Incorporating multiple a priori information for full waveform inversion

Da Li, Michael P. Lamoureux, Wenyuan Liao

Full waveform inversion (FWI) is a powerful data-fitting procedure for the seismic inversion problem. However, it suffers the local minimum problem when the accurate initial model is not available because of the nonlinear nonconvex structure of the objective function. Our initial idea in this work is that a better inverse result can be expected when more a priori information of the physical model is provided. We propose a numerical scheme which can incorporate multiple a priori information to the optimization problem. First, a scaled gradient projection method on adaptive constraint sets is provided which is compatible with the inexact projection algorithm. Next, we incorporate a priori information as convex constraint sets. Then, the FWI problem is solved as a constraint optimization problem on the intersection of the constraint sets as the feasible set. Numerical examples with box constraints, total variation constraints, and l1 constraints on the cross-well model and the reflective seismic wave model are provided.