Two-grid Full Waveform Rayleigh Wave Inversion by Means of Genetic Algorithm with Frequency Marching

We present a 2D elastic full waveform inversion (FWI) of Rayleigh waves (RW) with a genetic algorithm (GA) as the optimization tool and with a finite difference code as the forward modeling engine. To limit the computing time required by GA, we implement the RW FWI, making use of a two-grid parametrization of the subsurface model, one fine grid and one coarse grid, and of frequency marching during the evolution of the GA optimization. Forward modeling is performed on the fine grid to avoid numerical dispersion, while the GA inverts for the unknown velocities and densities at the nodes of the coarse grid. The coarser the grid the less the unknowns to be inverted for, at the expense of the final model resolution. Frequency marching also speeds up convergence because it has the ability of rejecting unrealistic models at the initial generations of the GA. Due to the very band-limited nature of RW, we suggest to start frequency marching from near the peak frequency of RW. Synthetic examples reproducing velocity inversions, lateral velocity variations and varying elevations show the feasibility of the proposed RW FWI, without any a-priori information and with shear-wave and compressional-wave velocities and densities as unknowns.