Efficient Wavefield Inversion With Outer Iterations and Total Variation Constraint

Full-waveform inversion (FWI) is popularly used to retrieve a high-resolution velocity model that maximizes the data fitting directly. It is a highly nonlinear optimization problem, and thus, FWI can easily fall into a local minimum. Wavefield reconstruction inversion (WRI) allows us to relax the wave equation constraint to provide a larger search space. However, it requires a high computational cost to update the velocity in each selected frequency through many expensive iterations. By recasting a linear optimization problem in terms of a modified source function (which includes the original source and secondary sources) and relying on the background velocity model, we end up with cheap inner iterations for inverting the wavefield. We refer to this setup as an efficient wavefield inversion (EWI). However, like WRI, EWI cannot mitigate the cycle-skipping problem completely when the background velocity model is far from the true one and low-frequency components in the data are missing. In this case, we propose to use additional outer iterations to better recover the velocity model. In the salt body inversion, we utilize a total variation (TV) regularization to constrain the inverted velocity model at each outer iteration. We demonstrate these features on a modified Marmousi model and a central part of the BP salt model. The application on a 2-D real data set also demonstrates the effectiveness of the proposed method.