Scattering of seismic waves by cracks in multi-layered geological regions: II. Numerical results

The mechanical model for plane strain, time-harmonic seismic wave propagation problems in cracked, multi-layered geological regions with surface topography and non-parallel interfaces was described in the first part of this work. Here, this model is used to investigate the response of such a region to the presence of traveling elastic waves generated by a seismic source. The computational methodology that was developed in the first part is based on a combination of both the regular (displacement-based) and the hypersingular (traction-based) Boundary Integral Equation Method (BIEM). First, the accuracy and convergence characteristics of this hybrid BIEM are studied. Then, a series of problems involving four different configurations of a reference geological deposit with both interface and internal cracks are solved, for a loading that is due to a seismically-induced pressure wave propagating upwards from the underlying rigid half-plane. The purpose of the numerical study is to investigate the influence of various key parameters of the problem, such as frequency and incidence angle of the incoming wave, size of the surface relief, location and size of the buried cracks, interaction effects between cracks and finally the presence of layers, on both the scattered displacement field and the stress concentration field.     

Rocking response of flexible circular foundations on layered media

The analysis of the response of a flexible circular foundation on layered media due to an arbitrarily distributed vertical loading is presented. The analysis is based on the ‘ring method’ approach, i.e. discretization of the foundation in a set of concentric rings. The arbitrarily distributed loading is expanded in the circumferential direction in a Fourier series. The influence coefficient matrix of soil for each element of the series is evaluated utilizing the stiffness matrix approach. The stiffness matrix of the foundation is obtained from the finite difference energy method approach. Numerical examples illustrate the influence of several soil-foundation parameters on the rocking response of a foundation. Results are presented in terms of displacement and soil reaction distributions and impedance functions point to significantly different responses of flexible and rigid foundations.     

对称化测量高频电磁波测井的优化组合研究

采用对称化测量可克服现有单发双收高频电磁波测井仪器（ＤＰＴ）由于收－发不对称结构导致的幅度比测井曲线严重失真的缺陷，提高ＤＰＴ的纵向分辨率．通过对二线非均质测井环境下ＤＰＴ响应的数值模拟，指出选用原频率较低、源距较长仪器的相位差测量与源频率较高、源距较短仪器的幅度比测量进行组合，可获得高品质的视介电常数和视电阻率曲线，显著提高ＤＰＴ的资料解释能力．这里源频率的恰当选择起着关键作用．     

The MT inversion for conductivity anisotropy and EDA precursor，stress field and deformationbandintheEarthsdeepcrust

ＴｈｅＭＴｉｎｖｅｒｓｉｏｎｆｏｒｃｏｎｄｕｃｔｉｖｉｔｙａｎｉｓｏｔｒｏｐｙａｎｄＥＤＡｐｒｅｃｕｒｓｏｒ，ｓｔｒｅｓｆｉｅｌｄａｎｄｄｅｆｏｒ┐ｍａｔｉｏｎｂａｎｄｉｎｔｈｅＥａｒｔｈｓｄｅｅｐｃｒｕｓｔＣＨＡＮＧ－ＹＯＵＬＩＮ（林长佑），Ｃ...     

Harmonic wave propagation through viscoelastic heterogeneous media exhibiting mild stochasticity - I. Fundamental solutions

This work examines the propagation of time harmonic, horizontally polarized shear waves through a naturally occurring heterogeneous medium that exhibits viscous behaviour as well as random fluctuations of its elastic modulus about a mean value. As a first step, the governing equation, which is a heterogeneous Helmholtz equation, is solved using algebraic transformations and the relevant Green's function is obtained for two sets of boundary conditions, one corresponding to a finite depth layer and the other to an infinite layer. Viscous material behaviour is introduced by considering the depth-dependent elastic modulus to be a complex quantity. Subsequently, material stochasticity in the medium is handled through the perturbation approach by assuming that the elastic modulus has a small random fluctuation about its mean value. The final results are closed-form expressions for the mean value and covariance matrix of both the wave speed profile in the medium and the corresponding Green's function. In Part II, (Soil Dynam. Earth. Engng, 1996,15, 129-39), two examples concerning seismic wave propagation in soft topsoil and in sandstone serve to illustrate the methodology and comparisons are made with Monte Carlo simulations.     

Spatial averaging of hydraulic conductivity in three-dimensional heterogeneous porous media

Numerical models of groundwater flow require the assignment of hydraulic conductivities to large grid blocks discretizing the flow domain; however, conductivity data is usually available only at the much smaller scale of core samples. This paper describes a geostatistical model for hydraulic conductivity at both the core or point scale and that of grid blocks. Conductivity at the block scale is obtained empirically as a spatial power-average of point scale values. Assuming a multivariate Gaussian model for point log-conductivity, expressions are derived for the ensemble mean and variance of block conductivity. The expression for the ensemble mean of block scale conductivity is found to be similar to an expression for the ensemble effective conductivity of an infinite field derived analytically by earlier authors. Here, block conductivities obtained by power averaging are compared with effective conductivities obtained from a numerical flow model and are found to be in excellent agreement for a suitably chosen averaging exponent. This agreement deteriorates gradually as the log variance of conductivity increases beyond 2. For arbitrary flow field geometry and anisotropic conductivity covariances, the averaging exponent can be calibrated by recourse to numerical flow experiments. For cubic fields and an isotropic spatial covariance, the averaging exponent is found to be 1/3. In this particular case, it was found that flow field discretization at the block scale through local averaging of point conductivities gave similar results to those obtained directly using a point scale discretization of the flow field.     

Flow Characteristics of Large-Scale Liquefaction-Slip of the Loess Strata in Shibei Tableland, Guyuan City, Induced by the 1920 Haiyuan M8 1/2 Earthquake

Based on the dynamic triaxial liquefaction test of the loess samples which are taken from Shibei tableland, Guyuan City, Ningxia, China, the characteristics of dynamic strain, dynamic stress and pore water pressure are studied under cyclic loading. Triaxial shear test is conducted immediately after the sample reaches liquefaction point. During the test, the property of the liquefied soil is analyzed through fluid mechanics method, whereby the fluidity of the liquefied soil is represented by apparent viscosity.The results show that the fluidity of liquefied loess changes from "shear thickening" to "shear thinning" as the shear force continues, and the fluidity of liquefied loess is closely related to its structure. In addition, in the process of forming a new stable state, the apparent viscosity and deviant stress change with axial strain in a similar approach. When the sample reaches its stable state, it meanwhile shows a relatively stable apparent viscosity. According to the fluid mechanics and the law of conservation of energy, the slip distance of the liquefied soil is estimated, and the results are in good agreement with the field investigation results.     

Another look at the conceptual fundamentals of porous media upscaling

We suggest a critical look at the epistemic foundations of the porous media upscaling problem that focuses on conceptual processes at work and not merely on form manipulations. We explore the way in which critical aspects of scientific methodology make their appearance in the upscaling context, thus generating useful effective parameters in practice. The fons et origo of our approach is a conceptual blending of knowledge states that requires the revision of the traditional method of scientific argument underlying most upscaling techniques. By contrast to previous techniques, the scientific reasoning of the proposed upscaling approach is based on a stochastic model that involves teleologic solutions and stochastic logic integration principles. The syllogistic form of the approach has important advantages over the traditional reasoning scheme of porous media upscaling, such as: it allows the rigorous derivation of the joint probability distributions of hydraulic gradients and conductivities across space; it imposes no restriction on the functional form of the effective parameters or the shape of the probability laws governing the random media (non-Gaussian distributions, multiple-point statistics and non-linear models are automatically incorporated); it relies on sound methodological principles rather than being ad hoc; and it offers the rational means for integrating the multifarious core knowledge bases and uncertain site-specific information sources about the subsurface system. Previous upscaling results are derived as special cases of the proposed upscaling approach under limited conditions of porous media flow, a fact that further demonstrates the generalization power of the approach. Our hope is that looking at the upscaling problem in this novel way will direct further attention to the methodological exploration of the problem at the length and the detail that it deserves.I would like to thank Drs. A. Kolovos and D.T. Hristopulos for their valuable comments. The work was supported by grants from the Army Research Office (Grant no. DAAG55–98–1-0289) and the National Institute of Environmental Health Sciences (P42-ES05948 & P30-ES10126).