Determination of source finiteness and depth of large earthquakes

In this thesis, a method to retrieve the source finiteness, depth of faulting, and the mechanisms of large earthquakes from long-period surface waves is developed and applied to several recent large events.

In Chapter 1, source finiteness parameters of eleven large earthquakes were determined from long-period Rayleigh waves recorded at IDA and GDSN stations. The basic data set is the seismic spectra of periods from 150 to 300 sec. Two simple models of source finiteness are studied. The first model is a point source with finite duration. In the determination of the duration or source-process times, we used Furumoto's phase method and a linear inversion method, in which we simultaneously inverted the spectra and determined the source-process time that minimizes the error in the inversion. These two methods yielded consistent results. The second model is the finite fault model. Source finiteness of large shallow earthquakes with rupture on a fault plane with a large aspect ratio was modeled with the source-finiteness function introduced by Ben-Menahem. The spectra were inverted to find the extent and direction of the rupture of the earthquake that minimize the error in the inversion. This method is applied to the 1977 Sumbawa, Indonesia, 1979 Colombia-Ecuador, 1983 Akita-Oki, Japan, 1985 Valparaiso, Chile, and 1985 Michoacan, Mexico earthquakes. The method yielded results consistent with the rupture extent inferred from the aftershock area of these earthquakes.

In Chapter 2, the depths and source mechanisms of nine large shallow earthquakes were determined. We inverted the data set of complex source spectra for a moment tensor (linear) or a double couple (nonlinear). By solving a least-squares problem, we obtained the centroid depth or the extent of the distributed source for each earthquake. The depths and source mechanisms of large shallow earthquakes determined from long-period Rayleigh waves depend on the models of source finiteness, wave propagation, and the excitation. We tested various models of the source finiteness, Q, the group velocity, and the excitation in the determination of earthquake depths.

The depth estimates obtained using the Q model of Dziewonski and Steim (1982) and the excitation functions computed for the average ocean model of Regan and Anderson (1984) are considered most reasonable. Dziewonski and Steim's Q model represents a good global average of Q determined over a period range of the Rayleigh waves used in this study. Since most of the earthquakes studied here occurred in subduction zones Regan and Anderson's average ocean model is considered most appropriate.

Our depth estimates are in general consistent with the Harvard CMT solutions. The centroid depths and their 90 % confidence intervals (numbers in the parentheses) determined by the Student's t test are: Colombia-Ecuador earthquake (12 December 1979), d = 11 km, (9, 24) km; Santa Cruz Is. earthquake (17 July 1980), d = 36 km, (18, 46) km; Samoa earthquake (1 September 1981), d = 15 km, (9, 26) km; Playa Azul, Mexico earthquake (25 October 1981), d = 41 km, (28, 49) km; El Salvador earthquake (19 June 1982), d = 49 km, (41, 55) km; New Ireland earthquake (18 March 1983), d = 75 km, (72, 79) km; Chagos Bank earthquake (30 November 1983), d = 31 km, (16, 41) km; Valparaiso, Chile earthquake (3 March 1985), d = 44 km, (15, 54) km; Michoacan, Mexico earthquake (19 September 1985), d = 24 km, (12, 34) km.

In Chapter 3, the vertical extent of faulting of the 1983 Akita-Oki, and 1977 Sumbawa, Indonesia earthquakes are determined from fundamental and overtone Rayleigh waves. Using fundamental Rayleigh waves, the depths are determined from the moment tensor inversion and fault inversion. The observed overtone Rayleigh waves are compared to the synthetic overtone seismograms to estimate the depth of faulting of these earthquakes. The depths obtained from overtone Rayleigh waves are consistent with the depths determined from fundamental Rayleigh waves for the two earthquakes. Appendix B gives the observed seismograms of fundamental and overtone Rayleigh waves for eleven large earthquakes.

I. Exact solution of some nonlinear evolution equations. II. The similarity solution for the Korteweg-De Vries equation and the related Painleve Transcendent

In Part I, a method for finding solutions of certain diffusive dispersive nonlinear evolution equations is introduced. The method consists of a straightforward iteration procedure, applied to the equation as it stands (in most cases), which can be carried out to all terms, followed by a summation of the resulting infinite series, sometimes directly and other times in terms of traces of inverses of operators in an appropriate space.

We first illustrate our method with Burgers' and Thomas' equations, and show how it quickly leads to the Cole-Hopft transformation, which is known to linearize these equations.

We also apply this method to the Korteweg and de Vries, nonlinear (cubic) Schrödinger, Sine-Gordon, modified KdV and Boussinesq equations. In all these cases the multisoliton solutions are easily obtained and new expressions for some of them follow. More generally we show that the Marcenko integral equations, together with the inverse problem that originates them, follow naturally from our expressions.

Only solutions that are small in some sense (i.e., they tend to zero as the independent variable goes to ∞) are covered by our methods. However, by the study of the effect of writing the initial iterate u_1 = u_(1)(x,t) as a sum u_1 = ^∼/u_1 + ^≈/u_1 when we know the solution which results if u_1 = ^∼/u_1, we are led to expressions that describe the interaction of two arbitrary solutions, only one of which is small. This should not be confused with Backlund transformations and is more in the direction of performing the inverse scattering over an arbitrary “base” solution. Thus we are able to write expressions for the interaction of a cnoidal wave with a multisoliton in the case of the KdV equation; these expressions are somewhat different from the ones obtained by Wahlquist (1976). Similarly, we find multi-dark-pulse solutions and solutions describing the interaction of envelope-solitons with a uniform wave train in the case of the Schrodinger equation.

Other equations tractable by our method are presented. These include the following equations: Self-induced transparency, reduced Maxwell-Bloch, and a two-dimensional nonlinear Schrodinger. Higher order and matrix-valued equations with nonscalar dispersion functions are also presented.

In Part II, the second Painleve transcendent is treated in conjunction with the similarity solutions of the Korteweg-de Vries equat ion and the modified Korteweg-de Vries equation.

Psychobiophysics of transcranial magnetic stimulation

Transcranial magnetic stimulation (TMS) is a technique that stimulates the brain using a magnetic coil placed on the scalp. Since it is applicable to humans non-invasively, directly interfering with neural electrical activity, it is potentially a good tool to study the direct relationship between perceptual experience and neural activity. However, it has been difficult to produce a clear perceptible phenomenon with TMS of sensory areas, especially using a single magnetic pulse. Also, the biophysical mechanisms of magnetic stimulation of single neurons have been poorly understood.

In the psychophysical part of this thesis, perceptual phenomena induced by TMS of the human visual cortex are demonstrated as results of the interactions with visual inputs. We first introduce a method to create a hole, or a scotoma, in a flashed, large-field visual pattern using single-pulse TMS. Spatial aspects of the interactions are explored using the distortion effect of the scotoma depending on the visual pattern, which can be luminance-defined or illusory. Its similarity to the distortion of afterimages is also discussed. Temporal interactions are demonstrated in the filling-in of the scotoma with temporally adjacent visual features, as well as in the effective suppression of transient visual features. Also, paired-pulse TMS is shown to lead to different brightness modulations in transient and sustained visual stimuli.

In the biophysical part, we first develop a biophysical theory to simulate the effect of magnetic stimulation on arbitrary neuronal structure. Computer simulations are performed on cortical neuron models with realistic structure and channels, combined with the current injection that simulates magnetic stimulation. The simulation results account for general and basic characteristics of the macroscopic effects of TMS including our psychophysical findings, such as a long inhibitory effect, dependence on the background activity, and dependence on the direction of the induced electric field.

The perceptual effects and the cortical neuron model presented here provide foundations for the study of the relationship between perception and neural activity. Further insights would be obtained from extension of our model to neuronal networks and psychophysical studies based on predictions of the biophysical model.

Analysis of temporal structure in spike trains of visual cortical area MT

The temporal structure of neuronal spike trains in the visual cortex can provide detailed information about the stimulus and about the neuronal implementation of visual processing. Spike trains recorded from the macaque motion area MT in previous studies (Newsome et al., 1989a; Britten et al., 1992; Zohary et al., 1994) are analyzed here in the context of the dynamic random dot stimulus which was used to evoke them. If the stimulus is incoherent, the spike trains can be highly modulated and precisely locked in time to the stimulus. In contrast, the coherent motion stimulus creates little or no temporal modulation and allows us to study patterns in the spike train that may be intrinsic to the cortical circuitry in area MT. Long gaps in the spike train evoked by the preferred direction motion stimulus are found, and they appear to be symmetrical to bursts in the response to the anti-preferred direction of motion. A novel cross-correlation technique is used to establish that the gaps are correlated between pairs of neurons. Temporal modulation is also found in psychophysical experiments using a modified stimulus. A model is made that can account for the temporal modulation in terms of the computational theory of biological image motion processing. A frequency domain analysis of the stimulus reveals that it contains a repeated power spectrum that may account for psychophysical and electrophysiological observations.

Some neurons tend to fire bursts of action potentials while others avoid burst firing. Using numerical and analytical models of spike trains as Poisson processes with the addition of refractory periods and bursting, we are able to account for peaks in the power spectrum near 40 Hz without assuming the existence of an underlying oscillatory signal. A preliminary examination of the local field potential reveals that stimulus-locked oscillation appears briefly at the beginning of the trial.

Pharmacology and pore-forming domains of the cystic fibrosis transmembrane conductance regulator

The cystic fibrosis transmembrane conductance regulator (CFTR) is a chloride channel member of the ATP-binding cassette (ABC) superfamily of membrane proteins. CFTR has two homologous halves, each consisting of six transmembrane spanning domains (TM) followed by a nucleotide binding fold, connected by a regulatory (R) domain. This thesis addresses the question of which domains are responsible for Cl^- selectivity, i.e., which domains line the channel pore.

To address this question, novel blockers of CFTR were characterized. CFTR was heterologously expressed in Xenopus oocytes to study the mechanism of block by two closely related arylaminobenzoates, diphenylamine-2-carboxylic acid (DPC) and flufenamic acid (FFA). Block by both is voltage-dependent, with a binding site ≈ 40% through the electric field of the membrane. DPC and FFA can both reach their binding site from either side of the membrane to produce a flickering block of CFTR single channels. In addition, DPC block is influenced by Cl^- concentration, and DPC blocks with a bimolecular forward binding rate and a unimolecular dissociation rate. Therefore, DPC and FFA are open-channel blockers of CFTR, and a residue of CFTR whose mutation affects their binding must line the pore.

Screening of site-directed mutants for altered DPC binding affinity reveals that TM-6 and TM-12 line the pore. Mutation of residue 5341 in TM-6 abolishes most DPC block, greatly reduces single-channel conductance, and alters the direction of current rectification. Additional residues are found in TM-6 (K335) and TM-12 (T1134) whose mutations weaken or strengthen DPC block; other mutations move the DPC binding site from TM-6 to TM-12. The strengthened block and lower conductance due to mutation T1134F is quantitated at the single-channel level. The geometry of DPC and of the residues mutated suggest α-helical structures for TM-6 and TM-12. Evidence is presented that the effects of the mutations are due to direct side-chain interaction, and not to allosteric effects propagated through the protein. Mutations are also made in TM-11, including mutation S1118F, which gives voltage-dependent current relaxations. The results may guide future studies on permeation through ABC transporters and through other Cl^- channels.

Teleseismic array analysis of upper mantle compressional velocity structure

Large quantities of teleseismic short-period seismograms recorded at SCARLET provide travel time, apparent velocity and waveform data for study of upper mantle compressional velocity structure. Relative array analysis of arrival times from distant (30° < Δ < 95°) earthquakes at all azimuths constrains lateral velocity variations beneath southern California. We compare dT/dΔ back azimuth and averaged arrival time estimates from the entire network for 154 events to the same parameters derived from small subsets of SCARLET. Patterns of mislocation vectors for over 100 overlapping subarrays delimit the spatial extent of an east-west striking, high-velocity anomaly beneath the Transverse Ranges. Thin lens analysis of the averaged arrival time differences, called 'net delay' data, requires the mean depth of the corresponding lens to be more than 100 km. Our results are consistent with the PKP-delay times of Hadley and Kanamori (1977), who first proposed the high-velocity feature, but we place the anomalous material at substantially greater depths than their 40-100 km estimate.

Detailed analysis of travel time, ray parameter and waveform data from 29 events occurring in the distance range 9° to 40° reveals the upper mantle structure beneath an oceanic ridge to depths of over 900 km. More than 1400 digital seismograms from earthquakes in Mexico and Central America yield 1753 travel times and 58 dT/dΔ measurements as well as high-quality, stable waveforms for investigation of the deep structure of the Gulf of California. The result of a travel time inversion with the tau method (Bessonova et al., 1976) is adjusted to fit the p(Δ) data, then further refined by incorporation of relative amplitude information through synthetic seismogram modeling. The application of a modified wave field continuation method (Clayton and McMechan, 1981) to the data with the final model confirms that GCA is consistent with the entire data set and also provides an estimate of the data resolution in velocity-depth space. We discover that the upper mantle under this spreading center has anomalously slow velocities to depths of 350 km, and place new constraints on the shape of the 660 km discontinuity.

Seismograms from 22 earthquakes along the northeast Pacific rim recorded in southern California form the data set for a comparative investigation of the upper mantle beneath the Cascade Ranges-Juan de Fuca region, an ocean-continent transit ion. These data consist of 853 seismograms (6° < Δ < 42°) which produce 1068 travel times and 40 ray parameter estimates. We use the spreading center model initially in synthetic seismogram modeling, and perturb GCA until the Cascade Ranges data are matched. Wave field continuation of both data sets with a common reference model confirms that real differences exist between the two suites of seismograms, implying lateral variation in the upper mantle. The ocean-continent transition model, CJF, features velocities from 200 and 350 km that are intermediate between GCA and T7 (Burdick and Helmberger, 1978), a model for the inland western United States. Models of continental shield regions (e.g., King and Calcagnile, 1976) have higher velocities in this depth range, but all four model types are similar below 400 km. This variation in rate of velocity increase with tectonic regime suggests an inverse relationship between velocity gradient and lithospheric age above 400 km depth.

The streaming of 1.3-2.3 MeV cosmic-ray protons during periods between prompt solar particle events

The anisotropy of 1.3 - 2.3 MeV protons in interplanetary space has been measured using the Caltech Electron/Isotope Spectrometer aboard IMP-7 for 317 6-hour periods from 72/273 to 74/2. Periods dominated by prompt solar particle events are not included. The convective and diffusive anisotropies are determined from the observed anisotropy using concurrent solar wind speed measurements and observed energy spectra. The diffusive flow of particles is found to be typically toward the sun, indicating a positive radial gradient in the particle density. This anisotropy is inconsistent with previously proposed sources of low-energy proton increases seen at 1 AU which involve continual solar acceleration.

The typical properties of this new component of low-energy cosmic rays have been determine d for this period which is near solar minimum. The particles have a median intensity of 0.06 protons/ cm^(2)-sec-sr-MeV and a mean spectral index of -3.15.The amplitude of the diffusive anisotropy is approximately proportional to the solar wind speed. The rate at which particles are diffusing toward the sun is larger than the rate at which the solar wind is convecting the particles away from the sun. The 20 to 1 proton to alpha ratio typical of this new component has been reported by Mewaldt, et al. (1975b).

A propagation model with κ_(rr) assumed independent of radius and energy is used to show that the anisotropy could be due to increases similar to those found by McDonald, et al. (1975) at ~3 AU. The interplanetary Fermi-acceleration model proposed by Fisk (1976) to explain the increases seen near 3 AU is not consistent with the ~12 per cent diffusive anisotropy found.

The dependence of the diffusive anisotropy on various parameters is shown. A strong dependence of the direction of the diffusive anisotropy on the concurrently measured magnetic field direction is found, indicating a κ_⊥ less than κ_∥ to be typical for this large data set.

I. Thermochemistry and reaction kinetics of disolvated protons by ion cyclotron resonance spectroscopy. II. Thermochemical studies of small fluorocarbons by photoionization mass spectrometry

The disolvated proton, H(OH₂)₂⁺ is employed as a chemical reagent in low pressure (˂ 10^-5 torr) investigations by ion cyclotron resonance spectroscopy. Since termolecular reactions are absent at low pressure, disolvated protons are not generally observed. However H(OH₂)₂⁺ is produced in a sequence of bimolecular reactions in mixtures containing H₂O and one of a small number of organohalide precursors. Then a series of hydrated Lewis bases is produced by H₃O⁺ transfer from H(OH₂)₂⁺. In Chapter II, the relative stability of hydrated bases containing heteroatoms of both first and second row elements is determined from the preferred direction of H₃O⁺ transfer between BH(OH₂)⁺ complexes. S and P containing bases are shown to bind H₃O⁺ more weakly than O and N bases with comparable proton affinities. A simple model of hydrogen bonding is proposed to account for these observations.

H⁺ transfer from H(OH₂)₂⁺ to several Lewis bases also occurs at low pressure. In Chapter III the relative importance of H₃O⁺ transfer and H⁺ transfer from H(OH₂)₂⁺ to a series of bases is observed to be a function of base strength. Beginning with CH₃COOH, the weakest base for which H⁺ transfer is observed, the importance of H⁺ transfer increases with increasing proton affinity of the acceptor base. The nature of neutral products formed from H(OH₂)₂⁺ by loss of H⁺ is also considered.

Chapters IV and V deal with thermochemistry of small fluorocarbons determined by photoionization mass spectrometry. The enthalpy of formation of CF₂ is considered in Chapter IV. Photoionization of perfluoropropylene, perfluorocyclopropane, and trifluoromethyl benzene yield onsets for ions formed by loss of a CF₂ neutral fragment. Earlier determinations of ΔH^°_f298 (CF₂) are reinterpreted using updated thermochemical values and compared with results of this study. The heat of formation of neutral perfluorocyclopropane is also derived. Finally, the energetics of interconversion of perfluoropropylene and perfluorocyclopropane are considered for both the neutrals and their molecular ions.

In Chapter V the heats of formation of CF₃⁺ and CF₃I⁺are derived from photoionization of CF₃I. These are considered with respect to ion-molecule reactions observed in CF₃I monitored by the techniques of ion cyclotron resonance spectroscopy. Results obtained in previous experiments are also compared.

A computer-aided investigation of motion detection units in the fly

This work deals with two related areas: processing of visual information in the central nervous system, and the application of computer systems to research in neurophysiology.

Certain classes of interneurons in the brain and optic lobes of the blowfly Calliphora phaenicia were previously shown to be sensitive to the direction of motion of visual stimuli. These units were identified by visual field, preferred direction of motion, and anatomical location from which recorded. The present work is addressed to the questions: (1) is there interaction between pairs of these units, and (2) if such relationships can be found, what is their nature. To answer these questions, it is essential to record from two or more units simultaneously, and to use more than a single recording electrode if recording points are to be chosen independently. Accordingly, such techniques were developed and are described.

One must also have practical, convenient means for analyzing the large volumes of data so obtained. It is shown that use of an appropriately designed computer system is a profitable approach to this problem. Both hardware and software requirements for a suitable system are discussed and an approach to computer-aided data analysis developed. A description is given of members of a collection of application programs developed for analysis of neuro-physiological data and operated in the environment of and with support from an appropriate computer system. In particular, techniques developed for classification of multiple units recorded on the same electrode are illustrated as are methods for convenient graphical manipulation of data via a computer-driven display.

By means of multiple electrode techniques and the computer-aided data acquisition and analysis system, the path followed by one of the motion detection units was traced from open optic lobe through the brain and into the opposite lobe. It is further shown that this unit and its mirror image in the opposite lobe have a mutually inhibitory relationship. This relationship is investigated. The existence of interaction between other pairs of units is also shown. For pairs of units responding to motion in the same direction, the relationship is of an excitatory nature; for those responding to motion in opposed directions, it is inhibitory.

Experience gained from use of the computer system is discussed and a critical review of the current system is given. The most useful features of the system were found to be the fast response, the ability to go from one analysis technique to another rapidly and conveniently, and the interactive nature of the display system. The shortcomings of the system were problems in real-time use and the programming barrier—the fact that building new analysis techniques requires a high degree of programming knowledge and skill. It is concluded that computer system of the kind discussed will play an increasingly important role in studies of the central nervous system.

Behavior of spherical particles at low Reynolds numbers in a fluctuating translational flow

The behavior of spheres in non-steady translational flow has been studied experimentally for values of Reynolds number from 0.2 to 3000. The aim of the work was to improve our qualitative understanding of particle transport in turbulent gaseous media, a process of extreme importance in power plants and energy transfer mechanisms.

Particles, subjected to sinusoidal oscillations parallel to the direction of steady translation, were found to have changes in average drag coefficient depending upon their translational Reynolds number, the density ratio, and the dimensionless frequency and amplitude of the oscillations. When the Reynolds number based on sphere diameter was less than 200, the oscillation had negligible effect on the average particle drag.

For Reynolds numbers exceeding 300, the coefficient of the mean drag was increased significantly in a particular frequency range. For example, at a Reynolds number of 3000, a 25 per cent increase in drag coefficient can be produced with an amplitude of oscillation of only 2 per cent of the sphere diameter, providing the frequency is near the frequency at which vortices would be shed in a steady flow at the mean speed. Flow visualization shows that over a wide range of frequencies, the vortex shedding frequency locks in to the oscillation frequency. Maximum effect at the natural frequency and lock-in show that a non-linear interaction between wake vortex shedding and the oscillation is responsible for the increase in drag.

Applications of plasticity theory to selected problems in soil mechanics

Two topics in plane strain perfect plasticity are studied using the method of characteristics. The first is the steady-state indentation of an infinite medium by either a rigid wedge having a triangular cross section or a smooth plate inclined to the direction of motion. Solutions are exact and results include deformation patterns and forces of resistance; the latter are also applicable for the case of incipient failure. Experiments on sharp wedges in clay, where forces and deformations are recorded, showed a good agreement with the mechanism of cutting assumed by the theory; on the other hand the indentation process for blunt wedges transforms into that of compression with a rigid part of clay moving with the wedge. Finite element solutions, for a bilinear material model, were obtained to establish a correspondence between the response of the plane strain wedge and its axi-symmetric counterpart, the cone. Results of the study afford a better understanding of the process of indentation of soils by penetrometers and piles as well as the mechanism of failure of deep foundations (piles and anchor plates).

The second topic concerns the plane strain steady-state free rolling of a rigid roller on clays. The problem is solved approximately for small loads by getting the exact solution of two problems that encompass the one of interest; the first is a steady-state with a geometry that approximates the one of the roller and the second is an instantaneous solution of the rolling process but is not a steady-state. Deformations and rolling resistance are derived. When compared with existing empirical formulae the latter was found to agree closely.

Finite-Element Simulations of Earthquakes

This thesis discusses simulations of earthquake ground motions using prescribed ruptures and dynamic failure. Introducing sliding degrees of freedom led to an innovative technique for numerical modeling of earthquake sources. This technique allows efficient implementation of both prescribed ruptures and dynamic failure on an arbitrarily oriented fault surface. Off the fault surface the solution of the three-dimensional, dynamic elasticity equation uses well known finite-element techniques. We employ parallel processing to efficiently compute the ground motions in domains containing millions of degrees of freedom.

Using prescribed ruptures we study the sensitivity of long-period near-source ground motions to five earthquake source parameters for hypothetical events on a strike-slip fault (M_w 7.0 to 7.1) and a thrust fault (M_w 6.6 to 7.0). The directivity of the ruptures creates large displacement and velocity pulses in the ground motions in the forward direction. We found a good match between the severity of the shaking and the shape of the near-source factor from the 1997 Uniform Building Code for strike-slip faults and thrust faults with surface rupture. However, for blind thrust faults the peak displacement and velocities occur up-dip from the region with the peak near-source factor. We assert that a simple modification to the formulation of the near-source factor improves the match between the severity of the ground motion and the shape of the near-source factor.

For simulations with dynamic failure on a strike-slip fault or a thrust fault, we examine what constraints must be imposed on the coefficient of friction to produce realistic ruptures under the application of reasonable shear and normal stress distributions with depth. We found that variation of the coefficient of friction with the shear modulus and the depth produces realistic rupture behavior in both homogeneous and layered half-spaces. Furthermore, we observed a dependence of the rupture speed on the direction of propagation and fluctuations in the rupture speed and slip rate as the rupture encountered changes in the stress field. Including such behavior in prescribed ruptures would yield more realistic ground motions.