Propagation of surface waves on a laterally heterogeneous earth: asymptotic solution of the two-dimensional wave equation

The two-dimensional wave equation is used to represent the propagation of surface waves on a laterally heterogeneous earth. Assuming sufficiently smooth variations in earth structure, expressions for the wavefield potentials and their associated displacement spectra are derived up to second-order scattering interactions. Up to first-order scattering, these expressions are shown to be equivalent to the results obtained from the coupling of normal modes along a common dispersion branch. The second-order scattering wavefield appears as a negatively phase-shifted perturbation which acts to decrease the apparent phase velocity of the arriving wavelet. Synthetic experiments demonstrate that significant bias in earth structure inversions may be introduced by neglecting such effects.