Near-surface velocity inversion from Rayleigh wave dispersion curves based on a differential evolution simulated annealing algorithm

The utilization of urban underground space in a smart city requires an accurate understanding of the underground structure. As an effective technique, Rayleigh wave exploration can accurately obtain information on the subsurface. In particular, Rayleigh wave dispersion curves can be used to determine the near-surface shear-wave velocity structure. This is a typical multiparameter, high-dimensional nonlinear inverse problem because the velocities and thickness of each layer must be inverted simultaneously. Nonlinear methods such as simulated annealing (SA) are commonly used to solve this inverse problem. However, SA controls the iterative process though temperature rather than the error, and the search direction is random; hence, SA always falls into a local optimum when the temperature setting is inaccurate. Specifically, for the inversion of Rayleigh wave dispersion curves, the inversion accuracy will decrease with an increasing number of layers due to the greater number of inversion parameters and large dimension. To solve the above problems, we convert the multiparameter, high-dimensional inverse problem into multiple low-dimensional optimizations to improve the algorithm accuracy by incorporating the principle of block coordinate descent (BCD) into SA. Then, we convert the temperature control conditions in the original SA method into error control conditions. At the same time, we introduce the differential evolution (DE) method to ensure that the iterative error steadily decreases by correcting the iterative error direction in each iteration. Finally, the inversion stability is improved, and the proposed inversion method, the block coordinate descent differential evolution simulated annealing (BCDESA) algorithm, is implemented. The performance of BCDESA is validated by using both synthetic data and field data from western China. The results show that the BCDESA algorithm has stronger global optimization capabilities than SA, and the inversion results have higher stability and accuracy. In addition, synthetic data analysis also shows that BCDESA can avoid the problems of the conventional SA method, which assumes the S-wave velocity structure in advance. The robustness and adaptability of the algorithm are improved, and more accurate shear-wave velocity and thickness information can be extracted from Rayleigh wave dispersion curves.