Three-dimensional dynamic responses of a layered transversely isotropic half-space with irregular interfaces using the thin layer method

This paper proposes a thin layer method (TLM) for computing 3D dynamic responses in a layered transversely isotropic (TI) half-space with irregular interfaces. Utilizing Fourier transforms and modal superposition, stiffness matrices for semi-infinite and finite-length thin layer elements are derived, enabling the simulation of wave propagation in the finite-depth domain with irregular interfaces. The complex frequency shifted perfectly matched layer (CFSPML) within the TLM framework is developed to simulate wave attenuation in the underlying TI half-space, addressing the instability issues of the classical PML in the TI medium. The finite-length thin layer element can be of arbitrary length and is independent of the frequency, thus enhancing computational efficiency compared to discrete numerical methods like the FEM. The accuracy of the proposed method is verified with existing methodologies. The dynamic responses of a two-layered TI half-space with a Gaussian-shaped interface induced by either surface or buried dynamic point loads are investigated. The influences of the position and size of the irregular interface, as well as the transversely isotropy, are analyzed. Numerical results demonstrate that the presence of the irregular interface significantly changes the distribution of displacement fields. The influence of the irregular interface is highly dependent on the loading frequency and observation position.