Three-dimensional inverse scattering for the wave equation with variable speed: near-field formulae using point sources

1989 ◽  
Vol 5 (1) ◽  
pp. 1-6 ◽  
Author(s):  
M Cheney ◽  
G Beylkin ◽  
E Somersalo ◽  
R Burridge
Keyword(s):  
Wave Equation ◽  
Inverse Scattering ◽  
Near Field ◽  
Three Dimensional ◽  
Point Sources ◽  
Variable Speed

scholarly journals Imaging of bi-anisotropic periodic structures from electromagnetic near-field data

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Dinh-Liem Nguyen ◽  
Trung Truong
Keyword(s):  
Inverse Scattering ◽  
Maxwell Equations ◽  
Field Data ◽  
Periodic Structures ◽  
Near Field ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Inverse Scattering Problem ◽  
Factorization Method ◽  
Unique Determination

AbstractThis paper is concerned with the inverse scattering problem for the three-dimensional Maxwell equations in bi-anisotropic periodic structures. The inverse scattering problem aims to determine the shape of bi-anisotropic periodic scatterers from electromagnetic near-field data at a fixed frequency. The factorization method is studied as an analytical and numerical tool for solving the inverse problem. We provide a rigorous justification of the factorization method which results in the unique determination and a fast imaging algorithm for the periodic scatterer. Numerical examples for imaging three-dimensional periodic structures are presented to examine the efficiency of the method.

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.

NUMERICAL SOLUTION OF THE ACOUSTIC WAVE EQUATION AT THE LIMIT BETWEEN NEAR AND FAR FIELD PROPAGATION

2001 ◽  
Vol 12 (10) ◽  
pp. 1497-1507 ◽  
Author(s):  
ERICH STOLL ◽  
STEFAN DANGEL
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Seismic Waves ◽  
Near Field ◽  
Three Dimensional ◽  
Low Frequency ◽  
Far Field ◽  
Acoustic Wave Equation ◽  
Sound Sources ◽  
Continuous Waves

The acoustic wave equation is solved numerically for two and three-dimensional systems at the limit between near and far field propagation. Our results show that for large sound velocities, corresponding to wavelengths larger than the system, near field properties are dominant. When the near field conditions are no longer satisfied, standing waves close to the sound emitters and interference patterns between the near field and far field solutions appear. Our procedure is applied to sound sources, which broadcast coherent and continuous waves as well as to sources emitting bursts of incoherent and uncorrelated waves. Both cases can be used to simulate the spreading of low frequency seismic waves observed close to volcanoes and hydrocarbon reservoirs.

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