The reconstruction of an obstacle in some background medium is of great importance in practical applications. Mathematically, such a kind of problem called inverse scattering problem, which aims to recover the scatterer from the information about scattered wave.
This paper considers the reconstruction of voids in a uniform semi-infinite solid from near-field elastodynamic wave form via the linear sampling method (LSM). The key idea of LSM is to reconstruct the scatterer boundary by the blowing-up property of some indicator function, which solves an integral equation of the first kind. To solve the cavity imaging problem characterized by a limited density of illuminating sources, this paper considers the existing formulation of LSM in its adjoint statement. That is, a new indicator function which is defined in the data measurement set is introduced. The injectivity, approximation and solution unboundedness of this indicator is proven. To overcome the difficulty of singular value decomposition for large systems arising in solving the indicator function, the preconditioned conjugate gradient method is applied. Numerical examples are presented to show the validity of the proposed method. The generalization of LSM in this paper gives some new directions for other singular source methods such as probe method and factorization method in inverse scattering.