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

Abstract

A necessary and sufficient condition for the validity of surface‐wave ray theory is ≪ 1, where is the root‐mean‐square degree of the phase‐velocity perturbation δc, and l is the degree of the equivalent mode nSl or nTl. 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 ≪ 1 is less well satisfied. The misfit of the ray approximation, which is dependent upon the quantity , 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. Copyright © 1995, Wiley Blackwell. All rights reserved