3D wave-equation dispersion inversion of surface waves

The 2D wave-equation dispersion inversion (WD) methodology is extended to the inversion of three-dimensional data for a 3D shear-wave velocity model. The objective function of 3D WD is the sum of the squared wavenumber differences along each azimuth angle between the predicted and observed 3D dispersion curves. The 3D dispersion curves are obtained by wavenumber-frequency analysis of the fundamental Rayleigh waves in each 3D shot gather. The S-wave velocity update is computed by a weighted zero-lag crosscorrelation between the source wavefield and the back-projected receiver-side wavefield for each azimuth angle. The synthetic and field data examples demonstrate that the 3D WD method can accurately estimate the 3D S-wave velocity model in laterally heterogeneous media.