Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userA non-iterative sampling method for inverse elastic wave scattering by rough surfaces
79
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Consider the two-dimensional inverse elastic wave scattering by an infinite rough surface with a Dirichlet boundary condition. A non-interative sampling technique is proposed for detecting the rough surface by taking elastic wave measurements on a bounded line segment above the surface, based on reconstructing a modified near-field equation associated with a special surface, which generalized our pervious work for the Helmholtz equation (SIAM J. IMAGING. SCI. 10(3)(2017), 1579-1602) to the Navier equation. Several numerical examples are carried out to illustrate the effectiveness of the inversion algorithm.
rate research
Read More
We consider the numerical algorithm for the two-dimensional time-harmonic elastic wave scattering by unbounded rough surfaces with Dirichlet boundary condition. A Nystr{o}m method is proposed for the scattering problem based on the integral equation method. Convergence of the Nystr{o}m method is established with convergence rate depending on the smoothness of the rough surfaces. In doing so, a crucial role is played by analyzing the singularities of the kernels of the relevant boundary integral operators. Numerical experiments are presented to demonstrate the effectiveness of the method.
This paper is concerned with the direct and inverse random source scattering problems for elastic waves where the source is assumed to be driven by an additive white noise. Given the source, the direct problem is to determine the displacement of the random wave field. The inverse problem is to reconstruct the mean and variance of the random source from the boundary measurement of the wave field at multiple frequencies. The direct problem is shown to have a unique mild solution by using a constructive proof. Based on the explicit mild solution, Fredholm integral equations of the first kind are deduced for the inverse problem. The regularized Kaczmarz method is presented to solve the ill-posed integral equations. Numerical experiments are included to demonstrate the effectiveness of the proposed method.
This document takes existing derivations of scattering loss from rough surfaces, and makes them more accessible as a tool to derive the total scattering loss from a rough mirror given its true surface profile. It does not contain any new results and is therefore not intended for submission to a scientific journal in the near future. A rough mirror will diffusively reflect part of an incident wave, limiting the effective specular reflectivity of the mirror. This in turn will limit the finesse of an optical resonator using this mirror. We ask this reflectivity depends on the roughness, in the limit of small roughness. The derivation we will use is based off a detailed and well-written book by JA Ogilvy which is almost always out of the library on loan, is out of print, and we cant find any second-hand copies on the internet. Note that nowhere does Ogilvy use the phrase Debye-Waller factor. We outline how this derivation of scattering loss can be used in practice to calculate the scattering loss given a high-precision experimental measure of mirror profile.
Inverse scattering problems have many important applications. In this paper, given limited aperture data, we propose a Bayesian method for the inverse acoustic scattering to reconstruct the shape of an obstacle. The inverse problem is formulated as a statistical model using the Bayes formula. The well-posedness is proved in the sense of the Hellinger metric. The extended sampling method is modified to provide the initial guess of the target location, which is critical to the fast convergence of the MCMC algorithm. An extensive numerical study is presented to illustrate the performance of the proposed method.
In this paper, we consider the direct and inverse problem of scattering of time-harmonic waves by an unbounded rough interface with a buried impenetrable obstacle. We first study the well-posedness of the direct problem with a local source by the variational method; the well-posedness result is then extended to scattering problems induced by point source waves (PSWs) and hyper-singular point source waves (HSPSWs). For PSW or HSPSW incident waves, the induced total field admits a uniformly bounded estimate in any compact subset far from the source position. Moreover, we show that the scattered field due to HSPSWs can be approximated by the scattered fields due to PSWs. With these properties and a novel reciprocity relation of the total field, we prove that the rough surface and the buried obstacle can be uniquely determined by the scattered near-field data measured only on a line segment above the rough surface. The proof substantially relies upon constructing a well-posed interior transmission problem for the Helmholtz equation.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
