Propagation Characteristics Of Seismic Waves Research Articles

Analytic formula for the group velocity and its derivatives with respect to elastic moduli for a general anisotropic medium

Studying the anisotropy of seismic wave velocity can provide a theoretical basis for understanding the characteristics of seismic wave propagation in anisotropic media, such as forward modeling of seismic wavefield and simultaneous inversion of anisotropic parameters. It is an important work to calculate the group velocities of three kinds of seismic waves (qP, qS1, and qS2) and the analytical expressions of the partial derivatives of the group velocities with respect to 21 elastic parameters in general anisotropic media. Therefore, a new relationship between the phase and group velocity in the general anisotropic medium is introduced first, and then the analytical expressions of the group velocity of three kinds of waves are deduced. Then, the analytical formulas of partial derivatives of the group (or phase) velocity with respect to 21 elastic parameters are derived. Finally, the distribution of partial derivatives of group slowness with respect to 21 elastic parameters with varied ray angles is analyzed and discussed. The final analytical expressions of group velocity and its partial derivatives are relatively concise and can deal with the singular points and multivalued problems of qS waves. By drawing comparison to the numerical solution of the eigenvector method, the accuracy of the analytical formula of group velocity and its partial derivatives with respect to elastic parameters are verified. The numerical simulation results indicate that the algorithm can accurately obtain the partial derivatives of group slowness with respect to 21 elastic parameters and would provide a theoretical basis for seismic ray tracing and traveltime inversion in general anisotropic media.

Propagation Characteristics of Seismic Waves in Shallow Sea Sedimentary Layers

Zhao, S.; Gu, D.; Guo, C.; Wang, X., and Zhang, J., 2023. Propagation characteristics of seismic waves in shallow sea sedimentary layers. Journal of Coastal Research, 39(1), 32–44. Charlotte (North Carolina), ISSN 0749-0208. To explore new techniques for detecting and identifying targets in water, the propagation characteristics of seismic waves in shallow sea were deeply studied. Wave theory and staggered grid finite difference method were employed to analyze the propagation characteristics of seismic waves in a layer of underwater medium with a sedimentary layer. The results show that a Scholte wave is prone to disperse in an underwater medium with a sedimentary layer. The sediment thickness and acoustic parameters have great influence on the propagation characteristics of seismic waves. Moreover, the seismic wave signals were mainly concentrated below 20 Hz by collecting the vibration velocity of underwater interface. Furthermore, Scholte wave signals in underwater experiments were determined by utilizing four filtering methods and Scholte polarization characteristics, and the Butterworth filtering method can better preserve the integrity of vibration velocity signal. The theoretical, numerical, and experimental polarization characteristic results are basically consistent, which indicate that Scholte wave can be well extracted by the method of polarization characteristics.

Investigation on the Seismic Wave Propagation Characteristics Excited by Explosion Source in High-Steep Rock Slope Site Using Discrete Element Method

The influence of seismic waves induced by explosion sources on the dynamic response characteristics of rock slope sites is one of the most important problems affecting engineering construction. To investigate the wave propagation characteristics and attenuation law of seismic waves induced by explosive sources in rock sites from the perspective of time and frequency domains, the high-performance matrix discrete element method (MatDEM) is used to carry out numerical simulation tests on a granite rock medium site. The discrete element model of the high-steep rock slope is established by MatDEM, and the dynamic analysis of the rock medium site is conducted by loading blasting vibration load to generate seismic waves. The results show that the seismic waves in the rock site present characteristics of arc propagation attenuation. The maximum attenuation rate of the dynamic response is the fastest within 0.3 s and 25 m from the explosion source. The slope region can weaken the dynamic response of seismic waves generated by the explosion source. In particular, the high-frequency band (>20 Hz) has an obvious filtering effect. The dynamic response of the P-wave induced by the explosive source is greater than that of the S-wave in the bedrock and surface region. The dynamic amplification effect of the P-wave is greater than that of the S-wave in the slope region. The seismic waves in the slope region show an attenuation effect along the slope surface and have a typical elevation amplification effect inside the slope.

Wave propagation at the welded interface of an elastic solid and unsaturated poro-thermoelastic solid

PurposeThe purpose of this paper is to investigate propagation characteristics of seismic waves at the welded interface of an elastic solid and unsaturated poro-thermoelastic solid.Design/methodology/approachA theoretical formulation of partially saturated poro-thermoelastic solid is used in this study established by Zhou et al. (2019). The incidence of two primary waves (P and SV) is taken. The incident wave from the elastic solid induces two reflected waves and five refracted waves. Due to viscous pore fluids, partially saturated poro-thermoelastic solid behave dissipative, whereas elastic solid behaves non-dissipative. As a result, both reflected and incident waves are homogeneous. However, all the refracted waves are inhomogeneous. A non-singular system of linear equations is formed by the coefficients of reflection and refraction for a specified incident wave. The energy shares of various reflected and refracted waves are determined by using these reflection and refraction factors. Finally, a sensitivity analysis is performed, and the effect of critical variables on energy partitioning at the interface is observed. The numerical example shows that throughout the process of reflection/refraction, the energy of incidence is conserved at all angles of incidences.FindingsThis study demonstrated two refracted (homogeneous) and five refracted (inhomogeneous) waves due to the incident wave from elastic solid. The reflection and refraction coefficients and partitioning of incident energy are acquired as a part of diverse physical parameters of the partially saturated poro-thermoelastic media. The interference energies between unlike pairs of refracted waves have been discovered due to the dissipative behavior of unsaturated poro-thermoelastic solid.Originality/valueThe sensitivity of different energy shares to various aspects of the considered model is graphically analyzed for a specific numerical model. The energy balance is maintained by combining interaction energy and bulk wave energy shares.

Propagating Seismic Waves in VTI Attenuating Media Using Fractional Viscoelastic Wave Equation

AbstractSeismic velocity and attenuation anisotropy are ubiquitous in the crust and upper mantle, significantly modulating the characteristics of seismic wave propagation in the Earth's interior. Accurate seismic wave modeling of velocity and attenuation anisotropy is essential for the understanding of wave propagation in the Earth's interior as well as constructing global and region‐scale seismic full waveform tomography. Here, we derive a decoupled fractional Laplacian (DFL) viscoelastic wave equation to characterize the Earth's frequency‐independent Q behavior in the vertical transversely isotropic (VTI) media. We verify the accuracy of the proposed viscoelastic wave equation by 2D synthetic examples; to show its applicability in crustal‐scale seismic modeling, we present an example of 3D seismic wave propagation in the realistic Salton Trough model. Through extensive numerical tests, we conclude that the proposed viscoelastic wave equation is superior in four aspects. First, the viscoelastic wave equation takes VTI anisotropy of both velocity and attenuation into account and can describe the strong direction‐dependent attenuation. Second, our derivation contains spatially independent Laplacians, and thus the proposed wave equation enjoys higher simulation accuracy for heterogeneous Q media. Third, the new viscoelastic wave equation can decouple the amplitude decay and the phase distortion, which is appealing for improving the resolution in seismic imaging and inversion. Lastly, compared to viscoelastic wave equations with time‐fractional operators, our scheme has higher computational efficiency by avoiding substantial wavefield storage.

Seismic Wave Propagation Characteristics and Their Effects on the Dynamic Response of Layered Rock Sites

To investigate the seismic response of layered rock sites, a multidomain analysis method was proposed. Three finite element models with infinite element boundaries for layered sites were analysed. The results of this multidomain analysis show that stratum properties and elevation have an impact on wave propagation characteristics and the dynamic response of layered sites. Compared with the rock mass, the overlying gravel soil has a greater dynamic amplification effect at the sites. A time domain analysis parameter PGA(IMF) was proposed to analyse the effects of different strata on the seismic magnification effect of layered sites, and its application was also discussed in comparison with PGA. According to the frequency domain analysis, the interface of the rock mass strata has a low impact on the Fourier spectrum characteristics of the sites, but gravel soil has a great magnification effect on the spectrum amplitude in the high-frequency band (≥30 Hz) of waves. Moreover, the stratum properties have a great influence on the shape and peak value of the Hilbert energy and marginal spectrum at layered sites. When waves propagate from hard rock to soft rock, the peak value of the Hilbert energy spectrum changes from single to multiple peaks; then, in gravelly soil, the Hilbert energy spectral peak, its nearby amplitude and the amplitude in the high-frequency band (28–36 Hz) are obviously amplified. The frequency components and amplitude of the marginal spectrum become more abundant and larger from rock to gravelly soil in the high-frequency band (28–35 Hz).

Shaking table test of acceleration response of surrounding rock of the 3D cross tunnel under earthquake

Taking the 3D cross-engineering of Caomeigou No.1 Tunnel and Pandaoling Tunnel as an example, a shaking table test was carried out to study the effect of tunnel spatial position on seismic wave propagation characteristics and acceleration response of surrounding rock under earthquake seismic excitation. Based on the influence of the spatial position of the tunnel, the characteristic form of the surrounding rock between the cross section and non-cross section is divided, and the accelerometer layout scheme is designed. Based on statistical probability, the ratio of peak ground velocity to peak ground acceleration (PGA) was introduced to quantitatively characterize the characteristics of seismic wave propagation spectrum. Furthermore, the SPECTR calculation was used to obtain the regional difference in the seismic wave propagation potential damage potential displacement parameter (P d ). Under the influence of the spatial location of the 3D cross tunnel, the peak acceleration and motion duration of the seismic wave are mainly reflected in the variation of the section along the elevation direction. Low-frequency (≤20 Hz) seismic waves have a greater impact on the tunnel structure, and peak ground velocity/peak ground acceleration ratio has a positive correlation with the peak input energy of ground motion. The ultra-small net-spacing cross tunnel has a spatially distributed coupling deformation effect. The crown of the upper-span tunnel is highly sensitive to earthquakes and becomes a weak link in seismic design. These results help us provide a theoretical basis for the seismic design of the cross-tunnel.

Numerical Investigation on Dynamic Response Characteristics and Deformation Mechanism of a Bedded Rock Mass Slope Subject to Earthquake Excitation

In order to systematically reveal the dynamic response characteristics of rock mass slopes subject to seismic excitation, time-domain and frequency-domain analyses are used to investigate the dynamic response of a bedded rock slope from multiple perspectives, using the two-dimensional numerical dynamic analyses. Based on the numerical simulation results, the influence of the weak bedded structural planes on the propagation characteristics of seismic waves in the slope is analyzed. The time-domain analysis suggests that the topographic and geological conditions have an influence on the dynamic response of the slope. The effects of ground motion direction on the dynamic response characteristics of the slope are identified. In addition, according to the frequency-domain analysis, the impacts of slope surface, elevation, and structural plane on the seismic response characteristics of the slope are also clarified. The intrinsic characteristics of the slope are investigated by using Fourier spectral analysis and modal analysis, and the deformation response characteristics of the slope are clarified. The relationship between different natural frequencies of the slope, the predominant frequency of the seismic wave, and the dynamic response characteristics of the slope is discussed. Moreover, the dynamic failure mechanism of the slope is analyzed. This work provides a reference for the seismic analysis of this type of slope.

A study on the characteristics of seismic wave propagation in fractured marlstone reservoirs based on mechanical principles

A study on the characteristics of seismic wave propagation in fractured marlstone reservoirs based on mechanical principles

Transmitting Characteristics of Seismic Motion in Super-Deep Overburden Layer Ground

Dynamic response characteristics and antiseismic performance of the structures which were constructed on the super-deep overburden layer are affected obviously by the seismic motion characteristics of the super-deep overburden layer foundation. In this paper, the seismic motion characteristics of horizontally stratified super-deep overburdenIn this paper, the seismic motion characteristics of horizontally stratified super-deep overburden based on the research results of on-site in situ tests and indoor material property tests, the horizontal shear layer method that can consider the nonlinear characteristics of dynamic soil deformation and the characteristics of seismic wave propagation in the soil is used to study the characteristics of ground motions of super-deep and thick overburden level of an earth-rock dam in China. The influence law of input ground motion characteristics and input ground motion position on seismic response analysis results of overburden ground is studied. Taking the uniform overburden layer model as an example, the coupling influence analysis of soil layer thickness and shear velocity on ground motion response are carried out, and the coupling influence law is proposed. The study shows that the seismic motion propagating characteristics of the earthquake in super-deep overburden layer is involved, inputting location of the seismic motion affects the results of ground seismic response greatly; super-deep overburden layer thickness and the soil shear wave velocity on influence law of ground motion characteristics have coupling. When the shear wave velocity of the soil layer is constant, the surface acceleration response has an inflection point with the change of the soil layer thickness; when the thickness of overburden is constant, the surface acceleration response also has an inflection point with the change of shear wave velocity of the soil layer; these inflexion values are influenced by both soil thickness and shear wave velocity.

Scattering of Plane P1 Wave by an Inclusion in a Three-Dimension Poroelastic Half-Space

Local inclusion topography has significant influence on seismic wave propagation, and the propagation characteristics of seismic waves in poroelastic soils are obviously different from those in single-phase media. Based on Biot’s theory, the scattering of plane P1 wave by inclusion in a three-dimensional poroelastic half-space is studied by using the indirect boundary element method (IBEM). The scattering field is constructed by introducing a virtual wave near the interface between inclusion and half-space and the surface of half-space, and the virtual wave density is obtained by establishing boundary integral equation based on the boundary conditions. The effects of the depth, geometric characteristics, boundary permeability, porosity, incident frequency, and incident angle of the inclusion on elastic wave scattering are systematically analyzed. The results show that due to the soil skeleton-pore water coupling effect, when the porosity is n = 0.3, the surface displacement amplitude of dry soil is larger than that of poroelastic soil. When the porosity is n = 0.36, the surface displacement amplitude of poroelastic soil is larger than that of dry soil. The surface displacement amplitude of poroelastic-drained condition is slightly larger than that of undrained condition. With the increase of inclusion depth, the scattering of elastic wave by inclusion decreases gradually. When P1 wave is incident, the surface displacement amplitude at the depth of H = 0.5 can be increased up to three times as much as that at the depth of H = 1.5. As the inclusion becomes narrower and flatter, the scattering of elastic waves by inclusion decreases gradually. When the ratio between height and length is S = 2/5, the surface displacement magnitude can reach up to 9.5.

Optimal Third-Order Symplectic Integration Modeling of Seismic Acoustic Wave Propagation

ABSTRACTSeismic wavefield modeling based on the wave equation is widely used in understanding and predicting the dynamic and kinematic characteristics of seismic wave propagation through media. This article presents an optimal numerical solution for the seismic acoustic wave equation in a Hamiltonian system based on the third-order symplectic integrator method. The least absolute truncation error analysis method is used to determine the optimal coefficients. The analysis of the third-order symplectic integrator shows that the proposed scheme exhibits high stability and minimal truncation error. To illustrate the accuracy of the algorithm, we compare the numerical solutions generated by the proposed method with the theoretical analysis solution for 2D and 3D seismic wave propagation tests. The results show that the proposed method reduced the phase error to the eighth-order magnitude accuracy relative to the exact solution. These simulations also demonstrated that the proposed third-order symplectic method can minimize numerical dispersion and preserve the waveforms during the simulation. In addition, comparing different central frequencies of the source and grid spaces (90, 60, and 20 m) for simulation of seismic wave propagation in 2D and 3D models using symplectic and nearly analytic discretization methods, we deduce that the suitable grid spaces are roughly equivalent to between one-fourth and one-fifth of the wavelength, which can provide a good compromise between accuracy and computational cost.

Q-Compensated Pre-stack Reverse Time Migration in Viscoelastic Media with an Irregular Free Surface

Pre-stack reverse time migration (RTM) is a powerful tool that provides better imaging of complex geological structures than traditional migration methods. An irregular free surface has significant impacts on the characteristics of seismic wave propagation and seismic imaging in mountain or basin areas. In addition, viscoelastic media produce a better representation of the earth than acoustic or elastic media. A main feature of RTM in viscoelastic media is that it can consider compensation for P- and S-wave attenuation effects. In this study, we develop an approach for Q-compensated pre-stack RTM in 2D viscoelastic isotropic media with an irregular free surface. Based on the boundary-conforming method, the viscoelastic model can be discretized to better match the irregular surface and interfaces. The 2D second-order viscoelastic equations and free surface boundary conditions are converted from the Cartesian coordinate system to the curvilinear coordinate system. The finite-difference operators are applied to approximate the viscoelastic wave equations and the irregular free surface in the curvilinear coordinate system. In addition, the convolutional perfectly matched layer (CPML) absorbing boundary condition is selected to effectively suppress artificial reflections from the model boundaries. In the numerical examples, the snapshots, shot gathers and Q-compensated pre-stack RTM results show that our algorithm can obtain an accurate structure image in viscoelastic media in the presence of surface topography.

Prestack AVA joint inversion of PP and PS waves using the vectorized reflectivity method

Most current prestack AVA joint inversion methods are based on the exact Zoeppritz equation and its various approximations. However, these equations only reflect the relation between reflection coefficients, incidence angles, and elastic parameters on either side of the interface, which means that wave-propagation effects, such as spherical spreading, attenuation, transmission loss, multiples, and event mismatching of P- and S-waves, are not considered and cannot accurately describe the true propagation characteristics of seismic waves. Conventional AVA inversion methods require that these wave-propagation effects have been fully corrected or attenuated before inversion but these requirements can hardly be satisfied in practice. Using a one-dimensional (1D) earth model, the reflectivity method can simulate the full wavefield response of seismic waves. Therefore, we propose a nonlinear multicomponent prestack AVA joint inversion method based on the vectorized reflectivity method, which uses a fast nondominated sorting genetic algorithm (NSGA II) to optimize the nonlinear multiobjective function to estimate multiple parameters, such as P- wave velocity, S-wave velocity, and density. This approach is robust because it can simultaneously cope with more than one objective function without introducing weight coefficients. Model tests prove the effectiveness of the proposed inversion method. Based on the inversion results, we find that the nonlinear prestack AVA joint inversion using the reflectivity method yields more accurate inversion results than the inversion by using the exact Zoeppritz equation when the wave-propagation effects of transmission loss and internal multiples are not completely corrected.

Simulating Seismic Wave Propagation in Viscoelastic Media with an Irregular Free Surface

In seismic numerical simulations of wave propagation, it is very important for us to consider surface topography and attenuation, which both have large effects (e.g., wave diffractions, conversion, amplitude/phase change) on seismic imaging and inversion. An irregular free surface provides significant information for interpreting the characteristics of seismic wave propagation in areas with rugged or rapidly varying topography, and viscoelastic media are a better representation of the earth’s properties than acoustic/elastic media. In this study, we develop an approach for seismic wavefield simulation in 2D viscoelastic isotropic media with an irregular free surface. Based on the boundary-conforming grid method, the 2D time-domain second-order viscoelastic isotropic equations and irregular free surface boundary conditions are transferred from a Cartesian coordinate system to a curvilinear coordinate system. Finite difference operators with second-order accuracy are applied to discretize the viscoelastic wave equations and the irregular free surface in the curvilinear coordinate system. In addition, we select the convolutional perfectly matched layer boundary condition in order to effectively suppress artificial reflections from the edges of the model. The snapshot and seismogram results from numerical tests show that our algorithm successfully simulates seismic wavefields (e.g., P-wave, Rayleigh wave and converted waves) in viscoelastic isotropic media with an irregular free surface.

Surface wave group velocity in the Osaka sedimentary basin, Japan, estimated using ambient noise cross-correlation functions

Inter-station cross-correlation functions estimated using continuous ambient noise or microtremor records were used to extract the seismic wave propagation characteristics of the Osaka sedimentary basin, Japan. Temporary continuous observations were conducted at 15 sites in the Osaka basin between 2011 and 2013. The data were analyzed using seismic interferometry. The target period range was 2–8 s. Cross-correlations between all of the possible station pairs were calculated and stacked to produce a year-long data set, and Rayleigh wave signals in the vertical and radial components and Love wave signals in the transverse component were identified from the results. Simulation of inter-station Green’s functions using the finite difference method was conducted to check the performance of the current three-dimensional velocity structure model. The measured time lag between the observed and theoretical Green’s functions was less than 2 s for most station pairs, which is less than the wave period of interest in the target frequency range. Group velocity tomography was applied to group delay times estimated by means of multiple filter analysis. The estimated group velocities for longer periods of 5–8 s exhibited spatial variation within the basin, which is consistent with the bedrock depth distribution; however, the group velocities for shorter periods of 2–3 s were almost constant over the studied area. The waveform and group velocity information obtained by seismic interferometry analysis can be useful for future reconstruction of a three-dimensional velocity structure model in the Osaka basin.Graphical .

The correlation between the characteristics of seismic wave propagation in Western Caucasus and the geological–tectonic features of the region

The relationship between the characteristics of seismic waves in the Western Caucasus and the geological-tectonic structure of the region is studied for identifying the specificity of seismic propagation in the mountainous regions with a complicated geological structure and forecasting the characteristics of the propagation from the geological and tectonic data. The interpretation is presented for the estimates of the Q-factor of the medium (Q(f) ~ 55f 0.9 in the region of Sochi and Q(f) ~ 90f 0.7 in the region of Anapa), seismic wave enhancement in the upper crustal layers (A(f) ~ 1), and peak ground acceleration residuals, which were previously determined from the records of the local earthquakes and show the distributions of local variations in the parameters of seismic wave radiation and propagation. The obtained characteristics are interpreted in the context of the up-to-date information about the tectonic, geological, and deep structure of the epicentral zones in the Western Caucasus and neighboring territory of the Black Sea. The discrepancies revealed in the low-frequency behavior of the Q-factor in the vicinities of Sochi and Anapa is accounted for by the spatial scale and character of tectonic dislocations of the rocks in these regions. The local variations in the parameters of seismic radiation and propagation are probably related to the geological features of the region such as the fault structures, including the thrusts, shatter zones, oblique seismic boundaries, variations in the thickness and consolidation of the sedimentary cover, as well as the peculiarities in the structure and material composition of the basement.

Basin‐scale Green's functions from the ambient seismic field recorded by MeSO‐net stations

AbstractSeismic waves propagating through the Earth can be significantly affected by velocity structures such as sedimentary basins. We investigate the propagation characteristics of seismic waves across the Kanto basin, Japan, using Green's functions extracted from the ambient seismic field. We use two stations situated on the eastern and southern edges of the basin as virtual sources, and approximately 420 stations, which are mainly a part of the Metropolitan Seismic Observation network (MeSO‐net), as receivers. Using seismometers aligned along two straight lines with the virtual sources, we find that several types of waves can be recovered, each with different sensitivities to the layers that compose the basin. We also show that after amplitude calibration, the extracted Green's functions can accurately simulate the seismic waves of two moderate Mw 4–5 shallow earthquakes that occurred close to the virtual sources. Furthermore, we find that the distribution of the 5% damped pseudovelocity response at a period of 6 s computed from the records of each event and the Green's function waveforms have similar amplification patterns. This study supports the fact that dense networks recording continuously the ambient seismic field in metropolitan areas can be used to accurately assess seismic hazard at high spatial resolution.

Propagation Characteristics of Seismic Waves Taking Stratigraphic Composition into Consideration

In this paper, soil-water coupled dynamic analyses are carried out to investigate the influence of stratigraphic composition on the propagation properties of the seismic waves. SYS Cam-clay model is used as the constitutive model which can describe the different state of clayey and sandy soils. Two cases are considered for the composition of ground: one is the sandy ground with diluvial sand, alluvial sand and reclaimed sand; the other one is the clayey layer at the ground surface. It is found that for the sandy ground even though there is certain amplification of the input acceleration wave during the dense sand layer the subsequent seismic waves through the loose sand layers are attenuated significantly due to the occurrence of the liquefaction. While for the clayey ground, even though there is no risk of liquefaction damages at the ground surface the acceleration amplitude is greatly amplified and there is a risk that the structure itself would fail in the strength.

Near-Surface Multi-Point Vibration Location Method Based on Seismic Depth Migration

This paper presents a method for multi-point vibration location near-surface. Unlike traditional source location technologies, it is not using travel times of seismic waves for positioning calculation, but according to the entire seismic data record, using the wave equation migration method to calculate the source location. Similar to exploration seismic, the records from a survey line within a certain period of time are data volumes with dimensions of time and ground coordinates. Based on the data, combined with surface seismic wave propagation characteristics, by using the improved seismic depth migration algorithm, the vibration energy will return to the starting position where exactly the source location is. The method can solve the problem of location calculation error by using traditional method when several vibration at the same time or continuous vibration occurs at some point.