  We consider an inverse elastic scattering problem of simultaneously
reconstructing a rigid obstacle and the excitation sources using near-field
measurements. A two-phase numerical method is proposed to achieve the
co-inversion of multiple targets. In the first phase, we develop several
indicator functionals to determine the source locations and the polarizations
from the total field data, and then we manage to obtain the approximate
scattered field. In this phase, only the inner products of the total field with
the fundamental solutions are involved in the computation, and thus it is
direct and computationally efficient. In the second phase, we propose an
iteration method of Newton's type to reconstruct the shape of the obstacle from
the approximate scattered field. Using the layer potential representations on
an auxiliary curve inside the obstacle, the scattered field together with its
derivative on each iteration surface can be easily derived. Theoretically, we
establish the uniqueness of the co-inversion problem and analyze the indicating
behavior of the sampling-type scheme. An explicit derivative is provided for
the Newton-type method. Numerical results are presented to corroborate the
effectiveness and efficiency of the proposed method.
