三维黏弹性人工边界地震波动输入方法研究

对三维黏弹性人工边界给出了一种实用的地震波动输入方法。用等效边界力法进行地震波动输入时,把入射地震波假设为竖直向上入射的平面波,使施加在人工边界上的总荷载可以由输入波位移和速度的关系式完全表达,使地震动输入更容易在有限元计算程序中实现。解决了三维黏弹性人工边界采用球面波进行地震波动输入会出现尚待确定的未知项,不易实现地震波动的输入的困难。数值算例表明,该地震波动输入方法是十分有效的。     

Finite element modeling of wave propagation problems in multilayered soils resting on a rigid base

A new finite element scheme is proposed, in this paper, for solving two-dimensional wave propagation problems in multilayered soils resting on a rigid base. The multilayered soils are treated as multiple horizontal layers of lateral infinite extension in geometry. Since these horizontal layers can be truncated by two artificially truncated vertical boundaries, two high-order artificial boundary conditions are applied for propagating the incoming waves from the interior domain into the far field of the system. Both the semi-analytical method and the truncated boundary migration procedure are used to derive the high-order artificial boundary conditions, which are comprised of a physically meaningful dashpot and a generalized energy absorber. The main advantage of using the proposed finite element scheme is that the derived artificial boundary condition can be straightforwardly implemented in the finite element analysis, without violating the band/sparse structure of the conventional finite element equation. The related numerical examples have demonstrated that the proposed finite element scheme is of high accuracy in dealing with wave propagation problems in multiple horizontal layers.     

Grain boundary plane populations in minerals: the example of wet NaCl after low strain deformation

Many physical properties of rocks are sensitive to grain size and hence to the structure of grain boundaries. Depending on their properties, such as deformation and transport behaviour, boundaries may be divided into two broad types, namely special and general grain boundaries. Electron backscattered diffraction (EBSD) is used to investigate the misorientation distributions of grain boundaries and, more recently, to determine the population of grain boundary planes. Studies on metals and ceramics suggest that the grain boundary plane, rather than the misorientation, is the key parameter when defining special and general grain boundaries. In this study, the distribution of grain boundary plane orientations has been successfully determined using EBSD for a slightly deformed, synthetic NaCl material containing 22 ppm water. Boundaries showed a preference for {100} planes, which occurred with twice the frequency of a random distribution. The grain boundary plane distributions found in NaCl were largely in agreement with studies on MgO. Grain boundaries, with a coincident site lattice (CSL) misorientation, also showed a preference for {100} planes, rather than the planes of high coincident density associated with the CSL. Three main types of boundary were identified, namely {100} twist boundaries, boundaries with {100}{hkl} planes and general {hkl}{hkl} boundaries. As the properties of these three types of boundary differ, then the transport and creep properties in wet NaCl will depend on the fraction of the different boundary types found in the grain boundary population.     

Boundary setting method for the seismic dynamic response analysis of engineering rock mass structures using the discontinuous deformation analysis method

Large deformations and discontinuous problems can be calculated using the discontinuous deformation analysis (DDA) method by solving time steps, and this method is suitable for simulating the seismic dynamic response of engineering rock mass structures. However, the boundary setting must be carefully analyzed. In this paper, four boundary settings for the DDA method are investigated. First, the contributions to the DDA equations for nonreflecting boundaries (including the viscous boundary and the viscoelastic boundary) are deduced based on the Newmark method. Second, a free‐field boundary is introduced in the DDA method with boundary grid generation and coupling calculation algorithms to accurately simulate external source wave motion, such as earthquakes. Third, seismic input boundary treatments are intensively examined, and the force input method is introduced based on nonreflecting boundaries. Finally, the static‐dynamic unified boundary is implemented to ensure consistent boundary transformation. The boundary setting method in the DDA method is discussed, and the suggested treatments are used to analyze the seismic dynamic response of underground caverns. Copyright © 2015 John Wiley & Sons, Ltd.     

Effects of annealing on deformation textures in galena

Experimental annealing of galena samples with known deformation histories shows that this mineral has the necessary properties to be a valuable source of information about low-grade deformational environments. Annealed galena displays recovery and/or recrystallization features dependent upon the type of texture inherited from the tectonic event, which in turn is closely linked to deformation temperatures.In samples deformed at temperatures less than 200 ° C in the laboratory, later annealing produced subgrains, mosaics of new grains, or rapid grain boundary migration as the annealing temperatures were varied from 200 ° C to 700 ° C. Kink bands maintained characteristic straight simple boundaries inherited from the deformation event. Samples deformed above 300 ° C developed syntectonically recrystallized textures. Kink bands had been converted to elongate grains with complex sutured grain boundaries during deformation, and mosaics of new grains were found in highly deformed regions. These textures were extremely stable through later annealing. Despite our changing annealing temperatures through 500 ° C, we did not produce similar textures from both low and high temperature deformation runs.Examination of polished and etched galena from low-grade tectonic settings may well be worth the effort since galena textures appear to display features indicative of deformational evironments, even after being subjected to considerable post-tectonic thermal perturbations.     

Boundary settings for the seismic dynamic response analysis of rock masses using the numerical manifold method

Aiming to accurately simulate seismic dynamic response of rock masses using the numerical manifold method (NMM), boundary settings must be treated carefully. In this paper, 4 issues in boundary settings are investigated to improve the performance of NMM: (1) Nonreflecting boundaries including the viscous boundary and viscoelastic boundary are considered; (2) A free‐field boundary is incorporated into NMM to accurately simulate external source wave motion; (3) A seismic input boundary is considered, and the force input method is introduced; and (4) A static‐dynamic unified boundary is incorporated for the convenience of transforming displacement boundary into other types of boundaries, such as nonreflecting boundaries and seismic input boundary. Several benchmark problems are solved to validate the improved NMM. Simulation results agree well with analytical ones, indicating that the improved NMM is able to simulate seismic dynamic response of rock masses reliably and correctly.     

反转构造模型的地震波模拟及成像

为了检验由地震剖面解释得出的反转构造的可靠性,探讨反转构造地区在地震数据采集,处理中应采用的有效方法,设计了一个典型的反转构造模型－突起构造。以该模型为基础,针对复杂构造地震波模拟中常见起源频散严重、人为边界反射吸收不理想两个问题,应用高阶差分法以及一种新的边界吸收条件,对反转模型进行了地震波场数值模拟和深度偏移成像处理。采用中心放炮两边接收的观测方式,共模拟了185炮地震记录。研究表明,波动方程高阶差分法是模拟复杂构造模型中地震波传播的有效方法,除了近于直立的断层因难以接收到其反射波而较难成像外,其余的反转断层及其组合在理论上是可以通过合适方法（如Fourier有限差分深度偏移）较好地成像的。     

自由边界形状与近边界裂纹相互作用模型研究

大量的研究表明, 岩爆发生条件与岩石的力学性能有关。岩体中微裂纹的形成、扩展和汇合对岩体的力学性能产生显著影响,可以导致材料的逐渐劣化直至破坏。对于单轴压缩的岩石试件,其破坏型式主要是微裂纹的摩擦滑移、自相似平面扩展和弯折扩展。基于断裂力学机制,对单轴压缩荷载下3种不同边界形状,即直边、凸形、凹形情况下近边界原生斜裂纹的扩展进行了理论研究,并运用FLAC数值模拟技术,建立了基于Interface界面单元的裂纹扩展数值模型。近直边界及凸形边界情况的裂纹扩展使用梁渐近模型来解析薄片岩层的屈曲断裂问题,对于近凹形边界情况给予简化,提出了裂纹－圆－椭圆相互作用的修正模型并进行理论分析。研究结果表明,基于Interface界面单元的裂纹扩展的数值模型正确,解析解与数值解吻合较好,相应的梁渐近模型及裂纹-圆-椭圆模型可以合理地分析应力调整过程中裂纹的扩展和裂纹与不同洞室表面形状的相互作用问题,为岩爆工程及理论研究提出了新的理论依据。     

Experiments with Higdon's absorbing boundary conditions for a number of wave equations

Simulation of wave propagation for seismic purposes is usually restricted to a small portion of the earth. Artificial boundary conditions are required where the subsurface model is truncated. Absorbing boundaries should ensure that waves hitting the artificial boundaries are not reflected. The vast amount of literature on the subject suggests that “good” conditions have not been found, and only “reasonable” solutions exist. A cursory overview of existing and a few new ideas is presented that may guide the construction of suitable boundary conditions. Because the intended application of the boundary conditions was a high-order finite-difference code that runs on a parallel computer, we have restricted our attention to local boundary conditions. A fundamental problem in the design of accurate local boundary conditions is pointed out: accuracy is required to keep the amount of reflected energy small, but at the same time allows for growing low-frequency modes. We have settled for Higdon’s boundary conditions. Higdon proposes to include some damping to suppress the growing low-frequency modes. We show that third-order conditions provide acceptable results for the simple scalar wave equation and the acoustic equation. In the elastic case, an additional low-frequency growing mode may occur. This mode can be suppressed by using a dissipative boundary scheme and by increasing the amount of damping. The increase in damping results in an increase in the amount of reflected energy, which is larger than in the scalar case. Numerical experiments exhibit a reasonable performance, although some improvement would be useful, particularly in the anisotropic elastic case. This revised version was published online in July 2006 with corrections to the Cover Date.     

Synthetic near Σ5 (210)/[100] grain boundary in YAG fabricated by direct bonding: structure and stability

Several macroscopic physical and chemical properties, such as rheology, elasticity, or transport properties are governed by grain boundary processes. An improved understanding of the structure and evolution of grain boundaries has thus become a key challenge in geosciences and material sciences. Here, we report the structure of near Σ5 (210)/[100] grain boundaries in Y₃Al₅O₁₂ (YAG), which were synthesised by the wafer direct bonding method. The produced grain boundaries were annealed at different temperatures, ranging from 673 to 1,873 K. The grain boundaries annealed at different temperatures are not distinguishable based on their flatness and apparent cohesiveness in high resolution TEM (HRTEM) micrographs, but show a considerable step in their mechanical stability at around 1,273 K, a temperature that corresponds to roughly half the melting temperature of YAG. This study further focuses on the effect of a slight misorientation of the two crystals on the grain boundary structure and we discuss if the boundary can reach a state of minimum energy configuration during annealing. Along the grain boundaries, we observed a long-range strain contrast with a periodicity of 40 nm, which has not been reported for high-angle grain boundaries so far. We conclude that this contrast is caused by faceting along the grain boundary plane, which is needed to achieve minimum energy configuration of the grain boundary plane.     

Crystallographic control on the development of foam textures in quartz, plagioclase and analogue material

The shape, pattern and crystallographic orientation of grain boundaries represent important characteristics of crystalline material and contain information about its deformation and annealing history. The present study includes measurements of grain boundaries from experimentally annealed analogue material as well as natural foam texture of quartz and plagioclase. The main subject is the relation between the development of a foam texture and the crystallographic orientation of its grain boundaries and their geometry. (1) During annealing, grain sizes stabilize at certain values. On a statistical basis, these values can be applied as a geothermometer. (2) On the light-microscope scale, the grain boundaries in foam textures commonly consist of two or several planar facets. They are preferentially oriented along specific crystallographic planes, namely in relation to both neighbouring crystals; for quartz they tend to be rhombohedral. (3) Even highly misoriented facets and dihedral angles largely deviating from the 'equilibrium angle' of 120° may be stable over long periods of annealing. (4) Parts of single boundaries may migrate, whereas other parts are stationary during annealing. The results of the present study suggest that the anisotropy of surface energy has a considerable influence on the development of foam textures and that modelling of texture development should include the influence of the crystallographic orientation of grain boundaries.     

The interaction of migrating grain boundaries with fluid inclusions in rock analogues: the effect of wetting angle and fluid inclusion velocity

The distribution of fluids in grain boundaries, fluid inclusion morphology and kinetics have important effects on the evolution of microstructure and transport properties and should be understood for correct interpretations for studies of thermobarometry and paleorheology. We compare results of in situ annealing experiments on rock analogues in the presence of different pore fluids in transmitted light: bischofite with saturated brine, camphor with ethanol, and camphor with ethylene glycol. The solid–liquid systems vary in terms of wettability and solubility, while homologous temperatures, strain rates, annealing times, and the initial textures are similar. In agreement with earlier work and theory, we observe different types of grain boundary–fluid inclusion interaction at sufficiently low grain boundary velocity such as drag and drop, necking, and the break up into arrays of smaller inclusions. In all three systems the maximum possible velocity of a fluid inclusion being dragged by a moving grain boundary is dependent on the fluid inclusion size. We interpret this to reflect the fluid inclusion mobility, and compare the trend with theoretical models which suggest that for all three systems the rate-limiting process is bulk diffusion and not surface diffusion or solution-precipitation.     

An approximate spring–dashpot artificial boundary for transient wave analysis of fluid-saturated porous media

Practical civil engineering problems are usually formulated in an infinite half-space domain, and a selected finite domain is required to analyze the dynamic responses of a fluid-saturated porous medium by the finite element method (FEM). Devising a method to deal with the boundaries of the finite domain is the key issue for this open system. In this paper, a two-dimensional spring–dashpot artificial boundary (SDAB) for transient analysis in a fluid-saturated porous media is developed. Based on Biot’s dynamic theory of fluid-saturated porous media, the normal and tangential boundary stress formulae are deduced for out-going cylindrical body waves. The boundary stress is proportional to displacement and velocity, thus continuously distributed dashpots and springs can be placed on the artificial boundaries in the normal and tangential directions to simulate the energy absorption of the infinite media outside of the finite domain for the interior distributed source problems. In this paper, the input seismic motion can be realized by applying an equivalent load on the SDAB for the seismic scattering problems of exterior distributed sources. Numerical examples are given and the analyzed results show that the SDAB and the method of wave motion input have good stability and acceptable accuracy.     

The most frequent interfaces in olivine aggregates: the GBCD and its importance for grain boundary related processes

Rocks consist of crystal grains separated by grain boundaries that impact the bulk rock properties. Recent studies on metals and ceramics showed that the grain boundary plane orientation is more significant for grain boundary properties than other characteristics such as the sigma value or disorientation (in the Earth’s science community more frequently termed misorientation). We determined the grain boundary character distribution (GBCD) of synthetic and natural polycrystalline olivine, the most abundant mineral of Earth’s upper mantle. We show that grain boundaries of olivine preferentially contain low index planes, in agreement with recent findings on other oxides (e.g. MgO, TiO₂, Al₂O₃ etc.). Furthermore, we find evidence for a preferred orientation relationship of 90° disorientations about the [001] direction forming tilt and twist grain boundaries, as well as a preference for the 60° disorientation about the [100] axis. Our data indicate that the GBCD, which is an intrinsic property of any mineral aggregate, is fundamental for understanding and predicting grain boundary related processes.     

双程声波方程逆时深度偏移

从双程声波方程出发,在交错网格空间中推导了地震波逆时延拓的高阶有限差分算子,依据最佳匹配层(PML)的方程分裂思路,得到了一阶声波方程的PML边界条件及其高阶差分格式,采用零时间成像条件和上行、下行波场互相关成像条件,实现了声波方程的叠后与叠前逆时深度偏移。逆时偏移对sigsbee_2b模型理论数据的偏移成像得到了满意效果。     

Preliminary investigation results on fabrics and related physical properties of an anisotropic gneiss

In order to evaluate the fabric-dependent anisotropy of a particular gneiss type, we assessed the quartz lattice and shape preferred orientations as well as the microcrack pattern statistics. In the rock mechanics laboratory, several strength and deformability tests on drilled rock samples were run and the seismic wave propagation properties along the rock’s principal strain axes were determined. In the mechanical tests it turned out that despite a distinct stretching lineation with initially extreme grain elongation, the rock performs for the larger part as a transversely isotropic material with the schistosity as plane of isotropy. The anisotropy in seismic wave propagation within the plane of schistosity is attributed primarily to a highly anisotropic microcrack pattern, the distinct gneissose banding and to a lower degree to the LPO of quartz.     

谱模拟频谱比法反演品质因子稳定性分析

地震波在粘弹性介质中传播的一个基本特征是能量的衰减及地震波的瞬时波形变化。从广义上说,衰减可分为两类：一类是与地震波传播特性有关的衰减|另一类是反映介质内在属性的地层本征衰减,地层的本征衰减通常用品质因子来度量。反演品质因子的方法有多种,常用的是谱模拟频谱比法。笔者的主要目的是通过模型试算来分析评价该方法在反演品质因子时对干涉和噪声的稳定性,得出有益的结论,用于指导反演计算。     

断层岩与断层模式

本文通过对断层岩的结构、构造特征及其力学成因研究现状的综述，提出以下几点看法：（１）断层岩是在特定的地质环境下形成的，其结构特征直接反映所处境的地质构造运动特性所以通过研究断层岩的内部组构可以直接了解形变环境及其区域地质构造发展史；（２）断层财的线理和面理结构既可以在韧塑性条件下形成，也可以在脆性条件下形成，因此是否具有线理与面理结构不能作支岩分类的决定性基准；（３）断层岩母岩结晶的大小直接影响断     

A New Viscous Boundary Condition in the Two-Dimensional Discontinuous Deformation Analysis Method for Wave Propagation Problems

Viscous boundaries are widely used in numerical simulations of wave propagation problems in rock mechanics and rock engineering. By using such boundaries, reflected waves from artificial boundaries can be eliminated; therefore, an infinite domain can be modeled as a finite domain more effectively and with a much greater accuracy. Little progress has been made, thus far, with the implementation and verification of a viscous boundary in the numerical, discrete element, discontinuous deformation analysis (DDA) method. We present in this paper a new viscous boundary condition for DDA with a higher absorbing efficiency in comparison to previously published solutions. The theoretical derivation of the new viscous boundary condition for DDA is presented in detail, starting from first principles. The accuracy of the new boundary condition is verified using a series of numerical benchmark tests. We show that the new viscous boundary condition works well with both P waves as well as S waves.     

Analysis of Stochastic Seismic Wave Interaction with a Slippery Rock Fault

Stochastic seismic wave interaction with a slippery rock fault is studied, based on the principle of conservation of momentum at the wave fronts along the fault. By using the displacement discontinuity method, the wave propagation equations are derived for incident longitudinal-(P-) and shear-(S-) waves, respectively. This is an extension of the study by Li and Ma (2010) for blast-induced wave propagation across a linear rock joint. Stochastic seismic waves are generated from a frequency spectrum and used to analyze the seismic wave interaction with a rock fault having a Coulomb-slip behavior. Parametric studies are carried out to investigate the effect of the intensity and impinging angle of the incident seismic waves on wave propagation across a slippery rock fault. Results show that the transmission of the incident P-wave is almost not affected by the fault, on the contrary, this is not the case for an incident S-wave, due to the occurrence of a relative slip which is related to the impinging angle of the incident S-wave. A quantitative study is presented which is of help in understanding the propagation and attenuation laws of seismic waves in discontinuous rock masses.