where represents the model, is the observed dataset, is the corresponding modeling operator, and stands for the L2-norm. In most FWI implementations, consists of a gridded velocity distribution that explains both propagation and reflection of the seismic data and forward modeling is done via a finite-difference implementation of the two-way wave equation (Virieux and Operto, 2009). Note that in most FWI implementations, density variations are neglected. Minimizing this misfit function is likely to suffer from ill-posedness and non-uniqueness because of limited input data and non-linearity of the forward modeling operator. Adding regularization to the objective function can be one effective way to mitigate the ill-posedness and non-uniqueness of this inverse problem.

2020-12-07