The reflection coefficient for S-waves at normal incidence:
where is the amplitude of a plane S-wave (normalized by the amplitude of the incident wave) reflected from the planar interface between isotropic layers 1 (upper), 2 (lower), , is the density of layers 1, 2, and VS1, VS2 is the S-wave velocity in layers 1, 2. Note the minus sign (the opposite sign convention than for P-waves); this is the standard convention for S-waves; see Aki and Richards (1980). It arises from the convention for amplitudes of transverse waves.
For vertical polar anisotropic media with the planar interface horizontal, the formula is the same, but with the velocities understood as vertical velocities.
For non-normal incidence, there is a difference in reflectivity, depending on the polarization (SH or SV) of the incident wave; the formula (for isotropic media) are given in Aki and Richards. But, since most crustal formations are anisotropic, and since the anisotropy affects S-waves much more than P-waves, these are not repeated here. For azimuthal anisotropy, the situation is even more complicated; see shear-wave_splitting.
- Aki, K, and PG Richards (1980). Quantitative Seismology: Theory and Methods. WH Freeman and Co.