Combined shape-material sensitivity approach for elastic-wave identification of penetrable obstacles

This study deals with elastic-wave identification of heterogeneities (inclusions) in an otherwise homogeneous "reference" solid from limited-aperture measurements taken on its surface. On adopting the boundary integral equation (BIE) framework for elastodynamic scattering, the inverse query is cast as a minimization problem involving experimental observations and their simulations for a trial inclusion defined through its boundary, elastic moduli, and mass density. Expressions for the shape and material sensitivities of the misfit functional are obtained via the adjoint field approach and direct differentiation of the governing BIE's, respectively. A constrained nonlinear optimization framework based on the direct BIE method and an augmented Lagrangian is implemented. Numerical results for the reconstruction of an ellipsoidal defect in a semi-infinite solid show the effectiveness of the proposed shape-material sensitivity formulation, which constitutes an essential computational component.