Validity of surface‐wave ray theory on a laterally heterogeneous earth

SUMMARY A necessary and sufficient condition for the validity of surface-wave ray theory is S/m << 1, where S is the root-mean-square degree of the phase-velocity perturbation 6c, and 1 is the degree of the equivalent mode ,,Sl or ,,T. This condition, which is independent of the number of orbits, is obtained by consideration of the Fresnel area along the surface-wave ray path between the source and receiver. We assess the accuracy of surface-wave ray theory by comparing the phase, arrival angle and amplitude anomalies obtained using the JWKB approximation with the corresponding quantities measured using 'ground-truth' synthetic coupled-mode seismograms on models of varying roughness. The JWKB results agree well with the coupled-mode results for model S12-WM13; on a contrived model with slightly rougher variations, however, the agreement deteriorates as the condition S/@ << 1 is less well satisfied. The misfit of the ray approximation, which is dependent upon the quantity S/@, can be attributed to diffraction and other finite-frequency effects within the Fresnel area along the ray path; these effects are ignored by the JWKB theory but are fully accounted for by the coupled-mode summation. The wavefront smoothing produced by this Fresnel-area averaging limits the resolution of surface-wave inversion studies based upon the JWKB approximation.