Eugene M. Lavely

Three-dimensional seismic models of the Earth's mantle

Accurate models of the distribution of elastic heterogeneity in the Earths mantle are important in many areas of geophysics. The purpose of this paper is to characterize and compare quantitatively a set of recent three-dimensional models of the elastic structure of the Earth, to assess their similarities and differences, and to analyze their fit to one class of data in order to highlight fruitful directions for future research. The aspherical models considered are the following: M84C (Woodhouse and Dziewonski, 1984), LO2.56 (Dziewonski, 1984), MDLSH (Tanimoto, 1990a), SH.10c.17 (Masters et al., 1992), and S12_WM13 (Su et al., 1994). Through much of the discussion, M84C and LO2.56 are combined into a single whole mantle model, M84C + LO2.56. The fit of each model to previously tabulated even degree normal mode structure coefficients taken from Smith and Masters (1989a) and Ritzwoller et al. (1988) for multiplets along the normal mode fundamental and first, second, and fifth overtone branches is also presented. Rather than concentrating on detailed comparisons of specific features of the models, analyses of these models are general and statistical in nature. In particular, we focus on a comparison of the amplitude and the radial and geographical distribution of heterogeneity in each model and how variations in each affect the fit to the normal mode observations. In general, the results of the comparisons between the models are encouraging, especially with respect to the geographical distribution of heterogeneity and in the fit to the normal mode data sensitive to the upper mantle and lowermost lower mantle. There remain, however, significant discrepancies in amplitude and in the radial distribution of heterogeneity, especially near the top of the upper mantle and near the top of the lower mantle. The confident use of these models to constrain compositional and dynamical information about the mantle will await the resolution of these discrepancies. The factors that may be responsible for the differences in the models and/or for the misfit between the observed and predicted normal mode data are divided into two types: intrinsic (or procedural) and extrinsic (or structural). We discuss only three extrinsic factors at length here, including errors in the reference crustal models, unmodeled topography on discontinuities in the interior of the mantle, and errors in the assumed relationships between shear (υs) and compressional (υp) heterogeneity.

A unified approach to the helioseismic forward and inverse problems of differential rotation

A general, degenerate perturbation theoretic treatment of the helioseismic forward and inverse problem for solar differential rotation is presented. For the forward problem, differential rotation is represented as the axisymmetric component of a general toroidal flow field using velocity spherical harmonics. This approach allows each degree of differential rotation to be estimated independently from all other degrees. In the inverse problem, the splitting caused by differential rotation is expressed as an expansion in a set of orthonormal polynomials that are intimately related to the solution of the forward problem. The combined use of vector spherical harmonics as basis functions for differential ratio and the Clebsch-Gordon coefficients to represent splitting provides a unified approach to the forward and inverse problems of differential rotation which greatly simplify inversion. 43 refs.

Study of surface nuclear magnetic resonance inverse problems

Abstract Motivated by the recent application of the Earth-field nuclear magnetic resonance (NMR) technique to the detection and mapping of subsurface groundwater (to depths of 100 m or so), and making use of a recently developed theory of the method, we consider in detail the resulting inverse problem, namely the inference of the subsurface water distribution from a given sequence of NMR voltage measurements. We consider the simplest case of horizontally stratified water distributions in a horizontally stratified conducting Earth. Inversion methods based both on the singular value decomposition (SVD) and Monte Carlo are used and compared. The effects of random measurement errors and of systematic errors in the assumed subsurface conductivity structure are studied. It is found that an incorrectly modeled highly conducting layer leads to a “screening effect” in which the water content of layers lying below it is severely underestimated. We investigate also the ability of different source-receiver loop geometries to provide complementary information that may improve a combined inversion. Finally, inversion of experimental data from Cherry Creek, CO, USA is performed. Since only the absolute magnitude of the NMR voltage is measured accurately, a nonlinear Monte Carlo inversion is performed.

Average effects of large-scale convection on helioseismic line widths and frequencies

We present the numerical application of the theoretical formalism of Lavely & Ritzwoller (1992) to the model of stationary, large-scale solar convection described by Glatzmaier (1984) in order to search for a useful characteristic signature of giant-cell convection in helioseismic data. The numerical results contain two major simplifications. First, they are based on degenerate perturbation theory rather than the more accurate quasidegenerate perturbation theory, with the consequence that only the toroidal component of flow has a helioseismic effect

Can the differential sensitivity of body wave, mantle wave, and normal mode data resolve the trade-off between transition zone structure and boundary topography?

Abstract Large-scale seismic models of the three-dimensional (3D) variations in elastic properties will be biased by topography on mantle boundaries to the extent that volumetric and topographic structures produce similar effects in the data. To date, seismic inversions for global-scale 3D elastic models of the mantle have largely ignored the effect that topography on the major mantle discontinuities would have on estimating these models. In this paper we address three questions: (1) to what extent does unmodeled structure on the 410 and 660 km boundaries bias volumetric structure in inversions based on normal mode-mantle wave structure coefficients, absolute S-wave travel times, and differential SS-S travel times? (2) Can the differences in the sensitivity of S waves, SS-S phase pairs, and normal mode-mantle wave data be exploited to estimate transition zone volumetric models that are relatively unbiased by topographic structure? (3) Have current volumetric models resolved the trade-off that exists between volumetric and topographic structures? To address question (1), synthetic experiments were performed which show that volumetric models inferred from normal mode-mantle wave data can be biased by an average value of 20–25% in r.m.s. amplitude in the transition zone relative to current aspherical Earth models, depending on the model parametrization employed. The average transition zone volumetric bias of models inverted from absolute travel times from both transition zone and lower-mantle bottoming S rays that are imprinted with the same topographic signatures is reduced by at least by a factor of five relative to models inverted from normal mode-mantle wave data alone. A reduction in bias by a factor of about four is obtained using SS-S phase pairs in which the SS legs bottom in both the transition zone and lower mantle. The use of lower-mantle bottoming S rays or SS-S phase pairs with the SS legs bottoming in the lower mantle reduces the bias only by an average factor of about two to three relative to the normal mode-mantle wave inversion. These estimates of bias reduction can vary with the type of damping or smoothness constraints that are applied in the inversion. With respect to question (2), these results suggest that, in principle, absolute S-wave travel time data can be used to desensitize volumetric inversions to the bias caused by topography on the transition zone boundaries. In practice, however, near-source structure that contaminates S-wave travel times would diminish this capability. The use of SS-S differential times for SS waves which bottom in the transition zone and mantle waves sensitive to transition zone structure but insensitive to the 660 km boundary, should be the most effective means of overcoming the trade-off. To address question (3), we adopt the criterion that the combination of an unbiased volumetric model with an accurate topographic model should provide a better fit to normal mode structure coefficients than the volumetric model alone. The boundary model Topo660a when added to the volumetric model S12_WM13 fits the normal mode structure coefficients significantly better than the volumetric model alone. However, more recent models of 410 and 660 km boundary topography degrade the fit of the volumetric models S12_WM13 and SH.10c.17 to the normal mode structure coefficients, suggesting that there is not yet a conclusive answer to this question.

Model-based and data-based approaches for ATR performance prediction

Performance of automatic target recognition (ATR) systems depends on numerous factors including the mission description, operating conditions, sensor modality, and ATR algorithm itself. Performance prediction models sensitive to these factors could be applied to ATR algorithm design, mission planning, sensor resource management, and data collection design for algorithm verification. Ideally, such a model would return measures of performance (MOPs) such as probability of detection (Pd), correct classification (Pc), and false alarm (Pfa), all as a function of the relevant predictor variables. Here we discuss the challenges of model-based and data-based approaches to performance prediction, concentrating especially on the synthetic aperture radar (SAR) modality. Our principal conclusion for model-based performance models (predictive models derived from fundamental physics- and statistics-based considerations) is that analytical progress can be made for performance of ATR system components, but that performance prediction for an entire ATR system under realistic conditions will likely require the combined use of Monte Carlo simulations, analytical development, and careful comparison to MOPs from real experiments. The latter are valuable for their high-fidelity, but have a limited range of applicability. Our principal conclusion for data-based performance models (that fit empirically derived MOPs) offer a potentially important means for extending the utility of empirical results. However, great care must be taken in their construction due to the necessarily sparse sampling of operating conditions, the high-dimensionality of the input space, and the diverse character of the predictor variables. Also the applicability of such models for extrapolation is an open question.

Feature association and occlusion model estimation for synthetic aperture radar

We develop a radar-based automatic target recognition approach for partially occluded objects. The approach may be variously posed as an optimization problem in the phase history, scene reflectivity and feature domains. The latter consists of point scattering features estimated from the phase histories or corresponding images. We adopt simple occlusion models in which the physical scattering responses (isotropic scattering centers, attributed scatterers, etc.) can be occluded in any combination. The formulation supports the use of prior occlusion models (e.g., that occlusion is spatially correlated rather than randomly distributed). We introduce a physics-based noise covariance model for use in cost or objective functions. Occlusion model estimation is a combinatorial problem since the optimal subset of scatterers must be discovered from a potentially much larger set. Further, the number of occluded scatterers must be estimated as a part of the solution. We apply a genetic algorithm to solve the combinatorial problem, and we provide a simple demonstration example using synthetic data.