Higher-order thin layer method as an efficient forward model for calculating dispersion curves of surface and Lamb waves in layered media

Abstract

The thin layer method (TLM) is an effective semi-discrete numerical tool for analyzing wave motion in stratified media. The TLM can calculate the eigenvalues and eigenvectors for both propagating and decaying waves, which is essential to simulate waves near the source. The eigenvectors are particularly useful in various applications, such as estimating modal contributions, calculating synthetic seismograms, determining Green’s function, analyzing site response, and solving wave amplification problems in earthquake engineering, to name a few. In practice, most engineering applications use linear element-based TLM. However, the overall performance of TLM depends upon the type of element and the number of thin layers. The linear element TLM requires relatively thin sub-layers to obtain an accurate solution, making it computationally expensive and time-consuming. This study explores the potential of using non-linear higher-order TLM (HTLM) for forward modeling. The mathematical framework of TLM is used to formulate the generalized HTLM in determining the multimodal dispersion curve of Rayleigh, Love, and Lamb waves. The convergence and computational efficiency of different orders of HTLM have been investigated on a diverse set of published soil profiles and plate-like structures. Since non-linear interpolation functions better capture the change in displacement and stress between the layers, the findings reveal that the HTLM consistently outperforms the linear element TLM in terms of accuracy. Furthermore, the computational efficiency of different order HTLM is analyzed by comparing the total degrees of freedom and CPU time. Remarkably, higher-order HTLMs exhibit improved accuracy without increasing the computational burden, making them an attractive option for practical applications such as global search-based inversion and full spectrum inversions where fast and economical forward modeling is essential. Therefore, the HTLM will become helpful in seismic wavefield modeling, dynamic soil characterization, non-destructive evaluation methods, wave propagation analysis through waveguides, seismic site response analysis, etc.