The problem of mapping underground cavities from surface seismic measurements is investigated within the framework of a regularized boundary integral equation (BIE) method. With the ground modeled as a uniform elastic half-space, the inverse analysis of elastic waves scattered by a three-dimensional void is formulated as a task of minimizing the misfit between experimental observations and theoretical predictions for an assumed void geometry. For an accurate treatment of the gradient search technique employed to solve the inverse problem, sensitivities of the predictive BIE model with respect to cavity parameters are evaluated semi-analytically using an adjoint problem approach and a continuum kinematics description. Several key features of the formulation, including the rigorous treatment of the radiation condition for semi-infinite solids, modeling of an illuminating seismic wave field, and treatment of the prior information, are highlighted. A set of numerical examples with spherical and ellipsoidal cavity geometries is included to illustrate the performance of the method. It is shown that the featured adjoint problem approach reduces the computational requirements by an order of magnitude relative to conventional finite-difference estimates, thus rendering the three-dimensional elastic-wave imaging of solids tractable for engineering applications

The problem of reconstructing underground obstacles from near-field, surface seismic measurements is investigated within the framework of a linear sampling method. Although the latter approach has been the subject of mounting attention in inverse acoustics dealing with far-field wave patterns in infinite domains, there have apparently not been any attempts to apply this new method to the interpretation of near-field elastic wave forms such as those relevant to the detection of subterranean objects. Aimed at closing this gap, a threedimensional inverse analysis of elastic waves scattered by an obstacle (or a system thereof ), manifest in the surface ground motion patterns, is formulated as a linear integral equation of the first kind whose solution becomes unbounded in the exterior of the hidden scatterer. To provide a comprehensive theoretical foundation for this class of imaging solutions, generalization of the linear sampling method to near-field elastodynamics and semi-infinite domains is highlighted in terms of its key aspects. A set of numerical examples is included to illustrate the performance of the method. On replacing the featured elastodynamic half-space Green function by its free-space counterpart, the proposed study is directly applicable to infinite media as well.

This paper is concerned with the development of a fast spectral method for solving direct and indirect boundary integral equations in 3D-potential theory. Based on a Galerkin approximation and the Fast Fourier Transform, the proposed method is a generalization of the precorrected-FFT technique to handle not only single-layer potentials but also double-layer potentials and higher-order basis functions. Numerical examples utilizing piecewise linear shape functions are presented to illustrate the performance of the method.

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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.