Eur. Phys. J. Plus (2022) 137: 657
https://doi.org/10.1140/epjp/s13360-022-02847-9

Regular Article

An efficient and accurate strategy of numerical simulation of 2D Rayleigh waves under arbitrary undulating surface conditions

¹ College of Petroleum Engineering, Guangdong University of Petrochemical Technology, 525000, Maoming, People’s Republic of China
² State Key Laboratory of Geomechanics and Geotechnical Engineering, Chinese Academy of Sciences, 430071, Wuhan, People’s Republic of China

^b jjliu@whrsm.ac.cn

Received: 26 November 2021
Accepted: 17 May 2022
Published online: 4 June 2022

Abstract

When the conventional staggered grid is utilized in the numerical simulation of elastic waves with irregular topography, the setting of the free-surface boundary condition is complicated and not conducive to dealing with surface elevation mutation. Therefore, this study uses an improved staggered grid to achieve numerical simulation of 2D Rayleigh waves on any undulating surface. By placing the normal stress node at the center of the grid and the shear stress node at the upper left corner of the grid, we simplify the classification and calculation of the grid on the free boundary. To solve the problem of reduced stability caused by discontinuous particle velocity, the calculation of the spatial derivative of the discontinuous velocity component is transformed into a spatial derivation of its orthogonal component, which improves the stability of this principal stress calculation. The numerical simulation strategy proposed in this study is easy to implement and suitable for any undulating surface conditions. Numerical calculation examples show that this method can significantly improve the calculation efficiency without reducing the simulation accuracy. The proposed method may be applied to the study requiring accurate characterization of the Rayleigh waves, such as parameter optimization of seismic acquisition in the loess overburden area in western China, and research on surface wave inversion method.