Relationship between regional stress field variation and earthquake activities from GPS data

IntroductionWith the development of science and technology, especially with the development of spatial geodetic technology (Tralli, Timothy, 1988), it is possible to precisely obtain the continuous geodetic data on the earth surface by Global Positioning System (GPS) observation. The spatial geodetic technology can be used to observe the deformation response on the earth surface caused by the stress field variation, and some deformation and movement feature in the earth crust during the pro…     

利用GPS资料研究区域地壳应力场变化与地震活动关系h

推导了地球内应力场变化与地面位移场和重力变化的关系;讨论了利用地面位移变化速率来计算地球内应力场变化的边界元方法;最后,利用中国新疆伽师地区的GPS观测资料,对该地区地壳内的应力场变化进行了计算,并分析和讨论了该地区地壳内的局部应力场变化与地震活动和断层构造活动的关系．      

时域瞬变电磁法三维有限差分正演技术研究

瞬变电磁法应用广泛,三维数值模拟是研究复杂地质模型异常响应规律的重要技术手段之一,也是反演的基础.目前瞬变电磁数值模拟的不足主要有两个方面：第一,场源是在地表水平、浅层介质均匀的条件下计算的,限制了应用范围;第二,地下边界采用Dirichlet边界条件,导致计算空间很大,耗时较长.针对上述问题,在三维正演时,场源采用有限长细导线模型,在Maxwell有源差分方程中直接加入电流密度进行计算.在地表面加入空气层,避免了复杂的向上延拓计算,也可以对地形影响下的响应规律进行分析.在空气边界和地下边界均采用CPML吸收边界条件,并改进了CPML的参数分布,能够吸收空气介质和大地介质中的低频电磁波而反射误差极小,在满足计算精度的条件下可以有效减小节点数量.对循环迭代方法进行优化,将计算域、CPML区域和场源的空间循环统一转化为矩阵方式,加快了计算速度,但是空间消耗增大了约4~5倍.采用三维有限差分正演算法对均匀半空间模型、层状模型和地形模型进行了计算,并与解析解进行了对比验证.

     

On the discrete outer gravity field

Summary In the present paper the gravity field of the earth in the neighbourhood of the local disturbing masses is studied. The object of the method presented consists of the approximation of the disturbing potentialT _h , which fulfils Laplace's equation outside disturbing masses, on the earth's surface the fundamental boundary value condition of gravity and in infinity it is to be regular by the approximation of the disturbing potential (or by the discrete disturbing potential)T _h , which fulfils the respective finite difference approximation of Laplace's equation and the boundary value conditions in infinity and on the earth's surface. It is also shown that the approximation of the disturbing potentialT _h has the same properties as the disturbing potentialT. The method under consideration will be derived quite generally without any hypothesis about the distribution of the mass between the earth's surface and the geoid. It commences from the gravity data related to the earth's surface only-from the given geodetic measurements.     

Improved treatments for evaluating horizontal magnetic components through the 3-D FDM in E -polarization induction problems

To improve the accuracy of the numerical evaluation through the 3-D finite difference method, the surface boundary conditions are added to modify the old program. The author has tested the new program by making calculations for the model constructed by Wanamaker, et al (1984). The comparison between the numerical results obtained from this paper and those by Wannamaker, et al (1984) indicates that a pronounced improvement is realized in the evaluation of the horizontal magnetic components. Moreover, better calculations for the vertical magnetic components are also obtainable by using the new program.     

Multiscale Gravitational Field Recovery from GPS-Satellite-to-Satellite Tracking

The purpose of GPS-satellite-to-satellite tracking (GPS-SST) is to determine the gravitational potential at the earth's surface from measured ranges (geometrical distances) between a low-flying satellite and the high-flying satellites of the Global Positioning System (GPS). In this paper, GPS-satellite-to-satellite tracking is reformulated as the problem of determining the gravitational potential of the earth from given gradients at satellite altitude. The uniqueness and stability of the solution are investigated. The essential tool is to split the gradient field into a normal part (i.e. the first-order radial derivative) and a tangential part (i.e. the surface gradient). Uniqueness is proved for polar, circular orbits corresponding to both types of data (first radial derivative and/or surface gradient). In both cases gravity recovery based on satellite-to-satellite tracking turns out to be an exponentially ill-posed problem. Regularization in terms of spherical wavelets is proposed as an appropriate solution method, based on the knowledge of the singular system. Finally, the extension of this method is generalized to a nonspherical earth and a non-spherical orbital surface, based on combined terrestrial and satellite data.     

Non-linear dynamic earth dam–foundation interaction using a BE–FE method

A general, rigorous, coupled Boundary Element–Finite Element (BE–FE) formulation is presented for non-linear seismic soil–structure interaction in two dimensions. The BE–FE method is applied to investigate the inelastic response of earth dams to transient SV waves. The dam body, consisting of heterogeneous materials modelled with a simple non-linear hysteretic model, is discretized with finite elements, whereas the elastic half-space is discretized with boundary elements. The study focuses on the combined effects of the material non-linearity and foundation flexibility. The results show the significant effect of the foundation flexibility in reducing the response through radiation of energy. For excitations with peak ground accelerations from 0·2gto 0·6g, the crest acceleration amplification ranges from 2·5 to 1·4 and seems to be comparable with field observations and results from other studies. Deamplification increasing with strain is reported at the lower part of the dam. The method is computationally powerful and can be used for efficient non-linear analysis of complex soil–structure systems. The efficiency of the BE–FE method allows further improvements with incorporation of a more advanced constitutive model and consideration of the generation and dissipation of pore-water pressures during the earthquake. © 1998 John Wiley & Sons, Ltd.     

地球外部扰动重力严密改化模型及分析检验

直接积分模型是计算地球外部扰动重力的主要数学工具,将全球积分模型改化为局域积分模型是实现地球外部重力场赋值的前提条件.相比表层积分模型和向上延拓积分模型,Stokes积分模型要求的输入信息种类最少,故在减轻数据保障压力方面具有比较明显的优势.在实施Stokes积分模型工程化应用过程中,我们发现扰动重力径向分量积分模型从地球外部逼近边界面时存在比较严重的数值不连续性问题,本文研究并指出了存在该问题的内在原因,同时提出了保持该模型连续性的修正方法;针对三分量计算模型存在的积分奇异性问题和传统改化方法存在的理论缺陷,提出综合采用移去恢复运算和积分恒等式转换技术,同时依据实测数据保障条件,分步实施扰动重力三分量全球积分模型改化的技术流程和方法,推出了三分量积分模型的分步改化公式,提出了补偿传统改化模型缺陷的修正公式.以超高阶地球位模型EGM2008作为检核参考位场,开展模型对比计算数值试验,分别对本文推出的扰动重力三分量不同阶段改化模型的计算精度进行了分析检验和评估,验证了采用严密改化模型的必要性和有效性.

     

Stationary approximation of the magnetotelluric field in a halfspace with a vertical boundary and three-dimensional perturbing body

Summary Based on the generalized potential of a double layer, integral formulae have been derived for calculating the stationary approximation of the magnetotelluric field in a halfspace divided by a vertical boundary into two quarterspaces, one of which contains a three-dimensional perturbing body. The appropriate boundary integral equation and other surface integrals have been computed for a perturbing body in the shape of the three-dimensional prism located at the vertical boundary, or in contact with the said boundary. The exciting electrical field is assumed to be homogeneous and perpendicular to the vertical boundary. Isoline graphs of the electrical and magnetic fields on the surface of the halfspace have been plotted and their anomalies are discussed.     

The GPS-gravimetry boundary value problem

Boundary value problem (BVP) plays a funda-mental role in physical geodesy that aims at determin-ing the earth’s shape and its external gravity field. TheMolodensky BVP and the Stokes BVP are typical inphysical geodesy, and the gravity anomaly is a kind ofbasic data. With the wide use of GPS, measurementaccuracy of the earth’s surface can reach one centime-ter, while that of the gravity measurement can reachμgals. Hence, it is necessary to establish a new kind ofBVP which can satisfy…     

Two-dimensional scattering of in-plane body waves due to a discontinuity in bedrock

The direct boundary integral equation technique is used to study in-plane surface amplification of in-plane seismic body waves for the case of an inhomogeneity in a bedrock half-space. In the studied soil configuration, a soil layer rests on a rock half-space which includes a rock inclusion. The rock inclusion considered is a semi-infinite horizontal rock layer in which its upper boundary borders the soil layer. Materials in the soil–rock configuration are considered viscoelastic except for the section of the rock half-space below the level of the rock inclusion which is considered elastic. A parametric study is performed to determine controlling factors for surface displacement due to in-plane body waves. The study investigates varying the stiffness and the thickness of the rock inclusion for a range of frequencies and wave incidence angles. Anti-plane waves for this type of soil-rock configuration have been addressed in a previous article by Heymsfield (Earthquake Engng. Struct. Dyn. 28 : 841–855 (1999)). Copyright © 1999 John Wiley & Sons, Ltd.     

A mathematical structure for a theory of electromagnetic induction in the Earth in low latitude

Summary In low latitude the spatial distribution functions of the source field over the surface and the dimensions of the source, are important in any theory of electromagnetic induction developed for studying the conductivity structure of the Earth. The author has built up a mathematical structure for a theory of electromagnetic induction in anyn-layered earth model in low latitude. No simple solution is assumed for the horizontal distribution function of the source field and no assumption is made about the horizontal gradients of the source. The mathematical structure involves the concept of downward continuity of the field equations inside then-layered earth model. The resulting mathematical functions derived for anyn-layered earth model are complex. Hence a new matrix algebra of complex numbers is introduced by the author and this is built into the theory. From the upward continuity of the field equations, an inequality equation is derived in order to determine the heighth ₀ at which the induction field of the earth becomes negligible compared with the source field. The comparison of such heights at two or more stations under the same influence of the source field can be used for the resolution of the lateral distribution of the earch conductivity structure at these stations. The application of the theory will follow in a subsequent paper.     

Meridian-scanning photometer, coherent HF radar, and magnetometer observations of the cusp: a case study

The dynamics of the cusp region and post-noon sector for an interval of predominantly IMF B_y, B_z < 0 nT are studied with the CUTLASS Finland coherent HF radar, a meridian-scanning photometer located at Ny Ålesund, Svalbard, and a meridional network of magnetometers. The scanning mode of the radar is such that one beam is sampled every 14 s, and a 30° azimuthal sweep is completed every 2 minutes, all at 15 km range resolution. Both the radar backscatter and red line (630 nm) optical observations are closely co-located, especially at their equatorward boundary. The optical and radar aurora reveal three different behaviours which can interchange on the scale of minutes, and which are believed to be related to the dynamic nature of energy and momentum transfer from the solar wind to the magnetosphere through transient dayside reconnection. Two interpretations of the observations are presented, based upon the assumed location of the open/closed field line boundary (OCFLB). In the first, the OCFLB is co-located with equatorward boundary of the optical and radar aurora, placing most of the observations on open field lines. In the second, the observed aurora are interpreted as the ionospheric footprint of the region 1 current system, and the OCFLB is placed near the poleward edge of the radar backscatter and visible aurora; in this interpretation, most of the observations are placed on closed field lines, though transient brightenings of the optical aurora occur on open field lines. The observations reveal several transient features, including poleward and equatorward steps in the observed boundaries, braiding of the backscatter power, and 2 minute quasi-periodic enhancements of the plasma drift and optical intensity, predominantly on closed field lines.     

Modelling Potential Field Sources in the Gelibolu Peninsula (Western Turkey) Using a Markov Random Field Approach

In this study, a Markov Random Field (MRF) approach is used to locate source boundary positions which are difficult to identify from Bouguer gravity and magnetic maps. As a generalized form of Markov Chains, the MRF approach is an unsupervised statistical model based algorithm and is applied to the analysis of images, particularly in the detection of visual patterns or textures. Here, we present a dynamic programming based on the MRF approach for boundary detection of noisy and super-positioned potential anomalies, which are produced by various geological structures. In the MRF method, gravity and magnetic maps are considered as two-dimensional (2-D) images with a matrix composed of N₁ × N₂ pixels. Each pixel value of the matrix is optimized in real time with no a priori processing by using two parameter sets; average steering vector (θ) and quantization level (M). They carry information about the correlation of neighboring pixels and the locality of their connections. We have chosen MRF as a processing approach for geophysical data since it is an unsupervised, efficient model for image enhancement, border detection and separation of 2-D potential anomalies. The main benefit of MRF is that an average steering vector and a quantization level are enough in evaluation of the potential anomaly maps. We have compared the MRF method to noise implemented synthetic potential field anomalies. After satisfactory results were found, the method has been applied to gravity and magnetic anomaly maps of Gelibolu Peninsula in Western Turkey. Here, we have observed Anafartalar thrust fault and another parallel fault northwest of Anafartalar thrust fault. We have modeled a geological structure including a lateral fault, which results in a higher susceptibility and anomaly amplitude increment. We have shown that the MRF method is effective to detect the broad-scale geological structures in the Gelibolu Peninsula, and thus to delineate the complex tectonic structure of Gelibolu Peninsula.     

3-D rheologic model of earthquake preparation （Ⅲ）： Precursor field

On the basis of the theory of viscoelastic displacement and strain field for the three-dimensional rheologic model of earthquake preparation, this paper mainly studies the theoretical solution of precursor field for the three-dimensional rheologic model of earthquake preparation. We derive the viscoelastic analytical expressions of the ground tilt, underground water level, earth resistivity at an arbitrary point （x, y, z） in the rheologic medium, and analyzed the earth resistivity preliminarily, providing a certain theoretical basis for the precursor analysis of seismogenic process.     

分段光滑曲线边界波动方程数值模拟研究

矩形网格有限差分法在地震波传播数值模拟方面具有计算速度快的显著优势,但该方法在处理复杂边界问题上存在着效率低的严重缺陷.本文针对分段光滑曲线边界定义了尖点处的一种正则导数,给出了矩形网格情形分段光滑曲线网格边界点法向导数的一种插值计算方法.采用矩形网格有限差分法对复杂边界地球介质模型进行地震波场数值模拟,并采用波场系列快照技术揭示地震波在起伏地表和复杂介质中的传播规律.模拟结果表明：法向导数插值计算方法为矩形网格有限差分法处理复杂边界提供了有效途径,采用波场系列快照技术可以清晰地展现地震波在反射界面的反射和透射规律、在尖点的绕射规律以及在自由表面的直达波和多次反射规律.     

Possible configurations of the magnetic field in the outer magnetosphere during geomagnetic polarity reversals

Possible configurations of the magnetic field in the outer magnetosphere during geomagnetic polarity reversals are investigated by considering the idealized problem of a magnetic multipole of order m and degree n located at the centre of a spherical cavity surrounded by a boundless perfect diamagnetic medium. In this illustrative idealization, the fixed spherical (magnetopause) boundary layer behaves as a perfectly conducting surface that shields the external diamagnetic medium from the compressed multipole magnetic field, which is therefore confined within the spherical cavity. For a general magnetic multipole of degree n, the non-radial components of magnetic induction just inside the magnetopause are increased by the factor 1 + [(n + 1)/n] relative to their corresponding values in the absence of the perfectly conducting spherical magnetopause. An exact equation is derived for the magnetic field lines of an individual zonal (m = 0), or axisymmetric, magnetic multipole of arbitrary degree n located at the centre of the magnetospheric cavity. For such a zonal magnetic multipole, there are always two neutral points and n – 1 neutral rings on the spherical magnetopause surface. The two neutral points are located at the poles of the spherical magnetopause. If n is even, one of the neutral rings is coincident with the equator; otherwise, the neutral rings are located symmetrically with respect to the equator. The actual existence of idealized higher-degree (n > 1) axisymmetric magnetospheres would necessarily imply multiple (n + 1) magnetospheric cusps and multiple (n) ring currents. Exact equations are also derived for the magnetic field lines of an individual non-axisymmetric magnetic multipole, confined by a perfectly conducting spherical magnetopause, in two special cases; namely, a symmetric sectorial multipole (m = n) and an antisymmetric sectorial multipole (m = n – 1). For both these non-axisymmetric magnetic multipoles, there exists on the spherical magnetopause surface a set of neutral points linked by a network of magnetic field lines. Novel magnetospheric processes are likely to arise from the existence of magnetic neutral lines that extend from the magnetopause to the surface of the Earth. Finally, magnetic field lines that are confined to, or perpendicular to, either special meridional planes or the equatorial plane, when the multipole is in free space, continue to be confined to, or perpendicular to, these same planes when the perfectly conducting magnetopause is present.Also Honorary Research Associate, Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, UK and Visiting Reader in Physics. University of Sussex, Falmer, Brighton BN1 9QH, UK     

三维复杂山谷地形SV波垂直输入地震反应分析

本文基于显式有限元法研究了地震波垂直入射时三维复杂山谷地形对地震地面运动的影响,在数值分析中应用了三维化二维的解法和黏弹性人工边界的处理方法,实现了地震波垂直输入下三维复杂场地地震动数值模拟,并验证了该方法的合理性.以四川桃坪地区一山谷地形作为研究对象,基于地表高程数据分别建立了二维和三维场地模型,对比研究表明：在复杂地形情况下考虑二、三维模型时具有明显差异,三维模型能更真实地反映地形变化对地震动的影响,复杂地形条件下有必要考虑三维实际场地模型.本文对边界自由场的处理方法也可用于处理三维复杂场地地震动斜入射问题,为三维复杂地形场地地震效应研究提供参考.

     

2维和2.5维起伏地表直流电法有限差分数值模拟

起伏地表直流电场数值模拟现多采用有限元法,主要是因为其有灵活的处理曲边界的能力,然而有限元法比有限差分法要复杂,如果让有限差分法也同样具有较好的处理曲边界的能力,那数值模拟将变得更为简单.本文通过在非正则内点处采用不等距差分,在起伏地表点处直接实现边界条件,克服转移法人为改变地表形状的弊端,使得基于笛卡尔网格的有限差分...     

Explicit solution of a free boundary problem for a nonlinear absorption model of mixed saturated-unsaturated flow

In wet soils, zones of saturation naturally develop in the vicinity of impermeable strata, surface ponds and subterranean cavities. Hydrology must be then concerned with transient flow through coexisting unsaturated and saturated zones. The models of advancing saturated zones necessarily involve a nonlinear free boundary problem.A closed-form analytic solution is presented for a nonlinear diffusion model under conditions of ponding at the surface. The soil water diffusivity is restricted to the special functional form D(θ) = a/(b − θ)², where θ is the water content field to be determined and a, b are positive constants. The explicit solution depends on a parameter C (determined by the data of the problem), according to two cases: 1 < C < C₁ or C ≥ C₁, where C₁ is a constant which is obtained as the unique solution of an equation. This result complements the study given in P. Broadbridge, Water Resources Research, 1990, 26, 2435–2443, in order to established when the explicit solution is available. The behavior of the bifurcation parameter C₁ as a function of the driving potential is studied with the corresponding limits for small and large values. Moreover, the sorptivity is proven to be continuously differentiable function of the variable C.