Computational framework for the BIE solution to inverse scattering problems in elastodynamics

Abstract

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. Abstract The focus of this paper is a computational platform for the non-intrusive, active seismic imaging of subterranean openings by means of an elastodynamic boundary integral equation (BIE) method. On simulating the ground response to steady-state seismic excitation as that of a uniform, semi-infinite elastic solid, solution to the 3D inverse scattering problem is contrived as a task of minimizing the misfit between experimental observations and BIE predictions of the surface ground motion. The forward elastodynamic solution revolves around the use of the half-space Green's functions, which analytically incorporate the traction-free boundary condition at the ground surface and thus allow the discretization and imaging effort to be focused on the surface of a hidden cavity. For a rigorous approach to the gradient-based minimization employed to resolve the cavity, sensitivities of the trial boundary element model with respect to (geometric) void parameters are evaluated using an adjoint field approach. Details of the computational treatment, including the regularized (i.e.Cauchy principal value-free) boundary integral equations for the primary and adjoint problem, the necessary evaluation of surface displacement gradients and their implementation into a parallel code, are highlighted. Through a suite of numerical examples involving the identification of an ellipsoidal cavity, a parametric study is presented which illustrates the importance of several key parameters on the imaging procedure including the prior information, "measurement" noise, and the amount of experimental input.

Partial-differential-equation-constrained amplitude-based shape detection in inverse acoustic scattering

“…Following the works of Bonnet, Guzina, and Fata [1][2][3][4], here too we adopt the concept of a moving boundary to describe the boundary shape evolution between successive updates of the boundary parameterization. In other words, we assume that between shape updates the boundary evolves or moves according to a transformation velocity v (Fig.…”

“…We remark that in both cases the model parameters are near identical. 4 Thus, when the frequency-continuation scheme is used, convergence is faster (Fig. 5).…”

“…One may roughly classify the approaches that have been followed, into methods that rely on optimization-based schemes (e.g. [1][2][3][4][11][12][13][14][15][16][17][18]), and methods that do not explicitly seek to minimize a misfit functional (e.g. [19][20][21][22][23]).…”

“…This study comes closest to the elegant treatment of similar inverse shape detection problems reported by Bonnet, Guzina, and their collaborators in [1][2][3][4]. Here we try to improve on the sensitivity to the initial guess they reported, by using amplitude-based misfit functionals, and continuation schemes.…”

Dynamical one-dimensional models of passive piezoelectric sensors

“…The development of practical and robust algorithms based on full-waveform (or partial) measurements has been the subject of intense studies over the last few decades. For instance, classical minimization-based approaches exploit the data through a misfit cost function [1][2][3][4]. Alternatively, so-called qualitative methods are commonly centered on the development of an indicator function of scattering obstacles [5][6][7][8][9][10].…”