Earth–rock dams are typical soil–rock mixtures with high heterogeneity. Mastering the effect of dam heterogeneity on seismic wavefields is the premise of accurately detecting hidden risks in dams. In this paper, based on the soil–rock mixture characteristics of actual dams, a soil–rock mixture model that can reflect the heterogeneity of dams is established through local segmentation and reassignment of random disturbances. The influence of local area size on model heterogeneity is described. The seismic wavefield in a soil–rock mixture dam is numerically simulated through a staggered-grid finite-difference algorithm with second-order accuracy in time and sixth-order accuracy in space. Then, the effect of dam heterogeneity on effective wavefields is analyzed. The results show that the heterogeneity of the earth–rock dam can lead to scattered waves in the seismic wavefield, and the scattered waves are mainly generated by Rayleigh surface waves. In the seismic record, scattered waves with strong energy appear in the region below the surface waves. The scattered wave energy is weak and close to that in the homogeneous media in the region above the surface waves. As the rock content in the dam increases, the scattering of seismic wavefields and the energy of scattered waves weaken gradually. The scattered waves generated by the heterogeneity of the dam significantly impact the reflected longitudinal wave and converted wave but, affect the reflected shear wave less. The numerical simulation results are consistent with the acquired seismic wavefield from the field test, proving the effectiveness of the numerical simulation for the seismic wavefield propagation characteristics of the earth–rock dam.

Numerical seismic wave field simulation is essential for studying the dynamic responses in semi-infinite space, and the absorbing boundary setting is critical for simulation accuracy. This study addresses spherical waves incident from the free boundary by applying dynamic equations and Rayleigh damping. A new multi-directional viscous damping absorbing boundary (MVDB) method is proposed based on regional attenuation. An approximate formula for the damping value is established, which can achieve absorbing the boundary setting by only solving the mass damping coefficients without increasing the absorbing region grid cells or depending on the spatial and temporal walking distance. The validity and stability of the proposed method are proven through numerical calculations with seismic sources incident from different angles. Meanwhile, the key parameters affecting the absorption of the MVDB are analyzed, and the best implementation scheme is provided. In order to meet the requirements of mediums with different elastic parameters for boundary absorption and ensure the high efficiency of numerical calculations, the damping amplitude control coefficients k can be set between 1.02 and 1.12, the thickness of the absorbing region L is set to 2–3 times of the wavelength of the incident transverse wave, and the thickness of the single absorbing layer is set to the size of the discrete mesh of the model Δl.

Precise surveys are indispensable in coastal engineering projects. The extensive presence of sand in the coastal area leads to significant attenuation of seismic waves within unsaturated loose sediments. As a result, it becomes challenging for seismic waves to penetrate the weathered zone and reach the desired depth with significant amount of energy. In this study, the application of three-dimensional (3D) cross-well elastic reverse time migration (RTM) imaging based on multi-wave and multi-component techniques in coastal engineering exploration is explored. Accurate decomposition of vector compressional (P) and shear (S) waves is achieved through two wavefield decoupling algorithms without any amplitude and phase distortion. Additionally, compressional wave pressure components are obtained, which facilitates subsequent independent imaging. This study discusses and analyzes the imaging results of four imaging strategies under cross-correlation imaging conditions in RTM imaging. The analysis leads to the conclusion that scalarizing vector wavefields imaging yields superior imaging of P- and S-waves. Furthermore, the imaging results obtained through this approach are of great physical significance. In order to validate the efficacy of this method in 3D geological structure imaging in coastal areas, RTM imaging experiments were performed on two representative models. The results indicate that the proposed 3D elastic wave imaging method effectively generates accurate 3D cross-well imaging of P- and S-waves. This method utilizes the multi-wave and multi-component elastic wave RTM imaging technique to effectively leverage the Earth’s elastic medium without increasing costs. It provides valuable information about the distribution of subsurface rock layers, interfaces, and other structures in coastal engineering projects. Importantly, this can be achieved without resorting to extensive excavation or drilling operations. This method addresses the limitations of current cross-well imaging techniques, thereby providing abundant and accurate geological and geophysical information for the analysis and interpretation of 3D geological structures in coastal engineering projects. It has important theoretical and practical significance in real-world production, as well as for the study of geological structures in coastal engineering.

In this paper, a single-tier beam-spring-damping system and a two-tier beam-spring-damping system are adopted to simulate the FT (fixed track) and FST (floating slab track) system, respectively. The tunnel is modeled as an infinitely long Euler—Bernoulli beam embedded in the layered saturated soil. By solving the governing equations of the saturated soil and employing the TRM (transmission and reflection matrices) method, the frequency response function of the tunnel-layered saturated soil model is obtained. Making use of the interaction between the tunnel and track systems, the track system is coupled with the tunnel-layered saturated ground model. The solutions for the dynamic response of the track system–tunnel-layered saturated ground model under moving loads in the time–space domain are obtained using the inverse Fourier integral transform. To evaluate the damping effect of the FST system on the vibration of tunnel and soil, four damping coefficients are defined and the vibration results of the FT system–tunnel-layered saturated soil model are compared with those of the FST system–tunnel-layered saturated soil under different moving loads and soil conditions. The numerical results show that both the vibration displacement and acceleration amplitude are attenuated after using the FST system, and the damping coefficient of acceleration is about 30% greater than that of the displacement. In addition, the damping effect of the FST system on the ground surface vibration is associated with the embedded depth of the tunnel and the soil stiffness.