Numerical Techniques for the Inverse Acoustical Scattering Problem in Layered Media

1982 ◽  
pp. 443-457 ◽  
Author(s):  
P. C. Pedersen ◽  
O. J. Tretiak ◽  
Ping He
Keyword(s):  
Scattering Problem ◽  
Layered Media ◽  
Numerical Techniques

Seismogram synthesis for multi-layered media with irregular interfaces by global generalized reflection/transmission matrices method. II. Applications for 2D SH case

1995 ◽  
Vol 85 (4) ◽  
pp. 1094-1106
Author(s):  
Xiaofei Chen
Keyword(s):  
Present Article ◽  
Analytical Solutions ◽  
Scattering Problem ◽  
Layered Media ◽  
Synthetic Seismograms ◽  
Numerical Results ◽  
New Method ◽  
New Formulation ◽  
Series Study

Abstract As the second part of a series study attempting to present a new method of seismogram synthesis for the irregular multi-layered media problems, the present article is devoted to discussing the aspects of the implementation of our new formulation developed earlier in part I of this series study (Chen, 1990). In this article, we have verified the validity of the formulation by comparing our numerical results with the existing analytical solutions for the scattering problem of a semi-circular canyon, and have shown its applicability by computing the synthetic seismograms for several selected irregular multi-layered media cases. Finally, applying our algorithm to the Whittier-Narrows earthquake of 1987, we have successfully interpreted the observed records.

Fast Frequency-Domain Forward and Inverse Methods for Acoustic Scattering from Inhomogeneous Objects in Layered Media

2016 ◽  
Vol 24 (03) ◽  
pp. 1650008 ◽  
Author(s):  
Jing He Li ◽  
Qing Huo Liu
Keyword(s):  
Inverse Scattering ◽  
Large Scale ◽  
Layered Medium ◽  
Scattering Problem ◽  
Acoustic Scattering ◽  
Layered Media ◽  
Source Inversion ◽  
Multiple Frequency ◽  
Stable Convergence ◽  
Forward Solution

The fast scattering and inverse scattering algorithms for acoustic wave propagation and scattering in a layered medium with buried objects are an important research topic, especially for large-scale geophysical applications and for target detection. There have been increasing efforts in the development of practical, accurate, and efficient means of imaging subsurface target anomalies. In this work, the acoustic scattering problem in layered media is formulated as a volume integral equation and is solved by the stabilized bi-conjugate gradient fast Fourier transform (BCGS-FFT) method. By splitting the layered medium Green’s function interacting with the induced source into a convolution and a correlation, the acoustic fields can be calculated efficiently by the FFT algorithm. This allows both the forward solution and inverse solution to be computed with only [Formula: see text] computation time per iteration, where [Formula: see text] is the number of degrees of freedom. The inverse scattering is solved using a simultaneous multiple frequency contrast source inversion (CSI). The stable convergence of this inversion process makes the multiple frequency simultaneous CSI reconstruction practical for large acoustic problems. Some representative examples are shown to demonstrate the effectiveness of the forward and inverse solvers for acoustic applications.

Exponential convergence of Cartesian PML method for Maxwell’s equations in a two-layer medium

2020 ◽  
Vol 54 (3) ◽  
pp. 929-956
Author(s):  
Xiaoqi Duan ◽  
Xue Jiang ◽  
Weiying Zheng
Keyword(s):  
Electromagnetic Scattering ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Numerical Solutions ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Layered Media ◽  
Theoretical Work ◽  
Scattering Problems ◽  
Layer Medium

The perfectly matched layer (PML) method is extensively studied for scattering problems in homogeneous background media. However, rigorous studies on the PML method in layered media are very rare in the literature, particularly, for three-dimensional electromagnetic scattering problems. Cartesian PML method is favorable in numerical solutions since it is apt to deal with anisotropic scatterers and to construct finite element meshes. Its theories are more difficult than circular PML method due to anisotropic wave-absorbing materials. This paper presents a systematic study on the Cartesian PML method for three-dimensional electromagnetic scattering problem in a two-layer medium. We prove the well-posedness of the PML truncated problem and that the PML solution converges exponentially to the exact solution as either the material parameter or the thickness of PML increases. To the best of the authors’ knowledge, this is the first theoretical work on Cartesian PML method for Maxwell’s equations in layered media.

Radiation characteristics of elastodynamic line sources buried in layered media with periodic interfaces. II. P- and SV-wave analysis

1987 ◽  
Vol 77 (6) ◽  
pp. 2192-2211
Author(s):  
Vijay K. Varadan ◽  
Akhlesh Lakhtakia ◽  
Vasundara V. Varadan ◽  
Charles A. Langston
Keyword(s):  
Half Space ◽  
Elastic Plate ◽  
Matrix Method ◽  
Scattering Problem ◽  
Finite Size ◽  
Layered Media ◽  
Elastic Half Space ◽  
P Wave ◽  
Radiation Characteristics ◽  
T Matrix

Abstract A method for determining for determining the elastodynamic (P and SV waves) radiation characteristics of finite-size sources buried in horizontally layered media, having periodically corrugated interfaces, is described. In particular, the example problem chosen to illustrate the procedure is as follows: a solid plate lies on top of a solid half-space; the solid-solid interface has been taken to be planar, but traction-free conditions prevail on the other boundary of the elastic plate, which surface is also periodically corrugated; and the source has been taken to be an isotropic, P-wave line source located inside the elastic plate. The technique presented utilizes the plane wave spectral decomposition of the relevant fields within the framework of the extended boundary condition method or the T matrix method. Since the T-matrix method is a matrix approach, it is very attractive computationally and is certainly more tractable than a method based on the direct solution of the integral equations involved in the scattering problem. Numerical results are given to delineate the various features of the field diffracted into the elastic half-space, as well as the displacement field induced on the traction-free boundary of the elastic plate. The specific example examined is directly related to regional wave propagation in a continental crustal wave guide.

Sign in / Sign up

Export Citation Format

Share Document