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To meet the United States Government nuclear explosion monitoring requirements with high confidence, the Air Force Technical Applications Center needs new and improved capabilities for analyzing regional seismic teleseismic, and infrasound event data. Recently, the National Nuclear Security Administration has decided to move toward 3D modeling to improve knowledge of the compressional and shear velocity structure and enable us to reduce uncertainty and more accurately detect, locate, and identify small (body wave magnitude mb4) seismic events. For seismically active areas, inaccurate models can be corrected using the kriging methodology and therefore, it is possible to detect, locate, and identify large events even with limited resolution models. This is not necessarily the case for smaller events, however, and it is even more of a challenge for aseismic regions. Furthermore, interest on near-regional to local monitoring demands that we address the Earth's heterogeneities and 3D complexities. Motivated by the shortcomings of existing single-parameter inversion methods in accurate prediction of other geophysical parameters, this research was mainly focused on the development and refinement of advanced multivariate inversion techniques to generate a realistic, comprehensive, and high-resolution 3D model of the seismic structure of the crust and upper mantle that satisfies multiple independent geophysical datasets. We present 3D seismic velocity models of the crust and upper mantle beneath three different regions (northwest China; the East Africa Rift System; and Utah) resulting from the simultaneous and joint use of seismic body wave arrival times surface wave dispersion measurements, and gravity data.

The objective of this work is to help improve seismic monitoring technology through the development and application of advanced multivariate inversion techniques to generate realistic, comprehensive, and high-resolution 3D models of the seismic structure of the crust and upper mantle that satisfy independent geophysical datasets. Our focus is on the region surrounding Iran from the east coast of the Mediterranean in the west, to Pakistan in the east, an area of prime importance to nuclear explosion monitoring (NEM), and a region with adequate calibration events to validate our model and to quantify its accuracy. Specifically, we plan to integrate surface-wave dispersion, receiver function, and satellite and ground-based gravity observations to help constrain the shallow seismic structure in the Arabian-Eurasian collision zone. Building on our earlier work combining receiver functions and surface wave dispersion, and surface-wave dispersion and gravity, we plan to continue to integrate geophysical data sets to create more compatible earth models. We also intend to explore geologically based smoothness constraints to help resolve sharp features in the underlying shallow 3D structure.

A dipole inversion method was developed and successfully applied to the discrimination and identification of unexploded ordnance using total-field magnetometry. A black-white classification of anomalies as ordnance/nonordnance is not possible using magnetics because some nonordnance items are indistinguishable from UXO. We found that the best strategy is to rank items according to the likelihood they are UXO. This ranking can be achieved by several methods: the best was to rank on the basis of the amount of remnant magnetization required to make the anomaly match one of the ordnance items in a predefined library. The discrimination method had the potential to reduce the number of excavations at an impact site in Montana (Guthrie Road) by half; yet still yielded all the ordnance. The method requires complete or a least partial shock demagnetization of ordnance, otherwise it is not possible to reliably rank the anomalies. Error analysis indicated that recovered dipole moments are relatively well constrained. However, identification of the anomaly source is difficult using the recovered dipole moment due to nonuniqueness. The dipole moment is the product of magnetization with volume, and a change in volume can be compensated by a change in magnetization by varying the orientation of the item relative to the Earth's field.

This paper presents a new method of constructing physical models in a geophysical inverse problem, when there are only a few possible physical property values in the model and they are reasonably known but the geometry of the target is sought. The model consists of a fixed background and many small "particles" as building blocks that float around in the background to resemble the target by clustering. This approach contrasts the conventional geometric inversions requiring the target to be regularly shaped bodies, since here the geometry of the target can be arbitrary and does not need to be known beforehand. Because of the lack of resolution in the data, the particles may not necessarily cluster when recovering compact targets. A model norm, called distribution norm, is introduced to quantify the spread of particles and incorporated into the objective function to encourage further clustering of the particles. As proof of concept, 1D magnetotelluric inversion is used as example. My experiments reveal that the particles, starting from a fully scattered distribution, are able to move towards the actual target location; the quality of recovery depends on whether there is enough material (vertical conductance in 1D) in the particles to build the target; and the use of distribution norm can help produce tightened clustering. When the inversion struggles to fit the data, it may indicate that the prior information about the particles' conductivity and size are incorrect.

This is the final report on a field and modeling study aimed at developing methods to map permeability by combining hydrologic and surface geophysical data. Results include: (1) recognizing variation in cobble and sand units with principal components analysis based on borehole geophysical logs; (2) demonstrating a method for recovery of core from these coarse deposits; (3) determining stiffness and damping coefficients by jointly inverting velocity dispersion and attenuation data from vertical seismic profiles (VSPs); (4) recognizing variation below the water table with VSPs, transient electromagnetic soundings, and ground penetrating radar; (5) demonstrating a method for modeling hydrologic responses at a well with MODFLOW; (6) generating program developments in MODFLOW and MODFLOWP to facilitate modeling 3-D heterogeneous aquifer systems. Also, findings from this project were the basis for a follow-on, five year URISP project to develop a field scale control volume (research wellfield) to continue research to develop methods for mapping permeability with non-invasive surface geophysical methods.

A dipole inversion method was developed and successfully applied to the discrimination and identification of unexploded ordnance using total-field magnetometry. A black-white classification of anomalies as ordnance/non-ordnance is not possible using magnetics; rather the items can be ranked according to the likelihood they are UXO. The discrimination method had the potential to reduce the number of excavations at an impact site in Montana (Guthrie Road) by half, yet still yielded all the ordnance. The method requires complete or at least partial shock demagnetization of ordnance, otherwise it is not possible to reliably rank the anomalies. Error analysis indicates that recovered dipole moments are relatively well constrained. However, identification of the anomaly source is difficult using the recovered dipole moment due to non-uniqueness. By recognizing that there are a finite number of ordnance types, correct identification could be achieved in about 55% of cases. Extension of the inversion method to recover either quadrupole of octupole moments did not improve our ability to discriminate or identify.

A joint effort with SACLANTCEN concerning inversion of geophysical parameters in shallow water regions was undertaken. Data from previous experiments were analyzed and techniques for inverting the data were modified and employed. The data acquisition system and computing facilities at SACLANTCEN were used in this effort. Nonlinear inversion techniques employing simulated annealing was also used.

Our geophysical modeling efforts have focused on a variety of special studies. We continue to develop models for Eastern Russia using the Michigan State Siberia database, for which we have expanded over previous Pn velocity tomography by also inverting Lg amplitudes for a regional attenuation study, and a preliminary tomographic image of Pg travel times in Eurasia, including the Siberia region. Both Lg attenuation and Pg velocity tomographic studies illuminate features consistent with known aspects of Siberian and Russian Far East tectonics and are consistent with features derived in our earlier Pn study. Lg attenuation studies will help to improve our understanding of phase amplitudes for calibration across eastern Russia, and an improved Pg model will allow us to better calibrate travel times in the area when secondary phase arrivals are needed for event location. We are exploring the effects of upper mantle velocity gradients on the two-dimensional (2-D) tomographic image for P-waves that travel through the upper mantle for regional-distance source-receiver pairs (2.5 to 18 degrees). By adding an upper mantle gradient term to the inversion for 2-D varying Pn velocity and crustal time terms, we are able to map a 2-D varying upper mantle gradient, based on travel times from high-quality event locations. Lateral gradients in the upper mantle across central and eastern Eurasia vary from -0.001 s(-1) to 0.003 s(-1). High gradients appear to be associated with regions of tectonic convergence, both continental and oceanic, as well as stable cratonic regions. Variance reduction is 63% with respect to Pn tomography without gradients. An improved mapping not only of Pn velocities but also of the upper mantle gradients that influence the travel times for this phase is important for ongoing efforts to improve event location throughout central and eastern Asia.

To meet the United States Government nuclear explosion monitoring requirements with high confidence, the Air Force Technical Applications Center needs new and improved capabilities for analyzing regional seismic teleseismic, and infrasound event data. Recently, the National Nuclear Security Administration has decided to investigate three-dimensional (3D) modeling in an effort to further improve knowledge of the compressional and shear-velocity structure as well as reduce uncertainty and more accurately detect, locate, and identify small (body wave magnitude mb4) seismic events. For seismically active areas, inaccurate models can be corrected using the kriging methodology; therefore, it is possible to detect, locate, and identify large events even with limited resolution models. This is not necessarily the case for smaller events, however, and it is even more of a challenge for aseismic regions. On the other hand, improving near-regional to local monitoring demands that we address the Earth's heterogeneities and 3D complexities. Motivated by the shortcomings of existing single-parameter inversion methods in accurate prediction of other geophysical parameters, this research was mainly focused during its first year on the development of advanced multivariate inversion techniques to generate a realistic, comprehensive, and high-resolution 3D model of the seismic structure of the crust and upper mantle that satisfies multiple independent geophysical datasets. During its second year, we have focused on the efficient implementation of the newly developed technique. Application to different areas around the globe with different sets of observations allows us to study sensitivities, trade-offs, and possible improvements of the methodology. We present 3D seismic velocity models of the crust and upper mantle beneath several regions, resulting from the simultaneous and joint use of seismic body-wave arrival times surface-wave dispersion measurements, and gravity data.

This report is motivated by the need to understand the possible applications of two-dimensional (2-D) modeling of stochastic processes and related techniques in signal processing to problems of inversion of geophysical data. Here we first provide a brief overview of 2-D modeling and signal processing techniques. We then address the problem of passing from free air gravity anomaly data (FAG) to bathymetry. We present an approach to this fundamental inversion problem, based on a systematic spatial segmentation of the 2-D data followed by statistical modeling within the segments. We also suggest possible improvements on current approaches based on transfer function methods.

This report is motivated by the need to understand the possible applications of two-dimensional (2-D) modeling of stochastic processes and related techniques in signal processing to problems of inversion of geophysical data. Here we first provide a brief overview of 2-D modeling and signal processing techniques. We then address the problem of passing from free air gravity anomaly data (FAG) to bathymetry. We present an approach to this fundamental inversion problem, based on a systematic spatial segmentation of the 2-D data followed by statistical modeling within the segments. We also suggest possible improvements on current approaches based on transfer function methods.

The objective of this work is to help improve seismic monitoring technology through the development and application of advanced multivariate inversion techniques to generate realistic, comprehensive, and high-resolution 3D models of the seismic structure of the crust and upper mantle that satisfy independent geophysical datasets. Our focus is on the region surrounding Iran from the east coast of the Mediterranean in the west, to Pakistan in the east, an area of prime importance to nuclear explosion monitoring (NEM), and a region with adequate calibration events to validate our model and to quantify its accuracy. Specifically, we plan to integrate surface-wave dispersion, receiver function, and satellite and ground-based gravity observations to help constrain the shallow seismic structure in the Arabian-Eurasian collision zone. Building on our earlier work combining receiver functions and surface wave dispersion, and surface-wave dispersion and gravity, we plan to continue to integrate geophysical data sets to create more compatible earth models. We also intend to explore geologically based smoothness constraints to help resolve sharp features in the underlying shallow 3D structure.

Many flexible parameterizations exist to represent data on the sphere. In addition to the venerable spherical harmonics, we have the Slepian basis, harmonic splines, wavelets and wavelet-like Slepian frames. In this paper we focus on the latter two: spherical wavelets developed for geophysical applications on the cubed sphere, and the Slepian "tree", a new construction that combines a quadratic concentration measure with wavelet-like multiresolution. We discuss the basic features of these mathematical tools, and illustrate their applicability in parameterizing large-scale global geophysical (inverse) problems.

The general principles of the use of known density anomalies for gravity field modelling are reviewed with special emphasis on local applications and utilization of high degree and order spherical harmonic reference fields. The natural extension to include also unknown density anomalies will be studied within the framework of geophysical inversion methods, and the prospects for hybrid gravity field modelling/inversion methods will be outlined. A very simple case of such methods is the determination of representative topographic densities through collocation with parameters.

The increased speed and resolution possible with MBGG(Moving-Base Gravity Gradiometers) comes at a price, i.e. the need to cope with an enormous volume of data in the 5 independent gradient tensor components and the need for non-conventional methods for extracting geophysical information from the MBGG data. To address these needs, we conducted a survey of conventional and non- conventional data processing methods which might be applied to MBGG data processing. The conventional approach of simply integrating the gradient along the track of the moving platform to obtain a gravity profile ignores the information contained in the cross-track and vertical gradients. Furthermore, since the geophysicist is less interested in the gravity than in the underlying density distributions, conversion of MBGG data to gravity is a step in the wrong direction because of the inherent smoothing that integration entails. We show that the MBGG data contain much more information regarding the size, shape, and depth of buried structure than do conventional gravity data. This holds even when such structures are in isostatic equilibrium, such as a neutrally buoyant submarine, provided that the structures are not spherically symmetric. Among the non-conventional methods which showed promise derive and demonstrate an adaption of these methods for direct recovery of the topographic profile which gives rise to the measured gravity gradients. One interesting application arising from the use of this technique is the rapid profiling of bathymetry via aircraft survey.

We discuss procedures for the iterative solution of an integral equation of the Fredholm type of generic kernel and provide details for two particular geophysical problems. We study the inversion of gravity data in order to retrieve the profile of the underlying topography by searching for solutions giving rise to the most compact configuration. We invert radar measurements to obtain ocean spectra: this is achieved according to a perturbation procedure by minimizing a functional of errors which also expresses the deviation of the solution from an expected spectral density. Keywords: Fredholm integral equation; Ocean bathymetry; Radar measurements; Calculus of variations; Minimization of functionals.

Joint inversion of magnetic, earth rotation, geoid, and seismic data for a unified model of the coupled core-mantle system is proposed and shown to be possible. A sample objective function is offered and simplified by targeting results from independent inversions and summary travel time residuals instead of original observations. These data are parameterized in terms of a very simple, closed model of the topographically coupled core-mantle system. Minimization of the simplified objective function leads to a nonlinear inverse problem; an iterative method for solution is presented. Parameterization and method are emphasized; numerical results are not presented.

The objective of this work is to help improve seismic monitoring technology through the development and application of advanced multivariate inversion techniques to generate realistic, comprehensive, and high-resolution 3D models of the seismic structure of the crust and upper mantle that satisfy independent geophysical datasets. The focus is on the region surrounding Iran from the east coast of the Mediterranean in the west, to Pakistan in the east, a region with adequate calibration events to validate our model and to quantify its accuracy. Specifically, the effort is to integrate surface-wave dispersion, receiver function, and satellite and ground-based gravity observations to help constrain the shallow seismic structure in the Arabian-Eurasian collision zone. Building on earlier work combining receiver functions and surface wave dispersion, and surface-wave dispersion and gravity, integration of geophysical data sets will continue to create more broadly compatible earth models. Geologically based smoothness constraints will be explored to help resolve sharp features in the underlying shallow 3D structure.

Joint inversion of magnetic, earth rotation, geoid, and seismic data for a unified model of the coupled core-mantle system is proposed and shown to be possible. A sample objective function is offered and simplified by targeting results from independent inversions and summary travel time residuals instead of original observations. These data are parameterized in terms of a very simple, closed model of the topographically coupled core-mantle system. Minimization of the simplified objective function leads to a nonlinear inverse problem; an iterative method for solution is presented. Parameterization and method are emphasized; numerical results are not presented.