Journal ArticleDOI
Formal solutions of inverse scattering problems. IV. Error estimates
TLDR
The formal solutions of certain three-dimensional inverse scattering problems presented in this paper were employed to obtain quantitative estimates on the error resulting from the use of the Born approximations in both direct and inverse potential scattering problems, and these estimates were uniformly valid at all energies, and for all sufficiently weak potentials.Abstract:
The formal solutions of certain three‐dimensional inverse scattering problems presented in papers I–III in this series [J. Math. Phys. 10, 1819 (1969); 17, 1175 (1976); 21, 2648 (1980)] are employed here to obtain quantitative estimates on the error resulting from the use of the Born approximations in both direct and inverse potential scattering problems. These estimates are uniformly valid at all energies, and for all sufficiently weak potentials.read more
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Journal ArticleDOI
Inverse scattering series and seismic exploration
Arthur B. Weglein,Fernanda Vieira Araujo,Paulo M. Carvalho,Robert H. Stolt,Kenneth H. Matson,Richard Coates,Dennis Corrigan,Douglas J. Foster,Simon A. Shaw,Haiyan Zhang +9 more
TL;DR: In this paper, the authors present an overview and a detailed description of the key logic steps and mathematical-physics framework behind the development of practical algorithms for seismic exploration derived from the inverse scattering series.
Journal ArticleDOI
Migration and inversion of seismic data
TL;DR: A principal part of a migration‐inversion algorithm is the migration, and by making use of amplitudes versus offset, it is, in principle, possible to determine the three elastic parameters from compressional data.
Journal ArticleDOI
The role of nonlinearity in inverse problems
TL;DR: In this article, the problem of model appraisal for nonlinear inverse problems is discussed, and three approaches are compared: an analytical approach, a numerical approach and a common sense approach.
Journal ArticleDOI
Multidimensional inverse problems and completeness of the products of solutions to PDE
TL;DR: In this article, a method is given for proving uniqueness theorems for some inverse problems, based on a result on completeness of the products of solutions to PDE problems.
Journal ArticleDOI
The Psychophysiological Implications of Soundscape: A Systematic Review of Empirical Literature and a Research Agenda.
TL;DR: This review aims to investigate the consistency of methodologies applied for the investigation of physiological aspects of soundscape, to underline the feasibility of physiological markers as biomarkers of sound landscape, and to explore the association between the physiological responses and the well-founded psychological components of the soundscape which are continually advancing.
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