Coherence-enhancing anisotropic diffusion filter for 3D high resolution reconstruction of P-wave velocity and density using full waveform inversion: application to a North Sea Ocean Bottom Cable dataset

Regularization is a central topic in the study of the solutions of ill-posed inverse problems. High resolution seismic imaging using full waveform inversion belongs to this category of problems. Regularization through anisotropic diffusion, a technique which emerged in the field of image processing, is an interesting alternative to conventional regularization strategies. Exploiting the structural information of a given image, it has the capability to smooth this image along its main structures. The main difficulty is how to design the anisotropic diffusion operator. The concept of coherence enhancing proposed in 2D is extended in 3D and applied so as to filter and enhance the structural coherence of the model updates within a full waveform inversion algorithm. The benefits of this strategy are investigated on a 2D synthetic experiment before considering the multi-parameter inversion of a 3D field dataset from the North sea up to 10 Hz. From this data, the vertical velocity and the density are simultaneously reconstructed. Compared with a conventional nonstationary Gaussian regularization strategy, the models obtained using the coherence enhancing anisotropic diffusion strategy show an enhanced resolution, especially for the density model. The high resolution reflectivity image computed from the impedance volume clearly illustrates the benefit this filtering approach can deliver in terms of structural interpretation.