Time-Domain Wavefield Reconstruction Inversion Solutions in the Weighted Full Waveform Inversion Form

Full waveform inversion (FWI) methods evaluate subsurface media properties by minimizing the misfit between synthetic and observed data. However, its derivation process omits measurement errors and physical assumptions in modeling, resulting in many problems in practical utilizations. Wavefield reconstruction inversion (WRI) can handle nonphysical data by combining theoretical and measurement errors but is computationally expensive in large-scale or 3-D cases. An alternative formula for WRI in the form of traditional FWI (WRI in the FWI form, FWRI) was developed. The new form includes a medium-dependent weight function or a data-domain Hessian matrix. Based on the data-domain Hessian matrix, a feasible accurate time-domain solution is provided for 2-D and 3-D FWRI. Specifically, the point spread function (PSF) method and anisotropic total variation (TV) regularization were used to calculate the weighted residuals. Furthermore, an approximate solution based on the forward operator is provided, considering the efficient application in 3-D. Numerical tests using the homogeneous model show that accurately computed residuals mitigate the effects of “cycle-skipping” and nonphysical data. Sensitivity kernel analysis demonstrates the low wavenumber update mechanism of FWRI and verifies the robustness of the data-domain Hessian to “cycle-skipping.” The robustness of the proposed algorithm is demonstrated using a 2-D Marmousi model with partially elastic perturbations and a visco-acoustic Red Sea model. Furthermore, the 3-D Overthrust model is solved with an approximate solution to demonstrate the feasibility of the proposed method in 3-D applications.