travel of P waves through oceanic mantle is delayed
by 0.65 to 0.95 sec relative to United States mid-continental
mantle. </p>
<p>A new P-wave velocity core model is constructed from observed
times, dt/dΔ's, and relative amplitudes of P'; the observed times of
SKS, SKKS, and PKiKP; and a new mantle-velocity determination by
Jordan and Anderson. The new core model is smooth except for a
discontinuity at the inner-core boundary determined to be at a
radius of 1215 km. Short-period amplitude data do not require the
inner core Q to be significantly lower than that of the outer core.
Several lines of evidence show that most, if not all, of the arrivals
preceding the DF branch of P' at distances shorter than 143° are
due to scattering as proposed by Haddon and not due to spherically
symmetric discontinuities just above the inner core as previously
believed. Calculation of the travel-time distribution of scattered
phases and comparison with published data show that the strongest
scattering takes place at or near the core-mantle boundary close to
the seismic station. </p>
<p>In Part II, the largest events in the San Fernando earthquake
series, initiated by the main shock at 14 00 41.8 GMT on February 9,
1971, were chosen for analysis from the first three months of
activity, 87 events in all. The initial rupture location coincides
with the lower, northernmost edge of the main north-dipping thrust
fault and the aftershock distribution. The best focal mechanism
fit to the main shock P-wave first motions constrains the fault
plane parameters to: strike, N 67° (± 6°) W; dip, 52° (± 3°) NE;
rake, 72° (67°-95°) left lateral. Focal mechanisms of the aftershocks
clearly outline a downstep of the western edge of the main thrust
fault surface along a northeast-trending flexure. Faulting on this
downstep is left-lateral strike-slip and dominates the strain release
of the aftershock series, which indicates that the downstep limited
the main event rupture on the west. The main thrust fault surface
dips at about 35° to the northeast at shallow depths and probably
steepens to 50° below a depth of 8 km. This steep dip at depth is a
characteristic of other thrust faults in the Transverse Ranges and
indicates the presence at depth of laterally-varying vertical
forces that are probably due to buckling or overriding that causes
some upward redirection of a dominant north-south horizontal
compression. Two sets of events exhibit normal dip-slip motion with
shallow hypocenters and correlate with areas of ground subsidence
deduced from gravity data. Several lines of evidence indicate that
a horizontal compressional stress in a north or north-northwest
direction was added to the stresses in the aftershock area 12 days
after the main shock. After this change, events were contained in
bursts along the downstep and sequencing within the bursts provides
evidence for an earthquake-triggering phenomenon that propagates
with speeds of 5 to 15 km/day. Seismicity before the San Fernando
series and the mapped structure of the area suggest that the downstep
of the main fault surface is not a localized discontinuity but is
part of a zone of weakness extending from Point Dume, near Malibu, to
Palmdale on the San Andreas fault. This zone is interpreted as a
decoupling boundary between crustal blocks that permits them to deform
separately in the prevalent crustal-shortening mode of the Transverse
Ranges region.</p>
https://thesis.library.caltech.edu/id/eprint/8090Part I: Temperature dependence of single crystal spinel (MgAl_2O_4) elastic constants from 293K to 423K measured by light-sound scattering in the Raman-Nath region. Part II: Effect of anelasticity on periods of earth's free oscillation (toroidal modes)
https://resolver.caltech.edu/CaltechTHESIS:01132011-114814151
Authors: {'items': [{'id': 'Liu-Hsi-Ping', 'name': {'family': 'Liu', 'given': 'Hsi-Ping'}, 'show_email': 'NO'}]}
Year: 1974
DOI: 10.7907/QYWT-AK53
<p>Part I:</p>
<p>The temperature dependence of single-crystal elastic constants of synthetic stoichiometric MgAl_2O_4 spinel has been measured by the light-sound scattering technique in the Raman-Nath region. The crystal is set into forced vibration by a single crystal LiNbO_3 transducer coupled to one crystal face. A He-Ne laser beam is diffracted by the stress-induced birefringence inside the crystal. The diffraction angle is determined from the distance of two spots exposed on a photographic plate by the first order diffracted beams as measured by a microdensitometer. The sound wavelength inside the crystal is then inferred from the laser diffraction angle. Combining the sound wavelength with the measured transducer driving frequency, the velocity inside the crystal is determined typically to a precision of 0.05%. In this method, the measurement of velocity is not dependent on either the determination of sample length or on phase shifts at sample-transducer interface. Velocities of four pure modes, L//[001], T//[001], L//[110], and T//[110] (P//[1^-_10]) are measured in the temperature range between 293K and 423K. A linear temperature dependence is fit to the data by a least square method. Values obtained at 25°C from this linear fit are V_p[001] = 8.869 ± 0.013 km/sec, (∂V/∂T)_p = -(3.14 ± 0.13) x 10^(-4)km/sec-K; V_s[001] = 6.5666 ± 0.0055 km/sec, (∂V/∂T)_p = -(1.47 ± 0.10) x 10^(-4)km/sec-K; V_p[110] = 10.199 ± 0.011 km/sec, (∂V/∂T)_p = -(3.20 ± 0.15) x 10^(-4)km/sec-K; V_s[110][P//[110]) = 4.2101 ± 0.0043 km/sec, (∂V/∂T)_p = -(2.07 ± 0.06) x 10^(-4)km/sec-K. The temperature dependence of the adiabatic elastic constants and bulk and shear (VRH average) moduli is computed using the density and literature value of thermal expansion coefficient. Values obtained are: C^s_(11) = 2814 ± 8 kb, (∂C^s_(11)/∂T)_p = -0.258 ± 0.018 kb/K; C^s_(12) = 1546 ± 9 kb, (∂C^s_(12)/∂T)_p = -0.107 ± 0.019 kb/K; C^s_(44) = 1543 ± 3 kb, (∂C^s_(44)/∂T)_p = -0.101 ± 0.010 kb/k; K_s = 1969 ± 6 kb, (∂K^s_/∂T)_p = -0.157 ± 0.014 kb/K; µ_(VRH) = 1080 ± 5 kb, (∂µ_(VRH)/∂T)_p = -0.094 ± 0.008 kb/K. A comparison with previous measurements by pulse superposition and ultrasonic interferometry methods is made. Disagreement, when present, is discussed in terms of the separate measuring techniques. An attempt has also been made to measure the pressure dependence of elastic constants of spinel with the same technique. It failed because of the large spurious diffraction introduced by the fluctuation in index of refraction of the pressure fluid. A method to eliminate this spurious effect is discussed. An optical interferometry method is devised to measure the pressure window distortion effect in the pressure dependence measurement. Finally, the present method with its possibility for further improvement is evaluated as a new method to measure temperature and pressure dependence of elastic constants. Other methods using light-sound scattering to measure sound velocities are also reviewed.</p>
<p>Part II:</p>
<p>It is known that the anelastic properties of the earth characterized
by a "Q" structure will affect the periods of free oscillation.
It is generally considered that the effect is negligible compared to the
other perturbing effects due to rotation, ellipticity, and lateral
inhomogeneities. Nevertheless, it is of some interest to investigate
the precise magnitude of this effect for the observed free oscillation
modes since it could provide us with another constraint in the determination
of the Q structure of the Earth. An application of perturbation
theory provides us with a good estimate of the magnitude of the
changes in the periods of an elastic model due to inclusion of anelastic
effects. Calculations based on currently accepted elastic and
anelastic models for the Earth show that the shift in period due to
anelasticity is at most 0.023 percent for the toroidal modes from
_oT_2 to o_T_(99) the maximum occurring near _oT_(60) This is smaller by a
factor of five than the present observational accuracy. Compared to
the other perturbing effects, the anelastic effect, when important, is
larger than the effect of ellipticity considered alone but smaller by
an order of magnitude when compared with ellipticity and rotational
effects coupled together or with the continent-ocean lateral inhomogeneity.
Since the frequency shift due to anelasticity is scaled by
(1/Q)^2, the anelastic effect can be within observational accuracy and
comparable to other perturbing effects for more extreme, yet acceptable,
Q models.</p>https://thesis.library.caltech.edu/id/eprint/6224I. CEDAR -- an approach to the computer automation of short-period local seismic networks. II. Seismotectonics of the Imperial Valley of southern California
https://resolver.caltech.edu/CaltechTHESIS:04232010-074317474
Authors: {'items': [{'id': 'Johnson-C-E', 'name': {'family': 'Johnson', 'given': 'Carl Edward'}, 'show_email': 'NO'}]}
Year: 1979
DOI: 10.7907/DBG9-3260
A real-time detection and recording system (CEDAR) is developed as a means of automating the acquisition and processing of data from short- period local networks. This system has been used for the past two years for the analysis of data from 150 stations in Southern California with an annual workload of about 7500 local events. Two minicomputers are used with one dedicated to the real-time detection and digital recording of local earthquakes while the other is used for timing, location, and data archiving based on interactive graphical techniques. The use of this system has substantially reduced the effort required for the routine analysis of local data. The discussion is kept at a general level so as to be useful to those setting up similar systems with somewhat different requirements. In support of the CEDAR system a magnitude scale, M_(CA), is developed that is particularly adapted to the needs of local digital seismic networks. The supporting algorithm is based on median absolute amplitudes of any on-scale portion of the post-S seismic coda. The use of a power law coda shape function in the form a(t) = a_ot^(-q) makes the proposed method directly commensurable with the already widely used and highly successful duration method. The MCA magnitude scale is predicated on the same short-term averages used by the event detection algorithm on the real- time system, permitting a direct stochastic analysis of the spatial magnitude thresholds of a particular configuration of the detection logic. Such an a priori evaluation of detection capability is necessary since detection failure results in considerable extraneous effort. The use of these techniques has permitted the compilation of a local earthquake catalog and attendant phase data base that are substantially more uniform and accurate than what is generally obtained using manual methods.
The nature of earthquake swarms in the Imperial Valley is investigated with the goal of placing specific constraints on the physical mechanisms governing their behavior. Within the Imperial Valley most earthquakes occur as swarms concentrated within a narrow, sharply bounded, spindle-shaped zone joining the northern terminus of the Imperial Fault with the southern end of the San Andreas Fault. Although over the past five years the seismicity within this zone, designated the Brawley Seismic Zone, is surprisingly uniform, on time scales of a few weeks activity is highly clustered in both space and time. Seismicity is not confined to a few "hot spots", as might be expected, but rather seems to move around, seldom if ever reactivating the site of a previous swarm. Seven sequences of swarms are analyzed in detail using a master event approach in order to provide some insight into supporting tectonic structures. It is generally observed that swarm sequences comprise discrete bursts of activity, each of which appears to "illuminate" a single planar fracture transverse to the major tectonic elements in the Imperial Valley such as the Imperial Fault and the Brawley Fault. Development of activity during a sequence of swarms generally begins with high clustered activity followed by continuous, progressive involvement of the transverse structures, and progressive but discontinuous development in the form of spatially and temporally isolated clusters along the major fault elements. Observed migration rates range from .5 km/hr to .5 km/day. The consistency observed with respect to the pattern of development of independent sequences strongly suggests that a deterministic, physical model can be obtained. One possible model is suggested that relates the swarms on transverse structures with propagating, episodic creep on the major transforms. In this model both the creep rate and the triggering of earthquake swarms is governed by perturbations of pore-pressure in a fluid-infiltrated elastic matrix.
https://thesis.library.caltech.edu/id/eprint/5740I. Great Earthquakes and Seismic Coupling at Subduction Zones. II. The Structure of the Lowermost Mantle Determined by Short Period P-Wave Amplitudes
https://resolver.caltech.edu/CaltechETD:etd-09062006-105439
Authors: {'items': [{'id': 'Ruff-Larry-John', 'name': {'family': 'Ruff', 'given': 'Larry John'}, 'show_email': 'NO'}]}
Year: 1982
DOI: 10.7907/YW3Y-AZ37
<p><u>Part I</u></p>
<p>Seismic coupling has been used as a qualitative measure of the "interaction" between the two plates at subduction zones. Kanamori (1971) introduced seismic coupling after noting that the characteristic size of earthquakes varies systematically for the northern Pacific subduction zones. Great earthquakes (M<sub>W</sub> > 8.5) occur in only a few subduction zones: notably the northern Pacific and South American subduction zones. A quantitative global comparison of many subduction zones reveals a strong correlation of earthquake size with two other subduction zone variables: age of the subducting lithosphere and convergence rate. The largest earthquakes occur in zones with young lithosphere and fast convergence rates, while zones with old lithosphere and slow rates are relatively aseismic for large earthquakes. Two other correlations are of interest; maximum depth of the continuous Benioff zone is correlated to lithosphere age, and horizontal length of the Benioff zone is correlated to convergence rate. The simplest explanation of these correlations is "preferred trajectory": the subducting slab descends into the mantle with the vertical and horizontal rates determined by the plate age and convergence rate respectively. The mechanism of preferred trajectory is also consistent with the obversation that back-arc spreading occurs behind subduction zones that are subducting old lithosphere at a slow rate.</p>
<p>The rupture process of a great earthquake indicates the distribution of weak and strong regions on the fault zone between the subducting and over-lying plates. The rupture process of three great earthquakes (1963 Kurile Islands, M<sub>W</sub> = 8.5; 1965 Rat Islands, M<sub>W</sub> = 8.7; 1964 Alaska, M<sub>W</sub> = 9.2) are studied by using WWSSN stations in the core shadow zone. The main result is that maximum earthquake size is determined by the asperity distribution on the fault plane (asperities are the strong regions that resist the motion between the two plates). The subduction zones with the largest earthquakes have very large asperities (the Alaskan earthquake is characterized by a giant asperity of length scale 150-200 km), while the zones with smaller earthquakes have small scattered asperities. This observation can be translated into a simple model of seismic coupling, where the horizontal compressive stress between the two plates is proportional to the ratio of the summed asperity area to the total area of the contact surface.</p>
<p>If asperity size determines earthquake size, and earthquake size is correlated to plate age and rate; then plate age and rate must be related to the asperity distribution. Plate age and rate can control asperity distribution directly by use of the horizontal compressive stress associated with the preferred trajectory. Indirect influences are many, including: oceanic plate topography and the amount of subducted sediments.</p>
<p>All subduction zones are apparently uncoupled below a depth of about 40 km, and the basalt to eclogite phase change in the down-going oceanic crust may be largely responsible. This phase change shouldstart at a depth of 30-35 km, and could at least partially uncouple the plates by superplastic deformation throughout the oceanic crust during the phase change.</p>
<p><u>Part II</u></p>
<p>The seismic velocities in the D" region (lowermost 200 km of the mantle) are recognized to be anomalously low, though the details of the velocity structure are not known. The details of D" are important, in particular whether a smooth velocity model is appropriate or not. A smooth decrease in the seismic velocities would be consistent with a thermal boundary layer at the base of the mantle. We have used the amplitudes of short period (T = 1 sec) P waves to investigate the internal structure of D". A short period amplitude data set is obtained by using underground nuclear events as sources and applying receiver corrections to the amplitudes. Receiver effects are largely responsible for the factor of ~ 8 scatter in the amplitudes of the North American WWSSN stations. Applying receiver corrections reduces the scatter to a factor of ~ 2, thereby providing a quantitatively useful amplitude profile into the core shadow. Using Soviet events and North American WWSSN statios, the D" layer beneath the north polar regio is well sampled. The core shadow (at T = 1 sec) begins sharply at a distance of Δ = 95.5 and the slope of the amplitude decay is well defined. Also, the amplitudes decrease slightly from Δ ~ 87 to Δ ~ 90, then increase to Δ = 95.5. Synthetic seismograms are used to test various earth models, with the important conclusion that the amplitudes from smooth D" models with a nearly constant velocity in D" decay too slowly in the shadow. This mismatch cannot be satisfactorily explained by random forward scattering or a thin low-Q layer within D". Anelastic calculations show that a thin low-Q layer in D" decreases the amplitudes gradually before the shadow, with little effect on the decay slope in the shadow. All of the features of the observed amplitude profile can be explained as the interference effects of a model that has a low velocity zone in the upper part of D" followed by a normal velocity gradient in the lower part of D". This type of model (POLAR series) also explains the scatter often observed in dT/dΔ beyond Δ ~ 90. The interference effects and required velocity changes in D" are small, and long period amplitudes will respond only to the averaged velocity gradient in D". The POLAR models imply a compositional and/or phase change at the top of D". Thus, the preferred seismological model does not allow the D" region to be interpreted as a single thermal boundary layer between the mantle and core.</p>
https://thesis.library.caltech.edu/id/eprint/3357The Energy Release in Earthquakes, and Subduction Zone Seismicity and Stress in Slabs
https://resolver.caltech.edu/CaltechTHESIS:10282019-161929138
Authors: {'items': [{'id': 'Vassiliou-Marios-Simou', 'name': {'family': 'Vassiliou', 'given': 'Marios Simou'}, 'show_email': 'NO'}]}
Year: 1983
DOI: 10.7907/yp4p-t246
<p>Part I</p>
<p>Earthquake energy calculations are generally made through an empirical application of the familiar Gutenberg-Richter energy-magnitude relationships. The precise physical significance of these relationships is somewhat uncertain. We make use here of the recent increases in knowledge about the earthquake source to place energy measurements on a sounder physical basis. For a simple trapezoidal far-field displacement source-time function with a ratio <i>x</i> of rise time to total duration <i>T<sub>0</sub></i>, the seismic energy <i>E</i> is proportional to 1/[<i>x</i>(1-<i>x</i>)<sup>2</sup>] <i>M<sup>2</sup><sub>0</sub></i>/<i>T<sup>3</sup><sub>0</sub></i>, where <i>M<sub>0</sub></i> is seismic moment. As long as <i>x</i> is greater than 0.1 or so, the effect of rise time is not important. The dynamic energies thus calculated for shallow events are in reasonable agreement with the estimate <i>E</i> ≈ (5 x 10<sup>-5</sup>)<i>M<sub>0</sub></i> based on elastostatic considerations. Deep events, despite their possibly different seismological character, yield dynamic energies which are compatible with a static prediction similar to that for shallow events. Studies of strong-motion velocity traces obtained near the sources of the 1971 San Fernando, 1966 Parkfield, and 1979 Imperial Valley earthquakes suggest that even in the distance range of 1-5 km., most of the radiated energy is below 1-2 Hz. in frequency. Far field energy determinations using long period WWSSN instruments are probably not in gross error despite their bandlimited nature. The strong motion record for the intermediate depth Bucharest earthquake of 1977 also suggests little teleseismic energy outside the pass-band of a long period WWSSN instrument.</p>
<p>Part II</p>
<p>The pattern of seismicity as a function of depth in the world, and the orientation of stress axes of deep and intermediate earthquakes, are explained using viscous fluid models of subducting slabs, with a barrier in the mantle at 670 km. 670 km is the depth of a seismic discontinuity, and also the depth below which earthquakes do not occur. The barrier in the models can be a viscosity increase of an order of magnitude or more, or a chemical discontinuity where vertical velocity is zero. Log <i>N</i> versus depth, where <i>N</i> is the number of earthquakes, shows (1) a linear decrease to about 250-300 km depth, (2) a minimum near that depth, and (3) an increase thereafter. Stress magnitude in a subducting slab versus depth, for a wide variety of models, shows the same pattern. Since there is some experimental evidence that <i>N</i> is proportional to <i>e<sup>kσ</sup></i>, where <i>k</i> is a constant and <i>σ</i> is the stress magnitude, the agreement is encouraging. In addition, the models predict down-dip compression in the slab at depths below 400 km. This has been observed in earlier studies of earthquake stress axes, and we have confirmed it via a survey of events occurring since 1977 which have been analyzed by moment tensor inversion. At intermediate depths, the models predict an approximate but not precise state of down-dip tension when the slab is dipping. The observations do not show an unambiguous state of down-dip tension at intermediate depths, but in the majority of regions the state of stress is decidedly closer to down-dip tension than it is to down-dip compression. Chemical discontinuities above 670 km, or phase transitions with an elevation of the boundary in the slab, predict, when incorporated into the models, stress peaks which are not mirrored in the profile of seismicity versus depth. Models with an asthenosphere and mesosphere of appropriate viscosity can not only explain the state of stress observed in double Benioff zones, but also yield stress magnitude profiles consistent with observed seismicity. Models where a nonlinear rheology is used are qualitatively consistent with the linear models.</p>https://thesis.library.caltech.edu/id/eprint/11869Investigations of Earthquakes and Other Seismic Sources in Regions of Volcanism
https://resolver.caltech.edu/CaltechTHESIS:10292023-222051513
Authors: {'items': [{'id': 'Eissler-Holly-Kathleen', 'name': {'family': 'Eissler', 'given': 'Holly Kathleen'}}]}
Year: 1986
DOI: 10.7907/wmxt-sv17
<p>Source properties of earthquakes in Hawaii and seismological aspects of explosive volcanic eruptions are examined in three chapters. In Chapter 1, source depths are estimated for all earthquakes larger than magnitude 6 on the island of Hawaii since 1940 by comparing relative amplitudes of short-period surface waves to body waves. Rayleigh wave excitation functions are calculated versus source depth, and the calculation is compared with observed data and calibrated using known depths of recent earthquakes. In general, results show that large earthquakes near the volcanic flanks and fault systems are shallow (≤ 20 km), but those near active volcanic centers can
be deeper (~ 50 km). Two earthquakes with the largest depth estimates (40-55 km and 35-50 km) occurred under the active volcanoes Mauna Loa and Kilauea, preceding eruptions by three days and 14 months respectively. As a check on the data set, which consisted of Pasadena seismograms alone, M_s values assigned from many global amplitude readings were compared with those from Pasadena amplitudes for worldwide earthquakes. Global M_s values on the average are 0.05 magnitude units larger than M_s values from Pasadena amplitudes.</p>
<p>In Chapter 2, the horizontal single-force source used to model seismic radiation from the Mt. St. Helens landslide is investigated as the source of the M_s = 7.1 Kalapana, Hawaii earthquake. The azimuthal radiation pattern of 100 s Love waves is two-lobed, consistent with a horizontal single-force source. The observed surface deformation is also more consistent with the single force than the conventional double-couple shear dislocation source. The single force is a crude representation of
motion of a large slide mass that is partially decoupled from the Earth. The interpretation is that the bulk of seismic radiation from the Kalapana earthquake was produced by large-scale slumping of the south flank of Kilauea volcano. The peak amplitude f₀ of the force time function is estimated at 1 x 10²⁰ dyne from Love and Rayleigh surface waves. The peak acceleration inferred from the seismic force is 10 - 100 cm s⁻², comparable to that of gravity on a gently inclined plane.</p>
<p>In Chapter 3, far-field seismograms were searched for signals associated with recent large volcanic eruptions to examine whether models of the volcano as a seismic source derived for Mt. St. Helens are applicable to other explosive volcanoes. The 1982 eruption of El Chich6n in Mexico produced Rayleigh waves and body waves that were marginally recorded at IDA and SRO stations less than 40° away; still, several characteristics of the eruption can be inferred from the seismic waves. Near-field seismograms of smaller eruptions at Mt. Asama, Japan, were found to be comparable in size to smaller secondary eruptions of Mt. St. Helens, and appear to have a more complicated source. Atmospheric pressure waves recorded on barographic instruments from several large explosive eruptions are compared and show differences in signal duration, amplitude, and characteristic period that are indicative of the overall size of the eruption.</p>https://thesis.library.caltech.edu/id/eprint/16217The interaction of subducting slabs and the 670 kilometer discontinuity
https://resolver.caltech.edu/CaltechTHESIS:04132011-101632415
Authors: {'items': [{'id': 'King-S-D', 'name': {'family': 'King', 'given': 'Scott David'}, 'show_email': 'NO'}]}
Year: 1991
DOI: 10.7907/pme7-gx03
The subduction of oceanic lithosphere plays a major role in the dynamics of the Earth. The dynamics of subduction are influenced both by variations in density (due to phase changes or compositional changes), and variations in viscosity encountered by the slab; the rheology of the slab and the coupling of the slab with the oceanic lithosphere also play important roles. Geoid and topography place fundamental constraints on subduction, and observations can be used to test various mantle models.
The effects of the rheology of slabs are considered using finite element convection calculations with Newtonian (linear) and non-Newtonian (power-law) temperature-dependent
rheology. Newtonian temperature-dependent fluids do not exhibit slab-like features without weakening the thermal boundary layer. Weak zones are imposed at the trench and ridge, and the effects of varying the size, location, and strength of the weak zones are studied. Non-Newtonian rheology provides a self-consistent mechanism for weakening the thermal boundary layer without imposing a weak zone at the trench. This self-consistency is not proof or confirmation of the importance of power-law deformation in the Earth. Even with non-Newtonian rheology, a weak
zone at the ridge is necessary for plate-like behavior.
The geoid and topography for slabs with a density discontinuity and a viscosity discontinuity are compared. Weak slabs deform rapidly by spreading out along the density discontinuity with little deformation of the boundary, while strong slabs deform slowly and locally depress the density boundary. However, the long wavelength
components of the geoid and topography are independent of the lateral variations in viscosity from the slab. Finite deformations of a compositional boundary are compared with an undeformable boundary approximation; the long wavelength components of the geoid and topography are indistinguishable for boundary deformations up to several hundred kilometers.
Subduction calculations are computationally intensive and high resolution is required to resolve deformation at the trench. The solutions are time-dependent, and a temperature-dependent rheology is required. Faster and more powerful numerical techniques are needed. A fast implementation of the finite element method is presented. Applied to creeping flow, this formulation allows large viscosity variations,
but is still efficient on a vector supercomputer.
https://thesis.library.caltech.edu/id/eprint/6321Three-Dimensional Seismic Velocity Structure of the Earth's Outermost Core and Mantle
https://resolver.caltech.edu/CaltechETD:etd-10312007-090136
Authors: {'items': [{'email': 'kohler@caltech.edu', 'id': 'Kohler-Monica-Diane', 'name': {'family': 'Kohler', 'given': 'Monica Diane'}, 'orcid': '0000-0002-4703-190X', 'show_email': 'YES'}]}
Year: 1995
DOI: 10.7907/q3fd-fd26
<p>Obtaining an accurate, detailed picture of deep-Earth structure is of fundamental importance in a wide range of geophysical applications such as fluid dynamic, magnetohydrodynamic, and mineral physics models of the Earth which incorporate properties determined from seismology. Because it is such a drastic chemical and thermal boundary layer, the nature of the core-mantle boundary has important implications for deep-Earth processes, particularly those which have their origin in the lower mantle or outer core. Seismic data provide the most direct method of sampling the Earth's interior and are, therefore, useful for determining deep-Earth material properties.</p>
<p>The goal of this work has been to present models of three-dimensional, shear and compressional velocity structure which are self-consistent with the data and which can be used in other geophysical applications. The numerical inversions consisted of determining the three-dimensional structure of the outermost core and mantle of the Earth from long-period seismic waveforms. This approach is distinct from other global models of deep-Earth heterogeneity because it accounts for possible lateral heterogeneity in an outermost core layer whose properties are constrained by seismic phases which travel through the core-mantle boundary region.</p>
<p>This method is different from previous core studies in several important ways: synthetic seismograms are constructed using short-period normal modes for the entire set of body-wave phases which travel through the interior of the Earth (e.g., P, PP, S, SS, SKS). Over 5000 seismograms from global digital seismic networks were collected and processed. First-order perturbations in P-wave velocities in one outermost core layer and S-wave velocities within 11 mantle layers of varying thicknesses comprised the least-squares solutions to the inverse problem. Spheroidal modes with periods between 33 and 100 sec were selected to model the body-wave portion of seismograms recorded from earthquakes which occurred globally.</p>
<p>The preferred model is a 12-layered model incorporating data weighted by inverse data variance. This model produces velocity anomalies in the mantle and outermost core which are acceptable for first-order perturbation methods. The results of one-layer inversions also point to the possible existence of lateral variations in the outermost core, most likely between ±0.5% but not as large as ±5%. This model suggests that outermost core P-wave velocity perturbations accompany S-wave velocity perturbations in the lowermost mantle to produce observed variations in SKS-S and SKKS-SKS travel times. In addition, the patterns of structure vary smoothly and exhibit both large and small scale features. The spectral amplitudes fall off more rapidly for the lower mantle layers than for the upper mantle. The depth resolution displayed by the c⁰₀ spherical harmonic term is 200-300 km for upper mantle layer midpoints and increases to 500-600 km for lower mantle layer midpoints.</p>
<p>The data variance reduction of entire body-wave portions as well as SnKS portions of seismograms are slightly better for the 12-layered model than for the 11-layered model; however, the total variance reductions were never very large. The results of the F ratio suggest that lateral velocity variations in the outermost core layer are not zero and that the deepest layer is statistically significant. This test does not require that the extra layer lie in the outermost core (as opposed to the lowermost mantle).</p>
<p>The results of pattern retrieval resolution tests support the conclusion that structure of the outermost core has been obtained independently from the mantle. Multiplicative factors have been calculated from the resolution tests using synthetic Earth models to place constraints on the amount of power leakage suspected from one region to another due to incomplete data coverage. An upper bound of 84% and a lower bound of 68% of the power of outermost core structure is, in fact, due to heterogeneity in the outermost core. By the same analysis, less than 100% of the power of structure initially placed in the lowermost mantle was retrieved in that layer after the resolution inversion. An upper bound of 60% and a lower bound of 53% of the power of lowermost mantle structure is, in fact, due to D" heterogeneity. Almost no leakage occurred from structure initially placed in the uppermost mantle layer.</p>
<p>Several possible sources of lateral velocity anomalies for the lowest layers are explored. Invoking thermal coupling between the mantle and core, one explanation is that the fluid surfaces are deformed due to cold downwellings of lower mantle, and as a result, outermost core fluid. This will give the appearance of lateral velocity anomalies. If lateral velocity anomalies indeed exist, they are likely to be due to a combination of lateral temperature variations and chemical inhomogeneity, suggested by mineral physics relationships.</p>
https://thesis.library.caltech.edu/id/eprint/4344Part I. Near-source acoustic coupling between the atmosphere and the solid earth during volcanic eruptions. Part II. Nearfield normal mode amplitude anomalies of the Landers earthquake
https://resolver.caltech.edu/CaltechETD:etd-10302007-082547
Authors: {'items': [{'email': 'watada@eri.u-tokyo.ac.jp', 'id': 'Watada-S', 'name': {'family': 'Watada', 'given': 'Shingo'}, 'show_email': 'YES'}]}
Year: 1995
DOI: 10.7907/JSE5-G397
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
<p>This thesis consists of two chapters. In the first chapter the normal mode theory of a spherical Earth model is extended to include the atmosphere and the theory is applied to understand the observation of air-ground acoustic coupling during volcanic eruptions and to construct synthetic ground motions. In chapter II, the fully developed normal mode theory of 3D Earth is applied to the nearfield amplitude anomalies of the surface waves of the Landers rearthquake. Synthetic seismograms for the recently-available three dimensional seismic global Earth models are constructed using the normal mode theory and compared with observations. The horizontal scale and the location of lateral seismic velocity variations which caused the amplitude anomalies are examined in detail.</p>
<p>Part I:</p>
<p>Long-period harmonic Rayleigh waves were observed by worldwide seismographic networks during the eruption of Mt. Pinatubo in 1991. It has been suggested that these Rayleigh waves were excited, through atmospheric-solid Earth coupling, by atmospheric oscillations set off by the eruption. We investigated this problem using the Earth's normal modes computed for a spherically symmetric Earth model with the solid (elastic) Earth, ocean and atmosphere. These normal modes represent Rayleigh waves in the solid Earth, tsunamis in the ocean, and Lamb waves, internal acoustic waves and internal gravity waves in the atmosphere. Since the atmosphere has a low sound velocity channel below the thermosphere (altitude 90 km), two characteristic acoustic modes with periods of 230 and 270 s exist. The energy coupling between atmospheric acoustic waves and Rayleigh waves is efficient because of the proximity of the horizontal phase velocities of these waves. The energy distribution suggests that a low altitude volcanic eruption would excite the 230 s mode more strongly than the 270 s mode. This is consistent with the observation for the Pinatubo eruption. In contrast, the internal gravity mode has a period of 300 s. The barographic oscillation at a period of 300 s observed for the 1980 Mt. St. Helens eruption is probably this mode. However, because of its slow phase velocity, it would not couple to Rayleigh waves efficiently, and cannot be detected with seismographs.</p>
<p>Part II-A:</p>
<p>The 1992 Landers earthquake ([...]=7.3) occurred in the middle of the TERRAscope network. Long-period Rayleigh waves recorded at TERRAscope stations [...] after travelling around the Earth show large amplitude anomalies, one order of magnitude larger than spherical Earth predictions up to a period of about 600 s. The ground motions over the epicentral region at and after the arrival of R4-5 are in phase at all stations. These observations are inconsistent with the nearly vertical strike slip mechanism of the Landers earthquake. Synthetic seismograms for a rotating, elliptic and laterally heterogeneous Earth model calculated by the variational method agree well with the observed waveforms. Calculations for various 3D Earth models demonstrate that the amplitudes are very sensitive to the large scale aspherical structure in the crust and the mantle. The anomalies for modes shorter than 300 s period can be explained by lateral heterogeneity shallower than the upper mantle. Rotation of the Earth and lower mantle heterogeneity are required to explain mode amplitudes at longer periods. Current whole mantle seismic tomographic models can fully explain the observed amplitudes longer than 300 s. To assess the effect of the high order lateral heterogeneity in the mantle, more precise estimate of the crustal correction is required.</p>
<p>Part II-B:</p>
<p>We modeled the interaction of the source mechanism and the station location with large-scale lateral heterogeneity using the splitting matrix of an isolated multiplet and the 'source-receiver function' whose spherical harmonic coefficients are given by [...] where s and t are angular and azimuthal order numbers respectively. For a short period of time waveform perturbation is proportional to the integral of products of the splitting function with harmonic coefficients [...] and the 'source-receiver' function. For the Landers earthquake and TERRAscope stations source-receiver geometry, the 'source-receiver function' is dominated by the low-order components, paticularly l = 2, m = ±2 in the epicentral coordinates. This beach-ball like pattern is the same for all the near-source stations located in different quadrants of the strike-slip mechanism. The two maxima of the 'beach ball' pattern coincide with the locations of the degree 2 maxima of the splitting functions; western Pacific and east of South America. These features explain the weak dependence of the waveforms on higher order lateral heterogeneity and similarity of waveforms over the epicentral region. The location and the source mechanism of the Landers earthquake relative to the large scale lateral heterogeneity l = 2, including the variations of the cruatal structures, are responsible for the cause of amplitude anomalies near the epicenter. However, the amplitude near the epicenter of an earthquake with a thrust fault type mechanism, for example the Northridge earthquake, is explained well with a spherical Earth model.</p>
https://thesis.library.caltech.edu/id/eprint/4331High Resolution Modeling of Regional Phases
https://resolver.caltech.edu/CaltechTHESIS:08302023-200342752
Authors: {'items': [{'id': 'Song-Xi', 'name': {'family': 'Song', 'given': 'Xi'}, 'show_email': 'NO'}]}
Year: 1997
DOI: 10.7907/qjr7-9471
<p>It has been a long-time goal of seismologists to decouple source phenomena from propagation effects. This thesis elaborates on our effort towards this goal.</p>
<p>We start by representing earthquakes as point-sources in space and using 1-D synthetics to resolve point-source parameters. Our trial-and-error approach to obtain 1-D crustal models is summarized in a set of sensitivity tests, where regional seismograms are decomposed into segments, i.e., the Pnl segment, the SV waves, the Love wave and the Rayleigh wave, so that the impact of model parameters on each segment is the most direct. In these tests, broadband waveform data is studied in a forward modeling approach, with synthetics computed using the reflectivity method and the generalized ray theory. Applying these tests to paths sampling the Basin and Range province, we find that a simple two-layer crustal model is effective in explaining regional seismograms. Our sensitivity tests also serve to help understand, and inter pret, the many results of a source estimation method we use to obtain point-source parameters. This method desensitizes the source mechanism result from the crustal model used to generate the 1-D synthetics, by allowing relative time shifts between the various segments. With this method, we obtain source mechanisms and seismic moments for a selection of Northridge aftershocks using broadband and long-period waveform data recorded by the TERRAscope array. The source duration of these earthquakes is measured by comparing the short-period to long-period energy ratio in the data to that in the synthetics. The seismic moment and source-duration are used to estimate the relative stress drop. The depth distribution of the relative stress drop indicates that the largest stress drops are in the depth range of 5-15 km for the 24 Northridge aftershocks in our study.</p>
<p>To obtain more detailed information about large earthquakes, such as fault dimension and rupture directivity, we develop a new method of using empirical Green's functions (eGf). As an example, the January 17, 1994 Northridge mainshock is studied with one of its aftershocks as an eGf. The source duration of the mainshock, as seen from the regional surface waves observed at various stations, is obtained by searching for the trapezoidal far-field source-time function for each station which, when convolved with the aftershock data, best simulates the mainshock data. Stations to the north see shorter source durations than those to the south. Modeling these with theoretical predictions of rupture on a square fault, we constrain the effective fault dimension to be 14 km with rupture along the direction of the average
rake vector. A moment of (1.4 ± 0.9) x 10²⁶ dyne•cm with a stress drop of ~120 bars is obtained for the mainshock from our eGf study.</p>
<p>When empirical Green's functions are not available due to a difference in the source mechanisms or in the source locations, theoretical modeling plays an important role. Our approach to develop high resolution Green's functions is to convert eGfs to pseudo Green's functions (pGf). This is done by modeling the eGfs with the generalized ray theory and consists of two major steps.</p>
<p>The first step is to shift individual ray responses to account for a difference in source location. This ray-shifting technique has its own use in fast generation of synthetic seismograms for finite sources. To study the directivity for a finite source, we discretize the fault region into a set of elements represented as point-sources. We then generate the generalized ray responses for the best-fitting point-source location, and derive for each separate ray the response for neighboring point-sources using power series expansions. The response for a finite fault is then a summation over rays and fault elements. If we sum over the elements first, we obtain an effective far field source-time function for each ray, which is sensitive to the direction of rupture. These far-field source-time functions are convolved with the corresponding rays and the results summed to form the total response. A simple application of the above method is demonstrated with the tangential motions observed from the 1991 Sierra Madre earthquake. For this event, we constrain the fault dimension to be about 3 km with rupture towards the west, which is compatible with other more detailed studies.</p>
<p>The second step in the modeling of the eGfs and the development of pseudo Green's functions is to account for variations in model structure by perturbing individual generalized ray responses calculated from a 1-D model. The model is divided into blocks and velocities in the blocks are allowed to vary, which shifts the arrival time of the individual rays. The amplitudes of the rays are perturbed independently to accommodate local velocity variations in the structure. For eGfs that are moderate-sized earthquakes with known source mechanism and time history, the velocity variation in each block and the amplification factor for individual rays can be optimized using a simulated annealing algorithm. The usefulness of the pGfs is demonstrated with the 1991 Sierra Madre earthquakes as examples. The pGf technique is also useful in retrieving 2-D structure, which is essentially waveform tomography. This is demonstrated with a study of a Tibetan profile.</p>https://thesis.library.caltech.edu/id/eprint/16168Plate Tectonics, Mantle Convection and D" Seismic Structures
https://resolver.caltech.edu/CaltechTHESIS:12012022-215809006
Authors: {'items': [{'id': 'Wen-Lianxing', 'name': {'family': 'Wen', 'given': 'Lianxing'}, 'orcid': '0000-0002-5344-6212', 'show_email': 'NO'}]}
Year: 1998
DOI: 10.7907/mn9a-ve49
<p>This thesis is directed at understanding dynamics of the Earth's mantle. I adopt multidisciplinary approaches toward the problem: geodynamical and seismological.</p>
<p>My approach in geodynamics is directed at understanding the relationship between large scale surface observables (geoid, topography, plate motions) and mantle rheology and convection of the present-day Earth. In chapter 2, I do best-fit correlations of shallow mantle structure with various tectonic features and remove them to generate what we call "residual tomography." In chapter 3, I show that the pattern, spectrum and amplitude of the "residual topography" are consistent with shallow origin of the "Earth surface dynamic topography;" the very long wavelength geoid and topography (l = 2 - 3) are successfully explained by density models inferred from the "residual tomography," assuming layered mantle convection stratified at the "920 km seismic discontinuity." In chapter 4, I develop a new method to calculate mantle flow in the spherical coordinates with lateral variation of viscosity. The viscosity contrast between continental and oceanic regions is identified to have dominating effects on both the observed poloidal/toroidal ratio and pattern of toroidal motions at long wavelengths. I show convection models with lateral variation of viscosity are capable of producing long wavelength plate motions observed in plate tectonics.</p>
<p>My approach in seismology is focused on exploring fine structures near the core mantle boundary and developing new techniques for computing synthetic seismograms. I discuss the method development and strategies to explore fine structures near the core-mantle boundary region in the following chapters. In chapter 5, I develop a hybrid method which can handle the seismic wave propagation in heterogeneous regions at large distances. The hybrid method is a combination of analytical and numerical methods, with numerical methods applied in heterogeneous regions only and analytical methods outside. In chapter 6, I discuss wave propagation of SKS and SPdKS phases through ultra-low velocity zones near the core-mantle boundary and constrain the general structures of ultra low velocity zones near the core-mantle boundary under Fiji subduction zone and Iceland. The long period SKS-SPdKS data are explained by ultra low velocity zones with P velocity reduction of 10% and horizontal length scales of about 250 km and height of about 40 km. S velocity reduction of 30% is consistent with the data, although the trade-offs between S velocity reduction and height of the structure exist. In chapter 7, I discuss wave propagation of PKP and its precursors and constrain the detailed structures of the ultra low velocity zones near the core-mantle boundary from observed broadband PKP precursors. The observed long period precursors are explained by the existence of ultra low velocity zones with P velocity reduction of at least 7% and horizontal length scales of 100-300 km and height of about 60-80 km, whereas short period precursors suggest that the structures have smooth edges and structures with smaller scale are adjacent to these large Gaussian-shaped structures. These fine structures may be indicatives of vigorous small-scale convection or the instabilities of the bottom thermal boundary layer of the mantle.</p>https://thesis.library.caltech.edu/id/eprint/15068Analysis of Complex Faulting: Wavelet Transform, Multiple Datasets and Realistic Fault Geometry
https://resolver.caltech.edu/CaltechTHESIS:02172012-155442347
Authors: {'items': [{'email': 'ji@geol.ucsb.edu', 'id': 'Ji-Chen', 'name': {'family': 'Ji', 'given': 'Chen'}, 'show_email': 'YES'}]}
Year: 2002
DOI: 10.7907/XYM3-4718
<p>This thesis presents the studies of two recent large and well-recorded earthquakes,
the 1999 Hector Mine and Chi-Chi earthquakes. A new procedure for the determination
of rupture complexity from a joint inversion of static and seismic data was
first developed. This procedure applies a wavelet transform to separate seismic information
related to the spatial and temporal slip history, then uses a simulated
annealing algorithm to determine the finite-fault model that minimizes the objective
function described in terms of wavelet coefficients. This method is then applied to
simultaneously invert the slip amplitude, slip direction, rise time and rupture velocity
distributions of the Hector Mine and Chi-Chi earthquakes with both seismic and
geodetic data. Two slip models are later verified with independent datasets. </p>
<p>Results indicate that the seismic moment of the Hector Mine earthquake is 6.28 x
10^(19) Nm, which is distributed along a "Y" shape fault geometry with three segments.
The average slip is 1.5 m with peak amplitudes as high as 7 m. The fault rupture has
an average slip duration of 3.5 sec and a slow average rupture velocity of 1.9 km/ sec,
resulting in a 14 sec rupture propagation history. The rise time appears to be roughly
proportional to slip, and the two branches of "Y" shape fault rupture together. The
Chi-Chi earthquake is the best-recorded large earthquake so far. Its seismic moment
of 2.7 x 10^(20) Nm is concentrated on the surface of a "wedge shaped" block. The rupture
front propagates with a slow rupture velocity of about 2.0 km/ sec. The average slip
duration is 7.2 sec. Four interesting results are obtained: (1) The sinuous fault plane
strongly affects both spatial and temporal variation in slip history; (2) Long-period
peak slip velocity increases as the rupture propagates; (3) The peak slip velocity
near the surface is in general higher than on the deeper portion of the fault plane as
predicted by dynamic modeling [e.g., Oglesby et al., 1998]; and (4) the complex fault
geometry and slip distribution are related to the two transfer zones obliquely across
Taiwan, which separate Taiwan into three regions with different tectonic activity. The transfer zone in the north can be explained by the slab breakoff mechanism proposed
by Teng et al. [2000] recently. </p>
https://thesis.library.caltech.edu/id/eprint/6828