Two-grid full-waveform Rayleigh-wave inversion via a genetic algorithm — Part 1: Method and synthetic examples

When reliable a priori information is not available, it is difficult to correctly predict near-surface shear wave velocity models from Rayleigh waves through existing techniques, especially in the case of complex geology. To tackle this issue, we propose a new method, two-grid genetic-algorithm Rayleigh-wave full-waveform inversion (FWI). Adopting a two-grid parameterization of the model, the genetic algorithm inverts for unknown velocities and densities at the nodes of a coarse grid, while forward modeling is performed on a fine grid to avoid numerical dispersion. A bilinear interpolation brings the coarse grid results into the fine grid models. The coarse inversion grid allows for a significant reduction of the computing time required by the genetic algorithm to converge. The coarser the grid, the less the unknowns, the less the required computing time, at the expense of the model resolution. To further increase efficiency, our inversion code can perform the optimization employing a frequency-marching strategy and/or an offset-marching strategy, can make use of different kind of objective function and it allows for parallel computing. We illustrate the effect of the proposed inversion method using three synthetic examples with rather complex near-surface models. Though no a priori information was used in all the three tests, the long-wavelength structures of the reference models were fairly predicted, and satisfactory matches between “observed” and predicted data were achieved. The fair predictions of the reference models suggest that the final models estimated by our genetic-algorithm FWI, which we call macro-models, would be suitable input to gradient-based Rayleigh-wave FWI for further refinement. Other issues related to the practical use of the method are presented in a companion paper that shows the applications of the method to field data.