Inverse problems for elastic wave from Partial Cauchy Data: Uniqueness and Co-inversion for Shape and Impedance Function (2401.00236v4)

Abstract: We consider an inverse problem for the elastic wave of simultaneously reconstructing the impedance and the geometric information of the bounded body that is occupied by a homogeneous and isotropic elastic medium from the measured Cauchy data. A two-stage reconstruction method is proposed to realize simultaneous reconstruction of multiple targets. In the first step, we restore the aperture information by utilizing the observed Cauchy data that is measured on an accessible part of the boundary. In the second step, we start with the boundary condition and propose a novel iterative method to simultaneously reconstruct the missing boundary and the impedance function. Theoretically, we establish the uniqueness result of the co-inversion problem based on analyzing the properties of the corresponding operators. An explicit derivative is computed for the iterative method. Numerical examples are presented to test the effectiveness and efficiency of the proposed method.