Explicit Control of Numerical Dispersion and Instability in Elastic Wavefield Modeling and Inversion

Summary Full-waveform inversion (FWI) is a nonlinear inverse problem that refines models by iteratively matching the recorded and modeled data. The success of FWI relies on accurate and efficient wavefield modeling. The finite-difference method (FDM) is one of the most popular techniques used for this purpose because of its easy implementation and low memory requirement. However, depending on the spatial and temporal discretization, FDM may encounter numerical dispersion and instabilities, which degrade the quality of the simulated wavefields. The FWI objective function formulated based on data misfit may lead to situations where the updated models violate necessary conditions to guarantee modeling stability. We propose to address this problem by explicitly incorporating a stability constraint into the inversion through a penalty term based on a probability density functions (PDF) that represents the range of velocities in which numerical dispersion and instabilities do not occur. This penalty term prevents updated models from entering into a configuration that leads to dispersion and instability for specific choices of sampling parameters. Through synthetic examples, we demonstrate the benefits of including this stability constraint into the FWI framework, as it ensures the efficiency of the FDM engine, while increasing the quality of the recovered models.