Weighted pseudo-hessian matrix for frequency-domain elastic full waveform inversion

The full waveform inversion (FWI) can obtain accurate estimates of the parameters of subsurface materials using the steepest descent method with iterative calculations. Applying the Hessian matrix as a pre-conditioner improves the results of FWI. However, obtaining the full or approximate Hessian matrix is not practical because of the intensive computational cost. The diagonal of the pseudo-Hessian matrix is widely used to scale the gradient at a reduced computing cost, but it has problems imaging the deep region of the model. In this study, we suggest a new scaling method for frequency-domain elastic FWI that uses a weighted pseudo-Hessian matrix to overcome the imaging problem caused by the limitations of the pseudo-Hessian matrix. To verify the proposed algorithm, a numerical test is performed with the Model 94 synthetic data.