The research on full-waveform inversion method and its application based on Hessian operator preprocessing

Full-waveform inversion (FWI) can provide accurate velocity field for fine imaging in depth domain of seismic data. Its mathematics foundation determines that FWI is a strong nonlinearity with the solution being non-unique and the function being difficult to converge. In this paper, adjoint gradient and Hessian operators are introduced into the calculation of FWI objective function to improve the inversion accuracy. Firstly, the adjoint gradient method is used to iteratively optimize the gradient of the model with respect to the residuals of the observed data when solving the objective function. Secondly, in view of the energy inconsistency gradient amplitudes across space, the diagonal elements of Hessian operator are used to scale the gradient, which ensures that the gradient amplitude is inversely proportional to the sensitivity of the synthesized data, thereby the imaging accuracy in deep and weak reflected areas. Finally, the sub-sag model and the overthrust model are used to perform the proposed method in this paper. The inversion results indicated that the FWI method with Hessian operator pre-processing significantly reduced the impact of abnormal amplitude of wave field gradient on structures near the shot detection point and deep structure, and enhanced the accuracy and resolution of FWI modeling. It provides a more accurate velocity model for fine imaging of deep complex structures.