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.

A mathematical study of finite-amplitude rock-folding

The problem of the finite-amplitude folding of an isolated, linearly viscous layer under compression and imbedded in a medium of lower viscosity is treated theoretically by using a variational method to derive finite difference equations which are solved on a digital computer. The problem depends on a single physical parameter, the ratio of the fold wavelength, L, to the "dominant wavelength" of the infinitesimal-amplitude treatment, L_d. Therefore, the natural range of physical parameters is covered by the computation of three folds, with L/L_d = 0, 1, and 4.6, up to a maximum dip of 90°.

Significant differences in fold shape are found among the three folds; folds with higher L/L_d have sharper crests. Folds with L/L_d = 0 and L/L_d = 1 become fan folds at high amplitude. A description of the shape in terms of a harmonic analysis of inclination as a function of arc length shows this systematic variation with L/L_d and is relatively insensitive to the initial shape of the layer. This method of shape description is proposed as a convenient way of measuring the shape of natural folds.

The infinitesimal-amplitude treatment does not predict fold-shape development satisfactorily beyond a limb-dip of 5°. A proposed extension of the treatment continues the wavelength-selection mechanism of the infinitesimal treatment up to a limb-dip of 15°; after this stage the wavelength-selection mechanism no longer operates and fold shape is mainly determined by L/L_d and limb-dip.

Strain-rates and finite strains in the medium are calculated f or all stages of the L/L_d = 1 and L/L_d = 4.6 folds. At limb-dips greater than 45° the planes of maximum flattening and maximum flattening rat e show the characteristic orientation and fanning of axial-plane cleavage.

Interaction of aqueous inorganic orthophosphate and phosphate rock

An experimental study was made of the interaction of phosphate rock and aqueous inorganic orthophosphate, calcium, and hydroxyl ions. A model of the reaction was developed by observing electron diffraction patterns in conjunction with concentration changes of chemical components. The model was applied in explaining the performance of batch suspensions of powdered phosphate rock and packed columns of granular phosphate rock. In both cases the reaction consisted initially of a rapid nucleation phase that occurred in a time period of minutes. In the batch system the calcium phosphate nuclei then ripened into larger micro-crystals of hydroxyapatite, which eventually became indistinguishable from the original phosphate rock surface. During column operation the high supersaturation ratio that existed after the rapid nucleation phase resulted in a layer of small nuclei that covered a slowly growing hydroxyapatite crystal.

The column steady-state rate constant was found to increase with increasing temperature, pH, and fluoride concentration, and to decrease with increasing concentrations of magnesium sulfate, ammonium chloride, and bicarbonate ion.

An engineering feasibility study indicated that, based on economic considerations, nucleation of apatite on phosphate rock ore has a potential use as a wastewater phosphate removal treatment process.

Reconstructing Past Depositional and Diagenetic Processes through Quantitative Stratigraphic Analysis of the Martian Sedimentary Rock Record

High-resolution orbital and in situ observations acquired of the Martian surface during the past two decades provide the opportunity to study the rock record of Mars at an unprecedented level of detail. This dissertation consists of four studies whose common goal is to establish new standards for the quantitative analysis of visible and near-infrared data from the surface of Mars. Through the compilation of global image inventories, application of stratigraphic and sedimentologic statistical methods, and use of laboratory analogs, this dissertation provides insight into the history of past depositional and diagenetic processes on Mars. The first study presents a global inventory of stratified deposits observed in images from the High Resolution Image Science Experiment (HiRISE) camera on-board the Mars Reconnaissance Orbiter. This work uses the widespread coverage of high-resolution orbital images to make global-scale observations about the processes controlling sediment transport and deposition on Mars. The next chapter presents a study of bed thickness distributions in Martian sedimentary deposits, showing how statistical methods can be used to establish quantitative criteria for evaluating the depositional history of stratified deposits observed in orbital images. The third study tests the ability of spectral mixing models to obtain quantitative mineral abundances from near-infrared reflectance spectra of clay and sulfate mixtures in the laboratory for application to the analysis of orbital spectra of sedimentary deposits on Mars. The final study employs a statistical analysis of the size, shape, and distribution of nodules observed by the Mars Science Laboratory Curiosity rover team in the Sheepbed mudstone at Yellowknife Bay in Gale crater. This analysis is used to evaluate hypotheses for nodule formation and to gain insight into the diagenetic history of an ancient habitable environment on Mars.

Source characteristics of recent and historic earthquakes in Central and Southern California: results from forward modeling

The long- and short-period body waves of a number of moderate earthquakes occurring in central and southern California recorded at regional (200-1400 km) and teleseismic (> 30°) distances are modeled to obtain the source parameters-focal mechanism, depth, seismic moment, and source time history. The modeling is done in the time domain using a forward modeling technique based on ray summation. A simple layer over a half space velocity model is used with additional layers being added if necessary-for example, in a basin with a low velocity lid.

The earthquakes studied fall into two geographic regions: 1) the western Transverse Ranges, and 2) the western Imperial Valley. Earthquakes in the western Transverse Ranges include the 1987 Whittier Narrows earthquake, several offshore earthquakes that occurred between 1969 and 1981, and aftershocks to the 1983 Coalinga earthquake (these actually occurred north of the Transverse Ranges but share many characteristics with those that occurred there). These earthquakes are predominantly thrust faulting events with the average strike being east-west, but with many variations. Of the six earthquakes which had sufficient short-period data to accurately determine the source time history, five were complex events. That is, they could not be modeled as a simple point source, but consisted of two or more subevents. The subevents of the Whittier Narrows earthquake had different focal mechanisms. In the other cases, the subevents appear to be the same, but small variations could not be ruled out.

The recent Imperial Valley earthquakes modeled include the two 1987 Superstition Hills earthquakes and the 1969 Coyote Mountain earthquake. All are strike-slip events, and the second 1987 earthquake is a complex event With non-identical subevents.

In all the earthquakes studied, and particularly the thrust events, constraining the source parameters required modeling several phases and distance ranges. Teleseismic P waves could provide only approximate solutions. P_(nl) waves were probably the most useful phase in determining the focal mechanism, with additional constraints supplied by the SH waves when available. Contamination of the SH waves by shear-coupled PL waves was a frequent problem. Short-period data were needed to obtain the source time function.

In addition to the earthquakes mentioned above, several historic earthquakes were also studied. Earthquakes that occurred before the existence of dense local and worldwide networks are difficult to model due to the sparse data set. It has been noticed that earthquakes that occur near each other often produce similar waveforms implying similar source parameters. By comparing recent well studied earthquakes to historic earthquakes in the same region, better constraints can be placed on the source parameters of the historic events.

The Lompoc earthquake (M=7) of 1927 is the largest offshore earthquake to occur in California this century. By direct comparison of waveforms and amplitudes with the Coalinga and Santa Lucia Banks earthquakes, the focal mechanism (thrust faulting on a northwest striking fault) and long-period seismic moment (10^(26) dyne cm) can be obtained. The S-P travel times are consistent with an offshore location, rather than one in the Hosgri fault zone.

Historic earthquakes in the western Imperial Valley were also studied. These events include the 1942 and 1954 earthquakes. The earthquakes were relocated by comparing S-P and R-S times to recent earthquakes. It was found that only minor changes in the epicenters were required but that the Coyote Mountain earthquake may have been more severely mislocated. The waveforms as expected indicated that all the events were strike-slip. Moment estimates were obtained by comparing the amplitudes of recent and historic events at stations which recorded both. The 1942 event was smaller than the 1968 Borrego Mountain earthquake although some previous studies suggested the reverse. The 1954 and 1937 earthquakes had moments close to the expected value. An aftershock of the 1942 earthquake appears to be larger than previously thought.

The Colorado River; a source of water and power for Los Angeles

The rapid growth and development of Los Angeles City and County has been one of the phenomena of the present age. The growth of a city from 50,600 to 576,000, an increase of over 1000% in thirty years is an unprecedented occurrence. It has given rise to a variety of problems of increasing magnitude.

Chief among these are: supply of food, water and shelter development of industry and markets, prevention and removal of downtown congestion and protection of life and property. These, of course, are the problems that any city must face. But in the case of a community which doubles its population every ten years, radical and heroic measures must often be taken.

An experimental study of a stellar neutron source: ^(13)C(α, n)^(16)O

Described in this thesis are measurements made of the thick-target neutron yield from the reaction ¹³C(α, n)¹⁶O. The yield was determined for laboratory bombarding energies between 0.475 and 0.700 MeV, using a stilbene crystal neutron detector and pulse-shape discrimination to eliminate gamma rays. Stellar temperatures between 2.5 and 4.5 x 10^{8 o}K are involved in this energy region. From the neutron yield was extracted the astrophysical cross-section factor S(E), which was found to fit a linear function: S(E) = [(5.48 ± 1.77) + (12.05 ± 3.91)E] x 10⁵ MeV-barns, center-of-mass system. The stellar rate of the ¹³C(α, n)¹⁶O reaction if calculated, and discussed with reference to helium burning and neutron production in the core of a giant star.

Results are also presented of measurements carried out on the reaction ⁹Be(α, n)¹²C, taken with a thin Be target. The bombarding energy-range covered was from 0.340 to 0.680 MeV, with excitation curves for the ground- and first excited-state neutrons being reported. Some angular distributions were also measured. Resonances were found at bombarding energies of E_LAB = 0.520 MeV (E_CM = 0.360 MeV, Γ ~ 55 keV CM, ωγ = 3.79 eV CM) and E_LAB = 0.600 MeV (E_CM = 0.415 MeV, Γ ˂ 4 keV CM, ωγ = 0.88 eV CM). The astrophysical rate of the ⁹Be(α, n)¹²C reaction due to these resonances is calculated.

Hydrothermal experiments on the thermal stability of amino substances in sediments

Aspartic acid, threonine, serine and other thermally unstable amino acids have been found in fine-grained elastic sediments of advanced geologic age. The presence of these compounds in ancient sediments conflicts with experimental data determined for their simple thermal decomposition.

Recent and Late Miocene sediments and their humic acid extracts, known to contain essentially complete suites of amino acids, were heated with H₂O in a bomb at temperatures up to 500°C in order to compare the thermal decomposition characteristics of the sedimentary amino compounds.

Most of the amino acids found in protein hydrolyzates are obtained from the Miocene rock in amounts 10 to 100 times less than from the Recent sediment. The two unheated humic acids are rather similar despite their great age difference. The Miocene rock appears uncontaminated by Recent carbon.

Yields of amino acids generally decline in the heated Recent sediment. Some amino compounds apparently increase with heating time in the Miocene rock.

Relative thermal stabilities of the amino acids in sediments are generally similar to those determined using pure aqueous solutions. The relative thermal stabilities of glutamic acid, glycine, and phenylalanine vary in the Recent sediment but are uniform in the Miocene rock.

Amino acids may occur in both proteins and humic complexes in the Recent sediment, while they are probably only present in stabilized organic substances in the Miocene rock. Thermal decomposition of protein amino acids may be affected by surface catalysis in the Recent sediment. The apparent activation energy for the decomposition of alanine in this sediment is 8400 calories per mole. Yields of amino compounds from the heated sediments are not affected by thermal decomposition only.

Amino acids in sediments may only be useful for geothermometry in a very general way.

A better picture of the amino acid content of older sedimentary rocks may be obtained if these sediments are heated in a bomb with H₂O at temperatures around 150°C prior to HCl hydrolysis.

Leucine-isoleucine ratios may prove to be useful as indicators of amino acid sources or for evaluating the fractionation of these substances during diagenesis. Leucine-isoleucine ratios of the Recent and Miocene sediments and humic acids are identical. The humic acids may have a continental source.

The carbon-nitrogen and carbon-hydrogen ratios of sediments and humic acids increase with heating time and temperature. Ratios comparable to those in some kerogens are found in the severely heated Miocene sediment and humic acid.

The geochronology of the plutonic and metamorphic rocks of New Zealand

Extensive Rubidium-Strontium age determinations on both mineral and total rock samples of the crystalline rocks of New Zealand, which almost solely crop out in the South Island, indicate widespread plutonic and metamorphic activity occurred during two periods, one about 100-118 million years ago and the other about 340-370 million years ago. The former results date the Rangitata Orogeny as Cretaceous. They associate extensive plutonic activity with this orogeny which uplifted and metamorphosed the rocks of the New Zealand Geosyncline, although no field association between the metamorphosed geosynclinal rocks and plutonic rocks has been found. The Cretaceous plutonic rocks occur to the west in the Foreland Province in Fiordland, Nelson, and Westland, geographically separated from the Geosynclinal Province. Because of this synchronous timing of plutonic and high pressure metamorphic activity in spatially separated belts, the Rangitata Orogeny in New Zealand is very similar to late Mesozoic orogenic activity in many other areas of the circum-Pacific margin (Miyashiro, 1961).

The 340-370 million year rocks, both plutonic and metamorphic, have been found only in that part of the Foreland Province north of the Alpine Fault. There, they are concentrated along the west coast over a distance of 500 km, and appear scattered inland from the coast. Probably this activity marks the outstanding Phanerozoic stratigraphic gap in New Zealand which occurred after the Lower Devonian.

A few crystalline rocks in the Foreland Province north of the Alpine Fault with measured ages intermediate between 340 and 120 million years have been found. Of these, those with more than one mineral examined give discordant results. All of these rocks are tentatively regarded as 340-370 million year old rocks that have been variously disturbed during the Rangitata Orogeny, 100-120 million years ago.

In addition to these two periods, plutonic activity, dominantly basic and ultrabasic, but including the development of some rocks of intermediate and acidic composition, occurred along the margin of the Geosynclinal Province at its border with the Foreland Province during Permian times about 245 million years ago, and this activity possibly extended into the Mesozoic.

Evidence from rubidium-strontium analyses of minerals and a total rock, and from uranium, thorium, and lead analyses of uniform euhedral zircons from a meta-igneous portion of the Charleston Gneiss, previously mapped as Precambrian, indicate that this rock is a 350-370 million year old plutonic rock metamorphosed 100 million yea rs ago during the Rangitata Orogeny. No crystalline rocks with primary Precambrian ages have been found in New Zealand. However, Pb²⁰⁷/Pb₂₀₆ ages of 1360 million years and 1370 million years have been determined for rounded detrital zircons separated from each of two hornfels samples of one of New Zealand's olde st sedimentary units, the Greenland Series. These two samples were metamorphosed 345- 370 million years ago. They occur along the west coast, north of the Alpine Fault, at Waitaha River and Moeraki River, separated by 135 km. The Precambrian measured ages are most likely minimum ages for the oldest source area which provided the detrital zircons because the uranium, thorium and lead data are highly discordant. These results are of fundamental importance for the tectonic picture of the Southwest Pacific margin and demonstrate the existence of relatively old continental crust of some lateral extent in the neighborhood of New Zealand.