Frequency-Domain Finite Element Modeling of Seismic Wave Propagation Under Different Boundary Conditions

Ying Zhang, Haiyang Liu, Shikun Dai () and Herui Zhang
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Ying Zhang: Key Laboratory of Metallogenic Prediction of Nonferrous Metals and Geological Environment Monitoring (Ministry of Education), Central South University, Changsha 410083, China
Haiyang Liu: Changjiang Geotechnical Engineering Co., Ltd., Wuhan 430010, China
Shikun Dai: Key Laboratory of Metallogenic Prediction of Nonferrous Metals and Geological Environment Monitoring (Ministry of Education), Central South University, Changsha 410083, China
Herui Zhang: School of Safety Engineering, China University of Mining and Technology, Xuzhou 221000, China

Mathematics, 2025, vol. 13, issue 4, 1-30

Abstract: Seismic wave propagation in complex terrains, especially in the presence of air layers, plays a crucial role in accurate subsurface imaging. However, the influence of different boundary conditions on seismic wave propagation characteristics has not been fully explored. This study employs the finite element method (FEM) to simulate and analyze seismic wavefields under different boundary conditions, including perfectly matched layer (PML), Neumann free boundary conditions, and air layer conditions. First, the finite element solution for the 2D frequency-domain acoustic wave equation is introduced, and the correctness of the algorithm is validated using a homogeneous model. Then, both horizontal and undulating terrain interfaces are designed to investigate the kinematic and dynamic characteristics of the wavefields under different boundary conditions. The results show that PML boundaries effectively absorb seismic waves, prevent reflections, and ensure stable wave propagation, making them an ideal choice for simulating open boundaries. In contrast, Neumann boundaries generate significant reflected waves, particularly in undulating terrains, complicating the wavefield characteristics. Introducing an air layer alters the dynamics of the wavefield, leading to energy leakage and multi-path effects, which are more consistent with real-world seismic-geophysical models. Finally, the computational results using the Overthrust model under different boundary conditions further demonstrate that different boundary conditions significantly affect wavefield morphology. It is essential to select appropriate boundary conditions based on the specific simulation requirements, and boundary conditions with an air layer are most consistent with real seismic geological models. This study provides new insights into the role of boundary conditions in seismic numerical simulations and offers theoretical guidance for improving the accuracy of wavefield simulations in realistic geological scenarios.

Keywords: acoustic wave; numerical simulation; PML boundary conditions; Neumann boundary conditions; air layer (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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