Mathematical Foundation of Elastic Wave Propagation
Seismic body waves – whether compressional or shear – are subjected to reflection and refraction at layer boundaries with impedance contrast and diffraction at a sharp discontinuity. Based on the elastic wave theory described in Appendix A, we now review the nature of P- and S-wave propagation. To a great extent, seismic waves traveling in the earth can be considered as elastic waves. Therefore, we can use the wave equation (A-30) for elastic solids to describe seismic wave propagation. As P- and S-waves travel within an elastic solid, they are called body waves. Source types used in seismic surveys often generate P-waves. Nevertheless, at non-normal incidence, part of the P-wave energy is converted to S-waves. The P-to-S conversion phenomenon is the basis for the multicomponent seismic method.