Spectral element based 3D elastic full waveform inversion of surface waves in the presence of complex topography using an envelope based misfit function
Full waveform inversion (FWI) is a data fitting technique used to estimate properties of the Earth from seismic data by minimizing the misfit between observed and simulated seismograms. Because of very high computational cost, this technique has so far been used either in a 2D fully elastic formulation or in a 3D acoustic formulation, when applied to active source surveys in order to image the shallow subsurface (i.e. down to the first few kilometers) However, the Earth is three dimensional, (visco)elastic and highly heterogeneous. Therefore, obtaining more accurate models requires solving the full 3D elastic wave equation. In this study, we use an envelope based misfit function to construct shallow 3D models of shear wavespeed while inverting surface waves. The envelope based misfit function has proven to be effective for inverting surface waves, which are particularly exposed to the cycle skipping problem. To accurately model the wavefield in the presence of complex topography, we use a spectral element wave propagation code. A synthetic example on the SEAM Phase II foothills model illustrates that inversion of surface waves at the initial stages in such a challenging environment allows us to obtain an improved shear wavespeed starting model for traditional FWI.