Broad Learning Framework for Search Space Design in Rayleigh Wave Inversion

Search space design is a fundamental procedure for the inverse problem in Rayleigh wave exploration. In practice, such a crucial task mainly depends on researchers’ experience-based judgment. However, intricate near-surface materials may lead to erroneous search space design, and consequently, accurate inversion results cannot always be ensured. By the forward calculation, it is found that there is a strong relationship between the fundamental dispersion curves of a given earth model and its miniature model; namely, if the parameters (layer thicknesses and $S$ -wave velocities) of the given earth model are shrunk at a certain scale, the phase velocities on the fundamental dispersion curve will decrease at the same scale. Taking advantage of this relation, we propose a broad learning framework for search space design in a data-driven manner. First, a training set of minified models is generated using the forward calculation of dispersion curves. Then, a mapping relationship between dispersion curves and minified earth models is built via a broad learning network. Finally, a search space for the actual earth model is designed using the minified model based on the relation. As the ranges of parameters in the minified model are much smaller, the network can find the model parameters for the corresponding dispersion curve quickly and easily. Numerical simulations and field data applications demonstrate the reliability and effectiveness of the proposed method for search space design. It is concluded that the proposed method can promote accurate estimation of $S$ -wave velocities by Rayleigh wave inversion without experience-based judgment.