Seismic waves in a stratified half-space — IV: P—SV wave decoupling and surface wave dispersion

Summary. In a region of smoothly varying seismic parameters, the seismic displacements can be transformed into portions depending principally on the P and SV parts of the wavefield. Although this representation has previously been used for body wave studies, it is also very suitable for understanding surface wave problems. With the aid of this transformation and the representation of Rayleigh wave dispersion in terms of reflection coefficients at the free-surface and from the stratification the behaviour of the Rayleigh wavefield with slowness can be related to the velocity structure. This allows the character of Rayleigh waves to be related to that of Love waves. There is very close correspondence when P-waves are evanescent throughout the stratification. In this case we can represent the Rayleigh wave behaviour in terms of a scalar eigenfunction which has simple, though approximate, orthogonality properties.