Combined Inversion of Early Arrival P-wave and Rayleigh Wave with Cross-gradient Constraint

We present a combined early arrival P-wave and Rayleigh wave inversion strategy that uses the cross-gradient between the P-velocity and S-velocity as a regularization term. First, the P-velocity model is inverted by the early arrival full wave inversion (FWI) method. Then the magnitude spectra of the surface waves in the frequency-wavenumber domain are inverted for the S-velocity model with a cross-gradient constraint. This constraint regularization insists that the S-velocity gradient is closely parallel to that of the P-velocity gradient. Results show that cross-gradient regularization provides a significant reduction in artifacts in the S-velocity tomogram.