Inverse Scattering in Acoustic Media Using Interior Transmission Eigenvalues

1997 ◽  
pp. 357-374 ◽  
Author(s):  
J. R. McLaughlin ◽  
P. E. Sacks ◽  
M. Somasundaram
Keyword(s):  
Inverse Scattering ◽  
Transmission Eigenvalues ◽  
Acoustic Media

Modified transmission eigenvalues in inverse scattering theory

2017 ◽  
Vol 33 (12) ◽  
pp. 125002 ◽  
Author(s):  
S Cogar ◽  
D Colton ◽  
S Meng ◽  
P Monk
Keyword(s):  
Inverse Scattering ◽  
Scattering Theory ◽  
Transmission Eigenvalues ◽  
Inverse Scattering Theory

Removing free-surface multiples from teleseismic transmission and constructed reflection responses using reciprocity and the inverse scattering series

Geophysics ◽  
2006 ◽  
Vol 71 (4) ◽  
pp. SI71-SI78 ◽  
Author(s):  
Chengliang Fan ◽  
Gary L. Pavlis ◽  
Arthur B. Weglein ◽  
Bogdan G. Nita
Keyword(s):  
Free Surface ◽  
Inverse Scattering ◽  
Synthetic Data ◽  
P Wave ◽  
Transmission Data ◽  
Before And After ◽  
Small Incidence ◽  
Inverse Scattering Series ◽  
Acoustic Media ◽  
The Difference

We develop a new way to remove free-surface multiples from teleseismic P- transmission and constructed reflection responses. We consider two types of teleseismic waves with the presence of the free surface: One is the recorded waves under the real transmission geometry; the other is the constructed waves under a virtual reflection geometry. The theory presented is limited to 1D plane wave acoustic media, but this approximation is reasonable for the teleseismic P-wave problem resulting from the steep emergence angle of the wavefield. Using one-way wavefield reciprocity, we show how the teleseismic reflection responses can be reconstructed from the teleseismic transmission responses. We use the inverse scattering series to remove free-surface multiples from the original transmission data and from the reconstructed reflection response. We derive an alternative algorithm for reconstructing the reflection response from the transmission data that is obtained by taking the difference between the teleseismic transmission waves before and after free-surface multiple removal. Numerical tests with 1D acoustic layered earth models demonstrate the validity of the theory we develop. Noise test shows that the algorithm can work with S/N ratio as low as 5 compared to actual data with S/N ratio from 30 to 50. Testing with elastic synthetic data indicates that the acoustic algorithm is still effective for small incidence angles of typical teleseismic wavefields.

scholarly journals On the inverse scattering from anisotropic periodic layers and transmission eigenvalues

2020 ◽  
pp. 1-17 ◽  
Author(s):  
Isaac Harris ◽  
Dinh-Liem Nguyen ◽  
Jonathan Sands ◽  
Trung Truong
Keyword(s):  
Inverse Scattering ◽  
Transmission Eigenvalues

Direct nonlinear inversion of 1D acoustic media using inverse scattering subseries

Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. WCD29-WCD39 ◽  
Author(s):  
Haiyan Zhang ◽  
Arthur B. Weglein
Keyword(s):  
Inverse Scattering ◽  
Target Identification ◽  
Numerical Test ◽  
Added Value ◽  
Acoustic Medium ◽  
Nonlinear Inversion ◽  
Model Matching ◽  
Inverse Scattering Series ◽  
Acoustic Media ◽  
Property Changes

A task-specific, multiparameter (more than one mechanical property changes across a reflector), direct nonlinear inversion subseries of the inverse-scattering series is derived and tested for an acoustic medium in which velocity and density vary vertically. Task-specific means that terms in the distinct subseries corresponding to tasks for imaging only and inversion only are identified and separated. Direct means there are formulas that solve explicitly for and output the physical properties, without, e.g., search algorithms, model matching and optimization schemes, and proxies that typically characterize indirect methods. Numerical test results with analytic data indicate that one term beyond linear provides added value beyond standard linear techniques, and the improved estimates are valid over a larger range of angles. The direct acoustic inversion is nonlinear. It serves as an important step for new concepts and methods to guide the much more complicated and minimally realistic elastic inverse for exploration seismology target identification purposes.

scholarly journals Important Issues on Spectral Properties of a Transmission Eigenvalue Problem

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Besiana Cobani ◽  
Aurora Simoni ◽  
Ledia Subashi
Keyword(s):  
Eigenvalue Problem ◽  
Inverse Scattering ◽  
Scattering Problem ◽  
Fredholm Property ◽  
Normal Derivative ◽  
Inhomogeneous Media ◽  
Transmission Eigenvalues ◽  
Transmission Eigenvalue ◽  
Transmission Eigenvalue Problem ◽  
The Difference

Nowadays, inverse scattering is an important field of interest for many mathematicians who deal with partial differential equations theory, and the research in inverse scattering is in continuous progress. There are many problems related to scattering by an inhomogeneous media. Here, we study the transmission eigenvalue problem corresponding to a new scattering problem, where boundary conditions differ from any other interior problem studied previously. more specifically, instead of prescribing the difference Cauchy data on the boundary which is the classical form of the problem, we consider the case when the difference of the trace of the fields is proportional to the normal derivative of the field. Typical concerns related to TEP (transmission eigenvalue problem) are Fredholm property and solvability, the discreteness of the transmission eigenvalues, and their existence. In this article, we provide answers for all these concerns in a given interior transmission problem for an inhomogeneous media. We use the variational method and a very important theorem on the existence of transmission eigenvalues to arrive at the conclusion of the existence of the transmission eigenvalues.

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