Analytical study of ground motion caused by seismic wave propagation across faulted rock masses

Studying seismic wave propagation across rock masses and the induced ground motion is an important topic, which receives considerable attention in design and construction of underground cavern/tunnel constructions and mining activities. The current study investigates wave propagation across a rock mass with one fault and the induced ground motion using a recursive approach. The rocks beside the fault are assumed as viscoelastic media with seismic quality factors, Q_p and Q_s. Two kinds of interactions between stress waves and a discontinuity and between stress waves and a free surface are analyzed, respectively. As the result of the wave superposition, the mathematical expressions for induced ground vibration are deduced. The proposed approach is then compared with the existing analysis for special cases. Finally, parametric studies are carried out, which includes the influences of fault stiffness, incident angle, and frequency of incident waves on the peak particle velocities of the ground motions.     

Three dimensional simulation of fluid flow in X‐ray CT images of porous media

A numerical scheme is developed in order to simulate fluid flow in three dimensional (3‐D) microstructures. The governing equations for steady incompressible flow are solved using the semi‐implicit method for pressure‐linked equations (SIMPLE) finite difference scheme within a non‐staggered grid system that represents the 3‐D microstructure. This system allows solving the governing equations using only one computational cell. The numerical scheme is verified through simulating fluid flow in idealized 3‐D microstructures with known closed form solutions for permeability. The numerical factors affecting the solution in terms of convergence and accuracy are also discussed. These factors include the resolution of the analysed microstructure and the truncation criterion. Fluid flow in 2‐D X‐ray computed tomography (CT) images of real porous media microstructure is also simulated using this numerical model. These real microstructures include field cores of asphalt mixes, laboratory linear kneading compactor (LKC) specimens, and laboratory Superpave gyratory compactor (SGC) specimens. The numerical results for the permeability of the real microstructures are compared with the results from closed form solutions. Copyright © 2004 John Wiley & Sons, Ltd.     

A continuum‐discrete hydromechanical analysis of granular deposit liquefaction

A coupled continuum‐discrete hydromechanical model was employed to analyse the liquefaction of a saturated loose deposit of cohesionless particles when subjected to a dynamic base excitation. The pore fluid flow was idealized using averaged Navier–Stokes equations and the discrete element method was employed to model the solid phase particles. A well established semi‐empirical relationship was utilized to quantify the fluid–particle interactions. The conducted simulations revealed a number of salient micro‐mechanical mechanisms and response patterns associated with the deposit liquefaction. Space and time variation of porosity was a major factor which affected the coupled response of the solid and fluid phases. Pore fluid flow was within Darcy's regime. The predicted response exhibited macroscopic patterns consistent with experimental results and case histories of the liquefaction of granular soil deposits. Copyright © 2004 John Wiley & Sons, Ltd.     

P‐wave transmission across fractures with nonlinear deformational behaviour

Stress wave attenuation across fractured rock masses is a great concern of underground structure safety. When the wave amplitude is large, fractures experience nonlinear deformation during the wave propagation. This paper presents a study on normal transmission of P‐wave across parallel fractures with nonlinear deformational behaviour (static Barton–Bandis model). The results show that the magnitude of transmission coefficient is a function of incident wave amplitude, nondimensional fracture spacing and number of fractures. Two important indices of nondimensional fracture spacing are identified, and they divide the area of nondimensional fracture spacing into three parts (individual fracture area, transition area and small spacing area). In the different areas, the magnitude of transmission coefficient has different trends with nondimensional fracture spacing and number of fractures. In addition, the study reveals that under some circumstances, the magnitude of transmission coefficient increases with increasing number of fractures, and is larger than 1. Copyright © 2006 John Wiley & Sons, Ltd.     

The response of an elastic half‐space under a momentary shear line impulse

The response of an ideal elastic half‐space to a line‐concentrated impulsive vector shear force applied momentarily is obtained by an analytical–numerical computational method based on the theory of characteristics in conjunction with kinematical relations derived across surfaces of strong discontinuities. The shear force is concentrated along an infinite line, drawn on the surface of the half‐space, while being normal to that line as well as to the axis of symmetry of the half‐space. An exact loading model is introduced and built into the computational method for this shear force. With this model, a compatibility exists among the prescribed applied force, the geometric decay of the shear stress component at the precursor shear wave, and the boundary conditions of the half‐space; in this sense, the source configuration is exact. For the transient boundary‐value problem described above, a wave characteristics formulation is presented, where its differential equations are extended to allow for strong discontinuities which occur in the material motion of the half‐space. A numerical integration of these extended differential equations is then carried out in a three‐dimensional spatiotemporal wavegrid formed by the Cartesian bicharacteristic curves of the wave characteristics formulation. This work is devoted to the construction of the computational method and to the concepts involved therein, whereas the interpretation of the resultant transient deformation of the half‐space is presented in a subsequent paper. Copyright © 2003 John Wiley & Sons, Ltd.     

The efifect of wave breaking on surface wave imaging by Synthetic Aperture Radar

The effect of ocean wave breaking as a non-Bragg mechanism on backscattering cross-section and modulation transfer functions (MTF) of radar was investigated based on Bragg resonance theory and parametric method. The result showed that the additional effect of wave breaking on backscattering cross-section is not more than 20% except for the small incident angle of VV polarized electromagnetic (e.m.) wave but is significant for HH polarized e.m. wave. Breaking waves lead to increase in the modulus of tilt modulation MTF and the larger the wind speed, the faster the increase. For large incident angle, the modulus of tilt modulation MTF with wave breaking decreases quickly with incident angle for HH polarization and approach to that without wave breaking for VV polarization. The hydrodynamic MTF increases 30%-60% when considering wave breaking and the increase is larger for HH polarization than for VV polarization.     

有限元法与伪谱法混合求解弹性波动方程

在地震波场数值模拟中,有限差分法、有限元法和伪谱法都是常用的基本方法,但它们各有不同的适应性和优缺点,如有限差分法、有限元法都存在减弱网格频散和提高计算效率的矛盾,而伪谱法的网格频散小且计算效率高.有限差分法和伪谱法在处理地表结构复杂或地表剧烈起伏以及地下结构复杂的情况时存在较大的难度,而有限元法可较为理想地拟合起伏地表和任意弯曲界面,且可方便地处理自由边界条件和界面边界条件.尝试将有限元法和伪谱法相结合,形成地震波场数值模拟的一种混合方法,利用二者的优点,克服二者的缺点,达到既减弱网格频散又提高计算精度和效率的目的.并采用所谓的‘过度区域‘技术解决两种不同算法的衔接问题.模拟实例表明,给出的混合模拟方法不失为弹性波场数值模拟的一种有效方法.     

Synthetic SH seismograms in a laterally varying medium by the discrete wavenumber method

Summary. We present a new method to calculate the SH wavefield produced by a seismic source in a half-space with an irregular buried interface. The diffracting interface is represented by a distribution of body forces. The Green's functions needed to solve the boundary conditions are evaluated using the discrete wavenumber method. Our approach relies on the introduction of a periodicity in the source-medium configuration and on the discretization of the interface at regular spacing. The technique developed is applicable to boundaries of arbitrary shapes and is valid at all frequencies. Some examples of calculation in simple configurations are presented showing the capabilities of the method.     

中国大陆科学钻探先导孔零偏VSP资料解释

用六级三分量检波器在中国大陆科学钻探先导孔中实施了零偏VSP测量.数据处理结果表明,中国大陆科学钻探孔区超高压变质岩石的地震波速度主要介于4500～7000m/s之间,显著高于一般的沉积岩地区,而且随深度变化不明显.声波测井速度系统地稍低于VSP层速度,可能是由于井壁处岩石的完整性受到破坏而造成的.地震波速度与岩石密度和岩性存在明确的对应关系,榴辉岩的密度和地震波速度均显著高于片麻岩类岩石;由榴辉岩退变生成的斜长角闪岩类岩石,其密度和地震波速度均呈现出较大的变化,主要与其退变质程度有关;超基性岩中的裂隙系统导致其密度和地震波速度大幅度下降.由于榴辉岩与其他岩石类型之间存在较大的波阻抗差异,因此用零偏VSP资料标定该区地震波的地质层位是有效的.关于地震波反射的原因,通过综合研究地震波(包括反射纵波、上行转换横波、井筒波)的特征、岩石速度和密度分布以及井径变化,认为主要是岩性分界面、韧性剪切带和断裂(带),但还有一些因素尚待进一步研究.     

富氏谱分析法模拟地壳垂直运动的地学依据及其策应力模型

应用地壳波浪与镶嵌构造学说对富氏谱分析法提取地壳垂直形变信息的科学性做了地质学意义上的阐释 ,并提出了根据多期形变资料提取特定波段上构造策应力的数学模型