Efficient Seismic Depth Imaging and Full-Waveform Inversion via Generalized Multiscale Finite Element

Reverse-time migration (RTM) and full-waveform inversion (FWI) are widely used because they are able to recover complex geological structures. However, these wave-equation based imaging techniques also have a drawback, as they require significant computational cost. In both methods, wave modeling accounts for the largest part of the computing cost for calculating forward-and backward-propagated wavefields before constructing an imaging condition or a model update term. For this reason, I applied a model reduction technique, the generalized multiscale finite el-ment method (GMsFEM), which solves local spectral problems on a fine grid for fast simulation of wave propagation on a coarser grid. This approach can enhance the speed of computation without sacrificing accuracy by utilizing coarser grids for lower frequency waves. In the proposed method, one can control the size of the coarse grid and level of heterogeneity of the wave solutions to tune the trade-off between speedup and accuracy. As I increase the expected level of complexity of the wave solutions, the GMsFEM wave modeling can capture more detailed features of waves by applying a finer coarse grid and a larger number of basis functions. After computing the forward-and backward-wavefield on the coarse grid, the coarse-scale solutions are projected onto the original fine grid. Therefore, although wave solutions are computed on a coarse grid, it still provides the images for RTM and FWI without reducing the image resolution by projecting coarse wave solutions to the fine grid. In the multiscale finite element approach, one can apply flexible wave modeling parameters (i.e., grid size, number of basis functions) according to the target frequency components, which makes the method an attractive tool for the practical applications of the RTM and FWI. I demonstrated the multiscale FWI using the BP and Marmousi-2 synthetic model. In addition, I show FWI examples of the field data obtained in the Gulf of Mexico region. In the field data examples, I demonstrate that applying the proposed multiscale RTM and FWI with a relatively small number of basis functions can quickly construct a macro velocity model using low frequency. I also propose a strategy to maximize the efficiency of the multiscale FWI by utilizing frequency-adaptive multiscale basis functions based on the target frequency group