Anisotropic diffusion filter for 3D full waveform inversion: application to a North Sea dataset

Regularization is central in full waveform inversion, specifically to remove spurious oscillations due to noisy data and to compensate the uneven illumination of the subsurface. Conventional strategies directly apply smoothing operators at each full waveform inversion iteration. Numerous of operators have been proposed in the literature, from Gaussian operators to more evolved structure preserving Laplacian operators. The former are easy to implement but might destroy the structural information embedded in the gradient. The latter require an external source of information related to the structure to be preserved. We propose to use an anisotropic diffusion filter which can directly enhance the structure of the gradient without using external prior information. We extend the 2D method presented at 2022 EAGE meeting in Madrid to 3D, use an adapted discretization scheme which guarantees numerical stability, and apply it to a 3D field data from the North Sea. We compare the results of inversion up to 10 Hz between a Gaussian smoothing and our anisotropic diffusion smoothing. The enhancement of the resolution and the structural coherence is striking, making full wavefield images much easier to interpret geologically. We believe this technique could be applied to a wide variety of field data in the future.