Bayesian approach for two-dimensional interior inverse scattering problem in elasticity

Abstract In this paper, we consider an inverse elastic scattering problem in an impenetrable cavity with Neumann boundary condition. We show that the shape of the cavity can be uniquely determined by the scattered fields measured on some curve in the interior of the cavity. The Bayesian method is used to reconstruct the shape of the cavity from scattered fields incited by point sources inside the cavity. We discuss the well-posedness of the posterior distribution in the sense of the Hellinger metric and employ the preconditioned Crank–Nicolson algorithm to generate the posterior distribution information. Numerical experiments are provided to demonstrate the effectiveness of the proposed method.