<p> Variations in density within the earth are the dominant cause of both surface topography--generating mountains, valleys, and plateaux&mdash;and convection, leading to plate tectonics. Density varies as a function of chemistry, mineralogy and temperature, containing information about physical state and history. I develop methods to estimate the density of the crust and upper mantle from seismic, gravity, heat flow, and topographic data. Decomposing density variations into thermal and compositional components provides insight into the origin of topography, tectonic history, and active processes. These techniques are applied to the inspiring landscapes of the western United States. The modern density structure of the Sierra Nevada, California, suggests that post-Miocene range uplift occurred in response to removal of dense mantle lithosphere. A numerical model of the flexural response of the surface to mantle loads shows that this material is likely now found in the upper mantle just west of the range, where it has created the Tulare basin. A broader density model of the entire western U.S. highlights a dichotomy in upper mantle buoyancy between the low-relief Great Plains and regions modified in the Cenozoic. Relief within the Cordillera is generated by varying degrees of crustal thermal and compositional buoyancy. A targeted thermal modeling study of the Colorado Plateau shows that ~2 km of Cenozoic uplift&mdash;in the absence of crustal shortening&mdash;can be ascribed to removal of tens of km of mantle lithosphere and related hydration of the lower crust. Overall, these four studies highlight the utility of density as a window into tectonic processes and a record of lithospheric history.</p>

<p> Well logs, measured in depth, must be tied to seismograms, processed in time, using a time-depth function. Well ties are commonly computed using manual techniques, and are therefore prone to human error. I first introduce an automatic single-well tie method that uses smooth dynamic time warping to compute time shifts that align a synthetic seismogram with a seismic trace. These time shifts are constrained to be smoothly varying. I also show that these well ties, in my example, are insensitive to the complexity of my synthetic seismogram modeling. Tying multiple wells compounds errors in single well ties, and maintaining consistency among multiple single well ties is difficult. I introduce an automatic approach to tying multiple wells that improves consistency among well ties. I first model synthetic seismograms for each well. I then create a synthetic image by interpolating the synthetic seismograms between the wells and along seismic image structure. I use smooth dynamic image warping to align the synthetic image to the seismic image and compute updated time-depth functions for each well. I then interpolate the updated time-depth functions between the wells, and map the time-migrated seismic image to depth.</p>

<p>Time Reversal can be used to time reverse and propagate the measured scattered wave- forms to a point in both time and space, ideally to a delta function &delta;([special characters omitted])&delta;(t). This is commonly referred to as time reversal focusing and has led to time reversal being applied in a wide variety of fields such as medicine, communications, nondestructive evaluation (NDE), and seismology. In practice, time reversal is not optimal for generating a delta function focus if certain conditions are not upheld. For time reversal to work perfectly, the following four conditions must be present: (1) one must record for an infinitely long period of time; (2) Green's functions must be assumed to contain infinite bandwidth; (3) attenuation must be absent within the medium; and (4) one must have full coverage of the wavefield. Due to the need for these conditions, much research is being carried out in order to enhance the time reversal process in practice. We introduce deconvolution, a simple and robust approach, in order to calculate an optimal signal for back propagation designed to give an improved focus. We demonstrate experimentally that deconvolution is able to dramatically improve the temporal focus com- pared to time reversal. Through a joint project with Los Alamos National Laboratory, we compared time reversal to deconvolution. The results showed that deconvolution was able to dramatically improve the temporal focus for a source and a receiver which were both located on the surface of our object. We then continued our experimental studies of deconvolution by doing a joint project with researcher Dr. Ernst Niederleithinger from the Federal Institute for Materials Research and Testing (BAM). For this experiment, we placed multiple sources within a concrete block and recorded the source wavefields on the surface with a single re- ceiver. This experiment was designed to further test the robust nature of deconvolution and compare its temporal focusing capability to that of time reversal. All of these experimental studies show that deconvolution was able to improve the temporal focus compared to time reversal. We continued our comparison study between time reversal and deconvolution and demon- strated theoretically, experimentally, and numerically that deconvolution also improves spa- tial focusing. We give a proof explaining why one would expect improved spatial focusing when there is improved temporal focusing for both a acoustic and elastic media. We then demonstrate in our experiments the improved spatial focus achieved using deconvolution by scanning around the source location with a laser vibrometer at the time of focus for an acoustic case. Finally, we use deconvolution to locate synthetic microseismic events to prove numerically that improved temporal focusing leads to improved spatial focusing for both acoustic and elastic media.</p>

<p> The analysis of passive source seismic data recorded by quasi-linear deployments of broadband stations at teleseismic distances has proven to be an effective means of probing the subsurface of the Earth. However, current methodologies are far from being able to exploit all the interpretable signal in these data sets. In this thesis, I describe a 2.5D, frequency domain, visco-elastic waveform tomography algorithm for imaging with this type of data. To compute synthetic seismograms (the forward problem), the general equations of motion are discretized with p-adaptive finite elements. This approach allows for geometric flexibility and accurate solutions as a function of wavelength. Artificial force distributions manifesting Huygen's principle for the teleseismic events are introduced locally through a Bielak layer. Because of the relatively low frequency content of teleseismic data, regional scale tectonic settings can be parameterized with a modest number of variables and perturbations can be determined directly from a regularized Gauss-Newton system of equations. Waveforms generated by the forward problem compare well with analytic solutions for simple 1D media and with those generated in heterogeneous structures by a finite difference technique. It is demonstrated through examples that the regularized approximate Hessian is particularly effective at focusing backpropagated residuals to their true location. It is observed that full waveform inversion can provide significantly better vertical resolution than arrival time tomography and significantly better lateral resolution than standard surface wave tomography. Used in tandem in a multi-scale approach, surface wave tomography followed by joint surface wave/body wave tomography is shown to be an effective strategy for image reconstruction from a simple starting model. This inversion strategy is then applied to body and surface wave teleseismic waves recorded in the Tien Shan. The work of previous investigators is both corroborated and better illuminated by starting from a 1D model and inverting with this joint multi-scale approach. The main results for this application are (1) that the Tarim basin appears to be underthrusting the Tien Shan from the south, (2) a thin crust overlaying a piece of suspected relict lithosphere exists below the Naryn valley, and (3) there is a south dipping high velocity zone on the north side of the Tien Shan suggesting consumption of the Chu depression and the Kazak shield. The north dipping high velocity feature in the south and south dipping high velocity feature in the north are consistent with the hypothesis of dual subduction beneath the Tien Shan.</p>

<p> Seismic images and the geologic information they provide contribute significantly to our understanding of the earth's subsurface. In this thesis, I focus on methods relevant for constructing and interpreting seismic images, including methods for velocity estimation, seismic imaging, and interpretation, which together address key aspects of reflection seismic data processing. Specifically, I propose improved methods for semblance-based normal-moveout velocity analysis, for seismic imaging by least-squares migration, and for the automatic extraction of geologic horizons. </p><p> To compute a seismic image, an estimate of the subsurface velocity is needed. One common method for constructing an initial velocity model is semblance-based normal-moveout (NMO) velocity analysis, in which semblance spectra are analyzed to identify peaks in semblance corresponding to effective NMO velocities. The accuracy of NMO velocities obtained from semblance spectra depends on the sensitivity of semblance to changes in velocity. By introducing a weighting function in the semblance calculation, I emphasize terms that are more sensitive to velocity changes, which, as a result, increases the resolution of semblance spectra and allows for more accurate NMO velocity estimates. </p><p> Following velocity analysis, a seismic image of the subsurface is computed by migrating the recorded data. However, while velocity analysis is an important step in processing reflection seismic data, in practice we expect errors in the velocity models we compute, and these errors can degrade a seismic image. Instead of minimizing the difference between predicted and observed seismic data as is done for conventional migration, I propose to minimize the difference between predicted and time-shifted observed data, where the time shifts are the traveltime differences between predicted and observed data. With this misfit function, an image computed for an erroneous velocity model contains features similar to those obtained using a more accurate velocity. </p><p> Once a seismic image is computed, a common task in interpreting the image is the identification of geologic horizons. As an alternative to manual picking or autotracking, I propose methods to automatically and simultaneously extract all horizons within an image. To extract geologic horizons, a seismic image is unfaulted and unfolded to restore horizons to an undeformed, horizontal state from which they can be easily identified and extracted.</p>

<p> Satellite and <i>in situ</i> observations of ice sheet outlet glaciers around the turn of the 21^st century showed that rapid changes in ice dynamics are possible and important for the evolution of ice sheets. When attempting to model these dynamic changes the conditions at the ice-bed interface are crucial. Inverse methods can be used to infer basal properties, such as the basal yield stress, from abundant surface velocity observations by using a physical model of ice flow. Inverse methods are very powerful, but they need to be applied with care, otherwise errors can dominate the solution. In this study we investigate the potentials and caveats of inverse methods.</p><p> Synthetic experiments can be designed where basal conditions are assumed and an ice flow model is used to produce a set of 'synthetic' surface velocities. These can then be used to examine and evaluate inverse methods. We find that in iterative inverse methods it is essential to use a stopping criterion that will prevent overfitting the data. We introduce a new and rapidly-converging iterative inverse method called Incomplete Gauss Newton method, where the linearized problem is partly minimized in each step.</p><p> In a practical application of inverse methods to the terminus region of Jakobshavn Isbr&aelig;, Greenland we investigate changes in basal conditions over time by performing inversions for different years of available surface velocity data. We find a decrease in basal yield stress in the lower areas of the glacier that agrees with effective pressure changes due to the changes in ice geometry. This supports an ocean and terminus driven system.</p><p> The difference between the modeled and observed velocity fields, called residual, contains information about the ability to reproduce the velocities when only adjustment of the basal condition is allowed. With a properly regularized inversion the residual patterns can be used to investigate sources of error in the system. We find that the ice geometry and the model simplifications influence the ability to reproduce observed velocity fields more than the error in observed velocity does. This indicates that further progress must come from model improvements and improved capabilities to measure bedrock geometry.</p>

The deformation of the Iranian plateau subject to the convergence of the Arabian shield and Eurasian plate, is studied by the "thin viscous sheet" numerical model. The lithosphere is approximated by a thin layer having a uniform initial thickness, and the flow of material is assumed to be governed by a power law rheology. The solutions are calculated for velocity fields, crustal thickness distributions, stress and strain rate fields, and topography variations. The effects of the physical parameters (rheology, density etc.) are investigated through two non-dimensional parameters: n, the power law exponent in the constitutive relation between stress and strain rate, and Argand number Ar, which is a measure of the relative importance of the buoyancy force to the viscous force. The lack of deformation in central Iran and the southern Caspian block, is considered, by including lateral heterogeneities in the rheology of the lithosphere. The results show that heterogeneous models with non-Newtonian materials for n greater than 3 and $ rm1<Ar<10$ can best approximate tectonic features of Iran. The models are successful in providing reasonable agreement between the estimates of crustal thickness and strain rates, obtained from seismic observations, and those predicted from the theory. The topography pattern and the style of faulting in different parts of the plateau, are explained through the effect of boundary conditions and lateral heterogeneities.

A 16-h real data numerical simulation of the growing and mature stages of the 15 December 1992 TOGA COARE mesoscale convective system is performed. One of the objectives of this study is to obtain a realistic simulation of the lifecycle and to determine the factors that regulated the convective onsets. Another objective is to document the impact of the mesoscale convective system and its embedded mesoscale precipitation features on the atmospheric heat and moisture budgets over the warm pool and the surface energy balance of the underlying ocean. The lifecycle of the mesoscale convective system was characterized by the initiation at 0530 UTC of two entities S1 and S2, which underwent development and eventually merged to form a large anvil cloud by 1830 UTC. To obtain a realistic simulation of the lifecycle, improvements to the initial moisture field, the convective and surface flux processes in the model were undertaken. / The lifecycle of the mesoscale convective system was realistically simulated, The growing stage was composed of three convective onsets at 0600, 1100, and 1400 UTC. The onsets were governed by three factors: occurrence of convective available potential energy, large scale ascent and a favorable surface potential temperature dropoff. / The calculated heat and moisture budgets of the mesoscale convective system were characterized by two heating and drying peaks (300 hPa and 925 hPa) with cooling and moistening occurring at midlevels (45--700 hPa). / The surface energy balance was not affected by solar radiation because the system evolved nocturnally. Latent heat flux and the net longwave radiation were the two largest components in the surface energy budget. During the second and third convective onsets, the net longwave radiation remained essentially unchanged but the latent and sensible heat fluxes increased. The enhanced surface fluxes during the onsets increased the residual ocean fluxes, particularly over the region occupied by the third convective onset. (Abstract shortened by UMI.)

This thesis focuses on a universal multifractal, Fractionally Integrated flux model. Although this type of model is one of the first continuous multiplicative cascade models developed, and in fact the first chapter of this thesis dates back six years, it still remains an excellent model for a wide range of systems. Using the framework of GSI, extended in this thesis, it has been shown here that sea ice, cloud radiances and topography are all fields that can be modeled by universal multifractals. The multifractal parameters of such fields are given, and classification of anisotropies using GSI parameters is made. In addition, the anisotropic universal multifractal model is used for magnetization, and the implications for magnetic anomaly field are examined. The model agrees not only with magnetization data, but with the magnetic field data, and correctly predicts what could otherwise be considered an anomalous scale break. This theory is easily generalized to gravitational potential fields and rock density, and has applications in the modeling of other physical systems.

Recently, there has been a dramatic increase in the use of scale invariance in the study of geophysical fields. However, very little attention has been paid to the anisotropy that is invariably present in these fields, in the form of stratification, differential rotation, texture and morphology. In order to account for scaling anisotropy, the formalism of Generalized Scale Invariance (GSI) was developed. Until now, only a single analysis technique has been developed which incorporates this formalism and which can be used to study the differential rotation of fields. / Using a two-dimensional representation of the linear approximation to GSI, a new, greatly improved, technique for quantifying anisotropic scale invariance in geophysical fields is developed: the Scale Invariant Generator technique (SIG). / The ability of the technique to yield valid estimates is tested by performing the analysis on multifractal (scale invariant) simulations. It was found that SIG yields reasonable estimates for fields with a diversity of anisotropic and statistical characteristics. The analysis is also performed on three satellite cloud radiances and three sea ice SAR reflectivities to test the applicability of the technique. SIG also produced reasonable estimates in these cases.