Elastic waves excited by a plane source on the surface of a multilayered medium

Elastic waves excited by a plane piezoelectric source with an arbitrary shape on the surface of a multilayered medium have been studied for the first time in this paper. On the basis of Abzo-zena [Geophys. J. R. Astron. Soc. 58, 91-105 (1979)] and Menke [Geophys. J. R. Astron. Soc. 59, 315-323 (1979)], the propagator matrix for the elastic wave field in multilayered medium is extended from two- to three-dimensional (3D) space. 3D elastic wave field is investigated and the displacement-stress response for the boundary conditions is obtained. The propagation of elastic wave in multilayered media is analyzed in 3D space in the frequency domain. The P-SV and SH modes corresponding to the poles are studied. The excitation and propagation of the modes are analyzed further. It is found that the propagation velocities of the P-SV and SH modes do not depend on the propagation azimuth theta in the plane parallel to the free surface of the multilayered medium while the displacement amplitudes are strongly dependent on the azimuth theta. The directional distribution functions of the modes are independent of the medium parameters and the modes and dependent on the shape and excitation fashion of the source. Finally, as an example, the displacement fields of the P-SV and SH modes excited by a rectangle source are analyzed. The displacement representation and numerical results of the directivity distribution functions for the P-SV and SH modes are obtained.