Many geophysical inverse problems are ill-posed and have to be regularized. The most often used solution methods for solving ill-posed problems are based on the use of quadratic regularization that results in smooth solutions. Solutions of this type are not to be suitable when the model parameter is piecewise continuous blocky and edges are desired in the regularized solution. To avoid the smoothing of edges, which are very important attributes of an image, an edge-preserving regularization (non-quadratic regularization) term has to be employed. Total Variation (TV) regularization is one of the most effective regularization techniques for allowing sharp edges and the existence of discontinuities in the solutions. The edge-preserving regularization based on the TV method for small-scale geophysical inverse problems to the problem of estimating the acoustic velocity perturbation from a multi-source-receiver geophysical experiment is studied. The acoustic velocity perturbation is assumed to be piecewise continuous and blocky. The problem is based on linearization acoustic modeling using the framework of the single-scattering Born approximation from a known constant background medium. To solve this non-linear and ill-posed problem, an iterative scheme based on the conjugate gradient method is employed. The TV regularization method provides us with the opportunity to recover more useful information of velocity profiles from the measured seismic data. Though it requires more effort in implementing the TV term to control the smoothing and regularization parameter, the algorithm possesses the strong ability of marking the discontinuities and ensures their preservation from over-smoothing. / Geophysics

Thesis (Ph.D.)--York University, 2007. Graduate Programme in Physics and Astronomy. / Typescript. Includes bibliographical references (leaves 99-102). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:NR29318

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Cengiz Esmersoy, Bernard C. Levy. / Bibliography: leaf 6. / "March 1985." / "...Army Research Office ... Grant no. DAAG29-84-K-0005."

Thin target L-Shell x-ray production cross sections for protons incident on ₆₂Sm and ₇₀Yb in the energy range of 0.3 to 2.4 MeV/amu, alpha particles incident on ₆₂Sm, ₇₀Yb, and ₈₂Pb in the energy range of 0.15 to 4.8 MeV/amu, and lithium ions incident on ₅₈Ce, ₆₀Nd, ₆₂Sm, ₆₆Dy, ₆₇Ho, ₇₀Yb, and ₈₂Pb in the energy range of 0.8 to 4.4 MeV/amu have been measured. The cross section data have been compared to the planewave Born approximation (PWBA) and the PWBA modified to include binding energy and Coulomb deflection effects. The Lα₁,₂ x-ray production cross sections are best represented by the PWBA modified to include both the binding energy and Coulomb deflection effects (PWBA-BC) over the entire incident ion, incident energy, and target ranges studied. However, the Lγ₁ and Lγ₂,₃,₍₆₎ x-ray production cross sections are best represented by the PWBA except at the lower ion energies, where both the PWBA and PWBA-BC are in disagreement with the data. The comparison of Lα₁,₂/Lγ₂,₃,₍₆₎ ratios to theory reveals that the PWBA-BC does not predict the inflection point substantiated by the data, and the agreement between the data and the PWBA-BC becomes worse as the atomic number of the incident ion increases. Comparison of the PWBA modified to include binding energy effects CPWBA-B) and the PWBA modified to include Coulomb deflection effects (PWBA-C) to the Lα₁,₂, Lγ₁, and the Lγ₂,₃ cross sections for protons, alpha particles, and lithium ions incident on ₇₀Yb indicates that the PWBA-C overestimates the magnitude of the data but does describe the shape of the L₁-associated cross section while the PWBA-B underestimates the magnitude of the data but fails to predict the proper shape of the L₁-associated data. In order to evaluate the ability of the PWBA and the presently accepted modifications to the PWBA to fit the experimental data, future experimentation should be conducted in the energy range that includes the point where the ratio of the incident ion velocity to the L-Shell electron velocity is equal to 0.19 (i.e., V₁/Vₗ = 0.19). This is where the L₁-associated cross sections begin to exhibit the shouldered structure and the cross section ratios L₃/L₁ and L₂/L₁ have inflection points.

Thesis (PhD)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: See fulltext for abstract. / AFRIKAANSE OPSOMMING: Sien volteks vir opsomming.

Title: Ray-based Born approximation Author: Libor Šachl Department: Department of Geophysics Supervisor: RNDr. Luděk Klimeš, DrSc. Supervisor's e-mail address: klimes@seis.karlov.mff.cuni.cz Abstract: One of the aims of this thesis was coding of program grdborn.for for computing the 2D and 3D ray-based Born approximation of the first order in an inhomoge- nous isotropic medium without attenuation. The computation of 3D amplitudes using the 2D Born approximation is based on the correction term, which is de- rived. The program is further used in computing the Born approximation in various models. We test its performance in three simple models. We study the effect of the discretization, the spurious waves introduced by the finite size of the grid etc. In the next step, we focus on the computations in more compli- cated models. We compute the Born seismograms in 2D heterogenous models. We study the diffracted waves, the effects of caustics etc. Keywords: Born approximation, ray theory, velocity model, perturbation 1

M. Tinkham and M.W.P. Strandberg. / "February 1, 1955"--Cover. "Reprinted from The Physical review, vol. 97, no. 4, 937-966, February 15, 1955." / Includes bibliographical references. / Army Signal Corps Contract DA36-039 sc-42607 Project 132B Dept. of the Army Project 3-99-12-022

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Thesis (Ph. D.)--University of Texas at Austin, 2007. / Vita. Includes bibliographical references.