Near-field imaging method for interior inverse elastic scattering problem.

The interior inverse elastic scattering problem is considered in this paper. The scattering in the cavity is illuminated by an time-harmonic elastic point source at fixed frequency. The boundary of the cavity is assumed to be a small and smooth perturbation of some circle. In this paper, we are interested in the reconstruction of the boundary according to the measured data on a closed curve inside the cavity. In implementation, we split the displacement field into compressional and shear waves by the Helmholtz decomposition. Then we use coordinate transformation, power series expansion based on perturbed parameters and Fourier expansion of corresponding power series coefficients to simplify the original boundary value problem to a successive sequence of one-dimensional boundary value problem. We linearize the inverse problem by eliminating the higher-order terms in the power series expansion; and design a reconstruction algorithm by the explicit relationship between the Fourier coefficients of the boundary function and the total field. In order to obtain better resolution, we also use a nonlinear correction method in the numerical experiments. The numerical results have shown the effectiveness and the stableness of the proposed method. [ABSTRACT FROM AUTHOR]