Full waveform inversion (FWI) is a computationally demanding procedure to estimate the velocity model for seismic imaging. We develop a new method to reduce computational cost of FWI by approximating the gradient vector and Hessian matrix with the help of a new forward solver. The proposed solver is based on special interface conditions that facilitate sequential solution of the wavefield, which is a good approximation of that from full wave equation. The proposed approximation, when incorporated into FWI framework, does not affect the convergence and improves FWI efficiency.


Building an accurate velocity model is still challenging and critical step in seismic imaging. Full waveform inversion (FWI) is an automatic but computationally challenging data-fitting process to determine the velocity model. FWI is a local optimization procedure that minimizes the misfit between recorded data and synthetic wavefield at the location of receivers. Similar to all local optimization procedure, a good estimation of gradient and Hessian operators is required at each iteration of nonlinear minimization. Therefore, the large number of forward simulations must be carried out at each step. Although recent advances in parallel computing and high-performance computing make the application of FWI in seismic imaging more feasible, more efficient methods are still required to reduce the computational cost of FWI.

In this study, we propose a novel method to approximately solve acoustic wave equation in frequency domain (i.e. Helmholtz equation). The key idea of the method is to partition the domain into smaller subdomains and solve each subdomain sequentially, facilitated by special interface (continuity) conditions. Later, we use the proposed method to estimate the gradient vector and the Hessian matrix in FWI framework. We show that cost of computing gradient and Hessian is reduced significantly, while the convergence rate of FWI procedure remains unchanged.

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