Wide Aperture Imaging Strategies for 3D Elastic Full-waveform Inversion: Application to the Marmousi model

An application of the 3D elastic full-waveform inversion (FWI) to wide-aperture seismic data obtained for a complex geological setting is presented. Imaging is implemented in the Fourier domain, exploiting damped wave fields. The modeling part is solved with a finite-difference method. The non-linear conjugate gradient method is used for the inverse problem solution. The nonlinearity of FWI leads to the presence of local and multiple minima in the least-squares error functional especially for large offset problems. That leads to the shutdown of the inverse problem convergence and uncertainty in the solution. An accurate starting velocity model can avoid this problem, but in many cases may not be available. Hence other strategies are necessary to address the problem.

We propose a robust inversion process for an arbitrary starting velocity model, which allows avoiding local minima and obtaining acceptable images of the deep seated structures defined by large offset data. We proceed from the assumption that decreasing data offset reduces local minima problems but decreases the depth of the recovered image. So, the inversion process is realized sequentially from small to large offsets, allowing recovery of geological structures over the entire depth range of interest from the near surface to deeper depths sensed only by large aperture offsets. Increasing of data offset is first performed at the lowest frequency and then proceeding with treatment of all data offsets from low to high frequencies. A reverse loop is also implemented in the laddering of frequencies, where after the inversion at high frequencies and all offsets we return to the lower frequencies data to continue the IP. Returning to lower frequency data provides helping to ameliorate multiple minima encountered in the inversion. The inversion then concludes by sweeping over higher frequency data, at all offsets.

We demonstrate our strategies for treating wide aperture offset data on the Marmousi model, using a linearly increasing starting velocity model with depth. Our results suggest that FWI exploiting variable data offsets, up to 10 km, can be applied successfully to frequencies up to 6 Hz, and it is possible to develop accurate 3D velocity images down to depths of 3.5 km at the resolution that approaches half the smallest wavelength utilized in FWI.