We consider a self-adjoint operator governing the propagation of elastic waves in stratified media _R_3, where Lame functions and a density are perturbed in a compact region. In this paper we prove the existence, the completeness, and the invariance principle of wave operators associated with the self-adjoint operator and a self-adjoint operator governing the propagation of elastic waves in unperturbed stratified media _R_3. The proof is based on an abstract scattering theory due to M. S. Birman.
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Senjo Shimizu, Scattering Theory for Elastic Wave Propagation Problems in Perturbed Stratified Media II. Publ. Res. Inst. Math. Sci. 33 (1997), no. 3, pp. 341–358DOI 10.2977/PRIMS/1195145319