Journal ArticleDOI
Velocity inversion procedure for acoustic waves
Jack K. Cohen,Norman Bleistein +1 more
TLDR
In this paper, an acoustic model is used, and the reflections are assumed to be sufficiently weak to allow a linearization procedure in the otherwise nonlinear inverse problem, which is given as a multiple integral over the reflection data observed at the upper surface.Abstract:
An approximate solution is presented to the seismic inverse problem for two‐dimensional (2-D) velocity variations. The solution is given as a multiple integral over the reflection data observed at the upper surface. An acoustic model is used, and the reflections are assumed to be sufficiently weak to allow a “linearization” procedure in the otherwise nonlinear inverse problem. Synthetic examples are presented demonstrating the accuracy of the method with dipping planes at angles up to 45 degrees and with velocity variations up to 20 percent. The method was also tested under automatic gain control, in which case velocity estimates were lost but the method nonetheless successfully migrated the data.read more
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Journal ArticleDOI
Nonlinear two-dimensional elastic inversion of multioffset seismic data
TL;DR: In this article, an elastic finite-difference method is used to perform an inversion for P-wave velocity, S-wave impedance, and density, which is based on nonlinear least squares and proceeds by iteratively updating the earth parameters.
Journal ArticleDOI
Imaging of discontinuities in the inverse scattering problem by inversion of a causal generalized Radon transform
TL;DR: In this paper, the linearized inverse scattering problem is formulated in terms of an integral equation in a form which covers wave propagation in fluids with constant and variable densities and in elastic solids.
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Inverse theory applied to multi‐source cross‐hole tomography.: part 1: acoustic wave‐equation method1
TL;DR: In this article, the use of high speed, high capacity vector computers allows the resultant finite-difference equations to be factored in-place, allowing inversions to be generated using data from a very large number of source positions.
Journal ArticleDOI
An acoustic wave equation for anisotropic media
TL;DR: In this paper, a wave equation, derived using the acoustic medium assumption for P-waves in transversely isotropic (TI) media with a vertical symmetry axis (VTI media), yields a good kinematic approximation to the familiar elastic wave equation for VTI media.
Journal ArticleDOI
On the imaging of reflectors in the earth
TL;DR: In this article, a modification of the Beylkin inversion operator was proposed to account for the band-limited nature of the data and make the role of discontinuities in the sound speed more precise.