A fast wavefield reconstruction inversion solution in the frequency domain

Full-waveform inversion (FWI) aims at estimating subsurface physical parameters by minimizing the misfit between simulated data and observations. FWI relies heavily on an accurate initial model and is less robust to measurement noise and physical assumptions in modeling. Compared with FWI, wavefield reconstruction inversion (WRI) is more robust to these uncertainties but faces high computational costs. To overcome these challenges, we have developed a new form of WRI. This reformulation takes the form of a traditional FWI formula, which includes a medium-dependent weight function, and can be easily incorporated into the current FWI workflow. This weight function contains the covariance matrices to characterize the distribution of uncertainties in measurements and physical assumptions. We discuss various options of the theoretical covariance matrix of the new inversion method and find how they relate to various well-known approaches, including FWI, WRI, and extended FWI. On the basis of the preceding comparison, we develop a theoretical covariance matrix definition based on the source. Numerical experiments demonstrate that our method with a source-dependent theoretical covariance matrix is more computationally efficient than conventional WRI while preserving a certain degree of robustness.