Full waveform inversion method based on vertical structural gradient optimization

Adjoint-state method is the mainstream gradient calculation method of full waveform inversion. Although adjoint-state method can realize accurate inversion of horizontal structures, it has limitations on vertical structure inversion. In order to effectively invert the vertical structure, a full waveform inversion method based on vertical structure gradient optimization is proposed. On the basis of the principle of adjoint-state method gradient calculation as well as the characteristics of the source-wavefield forward-time propagation and the residual-wavefield reverse-time propagation, the limitations of adjoint state method in calculating the gradient at the position of the vertical structure is first analyzed. Then, by constructing the autocorrelation term of the residual wavefield of the simulated and the observed data, the gradient obtained by adjoint-state method is compensated at the vertical structure position. Taking the maximum energy of autocorrelation gradient term as the normalization criterion, the weighting factor is introduced to realize the combination of autocorrelation term mentioned above and cross-correlation term calculated by adjoint-state method, to improve the inversion effect of vertical structure and retain the inversion effect of horizontal structure at the same time. The inversion results of single-layered and double-layered ladder model show that the proposed method not only effectively inverts the vertical structures, but also improves the inversion effect of horizontal structures. The inversion results of the main part of Marmousi model prove that the proposed method is also applicable to the inclined structure.