Regional Seismic Wavefield Computation on a 3-D Heterogeneous Earth Model by Means of Coupled Traveling Wave Synthesis

-- I present a new algorithm for calculating seismic wave propagation through a three-dimensional heterogeneous medium using the framework of mode coupling theory originally developed to perform very low frequency (f < ~0.01т.05 Hz) seismic wavefield computation. It is a Greens function approach for multiple scattering within a defined volume and employs a truncated traveling wave basis set using the locked mode approximation. Interactions between incident and scattered wavefields are prescribed by mode coupling theory and account for the coupling among surface waves, body waves, and evanescent waves. The described algorithm is, in principle, applicable to global and regional wave propagation problems, but I focus on higher frequency (typically f S ~0.25 Hz) applications at regional and local distances where the locked mode approximation is best utilized and which involve wavefields strongly shaped by propagation through a highly heterogeneous crust. Synthetic examples are shown for P-SV-wave propagation through a semi-ellipsoidal basin and SH-wave propagation through a fault zone.     

含泥质低孔渗各向异性黏弹性介质中的波频散和衰减研究

本文定义了各向异性黏弹性参数修正因子,并将其引入到黏弹性模型中以体现泥质含量对黏弹性机制的影响,同时将波传播过程中孔隙介质骨架黏弹性力学机制与两种孔隙流体流动力学机制（Biot流动和喷射流动机制）有机地统一起来处理,从而给出了描述含泥质低孔渗孔隙各向异性介质中波传播规律的黏弹性Biot/squirt (BISQ)模型.数值计算结果表明,入射波的方位角、各向异性渗透率以及泥质含量等对含流体复杂孔隙介质中波频散和衰减的影响具有显著的方位各向异性特征,在低频范围内（地震波勘探频率）黏弹性力学机制对波传播能量的衰减起主导作用.     

Harmonic wave propagation through viscoelastic heterogeneous media exhibiting mild stochasticity — II. Applications

The results obtained in Part I (Soil Dynam. Earth. Engng, 1996, 15, 119-27) of this work for modelling harmonic wave propagation through viscoelastic heterogeneous media that exhibit a small random fluctuation of their material properties about mean values are now used here to investigate SH wave propagation in two naturally occurring media, namely sandstone and topsoil. These results are in the form of depth dependent, deterministic mean values and non-isotropic covariances for both the wave speed profile in the medium and for the fundamental solution in terms of displacement due to a unit point source. The results are also compared against conventional Monte Carlo simulations.     

Viscoelastic representation of surface waves in patchy saturated poroelastic media

Wave-induced flow is observed as the dominated factor for P wave propagation at seismic frequencies. This mechanism has a mesoscopic scale nature. The inhomogeneous unsaturated patches are regarded larger than the pore size, but smaller than the wavelength. Surface wave, e.g., Rayleigh wave, which propagates along the free surface, generated by the interfering of body waves is also affected by the mesoscopic loss mechanisms. Recent studies have reported that the effect of the wave-induced flow in wave propagation shows a relaxation behavior. Viscoelastic equivalent relaxation function associated with the wave mode can describe the kinetic nature of the attenuation. In this paper, the equivalent viscoelastic relaxation functions are extended to take into account the free surface for the Rayleigh surface wave propagation in patchy saturated poroelastic media. Numerical results for the frequency-dependent velocity and attenuation and the time-dependent dynamical responses for the equivalent Rayleigh surface wave propagation along an interface between vacuum and patchy saturated porous media are reported in the low-frequency range (0.1–1,000 Hz). The results show that the dispersion and attenuation and kinetic characteristics of the mesoscopic loss effect for the surface wave can be effectively represented in the equivalent viscoelastic media. The simulation of surface wave propagation within mesoscopic patches requires solving Biot’s differential equations in very small grid spaces, involving the conversion of the fast P wave energy diffusion into the Biot slow wave. This procedure requires a very large amount of computer consumption. An efficient equivalent approach for this patchy saturated poroelastic media shows a more convenient way to solve the single phase viscoelastic differential equations.     

Seismic wave modeling in viscoelastic VTI media using spectral element method

Spectral element method (SEM) for elastic media is well known for its great flexibility and high accuracy in solving problems with complex geometries. It is an advanced choice for wave simulations. Due to anelasticity of earth media, SEM for elastic media is no longer appropriate. On fundamental of the second-order elastic SEM, this work takes the viscoelastic wave equations and the vertical transversely isotropic (VTI) media into consideration, and establishes the second-order SEM for wave modeling in viscoelastic VTI media. The second-order perfectly matched layer for viscoelastic VTI media is also introduced. The problem of handling the overlapped absorbed corners is solved. A comparison with the analytical solution in a two-dimensional viscoelastic homogeneous medium shows that the method is accurate in the wave-field modeling. Furtherly, numerical validation also presents its great flexibility in solving wave propagation problems in complex heterogeneous media. This second-order SEM with perfectly matched layer for viscoelastic VTI media can be easily applied in wave modeling in a limited region.     

粘弹性裂隙型单斜介质多方位地面三分量记录模拟

针对粘弹性裂隙型单斜介质,本文应用高阶交错网格差分法,对其传播快照以及多方位地面三分量记录进行模拟,结果证明了裂隙填充物的性质引起的各向异性与粘弹性性质对单斜介质波场有明显的影响,总结了不同观测方位地震记录呈现出的规律性,这为进一步了解波场在介质中的传播情况,提出更合理的理论模型,提供一种尝试。     

ulti-azimuth three-component surface seismic modeling for viscoelastic cracked monoclinic media

针对粘弹性裂隙型单斜介质,本文应用高阶交错网格差分法,对其传播快照以及多方位地面三分量记录进行模拟,结果证明了裂隙填充物的性质引起的各向异性与粘弹性性质对单斜介质波场有明显的影响,总结了不同观测方位地震记录呈现出的规律性,这为进一步了解波场在介质中的传播情况,提出更合理的理论模型,提供一种尝试.     

Converted T Phases Recorded on Hawaii from Polynesian Nuclear Tests: A Preliminary Report

v--vWe present a preliminary study of T waves from Polynesian nuclear tests at Mururoa, recorded on digital stations of the Hawaii Volcano Observatory network, following their conversion to seismic waves at the southern shore of the Island of Hawaii, and subsequent propagation to the recording stations. We show that seismograms are composed of several packets, which can be interpreted as resulting from TMP and TMS conversions, and which feature distinct spectral characteristics. As the distance from the shoreline to the station increases, the relative importance of the several wave packets changes; a prominent shadow for TMP is found at 8-12 km from the shore. This pattern is affected by the local crustal structure; in a favorable case, propagation in deep, low-attenuation layers resulted in a clear record as far as 76 km from the shoreline. While these results are generally robust, they can be moderately affected by a change of location of the source inside Mururoa Atoll.     

3-D Simulation of Earthquake Generation Cycles and Evolution of Fault Constitutitve Properties

--The earthquake generation cycle consists of tectonic loading, quasi-static rupture nucleation, dynamic rupture propagation and stop, and subsequent stress redistribution and fault restrengthening. From a macroscopic point of view, the entire process of earthquake generation cycles should be consistently described by a coupled nonlinear system of a slip-response function, a fault constitutive law and a driving force. On the basis of such a general idea, we constructed a realistic 3-D simulation model for earthquake generation cycles at a transcurrent plate boundary by combining the viscoelastic slip-response function derived for a two-layered elastic-viscoelastic structure model, the slip- and time-dependent fault constitutive law that has an inherent mechanism of fault restrengthening, and the steady relative plate motion as a driving force into a single closed system. With this model we numerically simulated the earthquake generation cycles repeated in a seismogenic region on a plate interface, and examined space-time changes in shear stress, slip deficits and fault constitutive properties during one complete cycle in detail. The occurrence of unstable dynamic slip brings about decrease both in fault strength and shear stress to a constant residual level. After the arrest of dynamic slip, the breakdown strength drop j†_p of fault is restored rapidly and the process of stress accumulation resumes in the seismogenic region. On the other hand, the restoration of the critical weakening displacement D_c proceeds gradually with time through the interseismic period. The restoration of D_c can be regarded as the macroscopic manifestation of the microscopic recovery process of fractal fault surface structure. Through numerical simulation with a multi-segmented fault model, we examined the effects of viscoelastic fault-to-fault interaction. The effect of transient viscoelastic stress transfer through the asthenosphere is significant as well as the direct effect of elastic stress transfer, and it possibly explains the time lag of the sequential occurrence of large events along a plate boundary.     

二维频率空间域25点优化系数差分格式弹性波数值模拟(英文)

频率空间域地震波数值模拟具有独特的优势:可以同时模拟多源的波传播、每个频率之间独立并行地计算、计算频带选择灵活、不存在累计误差、容易模拟粘弹性介质中地震波传播.但是该方法的最大瓶颈是对于计算机内存的巨大需求.我们使用压缩存储系数矩阵的方法,极大地减少了计算机内存的需求量.同时为了减少短筹分算子的数值频散,引用了频率空间域25点弹性波波动方程的差分格式,并使用了最小二乘意义下求出的优化差分系数.为了克服边界反射,采用了最佳匹配层吸收边界条件.数值模拟试验证明:用压缩存储系数矩阵及优化差分系数的频率空间域25点差分格式进行弹性波正演模拟,可以减少数值频散,提高计算精度.使用较大的网格间距,降低计算机内存需求,并保持较高的计算效率.该正演方法为后续弹性波偏移和弹性参数反演提供较好的基础.     

Sedimentary Basins and the Blockage of Lg Wave Propagation in the Continents

v--vThe phenomenon of "Lg blockage," where Lg is strongly attenuated by crustal heterogeneities, poses a serious problem to CTBT monitoring because Lg is an important seismic phase for discrimination. This paper examines blockage in three continental regions where the Lg blockages may be caused by large, enclosed sedimentary basins along the propagation path. The Barents Sea Basin blocks Lg propagation across the Barents Sea from the Russian nuclear test sites at Novaya Zemlya to Scandinavian stations. Also, "early Lg" waves are observed in Sn codas on NORSAR, NORESS, and ARCESS recordings of Novaya Zemlya explosions where direct Lg is blocked. Early Lg waves may have resulted from Sn-to-Lg mode conversion at the contact between the Barents Basin and the Kola Peninsula. The Northern and Southern Caspian Sea Basins also block Lg waves from PNEs and earthquakes, perhaps due to thick, low-velocity, low-Q sediments replacing the granitic layer rocks in the crust. Lg blockage has also been observed in the Western Mediterranean/Levantine Basin due to low-Q sediments and crustal thinning. A "basin capture" model is proposed to explain Lg blockage in sedimentary basins. In this model, shear waves that reverberate in the crust and constitute the Lg wave train are captured, delayed, and attenuated by thick, low-velocity sediments that replace the "granitic" layer rocks of the upper crust along part of the propagation path. Sn waves, which propagate below the basin, would not be blocked and in fact, the blocked Lg waves may be diverted downward into Sn waves by the low velocity sediments in the basin.     

基于Kelvin-Voigt黏弹性骨架的含非饱和流体孔隙介质BISQ模型(英文)

本文综合考虑了在波传播过程中孔隙介质的三种重要力学机制——"Biot流动机制一squirt流动机制-固体骨架黏弹性机制",借鉴等效介质思想,将含水饱和度引入波动力学控制方程,并考虑了不同波频率下孔隙流体分布模式对其等效体积模量的影响,给出了能处理含粘滞性非饱和流体孔隙介质中波传播问题的黏弹性Biot/squirt(BISQ)模型。推导了时间-空间域的波动力学方程组,由一组平面谐波解假设,给出频率-波数域黏弹性BISQ模型的相速度和衰减系数表达式。基于数值算例分析了含水饱和度、渗透率与频率对纵波速度和衰减的影响,并结合致密砂岩和碳酸盐岩的实测数据,对非饱和情况下的储层纵波速度进行了外推,碳酸盐岩储层中纵波速度对含气饱和度的敏感性明显低于砂岩储层。     

方位各向异性粘弹性介质波场数值模拟

当地震信号通过复杂地球介质时,地层除了表现为各向异性,还表现为内在的粘弹性特征.因此,为准确描述地震波在地球介质中的传播特征,理想的地球介质模型应该能够模拟岩石的各向异性特征和衰减特征.本文给出了各向异性粘弹性介质模型的波动方程及其差分格式,并利用有限差分法实现了地震波波场数值模拟.结果表明了该介质模型中地震波场特征与各向异性主轴方位和介质的粘滞性参数之间的关系.     

Parallel PSM/FDM Hybrid Simulation of Ground Motions from the 1999 Chi-Chi,Taiwan, Earthquake

-- A new technique for the parallel computing of 3-D seismic wave propagation simulation is developed by hybridizing the Fourier pseudospectral method (PSM) and the finite-difference method (FDM). This PSM/FDM hybrid offers a good speed-up rate using a large number of processors. To show the feasibility of the hybrid, a numerical 3-D simulation of strong ground motion was conducted for the 1999 Chi-Chi, Taiwan earthquake (M_w 7.6). Comparisons between the simulation results and observed waveforms from a dense strong ground motion network in Taiwan clearly demonstrate that the variation of the subsurface structure and the complex fault slip distribution greatly affect the damage during the Chi-Chi earthquake. The directivity effect of the fault rupture produced large S-wave pulses along the direction of the rupture propagation. Slips in the shallow part of the fault generate significant surface waves in Coastal Plain along the western coast. A large velocity gradient in the upper crust can propagate seismic waves to longer distances with minimum attenuation. The S waves and surface waves were finally amplified further by the site effect of low-velocity sediments in basins, and caused the significant disasters.     

Modified image algorithm to simulate seismic channel waves in 3D tunnel model with rugged free surfaces

The existence of rugged free‐surface three‐dimensional tunnel conditions in the coal seams, caused either by geological or mining processes, will inevitably influence wave propagation characteristics when the seismic waves go through the coal mines. Thus, a modified image algorithm has been developed to account for seismic channel waves propagating through this complicated topography with irregular free surfaces. Moreover, the seismic channel waves commonly exhibit damped and dispersive signatures, which is not only because of their own unique sandwich geometry of rock–coal–rock but also because of the viscoelastic behavior of coal. Considering the complexity of programming in three‐dimensional tunnel models with rugged free surfaces, an optimized vacuum grid search algorithm, enabling to model highly irregular topography and to compute efficiently, is also proposed when using high‐order staggered finite‐difference scheme to simulate seismic channel wave propagations in viscoelastic media. The numerical simulations are implemented to investigate the accuracy and stability of the method and the impact of coal's viscoelastic behavior on seismic channel wave propagation characteristics. The results indicate that the automatic vacuum grid search algorithm can be easily merged into high‐order staggered finite‐difference scheme, which can efficiently be applied to calculate three‐dimensional tunnel models with rugged free surfaces in the viscoelastic media. The simulation also suggests that the occurrence of a three‐dimensional tunnel with free surfaces has a remarkable influence on the seismic channel wave propagation characteristics and elastic energy distribution.     

Propagation of guided waves in a fluid layer bounded by two viscoelastic transversely isotropic solids

The analysis of Stoneley wave propagation in a fracture is essential for the identification and evaluation of fracture parameters from the borehole Stoneley wave. Also, it is important for many geophysics considerations, e.g. for tremor and long-period events observed in volcanoes and geothermal areas. In this paper, we investigate the guided waves propagation in a fluid layer lying between two viscoelastic vertically transversely isotropic media. The viscoelastic mechanism models the attenuation due to the presence of fluid saturation in the rock. A model based on the superposition of three inhomogeneous partial plane waves: one in the fluid and two heterogeneous waves in the solid is developed. The dispersion equation is obtained for this case. A numerical solution is carried out to obtain the guided wave velocity and attenuation coefficient. The results of this investigation show that there is a strong correlation between the velocity dispersion and attenuation of Stoneley wave and the anisotropic parameters of the medium especially in a sandstone (fast) medium.     

层状黏弹性介质中Rayleigh波频散曲线“交叉”现象分析

Rayleigh波勘探方法在探测近地表横波速度、动力学特征等环境与工程地球物理领域获得了广泛应用.这种方法以弹性层状介质理论为基础,然而实际介质具有黏弹性,研究面波在层状黏弹性介质中的传播特征,将为近地表面波勘探提供有益帮助.在某些弹性层状介质模型中,例如存在低速夹层和强波阻抗差异地层模型,Rayleigh波相邻两条频散曲线彼此会非常靠近,产生看似彼此"交叉"的现象,即"osculation"现象,但对于黏弹性介质中的这种现象并没有进行相关的研究.本文利用Muller法计算层状黏弹性介质Rayleigh波频散方程,基于层状介质模型中Rayleigh波频散和衰减曲线连续的性质,结合本征位移曲线特征,分析二层黏弹性介质模型中Rayleigh波频散曲线"交叉"现象以及"交叉"点附近的波动特性.结果表明:与弹性介质相比,黏弹性介质中Rayleigh波的波动特性存在明显差异,随着介质对地震波的损耗越来越强,将导致Rayleigh波频散曲线发生"交叉"现象.     

Pseudospectral modeling and dispersion analysis of Rayleigh waves in viscoelastic media

Multichannel Analysis of Surface Waves (MASW) is one of the most widely used techniques in environmental and engineering geophysics to determine shear-wave velocities and dynamic properties, which is based on the elastic layered system theory. Wave propagation in the Earth, however, has been recognized as viscoelastic and the propagation of Rayleigh waves presents substantial differences in viscoelastic media as compared with elastic media. Therefore, it is necessary to carry out numerical simulation and dispersion analysis of Rayleigh waves in viscoelastic media to better understand Rayleigh-wave behaviors in the real world. We apply a pseudospectral method to the calculation of the spatial derivatives using a Chebyshev difference operator in the vertical direction and a Fourier difference operator in the horizontal direction based on the velocity–stress elastodynamic equations and relations of linear viscoelastic solids. This approach stretches the spatial discrete grid to have a minimum grid size near the free surface so that high accuracy and resolution are achieved at the free surface, which allows an effective incorporation of the free surface boundary conditions since the Chebyshev method is nonperiodic. We first use an elastic homogeneous half-space model to demonstrate the accuracy of the pseudospectral method comparing with the analytical solution, and verify the correctness of the numerical modeling results for a viscoelastic half-space comparing the phase velocities of Rayleigh wave between the theoretical values and the dispersive image generated by high-resolution linear Radon transform. We then simulate three types of two-layer models to analyze dispersive-energy characteristics for near-surface applications. Results demonstrate that the phase velocity of Rayleigh waves in viscoelastic media is relatively higher than in elastic media and the fundamental mode increases by 10–16% when the frequency is above 10 Hz due to the velocity dispersion of P and S waves.     

Thermal-mechanical Coupling in Shear Deformation of Viscoelastic Material as a Model of Frictional Constitutive Relations

-- We propose a thermal-mechanical model of shear deformation of a viscoelastic material to describe the temperature-dependence of friction law. We consider shear deformation of one-dimensional layer composed of a Maxwell linear viscoelastic material under a constant velocity V and temperature T_w at the boundary. The strain rate due to viscous deformation depends both on temperature and shear stress. The temperature inside the layer changes owing to frictional heating and conductive cooling. Steady-state calculations show that the sign of d†^ss/dV, where †^ss is steady-state stress, changes from positive to negative as V increases, and that the threshold velocity above which the sign of d†^ss/dV is negative increases with increasing T_w. These results are in accordance with the conjecture that the downdip limit of seismogenic zones is marked by the transition in the sign of d†^ss/dV due to temperature rise with depth. We also find that the response of steady state to a step change in V is quite similar to the response of frictional slip with constitutive laws which employ state variables. These findings suggest that by further improving the present model a model of constitutive relations along faults or plate boundaries can be developed which contains temperature-dependence in a physically-sound manner.     

Ray Tracing in Elastic and Viscoelastic Media

—We consider several extensions of ray tracing (uniform asymptotics, complex rays, space-time rays) interrelated by the fact that they must be used jointly in order to deal with both focusing and attenuation. Two representative models of acoustic wave propagation are considered: elasticity and viscoelasticity. Basic ideas behind canonical functions and Maslov integrals for uniformly asymptotic evaluation of the wave field from ray field parameters are discussed. Complex space-time ray tracing algorithms for dispersive and attenuating media are presented. Two models of attenuation in a viscoelastic medium are compared: (1) complex space-time ray methods for general attenuation/dispersion, (2) real ray methods for weak attenuation.