Nearfield inverse scattering formalism for the three‐dimensional wave equation: The inclusion of a priori velocity information

1982 ◽  
Vol 71 (5) ◽  
pp. 1179-1182 ◽  
Author(s):  
A. B. Weglein
Keyword(s):  
Wave Equation ◽  
Inverse Scattering ◽  
A Priori ◽  
Three Dimensional ◽  
Velocity Information ◽  
Dimensional Wave

Obtaining three‐dimensional velocity information directly from reflection seismic data: An inverse scattering formalism

Geophysics ◽  
1981 ◽  
Vol 46 (8) ◽  
pp. 1116-1120 ◽  
Author(s):  
A. B. Weglein ◽  
W. E. Boyse ◽  
J. E. Anderson
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Inverse Scattering ◽  
Seismic Data ◽  
A Priori ◽  
Three Dimensional ◽  
Quantum Scattering ◽  
Acoustic Wave Equation ◽  
Reflection Seismic ◽  
The One

We present a formalism for obtaining the subsurface velocity configuration directly from reflection seismic data. Our approach is to apply the results obtained for inverse problems in quantum scattering theory to the reflection seismic problem. In particular, we extend the results of Moses (1956) for inverse quantum scattering and Razavy (1975) for the one‐dimensional (1-D) identification of the acoustic wave equation to the problem of identifying the velocity in the three‐dimensional (3-D) acoustic wave equation from boundary value measurements. No a priori knowledge of the subsurface velocity is assumed and all refraction, diffraction, and multiple reflection phenomena are taken into account. In addition, we explain how the idea of slant stack in processing seismic data is an important part of the proposed 3-D inverse scattering formalism.

Dielectric Metrology VIA Microwave Tomography: Present and Future

1994 ◽  
Vol 347 ◽  
Author(s):  
J.Ch. Bolomey ◽  
N. Joachimowicz
Keyword(s):  
Inverse Scattering ◽  
A Priori ◽  
Scattering Problem ◽  
Measurement Techniques ◽  
Three Dimensional ◽  
Inverse Scattering Problem ◽  
Dielectric Characterization ◽  
Sample Shape ◽  
Three Dimensional Configuration ◽  
Characterization Of Materials

ABSTRACTUntil now, the measurement techniques used for the dielectric characterization of materials require severe limitations in terms of sample shape, size and homogeneity. This paper considers the dielectric permittivity measurement as a non-linear inverse scattering problem. Such an approach allows to identify the quantities to be measured and suggests possible experimental arrangements. The problem is shown to be significantly simplified if the shape of the material is known and if some a priori knowledge of the averaged value of the permittivity in the material under test is available. Two test cases have been selected to illustrate the state of the art in solving such inverse problems. The first one consists of a two-dimensional configuration which is applicable to cylindrical objects, and the second one to a vector three-dimensional configuration applicable, for instance, to cubic samples. The main limitations of such an inverse scattering approach are discussed and expected improvements in the near future are analysed.

Compact High Order Accurate Schemes for the Three Dimensional Wave Equation

2019 ◽  
Vol 81 (3) ◽  
pp. 1181-1209 ◽  
Author(s):  
F. Smith ◽  
S. Tsynkov ◽  
E. Turkel
Keyword(s):  
Wave Equation ◽  
Three Dimensional ◽  
High Order ◽  
Dimensional Wave

scholarly journals A Comparison of Splitting Techniques for 3D Complex Padé Fourier Finite Difference Migration

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Jessé C. Costa ◽  
Débora Mondini ◽  
Jörg Schleicher ◽  
Amélia Novais
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Computational Cost ◽  
Three Dimensional ◽  
Depth Level ◽  
Numerical Examples ◽  
The Cost ◽  
Comparable Quality ◽  
3D Problem ◽  
Dimensional Wave

Three-dimensional wave-equation migration techniques are still quite expensive because of the huge matrices that need to be inverted. Several techniques have been proposed to reduce this cost by splitting the full 3D problem into a sequence of 2D problems. We compare the performance of splitting techniques for stable 3D Fourier finite-difference (FFD) migration techniques in terms of image quality and computational cost. The FFD methods are complex Padé FFD and FFD plus interpolation, and the compared splitting techniques are two- and four-way splitting as well as alternating four-way splitting, that is, splitting into the coordinate directions at one depth and the diagonal directions at the next depth level. From numerical examples in homogeneous and inhomogeneous media, we conclude that, though theoretically less accurate, alternate four-way splitting yields results of comparable quality as full four-way splitting at the cost of two-way splitting.

FREQUENCY DOMAIN RECONSTRUCTION FOR PHOTO- AND THERMOACOUSTIC TOMOGRAPHY WITH LINE DETECTORS

2009 ◽  
Vol 19 (02) ◽  
pp. 283-306 ◽  
Author(s):  
MARKUS HALTMEIER
Keyword(s):  
Wave Equation ◽  
Frequency Domain ◽  
Boundary Data ◽  
Three Dimensional ◽  
Photoacoustic Tomography ◽  
Two Dimensional ◽  
Reconstruction Problem ◽  
Acoustic Data ◽  
Dimensional Wave ◽  
Frequency Domain Reconstruction

This paper is concerned with a version of photoacoustic tomography, that uses line shaped detectors (instead of point-like ones) for the recording of acoustic data. The three-dimensional image reconstruction problem is reduced to a series of two-dimensional ones. First, the initial data of the two-dimensional wave equation is recovered from boundary data, and second, the classical two-dimensional Radon transform is inverted. We discuss uniqueness and stability of reconstruction, and compare frequency domain reconstruction formulas for various geometries.

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