A note on the interpretation of seismic surface waves over three-dimensional structures

In the 2-D acoustic case, the sound velocity of a heterogeneous medium can be determined from the amplitude and phase of almost any wavefield (but not from its phase alone) by inserting the wavefield into the Helmholtz equation and resolving for the wavenumber. Seismic surface waves in a laterally heterogeneous half-space do not obey the Helmholtz equation; however, when the heterogeneity is smooth, the Helmholtz equation is approximately valid for each mode separately. Using synthetic multimode wavefields, we investigate whether the same equation can be used to improve the structural interpretation of seismic surface waves. We find that the Helmholtz equation images lateral heterogeneity much better than the eikonal equation on which the conventional interpretation of surface wave dispersion is based.