Interface waves are widely utilized for applications in ground motion analysis and geophysical exploration. To enhance understanding of seismic wave propagation in marine environments, this study derives, for the first time, the dispersion equation for interface waves at the fluid / transversely isotropic solid half-space interface within a submarine slope region. Results indicate that a more rigid seafloor basement amplifies the effect of the slope angle on interface wave propagation. Slope angle significantly affects dispersion curves within specific frequency-thickness ranges. For a 4° basaltic slope, the calculated differences in fundamental mode phase and group velocities between horizontal and inclined models reached 8.01% and 25.52%, respectively. These significant discrepancies demonstrate the critical importance of accounting for slope effects. Notably, while the interface wavenumber is a real number in the horizontal model, it becomes complex in the inclined model, indicating that interface waves exhibit a slight leakage property. Furthermore, anisotropy influences interface wave dispersion; however, as the degree of anisotropy increases, the impact of the slope angle on both phase and group velocity dispersion characteristics diminishes. This study provides a new theoretical basis for understanding seismic responses in submarine slope regions.

Numerous scientific studies and industrial fields, including geology, geophysics, mining, etc., rely heavily on seismic waves. Seismic wave analysis provides information that helps us better manage and use natural resources by enhancing our understanding of their structure. With this objective, this study presents a comprehensive mathematical model for Love-type seismic wave propagation in a transversely isotropic fluid-saturated poroelastic (TIFSP) layer bonded to an elastic half-space through spring–membrane interfacial foundations. More precisely, Classical (CL), Spring (SPR), Membrane (MBR), and Combined (CB) elastic foundation models are discussed. Implementing analytical mathematical techniques and complex continuity conditions across the different interfaces, the hyperbolic boundary value problem is solved, and the closed-form expressions of dispersion relations for all four models are obtained. The obtained dispersion relations are also reduced as special cases and matched with the results in the literature. Noteworthy influences of prevalent parameters such as anisotropy, porosity, spring constant, surface/interface Lame and density constants, etc., on Love wave phase velocity are examined graphically and discussed. The results demonstrate that spring–membrane interfacial foundations provide an effective mechanism for tailoring Love-wave dispersion in fluid-saturated media, offering valuable insights for subsurface sensing, geophysical waveguides, and engineered layered composites with imperfect interfaces.

The seismic response of terrain sites has long been a hot topic in the field of geophysics and earthquake engineering over decades, which plays a critical role in evaluating the seismic safety of major engineering in mountain areas. In current practice, rocky mountain structures are often treated as a homogeneous body for the simulation of seismic wave propagation, with only the topographic effects taken into account. However, the in–situ stress field can introduce spatial heterogeneity in wave velocity in the hilly body, which may have a significant influence on the seismic wave propagation. In this study, a three–dimensional (3–D) finite element model of a homogeneous Gaussian–shaped hill was first constructed and validated against existing simulations using the boundary element method. Then, an empirical model for the hilly body with shear wave velocity varying with depth in gradients is established based on the results of laboratory tests from the literature. Finally, with the validated model and the empirical relationship, the seismic wave propagation of the 3–D Gaussian–shaped rocky hilly body with gradient shear wave velocity was investigated numerically via the finite element method. The results show that: (1) The gradient shear wave velocity structure of hilly body can significantly influence the seismic wave propagation and alter the spatial distribution of seismic motion near the hilly surface; (2) As the gradient of shear wave velocity structure intensifies, the amplification of surface ground motion on hill generally increases, accompanied by a shift of the transfer function toward lower frequencies; (3) For the complex site effects of rocky hilly body, there exists a complicated interaction effect between the topography and the gradient shear wave velocity structure.

Abstract Stress-induced anisotropy is prevalent in the subsurface and has a significant impact on seismic wave propagation. Employing the framework of acoustoelastic theory, we establish velocity-stress formulations in the first-order form tailored for media exhibiting stress-induced anisotropy. A numerical implementation based on high-order staggered-grid finite-difference is proposed for wavefield simulation. The study demonstrates that isotropic media subjected to overburden stress exhibit an effective elastic stiffness tensor with VTI (Vertical Transverse Isotropy) symmetry, and the degree of anisotropy scales proportionally with the applied stress level. Numerical simulation results indicate that as the overburden stress increases, the wavefront morphology gradually transitions from circular (isotropic) to elliptical (anisotropic). This research provides a theoretical foundation for understanding seismic wave propagation in stressed media and for subsequent inversion of stress parameters.

Coalbed methane, a key resource in natural gas exploration, is closely linked to the fracture networks within coal beds. Unlike shale or tight sandstone reservoirs, coalbed methane reservoirs feature a dual-porosity/fracture system consisting of matrix pores and cleats. While prior studies have examined the impact of cleat orientation on P-wave velocity and permeability anisotropy, joint frequency-direction analyses of dispersion and attenuation are limited. This study fills this gap by analyzing dispersion and attenuation characteristics in coalbed methane reservoirs, focusing on the cleat system's role in reservoir characterization and gas extraction. Using Biot's quasi-static pore elastic consolidation equation coupled with finite element modeling and numerical upscaling, we investigated the cleat system's influence on seismic signals at the representative elementary volume (REV). Digital rock samples incorporating cleat features were constructed, and their attenuation and velocity dispersion were calculated perpendicular to butt and face cleat directions. A sensitivity analysis assessed the effect of cleat characteristics on seismic signals. Results show that seismic wave dispersion and attenuation are primarily driven by the wave-induced fluid flow (WIFF) effect, with the cleat system's characteristics influencing seismic signal propagation. Directional variations in seismic wave propagation significantly affect dispersion and attenuation, with fracture aspect ratio and infills playing key roles. These findings enhance our understanding of seismic wave anisotropy and provide a foundation for interpreting seismic data in porous media.

The development of coalbed methane (CBM) relies on high-precision reservoir prediction and lithological inversion. Seismic amplitude variation with offset (AVO) technology is an important tool for fine-scale reservoir characterization. However, the seismic AVO response of CBM reservoirs is complex and is affected by seismic rock physics parameters at different scales. Microscopically, aligned fractures in CBM reservoirs produce complex anisotropy due to formation inclination. At the macroscopic scale, the thickness of CBM reservoirs within seismic frequency bands is comparable to the seismic wavelength and should therefore be treated as a layered medium. In addition, pore fluid significantly affects seismic wave propagation. Consequently, determining the azimuthal AVO response of CBM reservoirs in relation to seismic rock physics parameters at different scales can support high-precision reservoir prediction and lithological inversion. In this study, the primary–primary wave reflection coefficient for a two-phase layered medium was derived using Biot’s theory. Using this model, the response characteristics of the reflection coefficients with respect to seismic azimuth, aligned fracture parameters, reservoir thickness, and seismic main frequency were analyzed. A rotated staggered–grid finite–difference algorithm was employed to simulate wavefield characteristics separately for coal seams and surrounding strata. Seismic attributes were then used to characterize the seismic AVO response. The Z-direction seismic amplitude attributes and reflection coefficients showed similar trends in their responses to seismic rockphysical parameters. This study contributes to establishing a more precise seismic AVO response framework to support CBM reservoir prediction and high-quality lithological inversion.

Experimental and Numerical Investigation of Segment Response to Seismic Wave Propagation for Advanced Geological Detection in Shield Tunnels

Abstract Understanding fault‐zone permeability is crucial in model‐based assessment of fluid migration, earthquake nucleation, and hydrothermal or hydrocarbon systems. Vertical seismic profiling (VSP) often captures Stoneley (tube) waves generated by fluid‐formation coupling in and around a borehole. Tube waves offer valuable constrains to local hydraulic properties. Full simulation of the generation of tube waves using Biot's poroelastic equations is very important, but computationally demanding due to the multiscale nature of the problem, involving fine‐scale borehole geometry and long‐wavelength seismic wave propagation in the layered media. We develop a semi‐analytical approach that can predict borehole pressure response of a normally incident plane P wave in layered poroelastic media, including irregularities in the borehole radius. The model accounts for three key mechanisms for tube‐wave generation: (a) due to elastic impedance contrasts, (b) due to fluid infiltration from poroelastic layers, and (c) due to borehole‐radius changes. Using a propagator‐matrix formulation under low‐frequency assumptions, we derive closed‐form expressions for the tube‐wave amplitudes and validate them using finite‐difference poroelastic simulations. The results show that elastic boundaries produce tube waves with opposite polarities, while a thin porous layer and a thin elastic layer generate asymmetric responses with notably different frequency spectra. Our approach improves upon previous effective‐source models by accounting for the tube‐wave velocity contrasts and ensuring the consistency with the poroelastic theory. This efficient modeling framework enables clearer interpretation of VSP data in fault zones, providing insights that aid in quantitative estimation of the local hydraulic properties.

ABSTRACT This paper is concerned with the existence of periodic vibrations of the nonhomogeneous strings with linear and nonlinear couplings under some Sturm–Liouville boundary conditions. Such a model is governed by the variable coefficients wave equations and can also be used to describe the simultaneous propagation of seismic waves in nonisotropic media. In the case of linear couplings, the nonlinear self‐interactions exhibit sublinear growth with different powers. In the case of nonlinear coupling, the nonlinear self‐interactions are characterized by superlinear growth with the same powers as the coupling terms. We prove the existence of infinitely many periodic solutions for these two classes of problems by variational methods and Galerkin approximations under the same working space. Our results are applicable to the uncoupled problems of either homogeneous or nonhomogeneous strings and the coupled problems of the homogeneous strings.

The mobilization of near-surface regolith beneath Apollo seismic stations represents a significant source of noise in lunar seismic records, particularly for low-amplitude deep moonquake signals. These shallow layers strongly affect seismic wave propagation, producing detectable ground motion beneath the instruments and modulating recorded amplitudes and frequency content. In addition to seismic sources, lunar records are influenced by surface thermal expansion driven by solar illumination, tidal stresses associated with the Moon’s orbital motion, meteoroid impacts, and local surface adjustments. Deep moonquake clusters are commonly enhanced through waveform stacking to improve the signal-to-noise ratio. In this study, we analyze deep moonquake clusters previously identified in relation to lunar orbital periods, focusing on variations in frequency content across the three seismometer components. Using the Fast Fourier Transform (FFT), spectrogram analysis, and the Hilbert–Huang transform, we examine clustered seismograms recorded at Apollo stations 12, 14, 15, and 16. Our results show that the y-component consistently exhibits higher high-frequency content than the x-component. The orientation of the y-component, aligned with the lunar east–west axis and parallel to the direction of orbital motion, suggests that frequency dispersion may be sensitive to changes in the Moon’s position within the celestial plane. In contrast, the observed high-frequency variability is likely associated with surface thermal effects linked to solar exposure. These findings indicate that sensors more susceptible to orbital variability are also more sensitive to surface and regolith-related motion, emphasizing the combined influence of orbital dynamics, thermal forcing, and local geological conditions on lunar seismic records.

Abstract Seismic wavefield visualization plays a crucial role in both seismology education and regional seismic studies. Realistic visualization enables users to intuitively observe how seismic waves propagate through different landscapes, making it easier to understand the ground-motion dynamics. With this motivation, we developed Seismic-XR. Seismic-XR is a mixed-reality (XR) educational tool designed to visualize seismic ground motions, providing an interactive platform for exploring seismic-wave propagation and its interactions with diverse topographies. We present a case study using Seismic-XR on an earthquake in Uttarakhand, a seismically active region of the Himalayas characterized by complex geological structures. This study discusses how computational modeling, geospatial data sets, and XR technologies together can transform seismic data sets into accessible and engaging visual experiences. Seismic-XR has the potential to enhance user engagement and provide an intuitive exploration of seismic waves. However, the extent to which XR-driven visualization leads to measurable improvements in conceptual understanding is still an open question. This article presents the methodology, visualization workflow, and results of Seismic-XR while discussing its broader applications.

Sensitivity analysis of SSI effects on nuclear power plants in layered soils using efficient ground motion inputs in OpenSees

Abstract Surge‐type debris flows propagate as a sequence of surges, forming gradually thickening in situ deposition layers between surges that dynamically alter channel‐bed conditions. Seismic recordings from Jiangjia Ravine reveal a progressive attenuation of ground motion amplitude with surge sequence, despite comparable flow magnitudes—indicating a decoupling between flow scale and seismic response. We attribute this to the accumulation and liquefaction of inter‐surge deposition layers, rather than pre‐existing deposits. To quantify this mechanism, we adopt an effective transmission parameter ( ξ ) within a fluvial seismology‐based framework, and propose a sigmoid function linking ξ to normalized deposition layer thickness ( H *). This formulation significantly improves the prediction of seismic power spectral density (PSD) across surges and provides a transferable approach to characterize subsurface flow–bed interactions. Our findings underscore the critical role of bed structure evolution during flow in modulating debris‐flow‐induced seismic signals, with implications for real‐time monitoring and early warning in sediment‐rich catchments.

Abstract Fault damage zones critically influence seismic wave propagation, rupture dynamics, and seismic hazard assessment, yet the relationship between damage zone width and cumulative fault displacement remains uncertain. In this study, we investigate the internal structures of the Jiangcuo fault that ruptured in the 2021 Mw 7.4 Maduo earthquake in the northern Tibetan plateau, Western China. A 60-station dense linear seismic array was deployed across the Jiangcuo fault, 30 km east of the epicenter. Utilizing teleseismic P-wave delays recorded by the array, we identify a low-velocity zone (LVZ) approximately 2.5–3.3 km wide situated asymmetrically south of the 2021 earthquake surface rupture. This wide damage zone is inconsistent with the expectations of the immature Jiangcuo fault but is best explained by the asymmetrically growing Jiangcuo fault zone, where abandoned fault strands preserve damage accumulated from past ruptures. We suggest that comparisons of LVZ widths are only meaningful when the same method and similar array geometry are employed. Our findings highlight the importance of incorporating structural complexities and geological history when evaluating rupture dynamics and fault zone properties in strike-slip tectonic environments.

Summary We simulate an instantaneous time mirror (ITM), i.e., a rapid short duration change in elastic material properties, using numerical experiments in time-varying isotropic elastic media. Our implementation in the seismic wave propagation software SeisSol is based on high-order discontinuous Galerkin discretization with ADER time stepping. We develop an eigenvector-based analytical solution for time interfaces for general linear hyperbolic wave systems and apply it to analyze the energy balance at time boundaries and ITMs. The energy increases for all intermittent medium changes for all impedance scaling factors. Our numerical implementation is validated against these analytical solutions and achieves high-order convergence. Its accuracy is further corroborated by estimates of reflection and transmission coefficients and observed frequency shifts across time boundaries, and by acoustic wave speed estimates obtained from focal spots associated with ITM-generated converging P waves that are consistent with theoretical predictions and ground truth values, respectively. We use the ITM implementation to simulate the partitioning of seismic body waves excited by a point source in a spatially homogeneous elastic full space. The response to an intermittent short change in the elastic parameters yields a diverging and converging P and S wavefield. A systematic scaling of the elastic parameters is then used to steer independent ITM reflections of either P or S waves. Numerical ITM solutions as developed here can be used to synthesize converging wavefields in seismic imaging applications, and more generally to analyze the behavior and manipulation of seismic wavefields in space-time varying media.

To study the complex dynamic response characteristics of spatial crossing tunnels under seismic loads, shaking table model tests were carried out for typical spatial parallel, orthogonal, and oblique crossing tunnels. The propagation and energy distribution characteristics of seismic waves were quantitatively analyzed according to the fundamental frequency, acceleration, and strain response of the system. The results show the following: the addition of a tunnel structure significantly reduces the natural frequency of the system. In spatial crossing tunnel engineering, the axial acceleration responses of the arch top and arch bottom of the tunnel both exhibit the characteristic of a linear distribution, presenting a ‘linear’ shape. For spatial parallel-type and spatial orthogonal-type tunnels, the peak acceleration at the same measurement point of the overcrossing tunnel under the same working condition is generally greater than that of the undercrossing tunnel. However, for the spatial oblique intersection-type structure, the result is just the opposite, that is, the peak acceleration of the overcrossing tunnel is generally less than that of the undercrossing tunnel. For spatial crossing tunnels, unlike the amplification effect of acceleration in a single tunnel, due to the reflection and refraction of seismic waves between the two tunnels, a ‘superposition effect’ of acceleration is generated in space, resulting in an abnormal increase in the acceleration response within the crossing section, which is prone to becoming a weak link in the seismic resistance of the tunnel structure. The strain response of both spatially parallel and orthogonal overcrossing tunnels is greater at the central section than that of undercrossing tunnels and less on both sides. The strain response of the spatial oblique intersection-type overcrossing tunnel is generally greater than that of the undercrossing tunnel.

ABSTRACT Most existing power spectral models used in structural stochastic response analyses only account for site effects through parameters such as fundamental period and damping ratio. However, these site-based models lack an explicit consideration of seismic source and path characteristics, which are inherently critical factors. With the accumulation of knowledge and advancements in seismic exploration technologies in recent decades, detailed seismic source information has become increasingly accessible, making it now both desirable and feasible to conduct stochastic response analyses that integrate not only site conditions but also source and path effects. Therefore, this study proposes an end-to-end analytical framework that simultaneously accounts for source, path, and site effects to efficiently compute the structural stochastic responses, thereby achieving direct prediction from specific seismic source conditions to structural responses. The proposed framework employs a source-based Fourier amplitude spectrum (FAS) model coupled with a ground motion duration model to represent the entire seismic wave propagation process, which has been thoroughly investigated and validated using real seismic records. The FAS parameters can be adjusted to simulate specific seismic sources of interest in earthquake engineering. Then, analytical formulations are derived for the stochastic response analyses of widely used multiple-degree-of-freedom structural systems in the frequency domain, which also supports time-domain stochastic response analysis by converting FAS into time series. Finally, the proposed method is applied to a series of numerical examples for reliability analysis, and the results are validated against time-domain analyses, demonstrating the applicability and accuracy of the method under varying seismic source conditions.

The heterogeneous spatial distribution of fluids induced by capillarity leads to the difficulty to accurate describe seismic wave dispersion and attenuation in partially saturated rocks, affecting the precision of hydrocarbon reservoir exploration. In this work, based on the Santos framework, a modified Santos-Rayleigh model was developed for partially saturated double-porosity medium by reformulating the Biot-Rayleigh equations to incorporate capillarity and kinetic energy effects within fluid inclusions. Numerical analysis reveals that the presence of capillarity induces an additional enhancement of P-wave velocity within low-frequency. Furthermore, under varying configurations of water, oil and gas, the P-wave velocities in the low-frequency band fall below the Gassmann-Wood limit due to coupled capillarity and mesoscopic flow. Significant dispersion and attenuation occur when gas serves as the inclusion, and a smaller modulus contrast between the host and inclusions leads to weaker low-frequency dispersion. The internal kinetic energy of inclusion gives rise to a shift of both dispersion and attenuation toward lower frequencies. Comparison with the experimental data confirms that the modified model exhibits a good low-frequency agreement, providing reliable velocity predictions under varying water saturation levels. Document Type: Original article Cited as: Yang, B., Ba, J., Zhang, L., Jiang, Q., Duan, M., Santos, J. E. Seismic wave propagation in partially saturated double-porosity media: The role of capillarity. Advances in Geo-Energy Research, 2026, 19(1): 72-82. https://doi.org/10.46690/ager.2026.01.06

Shaking table test on the topographic effect of a symmetrical V-shaped canyon under streamwise excitation

ABSTRACT Traveltime computation is an effective way to simulate seismic wave propagation in isotropic and anisotropic media. It often requires the phase and group velocities along a ray direction. The phase and group velocities are not functions of the ray direction, but functions of the slowness direction, which motivates the need for efficient numerical approaches for computing the slowness direction. A generalized method was proposed to achieve this goal in 3D tilted transverse isotropic media, which involves solving a nonlinear equation of two unknowns, the inclination and azimuthal angles of the slowness direction, and is computationally demanding. To overcome the difficulty, the equation was recast by projecting it onto the local coordinates that align with the axis of symmetry of the medium. Under the local coordinate system, the nonlinear equation reduces to an equation of one unknown, the inclination angle, with the azimuthal angle obtained from the given ray direction. Hence, the nonlinear equation can be solved efficiently and its solutions can be used to calculate the phase and group velocities. As an application, the proposed method was used to compute traveltimes in 3D vertical transverse isotropic (VTI) media. The calculated group velocities are incorporated into the fast sweeping method to solve the original anisotropic Eikonal equation directly on uniform meshes. The feasibility of the proposed group velocity calculation method is evaluated in three 3D homogeneous anisotropic models, and the application on traveltime computation is tested on a 3D homogeneous VTI model and the British Petroleum anisotropic VTI model.