Full-waveform inversion (FWI) is widely used to infer earth structures and rock properties. In FWI, most of the computation arises from the repeated simulations of wave propagation. Although frequency-domain implementations have several advantages, solving the Helmholtz equation incurs a major computational cost associated with the inversion of large matrices. Hence, we have used a new model reduction technique called the generalized multiscale finite-element method (GM FEM) to perform this task rapidly for forward and backward simulations. This in turn leads to the acceleration of the FWI. In addition, the multiscale finite-element approach allows flexible, adaptive selection of modeling parameters (i.e., grid size, number of basis functions) for different target frequencies, providing further speed up. We apply this frequency-domain, multiscale FEM approach to the Marmousi-2 model, and the FWI results indicated how varying the number of basis functions can control the trade-off between the accuracy and computational speed. In addition, we introduced FWI examples applied to field data from the Gulf of Mexico. These field data examples indicate that applying our multiscale FWI with a relatively small number of basis functions can quickly construct a macrovelocity model using low frequencies. We also evaluate a strategy to optimize the FWI procedure by using frequency-adaptive multiscale basis functions based on the target frequency group. In general, we can reduce the run time by up to 30% through the application of GM FEM wave modeling in FWI.

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