Anisotropy Versus Heterogeneity in Continental Solid Earth Electromagnetic Studies: Fundamental Response Characteristics and Implications for Physicochemical State

Electrical anisotropy, the effect of current density in a medium being a function of the orientation of the electric field, is being recognized increasingly as an important effect in explaining Earth electromagnetic observations. A consideration of anisotropy, however, in most cases is an admission of spatial aliasing in earth structure, wherein the averaging volume of diffusive EM fields may be greater than the characteristic dimensions of a family of oriented structures, thus leading to a response which is equivalent to a bulk anisotropic medium. Even for two-dimensional geometries, there can be strong non-parallelism of principal axes of vertical magnetic field relative to the impedance over broad areas, as well as impedance phase variations which leave normal quadrants, if there are multiple directions of anisotropy or anisotropy strike distinct from bulk geometric (2D) strike. This paper concentrates on experience with regional field studies in continental settings where bulk anisotropy is apparent. Upper crustal anisotropy may result from preferred orientations of fracture porosity, or lithologic layering, or oriented heterogeneity. Lower crustal anisotropy may result from preferred orientations of fluidized/melt-bearing or graphitized shear zones, but does not necessarily reflect current state of stress per se. In the upper mantle, the prior causes all may act in pertinent domains, but added to these is the possibility of strong electrical anisotropy due to hydrous defects within shear-aligned olivine crystals (solid-state conduction). Several field examples from continental MT investigations will be discussed, which roughly fall into active transpressional, active transtensional, and fossil transpressional regimes. A general challenge in interpreting data with apparent anisotropic effects is to establish the tradeoff between heterogeneity and anisotropy in the inversion of EM responses.     

非均匀正交各向异性特征参数地震散射反演方法研究

在长波长假设条件下,水平层状地层中发育一组垂直排列的裂缝构成了等效正交各向异性介质.各向异性参数与裂缝弱度参数的估算有助于非均匀各向异性介质的各向异性特征描述,而弹性逆散射理论是非均匀介质参数反演的有效途径.基于地震散射理论,我们首先推导了非均匀正交介质中纵波散射系数方程,并通过引入正交各向异性特征参数,提出了一种新颖的正交各向异性方位弹性阻抗参数化方法.为了提高反演的稳定性与横向连续性,我们发展了贝叶斯框架下的正交各向异性方位弹性阻抗反演方法,同时考虑了柯西稀疏约束正则化和平滑模型约束正则化,最终使用非线性的迭代重加权最小二乘策略实现了各向异性特征参数的稳定估算.模型和实际资料处理表明,反演结果与测井解释数据相吻合,证明了该方法能够稳定可靠地从方位叠前地震资料中获取各向异性特征参数,减小参数估算的不确定性,为非均匀正交介质的各向异性预测提供了一种高可靠性的地震反演方法.     

各向异性介质中地震波前面的偏微分方程

从含２１个弹性参数的各向异性介质中关于位移分量ｕ_ｘ、ｕ_ｙ与ｕ_ｚ的偏微分波动方程组出发，通过假定平面波位移函数解，导出准Ｐ波、准ＳＶ波与准ＳＨ波的波前面偏微分控制方程，进而对各类特殊各向异性介质（横向各向同性介质、椭圆及立方体各向异性介质）中地震波前面偏微分方程进行了讨论．以上结果为研究各向异性介质中地震波传播规律以及进行正、反演研究奠定了理论基础．     

网式大地电磁阻抗张量及其影响因素分析

网式大地电磁（Network-MT,N-MT）法采用长数公里至数十公里的电话线为电极线测量电场,很难形成两条笔直且相互垂直的电极线,因此阻抗张量的计算不如大地电磁法中直接.本文依据阻抗张量的旋转规则提出了一种计算N-MT阻抗张量的简便算法.依据该算法计算了中国东北地区5个N-MT测站的阻抗张量,获得了基于阻抗张量的视电阻率、相位曲线和最佳主轴方位角分布图像,为我国东北N-MT资料的进一步处理和解释提供了基础性数据.此外,本文对比分析了朝阳测站中6条N-MT观测电极线上阻抗张量旋转值与观测值之间的差异,重点讨论了产生这种系统性偏差的各种因素,提出其主要因素可能来自“电场等效各向异性”效应,即测站附近的地壳内部存在与观测电极线尺度相比拟的横向非均匀构造,而测站各电极线沿不同方向跨越不均匀构造,此时各电极线上的电场分量不遵循同一电场矢量的分解准则,导致地表观测三角形内阻抗分量不满足统一的阻抗张量旋转规则.     

Matrix polynomial representation of the anisotropic magnetotelluric impedance tensor

A formalism based upon the equal penetration depth stratification assumption is extended to a layered anisotropic medium, yielding a recursive algorithm for the computation of the magnetotelluric impedance tensor elements. The development of this new procedure requires an appropriate layer-discretization as well as an extension of the reflection coefficient definition for the anisotropic layered model.This method transfers the differential problem into an algebraic one, and is independent of the electric and magnetic field vectors. The technique is a recursive process which gives a rational matrix polynomial representation for the magnetotelluric impedance tensor.The procedure involves the use of second-order matrices, rather than the fourth-order ones normally used for such a case. Using this representation, a separation of the contribution of the model parameters from that of the frequency is achieved. Consequently the elements of the magnetotelluric impedance tensor are computed, for each frequency, using coefficients which are evaluated just once for a given model.     

Mohr圆分析方法在川西-藏东MT剖面资料解释中的应用

用Mohr圆分析法对川西—藏东全测区 76个大地电磁测深点的资料进行了分析 ,结果表明 :测区以 2D区域构造为主要特征 ,横向各向异性不太强 ;区域构造走向大致呈近SN向 ,最大偏离不超过± 30°。文中介绍了 4个测点的分析结果     

地球物理问题中电磁感应的实验室模拟模型研究

在地球物理问题中,有两种方法通常用于解释地磁和地电异常,这就是数字模型技术和实验室模拟模型法。实验室模拟模型对于分析不易求得数学解的问题非常有用,并且已经广泛用于研究复杂的地球物理问题。本文评述了国外特别是加拿大开展模拟模型研究的情况;描述了平面波、线电流、磁偶极等各种类型的场源模型;给出了该法在研究海岸效应、岛陆通道电流、海浪电磁效应和各向异性导体等方面的应用。模拟模型测量和数字计算的比较结果显示了非常好的一致性,这就进一步证实了模拟模型法对于研究复杂二维和三维感应问题的可靠性。该项研究工作对于了解天然电磁场源的性质、进行地球物理勘探以及研究地球地壳和地幔的电性结构都十分有益。     

VTI介质中的弹性阻抗与参数提取

弹性阻抗是波阻抗的扩展,可以更好的反映储层和流体性质.常规弹性阻抗方程忽略了各向异性的影响,不能正确地描述各向异性介质中弹性阻抗的性质.本文基于Ruger给出的VTI介质反射系数近似公式,结合Connolly推导弹性阻抗的思想,推导出了一种VTI介质中的弹性阻抗方程.通过引入归一化常数,对方程进行了标准化,消除了方程量纲随角度变化而变化的不足.结合常规弹性阻抗反演的流程,得出了VTI介质中弹性阻抗反演的流程.最后,开展了从VTI介质弹性阻抗数据体中提取岩石物性参数的方法研究.数值测试表明,所讨论的参数提取方法具有一定的理论和应用价值.     

Analytical solution for the electric potential in arbitrary anisotropic layered media applying the set of Hankel transforms of integer order

The analytical solution and algorithm for simulating the electric potential in an arbitrarily anisotropic multilayered medium produced by a point DC source is here proposed. The solution is presented as a combination of Hankel transforms of integer order and Fourier transforms based on the analytical recurrent equations obtained for the potential spectrum. For the conversion of the potential spectrum into the space domain, we have applied the algorithm of the Fast Fourier Transform for logarithmically spaced points. A comparison of the modelling results with the power‐series solution for two‐layered anisotropic structures demonstrated the high accuracy and computing‐time efficiency of the method proposed. The results of the apparent‐resistivity calculation for both traditional pole‐pole and tensor arrays above three‐layered sequence with an azimuthally anisotropic second layer are presented. The numerical simulations show that both arrays have the same sensitivity to the anisotropy parameters. This sensitivity depends significantly on the resistivity ratio between anisotropic and adjacent layers and increases for the models with a conductive second layer.     

Depth migration anisotropy analysis in the time domain

In areas of complex geology such as the Canadian Foothills, the effects of anisotropy are apparent in seismic data and estimation of anisotropic parameters for use in seismic imaging is not a trivial task. Here we explore the applicability of common‐focus point (CFP)‐based velocity analysis to estimate anisotropic parameters for the variably tilted shale thrust sheet in the Canadian Foothills model. To avoid the inherent velocity‐depth ambiguity, we assume that the elastic properties of thrust‐sheet with respect to transverse isotropy symmetry axis are homogeneous, the reflector below the thrust‐sheet is flat, and that the anisotropy is weak. In our CFP approach to velocity analysis, for a poorly imaged reflection point, a traveltime residual is obtained as the time difference between the focusing operator for an assumed subsurface velocity model and the corresponding CFP response obtained from the reflection data. We assume that this residual is due to unknown values for anisotropy, and we perform an iterative linear inversion to obtain new model parameters that minimize the residuals. Migration of the data using parameters obtained from our inversion results in a correctly positioned and better focused reflector below the thrust sheet. For traveltime computation we use a brute force mapping scheme that takes into account weakly tilted transverse isotropy media. For inversion, the problem is set up as a generalized Newton's equation where traveltime error (differential time shift) is linearly dependent on the parameter updates. The iterative updates of parameters are obtained by a least‐squares solution of Newton's equations. The significance of this work lies in its applicability to areas where transverse isotropy layers are heterogeneous laterally, and where transverse isotropy layers are overlain by complex structures that preclude a moveout curve fitting.     

基于构造约束的波阻抗边界刻画

通过边界保护正则化和约束反演,在反演的目标函数中引入各种先验信息约束,以解决波阻抗反演的病态问题和带限问题.为了克服波阻抗模型边界过于平滑,在反演中引入地层和断层等构造信息约束,并且通过调整地层分界面和断层处的正则参数值来实现构造约束.此外,采用各向异性扩散法进行平滑处理,改善反演结果.通过合成数据测试和实际资料反演,证明了本文提出的方法对刻画模型边界是有效的.     

Exact elastic impedance tensor for isotropic media

The existing expressions of elastic impedance,as the generalized form of acoustic impedance,represent the resistance of subsurface media to seismic waves of non-normal incidence,and thus include information on the shear-wave velocity.In this sense,conventional elastic impedance is an attribute of the seismic reflection and not an intrinsic physical property of the subsurface media.The derivation of these expressions shares the approximations made for reflectivity,such as weak impedance contrast andisotropic or weakly anisotropic media,which limits the accuracy of reflectivity reconstruction and seismic inversion.In this paper,we derive exact elastic impedance tensors of seismic P-and S-waves for isotropic media based on the stress-velocity law.Each componentof the impedance tensor represents a unique mechanical property of the medium.Approximations of P-wave elastic impedance tensor components are discussed for seismic inversion and interpretation.Application to synthetic data and real data shows the accuracy and robust interpretation capability of the derived elastic impedance in lithology characterizations.     

Numerical simulation of the mutual conversion of ordinary and extraordinary waves in a magnetised plasma by artificial ionospheric turbulence

Some effects of normal mode coupling in weakly anisotropic inhomogeneous plasma are analysed on the basis of the numerical solution of transfer equations for the Stokes parameters. The numerical analysis of normal mode conversion on a set of isolated irregularities demonstrates the possibility of an effective polarisation transformation on such structures. It is shown that by the appropriate selection of discrete irregularities of the external magnetic field direction or plasma electron concentration resulting in radio-wave refraction, one can control electromagnetic radiation polarisation characteristics. Analytical expressions for mean Stokes parameters have been obtained for the rare isolated irregularities. The opportunity for the simulation of mutual wave conversion processes in the ionospheric heating experiments is discussed.     

Upper mantle seismic anisotropy beneath a convergent boundary: SKS waveform modeling in central Tibet

This study used SKS waveforms from the International Deep Profiling of Tibet and the Himalayas (INDEPTH) III dataset and a new 2D method for modeling seismic waves in anisotropic media to construct an image of anisotropic structures beneath central Tibet. A preferred model revealed three-segment anisotropic structures in the upper mantle beneath the study region. Waveform modeling demonstrated that the anisotropy was mainly generated by the lithosphere but not the asthenosphere, and that an anisotropic model with a flatter axis of symmetry provides a more consistent interpretation of the observations than models having steeply dipping symmetry axes. A relatively low velocity zone may underlie or intermingle with the anisotropic structures in the northern portion of the region. Synthetic tests also indicate that variations in the elastic constants and depth extent of the anisotropy assumed by the calculations do not affect the general conclusions, although trade-offs exist among certain model parameters. The modeling results suggest that the complex seismic structures in central Tibet were associated with underthrusting of the Indian lithosphere beneath the Asian lithosphere; the inferred flat symmetry axis of the anisotropy was likely generated during this collision process. If this were not the case, the inherited anisotropy would exhibit a steeply dipping axis of symmetry, parallel to the direction of underthrusting.     

1-D DC Resistivity Modeling and Interpretation in Anisotropic Media Using Particle Swarm Optimization

We examine the one-dimensional direct current method in anisotropic earth formation. We derive an analytic expression of a simple, two-layered anisotropic earth model. Further, we also consider a horizontally layered anisotropic earth response with respect to the digital filter method, which yields a quasi-analytic solution over anisotropic media. These analytic and quasi-analytic solutions are useful tests for numerical codes. A two-dimensional finite difference earth model in anisotropic media is presented in order to generate a synthetic data set for a simple one-dimensional earth. Further, we propose a particle swarm optimization method for estimating the model parameters of a layered anisotropic earth model such as horizontal and vertical resistivities, and thickness. The particle swarm optimization is a naturally inspired meta-heuristic algorithm. The proposed method finds model parameters quite successfully based on synthetic and field data. However, adding 5 % Gaussian noise to the synthetic data increases the ambiguity of the value of the model parameters. For this reason, the results should be controlled by a number of statistical tests. In this study, we use probability density function within 95 % confidence interval, parameter variation of each iteration and frequency distribution of the model parameters to reduce the ambiguity. The result is promising and the proposed method can be used for evaluating one-dimensional direct current data in anisotropic media.     

Analysis of the earth resistivity response of buried cables

Current flow in homogeneous and layered conducting media is analyzed for the case where an axial conductor or cable is present. The cable is characterized by a specified axial impedance and is assumed to be infinite in length. Various configurations are chosen such as a current point source in an infinite, semi-infinite, and layered region where the cable is taken parallel to the interface(s). The resulting formulas for the potentials reduce to known cases in the absence of the cable. Using these formulations, we present some concrete calculated examples that are relevant to resistivity probing of perturbed homogeneous and layered structures. Only the two-electrode array is treated, but various cable orientations are considered. In general, it is found that a long axial conductor such as a bare cable will distort the potential distribution of the current in a major way. This leads to profound departures from the apparent resistivity curves calculated for idealized homogeneous and layered structures.U.S. Government Work not subject to U.S. copyright.     

地壳分层各向异性介质接收函数及其粒子群反演

地壳不同深度介质的地震各向异性是研究地壳不同深度范围变形方式的重要依据.鉴于地壳介质的复杂性,如何从远震体波接收函数中提取不同深度的各向异性参数仍是一个有待深入研究的课题.在已有研究的基础上,本文利用广义反射-透射系数矩阵方法计算的合成地震图,研究了复杂地壳分层各向异性介质的接收函数随反方位角(back azimuth)变化及不同层位各向异性参数对接收函数波场的影响,为各向异性介质接收函数的解释提供了新的理论依据.通过引入粒子群优化理论,发展了分层各向异性介质接收函数全局反演算法.数值及观测数据的验证结果表明,在各向同性速度模型确定的前提下,我们的方法能够可靠地提取地壳分层各向异性参数;在反演中引入曲波变换去噪技术,对于正确解析不同层位的各向异性参数具有重要价值.     

一种基于3D复杂介质的弹性建模数值方法

储层中的裂隙会导致介质表现出各向异性.传统等效介质方法假定储层可以被等效成为横向各向同性介质,不适用于复杂裂缝储层的弹性等效建模和各向异性特征分析.本文在前人研究基础上,利用最小二乘方法开展3D复杂裂隙弹性等效数值模拟研究,并与常规等效介质理论方法进行比较,验证数值方法的精确性.数值方法不仅能有效避免Hudson理论和Eshelby-Cheng理论等解析方法在大裂隙密度条件下的参数估计误差,而且兼顾裂隙扰动作用对等效介质参数的影响.数值研究表明,数值方法能够较好地描述复杂裂缝介质的各向异性特征,为复杂裂缝储层地震波各向异性参数反演提供依据.     

横观各向同性岩土材料的应变局部化分析

为分析横观各向同性岩土材料的应变局部化行为,推导对应于Lade横观各向同性屈服准则向前欧拉算法的迭代格式及本构矩阵,通过有限元软件ABAQUS的UMAT接口实现相应的程序代码。数值算例调查分析材料主方向对横观各向同性岩土结构的极限承载力和变形局部化模式的影响。结果表明该模型能较好地模拟横观各向同性岩土结构的应变局部化行为。     

Seismoelectric numerical simulation in 2D vertical transverse isotropic poroelastic medium

Seismoelectric coupling in an electric isotropic and elastic anisotropic medium is developed using a primary–secondary formulation. The anisotropy is of vertical transverse isotropic type and concerns only the poroelastic parameters. Based on our finite difference time domain algorithm, we solve the seismoelectric response to an explosive source. The seismic wavefields are computed as the primary field. The electric field is then obtained as a secondary field by solving the Poisson equation for the electric potential. To test our numerical algorithm, we compared our seismoelectric numerical results with analytical results obtained from Pride's equation. The comparison shows that the numerical solution gives a good approximation to the analytical solution. We then simulate the seismoelectric wavefields in different models. Simulated results show that four types of seismic waves are generated in anisotropic poroelastic medium. These are the fast and slow longitudinal waves and two separable transverse waves. All of these seismic waves generate coseismic electric fields in a homogenous anisotropic poroelastic medium. The tortuosity has an effect on the propagation of the slow longitudinal wave. The snapshot of the slow longitudinal wave has an oval shape when the tortuosity is anisotropic, whereas it has a circular shape when the tortuosity is isotropic. In terms of the Thomsen parameters, the radiation anisotropy of the fast longitudinal wave is more sensitive to the value of ε, while the radiation anisotropy of the transverse wave is more sensitive to the value of δ.