Full waveform inversion guided by travel time tomography

Full waveform inversion (FWI) is a process in which seismic data in time or frequency domain is fit by changing the velocity of the media under investigation. The problem is non-linear, and therefore optimization techniques have been used to find a geological solution to the problem. The main problem in fitting the data is the lack of low spatial frequencies. This deficiency often leads to a local minimum and to non-geologic solutions. In this work we explore how to obtain low frequency information for FWI. Our approach involves augmenting FWI with travel time tomography, which has low-frequency features. By jointly inverting these two problems we enrich FWI with information that can replace low frequency data. In addition, we use high order regularization in a preliminary inversion stage to prevent high frequency features from polluting our model in the initial stages of the reconstruction. This regularization also promote the low-frequencies non-dominant modes that exist in the FWI sensitivity. By applying a smoothly regularized joint inversion we are able to obtain a smooth model than can later be used to recover a good approximation for the true model. A second contribution of this paper involves the acceleration of the main computational bottleneck in FWI–the solution of the Helmholtz equation. We show that the solution time can be significantly reduced by solving the equation for multiple right hand sides using block multigrid preconditioned Krylov methods.