利用Cole-Cole模型组合得到SIP真参数的联合频谱最优化反演

利用Cole-Cole模型组合和稀释系数理论，可以描述测量得到的视复电阻率频谱与地下多个电性体SIP真参数之间的正演关系。本利用此正演关系进行反演试算，并比较了几种Cole-Cole模型反演方案的效果；提出固定极化目标体和围岩体的极化率同时反演其它各SIP真参数的反演方案。结果表明在固定极化率为真值时，利用此反演方案可以稳定、准确、快速地得出地下电性体SIP真参数。     

一种真复电阻率谱参数的求解方法

本文建立了地下半空间中存在二种可极化介质时,真谱与视谱间一种新的关系式,它将视谱直接以待求的真谱参数表出,而无需任何中间量的介入.在此基础上利用改进的广义逆法实现真谱的反演.文中以四种简单地电模型为例,考察了极化体形态、规模、产状、埋深、测点位置、装置类型和大小以及极化体相对围岩的电阻率不同时的反演效果.结果表明,只要初值选择合适,真谱参数的反演效果是良好的.     

复电阻率法二维有限元数值模拟

伴随着复电阻率法的广泛应用，发展精确和快速的正演和反演算法成为复电阻率法研究的重点.本文采用基于三角单元剖分的有限单元法进行了复电阻率二维数值模拟研究.为了提高计算速度，对无穷远边界进行了近似处理.整个正演计算过程分为两步，首先采用有限单元法计算四个不同频率的视复电阻率数据，然后对前一步得到的视复电阻率数据采用递推算法计算视Cole-Cole参数.采用这种正演算法与一维正演的结果进行了对比，验证了本文方法的正确性.设计了两个二维极化模型，数值模拟结果表明视复电阻率和Cole-Cole视参数等值线断面图对于异常目标体都有比较明显的反映.     

1D and 2D Cole-Cole-inversion of time-domain induced-polarization data

A new method for the 2D inversion of induced polarization (IP) data in the time domain has been developed. The entire IP transients were observed and inverted into 2D Cole-Cole earth models, including resistivity, chargeability, relaxation time and the frequency constant. Firstly, a modified 1D time-domain electromagnetic algorithm was used to calculate the response of a layered polarizable ground. The transient signals were then inverted using the Marquardt method to derive the Cole-Cole parameters of each layer. However, model calculations showed that the EM effects could be neglected for the time range (>1 ms) and for the transmitter–receiver distances (<50 m) used in this study. Therefore, the induction effects were not considered for the solution of the 2D inverse problem and a DC solution was applied. An approximative forward algorithm was introduced in order to calculate the IP transients directly in the time domain and in order to speed up the inverse procedure. The approximation is highly accurate, and this is demonstrated by comparing the approximations with their exact solutions up to 3D. The inverse algorithm presented consists of two steps. The transient voltages of an array data set were inverted separately into a two-dimensional resistivity model for each time channel. The time-dependent resistivity of each cell was then interpreted as the response of a homogeneous half-space. In the 2D inversion algorithm, a 3D DC algorithm was used as a forward operator. The method only requires a standard 2D DC inversion and a homogenous half-space Cole-Cole inversion. The developed algorithm has been successfully applied to synthetic data sets and to a field data set obtained from a waste site situated close to Düren in Germany.     

计算视复电阻率的新的近似公式

本文推导并评价了一个新的计算视复电阻率的近似公式,其视振幅表达式为|ρ_s（ω）|≈ρ_s（ω）|_{ρs（ω）=ρs（ω）|},视相位表达式为φ_s（ω）≈sum from i=1 to n（B_i（ω）φ_i（ω））,这里B_i（ω）是按各介质复电阻率振幅计算的稀释系数。此近似公式比迄今为止已发表过的同类近似公式都精确,可在频率域激电法数值模拟计算视复电阻率时应用。     

三维大地电磁激电效应特征研究

在积分方程法的大地电磁三维正演模拟中引入Cole-Cole模型研究激电效应特征,对均匀半空间中存在极化体时的三维大地电磁测深响应进行了理论计算,分析了极化参数的影响规律.结果表明:激电效应使观测视电阻率值变低;地下高阻极化体比低阻极化体的激电效应强,特别是极化率大的高阻极化体对大地电磁响应影响大,使观测结果出现假异常.     

Determination of the Cole-Cole parameters in polarizable media from logging data

The paper presents the solution to an axially symmetric problem of the electromagnetic field excited by an electric dipole and a current in a half-infinite cable in a cylindrically layered polarizable medium. The polarization of the medium is described by the Cole-Cole formula, including such parameters as the conductance, polarizability, response time, and attenuation coefficient. The spatiotemporal structures of the field in polarizable and nonpolarizable homogeneous media are compared. The apparent Cole-Cole parameters are defined and determined for a model problem of a cylindrically layered medium.     

MT激电效应的模拟研究及在油气检测中的应用

本文引入Cole-Cole模型来模拟大地的激发极化效应,对三层水平地层且中间层为极化层的大地电磁测深的视电阻率进行了理论计算,分析了极化参数对视电阻率曲线的影响规律.采用广义逆方法对三层水平地层且中间层为极化层的模型进行了反演研究,结果表明该反演方法能够较好地确定地层电阻率的同时获得地层激电参数,应用于实际资料的反演时,反演结果与已知含油气地层的实际参数十分吻合.     

THE DISPERSION RELATION, OF EARTH''S ELECTROMAGNETIC RESPONSE FUNCTIONS AND THE JOINT INVERSION OF DATA

On the basis of the dispersion relations of MT field, the necessity and applied prospects of the joint inversions using a pair of MT response functions which are correlative with the dispersion relations, are infered. A filter coefficient algorithm is made, with which the corresponding impedance phase data can be estimated using a set of apparent resistivities. The tests for the observed MT data show that when comparing the impedance phase estimated using the dispersion relation with the ob served phase, it can be checked whether the dispersion relation between observed apparent resistivity and phase data is satisfied or not, and that the use of the phase data corrected using the dispersion relation in the joint inversion is advantageous to obtain more confident results. It is shown that joint inversions are more advantageous than single parameter inversions, and that in the most case the joint inversion using the apparent resistivities of impedance real and imaginary parts is more advantageous than the jointinversion using the normal apparent resistivity and impedance phase. The existence of the dipersion relations between the ratio apparent resistivity and corresponding impedance phase of the orthogonal electric and magnetic field horizontal Components in the frequency EM sounding with horizontal electric dipole(FEMS) are discussed, the better effect of the joint inversion using the pair of EM response functions is obtained. The problems on the one-dimensional joint inversion for the MT and FEMS apparent resistivities, for which the observed frequency bands partly overlape each other, are studied. It is shown that this joint inversion is applicable and effective:the joint inversions of the practical data for two kinds of EM methods at two sites give the results well corresponding to the drilling data. The simulated MT inversions for the data of two kinds of EM methods are made, and more confident results also are obtained.     

快速拟线性近似方法及三维频谱激电反演研究

Zhdanov提出的拟线性(QL)近似方法有效解决了积分方程计算速度慢、占用内存多的缺陷,但因为三维频谱激电(SIP)换源频繁,每次换源都需要重新计算剖分单元的并矢格林函数和一次场,所以用该方法模拟三维SIP的速度仍然缓慢.本文根据一次场及格林函数的空间对称性,提出了一种适用于多源电磁法的快速QL近似正演方法.在此基础上,实现了Cole-Cole参数范围约束的三维SIP共轭梯度反演方法.理论试算结果表明:快速QL近似方法适用于三维SIP正演模拟,计算速度较QL近似方法有了很大提高;Cole-Cole参数范围约束的三维SIP共轭梯度反演方法对零频电阻率、极化率等参数的反演效果良好,将异常区域剖分成2000块时迭代一次只需约0.2s的时间,占用内存大约为140 MB.     

频域激发极化法中体极化与面极化内在联系的探讨

矿化的体极化介质,其激发极化效应来自其中所含电子导电矿物颗粒的表面极化效应。基于上述认识,本文从理论上推导出含球状电子导体的体极化介质复电阻率的“微观”数学表达式。将它与体极化介质复电阻率的“宏观”表达式--Cole-Cole模型相比较,得出了:1.Cole-Cole模型中的特征参量与球状电子导体的表面极化系数、含量以及导体半径等的综合关系式;2.电子导体表面极化系数在频域中的一般表达式。这表达式同目前在实验室中观测到的结果是一致的。     

从瞬变电磁响应中提取IP信息的研究(英文)

在对浙江省某铜矿进行瞬变电磁勘查时,由于感应激发极化效应的影响,造成瞬变电磁晚期测道的数据发生倒转。采用常规的瞬变电磁数据处理方法难以处理,造成晚期测道数据不可用,影响TEM的探测深度及精度。针对这个情况,采用Cole.Cole模型分析了均匀半空问模型中直流电阻率、充电率、时间常数以及频率相关系数对磁性源瞬变电磁响应的影响规律。利用奇异值分解法(The Singular Value Decomposition,简称SVD)对实测TEM数据进行分析及反演,并且从瞬变电磁响应数据中分离出勘探区瞬变电磁测量数据Cole—Cole模型的各参数,将分离出来的参数用于探测结果的辅助解释。经过分析得出充电率和频率相关系数对瞬变电磁响应的影响较大,而直流电阻率和时间常数对其影响较小的结论。通过常规方法和奇异值分解法对实测数据分别进行处理,发现后者视电阻率断面图的异常更加突出,从而较准确的圈定了铜矿体地范围,此结论得到_『钻孔的验证,与实际地质情况吻合较好。     

地电阻率多极距观测反演初步研究

地电阻率多极距观测的目的是借助对观测数据的反演获得地下介质中不同层位真电阻率的变化.本文以3层结构为例,对地电阻率多极距观测的一维反演的效果进行了初步地理论研究.首先研究了一维地电阻率结构下观测数据一维反演的模拟效果,得到了各层电阻率值,且与真电阻率值很接近,说明在地下电性结构为一维的情况下,电阻率多极距观测可以区分出不同地层的电阻率变化.其次,考虑到台址下电阻率结构的复杂性,研究了上两层界面存在起伏的情况下,多极距观测数据一维反演的效果,结果显示:当电阻率变化较小时,各层反演得到的电阻率的变化与真电阻率十分符合;当上两层介质的电阻率变化较大时,各层反演得到的电阻率出现畸变,与真实电阻率的变化情况存在一定差别,表明浅层电阻率变化达到一定程度后将会影响对深部电阻率变化情况的正确判断.一般情况下,观测的时间间隔越短,则连续两次观测时段内各层介质的电阻率变化越小,因此缩短多极距观测的时间间隔可能是避免出现上述畸变现象的有效观测手段.      

The magnetotelluric response over 2D media with resistivity frequency dispersion1

We investigate the magnetotelluric response of two-dimensional bodies, characterized by the presence of low-frequency dispersion phenomena of the electrical parameters. The Cole-Cole dispersion model is assumed to represent the frequency dependence of the ‘impedivity’ complex function, defined as the inverse of Stoyer's ‘admittivity’ complex parameter. To simulate real geological situations, we consider three structural models, representing a sedimentary basin, a geothermal system and a magma chamber, assumed to be partially or totally dispersive. From a detailed study of the frequency and space behaviours of the magnetotelluric parameters, taking known non-dispersive results as reference, we outline the main peculiarities of the local distortion effects, caused by the presence of dispersion in the target media. Finally, we discuss the interpretative errors which can be made by neglecting the dispersion phenomena. The apparent dispersion function, which was defined in a previous paper to describe similar effects in the one-dimensional case, is again used as a reliable indicator of location, shape and spatial extent of the dispersive bodies. The general result of this study is a marked improvement in the resolution power of the magnetotelluric method.     

基于Pade逼近的Cole-Cole频散介质GPR有限元正演

针对Cole-Cole频散介质中的复介电常数是jω的分数次幂函数,传统的时域有限元法难以离散及计算时间域分数阶导数,本文采用Pade逼近算法将含有时间分数阶导数的Cole-Cole频散介质电磁波方程推导为一组整数阶辅助微分方程,提出了一种适用于Cole-Cole频散介质的GPR有限元正演模拟算法.在复数伸展坐标系下,通过在频率域Cole-Cole频散介质电磁波方程中引入2个中间变量,并将其变换到时间域,从而以变分形式将PML边界条件加载到Cole-Cole频散介质GPR有限元方程组中,并给出了详细的求解公式.在此基础上,编制了基于Pade逼近的Cole-Cole频散介质GPR有限元正演程序,利用该程序对均匀模型进行计算,并与解析解进行对比,验证了本文构建的GPR有限元正演算法的正确性和有效性.设计了一个复杂Cole-Cole频散介质GPR模型,利用本文构建的GPR有限元正演算法进行模拟并与非频散介质模型的模拟结果进行对比,分析了电磁波在Cole-Cole频散介质中传播衰减增强、子波延伸,分辨率降低等传播规律,有助于实测雷达资料更可靠、更准确的解释.模拟结果表明,基于Pade逼近的GPR有限元正演算法可用于复杂Cole-Cole频散介质结构模拟,且具有较高的计算精度.     

谱激电法中频率相关系数的应用

从电子导体激发极化（过电位）的电化学机理出发,导出了面极化系数的频谱表示式,得出面极化频率相关系数 c^（s）=0.5-1;从理论上证明了利用Cole-Cole模型描述体极化激电频谱的合理性,说明体极化频率相关系数c≤c^（s）.理论算例和实测结果表明,可以利用视频率相关系数在极化围岩背景上划分局部异常体,并按结构（矿物颗粒均匀程度和连通情况）区分引起激电异常的极化体.因此,在谱激电法中应重视这一参数的应用.     

基于电震耦合理论研究电极法储层岩石复电阻率频散特性

复电阻率测井在识别油水层的能力上优于常规电阻率测井,然而储层岩石复电阻率特性的微观机理还没有统一完整的解释和数学模拟方法,致使复电阻率测井技术的开发缺乏足够的理论基础.本文基于孔隙介质Pride电震耦合理论,结合谐变信号激励下渗流场与电流场的耦合理论,推导出一级近似条件下的Pride电震耦合理论.采用格林函数方法建立了一维电震波场的波动方程及其解.构造了双电极法测量储层岩石复电阻率的物理模型和数学模型,从理论上阐明了岩石复电阻率频散特性的微观机制与电震效应的关系,定量分析了储层岩石复电阻率频散特性的影响因素.数学模拟结果表明:储层岩石复电阻率的频散现象是在电震快纵波和电震慢纵波的共同作用下,由孔隙介质中的电渗流机制形成的;储层岩石的复电阻率随孔隙度的增大而减小,随渗透率的增大而增大,地层水矿化度的增加或阳离子交换量的增大使得同频率的复电阻率减小.慢纵波界面极化频率受孔隙度、渗透率和地层弹性模量的影响较大,而快纵波界面极化频率受地层弹性模量的影响较大.     

Effect of clayey media parameters on the negative response of a coincident loop1

The aim of this work is to consider the phenomenon of negative response and its detectability in a polarizable half-space formed of Clay-water mixture which commonly exists in water aquifers and which can be used as a simple indicator of the presence of Underground water. We make use of an analytical treatment for the transient voltage induced in a coincident loop lying on a half-space as a basis for our computations. A Cole-Cole model is used to represent the Clay with appropriate parameters. As saturated Clay is characterized by high conductivity and moderate chargeability, it is hardly detectable relative to the practical noise level. However, there are optimum Clay parameters that offer a maximum negative response. It is also observed that for a very short time constant τ in the Cole-Cole model, the amplitude of the negative response decreases with the decrease of the time constant due to the fast decay of the polarization current. Finally, it is found that there is an optimum value for the loop radius which gives the largest value of the negative response and this loop radius depends on the model parameters.     

The inversion of the data of magnetotelluric sounding and electromagnetic frequency sounding with horizontal electric dipole

On the basis of the dispersion relation of magnetotelluric response functions (MTRF), a filter coefficient algorithm has been made, with which the corresponding impedance phase data can be estimated using a set of apparent resistivity data. The tests of theoretical models and observed magnetotelluric (MT) data show that this algorithm is effective. Comparing the impedance phase estimated using dispersion relation with the observed phase, it can be checked whether the dispersion relation between the observed apparent resistivities and phase data was satisfied. The use of phase data corrected using the dispersion relation in the joint inversion for MT impedance is advantageous to obtain more reliable inversion results. The problems on the one-dimensional joint inversion for the (MT) apparent resistivity and the apparent resistivity of the frequency electromagnetic sounding (FEMS) with horizontal electric dipole, whose observed frequency bands are linked up each other, are studied. The observed data of two kinds of electromagnetic (EM) methods at two sites are used to inverse, the comparison with the drilling data show the results are more reliable. To supply the phase data of FEMS using the dispersion relation, for the apparent resistivity-phase data and impedance real part-imaginary part apparent resistivities of two kinds of EM methods the imitated MT joint inversions are made, and more similar results also are obtained. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,15, 91–96, 1993. The projects sponsored by the Chinese Joint Seismological Science Foundation.     

用梯度和感应测井联合确定地层电阻率各向异性

实际地层可能出现2种电阻率的宏观各向异性:微观的统计平均效应和裂缝走向等因素的构造效应.三分量感应测井方法可能是确定地层电阻率各向异性的最好方法,但是,该仪器目前在中国还没有应用.已有的数据一般是梯度和双感应曲线,梯度和双感应曲线单独使用都难以揭示各向异性,但是,将二者联合使用则有可能.在反演模型中考虑了电阻率各向异性的存在,给出了梯度和双感应曲线联合求地层电阻率各向异性的方法.通过直井水平层的二维人工模型表明,用感应方法可确定地层的水平电阻率和厚度.而梯度方法的视电阻率可以近似看作水平电阻率和纵向电阻率的几何平均值,梯度方法的视厚度是各向异性参数和真实厚度的乘积.因而不能用梯度方法单独确定各向异性参数和真实厚度2个参数中的任何1个.然而,联合梯度和双感应的方法则可能确定3个参数:各向异性参数,水平电阻率和地层厚度.人工数据的例子表明了这种联合的可行性.