Structure-Smoothing Bessel Filter for Finite Element Mesh - Application on 3D Elastic FWI
Résumé
Smoothing filters are extremely important tools in seismic imaging and especially in full waveform inversion. For complex geological structures with variable heterogeneities, these filters should be able to incorporate efficiently geological prior information of the target medium, through coherent lengths and 3D orientation, which are expected to vary in space. In this study, we introduce a novel smoothing strategy based on the Bessel filter, for which we are able to design a highly efficient implementation. Its application is performed by solving the elliptic partial differential equation associated to its sparse inverse operator. The development of this equation in any discretization method naturally yields a symmetric and well-conditioned linear system. We develop this smoothing strategy within an elastic spectral-element-based full-waveform-inversion framework. The associated linear system can be solved efficiently through a parallel conjugate-gradient algorithm, in which the matrix-vector product is factorized and optimized in a similar way as the one used for solving the elastodynamic system. By doing so, we avoid expensive explicit-windowed-convolution over the finite element mesh. The efficiency and the flexibility of the proposed smoothing method are illustrated through various schematic examples, and on a more realistic elastic full waveform inversion problem on the SEAM II benchmark model.