Three‐dimensional inverse scattering tomography using elastic waves

Inverse obstacle scattering for elastic waves

Topological Derivative for the Inverse Scattering of Elastic Waves

To establish an alternative analytical framework for the elastic-wave imaging of underground cavities, the focus of this study is an extension of the concept of topological derivative, rooted in elastostatics and shape optimization, to three-dimensional elastodynamics involving semiinfinite and infinite solids. The main result of the proposed boundary integral approach is a formula for topologi...

On the inverse elastic scattering by interfaces using one type of scattered waves

We deal with the problem of the linearized and isotropic elastic inverse scattering by interfaces. We prove that the scattered P -parts or S-parts of the far field pattern, corresponding to all the incident plane waves of pressure or shear types, uniquely determine the obstacles for both the penetrable and impenetrable obstacles. In the analysis, we assume only the Lipschitz regularity of the i...

Inverse scattering with diffusing waves.

We consider the problem of imaging the optical properties of a highly scattering medium probed by diffuse light. An analytic solution to this problem is derived from the singular value decomposition of the forward-scattering operator, which leads to explicit inversion formulas for the inverse scattering problem with diffusing waves. Computer simulations are used to illustrate these results in m...

Inverse scattering as nonlinear tomography

Abstract. The reconstruction problem for the acoustic tomography with non-homogeneous background is discussed. We develop a method of beamlike solutions of a Helmholtz equation which is not sensitive to caustics. For small perturbations of the speed the inverse scattering problem is reduced to inversion of a ray integral transform. An explicit formula is given for beam-like solutions in a homog...