Joint inversion of first arrival P waves and Rayleigh waves based on cross-gradient constraint

In seismic exploration, knowledge of the near-surface velocity can improve the construction of an accurate geological model. Until recently, most surface-wave inversion approaches assumed a layered model, which is not justified in a complex geological environment. To overcome this 1D limitation, researchers have begun to explore the benefits of 2D waveform inversion of surface waves. Windowed-Amplitude waveform inversion is a replacement to classical Full Wave form Inversion (FWI), which has faster convergence, however, lower spatial resolution in the tomogram is deduced. To partly recover this lost resolution, we propose a joint inversion of first arrival P-wave data and Rayleigh wave data that uses the cross-product between the P-velocity and S-velocity gradients as a regularization term. First, the P-velocity model is inverted by the full waveform inversion method, in which the first arrivals are those of the refraction and direct arrivals. Then, the amplitude spectra of the surface waves in the frequency-wavenumber domain are inverted for the S-velocity model with a cross-product constraint. This constraint regularization insists that the S-velocity gradient is closely parallel to that of the P-velocity gradient. Results show that cross-product regularization provides a significant reduction in artifacts in the S-velocity tomogram. In this case the less robust inversion of surface waves is combined with high resolution P-wave tomography to achieve better spatial resolution of the S-wave velocity tomogram.