I develop a number of new methods for performing slant stacking and its variants suitable to the processing of ocean bottom seismograph (OBS) data. I develop two versions of the discrete Radon transform (DRT) pair, a generalization of slant stacking, which can handle data unevenly spaced in both offset (x) and ray parameter (p). The discrete Radon transform matrix consists of two parts: a scaling matrix and a phase shift matrix. The elements in the phase shift matrix determine the amounts of the shift of given frequencies for stacking. I develop an iterative approach to perform velocity stacking, a parabolic variant of slant stacking, in the time domain. Invertibility of the transform is secured by iteration over the residual energy. A better focused version of the velocity profile is achieved. I extend conventional slant stacking of single component data to multicomponent data by performing a "vector" slant stack. The vector slant stack is performed by first transforming each component of the data, then combining the components in the $\tau$-p. This transform produces a vector field in $\tau$ and p. A color scheme using RGB intensity respectively to represent the vertical, radial and transverse components in either the x-t or the $\tau$-p domain is developed for displaying three component seismic data. I develop a technique to separate P-wave and S-waves arriving at the receiver in the vector $\tau$-p domain. I have designed an algorithm to decompose a vector common-p trace into P, SV, and SH traces. The result will be three sections in the $\tau$-p domain which can be inverse transformed to the x-t domain. (Abstract shortened by UMI.)

I present synthetics of seismic wave propagation near free surface topography. The velocity-stress formulations of both the full elastic and viscoelastic wave equations are used, and I have derived exact boundary conditions for any arbitrary, smooth topography in terms of the particle velocities. Program codes are developed for 2 and 3 dimensions (2-D and 3-D) using finite-difference (F-D) methods for both spatial and temporal numerical discretizations. An 8th order F-D method is used inside the physical model space, and the spatial F-D order decreases gradually towards the free surface topography. The discretization of the medium equations along the side and bottom boundaries, the free surface topography boundary conditions, and the forward time stepping, are all by 2nd order F-D methods. The leap-frog technique is used for time stepping everywhere except for the memory variable equations in the viscoelastic cases, where an explicit version of the unconditionally stable Crank-Nicholson method is used. I show synthetics applying the schemes to isotropic 2-D and 3-D media covered by topographies that are either described by analytic expressions or by real elevation data. These data are taken from an area in South-Eastern Norway that contains the NORESS seismic receiver array. Domains up to 60 x 60 kilometers are used in 3-D simulations, and the applied sources are plane waves generated by a plane of Ricker type point sources. These sources represent earthquakes or teleseismic explosions. For 2-D simulations I have used both plane waves and point sources, since the larger models permissible in 2-D allow for point sources to represent earthquakes or teleseismic explosions quite well. For 2-D simulations I have also included examples using layered media with randomization by a 2-D von Karman function with and without apparent anisotropy. Synthetic snapshots and seismograms show Rayleigh (Rg)-waves emanating from areas of prominent topography as well as strong surface wave directivity from some topographic features. Full viscoelastic modeling with relatively low Q-values, describing near-surface sedimentary layers, exhibit intrinsic attenuation and physical dispersion of the wavefield. Results coincide with numerous observations. 3-D simulations are performed using domain decomposition parallelization implemented by Message Passing Interface (MPI).

Prestack migration of seismic data is a dominant tool for imaging hydrocarbon bearing structures in the Earth. The standard prestack depth migration is a Kirchhoff approach using single-valued traveltimes computed from eikonal solvers or ray tracing. In simple structures with only one ray path between a surface location and a subsurface point, the single-valued assumption is valid, and the migration yields an acceptable image. However, in complex structures more than one ray path may exist between any image point and any surface location. Although it would be ideal to use all the ray paths, standard practice is to choose a single ray from the multiple arrivals to represent the wave propagation between two points. Standard choices include the ray having the minimum arrival time, the ray with the greatest amplitude or the ray traveling the shortest distance. We are critical of these standard selection rules as these are local comparisons of individual rays of the multi-valued traveltime operator. Single-valued migration operators based upon these selection rules can lead to uncontrolled jumps between the branches of the multi-valued traveltime operator, resulting in poor image quality. In this work we improve the Kirchhoff approach using single-valued traveltimes. We expect that better images can result from selection rules based on analysis of the full multi-valued operator, selecting rays yielding more continuous, yet energetic single-valued operators. We examine a particular selection rule of this type: choosing rays associated with branches of the multi-valued operator having the maximum angular aperture (MAA) about the image point. We provide several examples in 2D and 3D on synthetic and real data comparing the MAA selection rule with standard selection choices. Our results demonstrate that the MAA single-valued operator performs consistently as well as standard single-valued operators.

Seismic amplitude-versus-offset (AVO) analysis is a powerful geophysical technique for direct detection of gas on seismic records, and has increased the drilling success ratio in many areas. Due to the shifting of focus from 2-D migration to 3-D migration, to image correctly in regions with complex geological structures, full-volume AVO analysis of seismic reflection data is useful in detecting areas of anomalous AVO attributes (intercept and gradient), in a 3-D seismic data volume. Gardner et al. (1986) introduced 3-D dip moveout (DMO) and 3-D pre-stack imaging (PSI) as an alternative approach to 3-D time migration. One objective of this thesis is to study the amplitude behavior of the DMO and PSI methods, and show that PSI can be used to preserve the amplitude information. This thesis presents a new implementation of the PSI method. The kinematic correctness of this new PSI implementation, and the existing DMO implementation (Canning, 1993) is illustrated using examples from their application to three-dimensional synthetic data. The amplitude behavior of the both these implementations are illustrated using several examples. Based on the amplitude behavior, two different schemes to estimate the AVO attributes (intercept and gradient) are presented. Both these schemes provide reliable estimates of the AVO attributes, for reflection events with dip angles less than 30 degrees. (Abstract shortened by UMI.)

New quantitative methods of determining plate motions with respect to the hotspots, and their associated uncertainties are presented. These methods are then applied to Pacific hotspot data and combined with the global plate circuit to make estimates of the Cenozoic motion between Pacific and Indo-Atlantic hotspots. It is found that Pacific and Indo-Atlantic hotspots have little to no resolvable motion, about 3 +/- 6 mm yr-1, since 48 million years before present (Ma), but do show large motions, about 50 +/- 15 mm yr-1, between 48 and 68 Ma. This implies that a global hotspot reference frame for plate motions is attainable, at least since 48 Ma. It is also demonstrated, with the aid of paleomagnetic data that the observed large scale motions prior to 48 Ma are likely, at least in part, a result of unresolved links in the global plate circuit across Antarctica before 48 Ma.

Three different aspects of estimating properties from seismic data are treated in this thesis: (1) Deterministic processing of a high resolution shallow seismic data set with good geologic control, (2) traveltime estimation from complicated models described statistically, and (3) estimation of a the vertical autocorrelation length of such models. The first part of this thesis is the processing and interpretation of a shallow seismic dataset collected in an open pit copper mine near Tyrone, New Mexico. The seismic image is compared with the outcrop in the open pit mine wall along which the seismic line was collected, and with drill data obtained from the mine operators. Specific features imaged by the experiment include the base of the overlaying sediment, the base of the leached capping, and fractures and shear zones that control local ground water flow. The features in the migrated section compare well with outcrop and drill data. The second part of the thesis studies the systematic bias of velocities estimated from first arrival travel times measured from a class of very complicated velocity models. Traveltimes were computed for statistically described velocity models with anisotropic von Karman correlation functions. The results of a finite difference eikonal solver, corresponding to very small wavelength experiments, are compared to results from picking first arrivals of full wavefield finite difference simulations. The eikonal solver results show the largest systematic bias, corresponding to the ray theoretical limit, and the results from the full wavefield experiments are smaller, but with very similar dependence on aspect ratio of the anisotropic correlation function. The third part defines two methods to obtain the vertical correlation length from seismic data approximated by the primary reflectivity series, which conventionally is used as the ideal result of seismic imaging. The first method is based on fitting a theoretical power spectrum based on the known source spectrum and fractal dimension to the average vertical power spectrum of the seismograms. This method works for a range of conditions where the correlation length is relatively small compared to the wavelength. Larger correlation lengths can be estimated by a second method based on deconvolving and integrating the seismogram to obtain an approximation of a vertical slice of the velocity model.

The early version of the Toffoletto - Hill - Ding open magnetosphere model is improved and generalized in this thesis. This model computes the interplanetary magnetic field (IMF) dependent magnetic and electric fields in the Earth's magnetosphere. The magnetospheric magnetic fields contain contributions from the Earth's dipole field, the ring current, the tail field, and the interconnection magnetic field that represents the effect of an open magnetosphere. The solar wind electric field is mapped along open magnetic field lines into the polar cap ionosphere and acts as a driver for magnetospheric convection. We show that the influence of the IMF on the plasma convection in the magnetosphere as given by the new model is consistent with observations. The tail field is modified to be consistent with the interconnection field.

We use gravity to estimate rifted margin deep structure with an inversion method that links parameters in the shallow parts of the model to those in the deep parts through an isostatic, uniform extension model. The method provides for variable weighting of prior information, estimates densities and shapes simultaneously, and can be used in the presence and absence of deep seismic data. Synthetic tests of sensitivity to noise indicate that the isostatic extension constraint promotes the recovery of the short wavelength Moho topography, eliminates spatial undulations in deep structure due to noise in the data, and increases the range of acceptable recovered models over no isostatic extension constraint. In application to real data from the Carolina trough, the method recovers models that exhibit anomalously high density in the hinge zone area, apparently anomalously thick crust, and anticorrelation of subcrustal lithospheric densities with crustal densities. The first two features are observed in deep seismic studies. The latter is consistent with melting model predictions. We then present a unified view of the traditional gradiometric observables---differential curvature, horizontal gradient of vertical gravity, and vertical gradient of vertical gravity, in terms of invariants of the full gradient tensor, and examine their ability to recover subsurface structure through an efficient inversion method. Results of synthetic tests performed on selected complex bodies and noise free data indicate differential curvature and the horizontal gradient of vertical gravity do as well as the full tensor in recovering subsurface structure. In the presence of noise, we find that a mass constraint promotes recovery of smooth models and may be more appropriate than finite difference smoothing. Differential curvature appears to be a useful observable when inverted alone and as an early search technique in full tensor inversion.

The Iberia Margin is an excellent example of a passive rift. Multi-Channel Seismic (MCS) data consisting of the Line 14 reflection profile from the 1997 Iberia Seismic Experiment were processed and interpreted. Enhanced processing attenuated pervasive water-bottom multiple noise. MCS data image an extensional terrain that includes the Ocean-Continent Transition (OCT). The Moho is imaged locally. Extended crust was restored to an unextended state to quantify deformation. Horizontal strain tends to increase seaward along dip; the average strain is 46%. Crustal-thickness data indicate an average crustal thickness of 9.9 km. With certain assumptions regarding the observability of extension, the presence of 'pure shear' exclusively, and initial crustal thickness, there is a major discrepancy between the observed average crustal thickness and the average crustal thickness predicted by observed strain. The only satisfactory explanation is that crust has been removed by asymmetrical extension (simple shear).

This research investigates the different scales of crustal heterogeneity. A method for estimating the characteristic smaller scales of crustal heterogeneity directly from reflection seismic data is applied to the COCORP dataset. Smaller scales of crustal heterogeneity range between 250-800 m. The method is also applied to another reflection dataset that images extended crust similar to the Basin and Range and the results are compared. To determine the larger scale of heterogeneity, 2-D velocity models for the PASSCAL Basin and Range E-W refraction profile are derived using 2-D traveltime inversion. Combined stochastic and deterministic models that represent crustal velocity heterogeneity are generated using the results from the characteristic scale estimation and 2-D inversion. From these models, finite-difference synthetic seismograms are generated and a preferred model is chosen because the corresponding synthetic seismograms reproduce well the characteristic features of the seismic wavefield seen in the PASSCAL data.