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.     

一种利用频谱激电数据实部和虚部加权反演Cole-Cole模型参数的方法

频谱激电法(SIP)因具有多参数(Cole-Cole参数)解释异常的能力,一直受到电法工作者的关注.一些学者提出了用电场振幅和相位反演Cole-Cole参数的方法,但由于电场振幅和相位对不同Cole-Cole参数的敏感程度不同,往往导致有些Cole-Cole参数较难反演,特别是频率相关系数和时间常数.本文提出了利用视复电阻率的实部和虚部加权反演的方法.该方法采用视复电阻率实部和虚部联合反演的策略,并在反演不同Cole-Cole参数时对实部和虚部的目标函数进行不同的加权.模型试算结果表明:这种反演方法不仅可以很好的反演零频电阻率和极化率,还可以显著提高频率相关系数和时间常数的反演效果.     

2.5维可控源音频大地电磁法Occam反演理论及应用

Occam反演是一种正则化的光滑模型反演方法,它在寻找最小拟合差的同时追求最光滑模型.因地下介质的电性通常是连续变化的,Occam反演考虑了地下介质横向和纵向的光滑情况,应用Occam反演避免了模型电性参数被随意间断.通过建立层状和存在两个异常体的模型,利用2.5维可控源音频大地电磁有限元法作正演响应计算,对响应数据基...     

时间域航空电磁法激电信息提取研究

时间域航空电磁晚期道数据中常出现符号反转现象,该现象被证明是由激电效应引起.鉴于利用传统实电阻率模型的成像和反演技术处理该类数据无法得到正确的反演结果,本文提出基于Occam理论的反演方法,对层状模型电阻率和充电率参数进行同时反演.本文首先通过正演模拟极化介质中电流密度的分布情况,对时间域航空电磁信号出现多次符号反转现象做出合理解释;然后通过链式法则和波形褶积技术计算Cole-Cole模型参数灵敏度,进而探讨不同Cole-Cole模型参数灵敏度差异及其对反演结果的影响.为了提高多参数反演的稳定性和准确性,在反演过程中对参数采取上下限约束,最后对B_z、dB_z/dt响应单独反演结果和联合反演结果进行对比和分析,发现联合反演可以有效地降低反演结果的多解性.     

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.     

二维激电中梯数据磁类比拟合反演研究

本文通过柯尔-柯尔模型研究地下不同几何参数的极化椭球体在地表的中梯双频激电响应,从而了解不同产状极化体产生极化率的特征,便于后期交互建模。由理论推导可知,任何具有激发极化特征的地质体在地表产生的激电异常都可近似为一个地下电偶极子的三维空间积分,这个积分形式与磁场正演计算公式一致,这意味着我们可以用解释磁法异常的方法解释激电异常,即磁类比法。只要根据先验信息实时改变模型,使激电正演得到的曲线与实测激电曲线逼近,当拟合差小于均方误差时,我们将最后一次模型近似看作是真实模型,由此获得地下极化体的顶埋深、倾角和几何大小等空间参数。实测数据测试表明,这种磁类比人机交互方法加入矿体的一些已知信息后,其拟合反演结果比自动反演更具合理性。      

基于Cole-Cole模型的中间极化水平层大地电磁IP效应研究

利用Cole-Cole模型的复电阻率公式表征的介质激电效应,对一维层状介质O型、H型、A型、K型和Q型地电断面中间极化的大地电磁模型进行了正演计算.利用视电阻率比值和相位比值参数来表征IP效应,详细讨论了各地电类型的激发极化效应.对大地电磁场激发极化效应与极化体厚度和埋深的关系进行了讨论.     

基于富有机质页岩复电阻率的几种导电模型的探讨

利用SI-1260阻抗分析仪在室温常压下对南方页岩气探区中某井多块富总有机碳(TOC)含量的饱和页岩岩芯进行多次复电阻率扫频测量,最终选择一组数据分别使用单Cole-Cole、双ColeCole、Cole-Cole乘Brown以及Dias模型对其复电阻率幅值以及相位进行频谱参数联合反演。反演结果表明双Cole-Cole和Cole-Cole乘Brown模型相对于其他模型具有较小拟合误差,能够很好地描述页岩岩芯的复电阻率以及相位曲线,且能从反演结果中较准确地得到各频谱参数。测试与分析结果表明高TOC的页岩岩样的宽频复电阻率参数表现为低频时的高极化率异常,总结出高TOC页岩储层具有低电阻率、高极化率的异常特征。其对使用时频电磁勘探技术和频谱激电法寻找富总有机碳含量的优质页岩储层以及页岩储层复电阻率测井方法的实现都具有重要的指导与借鉴意义。     

SOTEM多分量激电响应特性分析

电性源短偏移距瞬变电磁法(SOTEM)具有探测深度大、分辨率高、施工方便等特点,在第二深度空间(500～2000 m)金属矿勘探中发挥了重要作用.实际测量中,当遇到具有激发极化效应的岩矿石时,SOTEM观测曲线会出现畸变和负值响应(符号反转)的现象.SOTEM激电效应的研究对金属矿勘探具有重要意义,为此,本文对SOTEM多分量激电响应特性进行分析.通过基于Cole-Cole模型的SOTEM一维正演计算,分析了不同装置参数(收发距,极化体埋深)和极化参数(极化体电阻率、极化率,频率相关系数以及时间常数)对常用的E_x、H_z和dH_z/dt电磁场的影响规律,研究结果表明水平电场分量受激电效应的影响最大,垂直磁场分量和垂直磁场分量的时间导数受到的影响要小得多,研究结果将有助于指导野外实际生产.     

含激电效应的航空瞬变电磁数据横向约束反演

受激电效应影响,航空瞬变电磁响应曲线经常出现异常快速衰减和符号反转现象,使用Cole-Cole模型的等效电阻率代替原模型实电阻率能很好的解释该现象,但由于激电多个参数的引入,使得反演多解性问题更加严重.本文基于Cole-Cole模型实现了航空瞬变电磁一维正演,采用横向约束反演同时计算激电参数及层厚,增加约束条件改善多解...     

THE COMPLEX RESISTIVITY SPECTRA OF MODELS CONSISTING OF TWO POLARIZABLE MEDIA OF DIFFERENT INTRINSIC PROPERTIES*

Theoretical model study shows that when an earth model is composed of two (Cole-Cole) polarizable media, its normalized complex resistivity spectrum is approximately a multiplicative combination of the contributions of the two media. This also applies on inversion, but the two dispersions thus obtained are apparent rather than intrinsic dispersions. In models consisting of two media, either a multiplicative or an additive combination of Cole-Cole functions fits the complex apparent resistivity spectrum. On inversion each combination gives similar parameters except for the apparent chargeability of the component with the shorter time constant. However, this can be compensated simply. In this sense the two representations are almost equivalent. We show that the apparent spectrum due to a finite polarizable body is actually a true Cole-Cole dispersion, as is usually assumed in practice. The behavior of a complex apparent resistivity spectrum and its corresponding apparent Cole-Cole dispersion parameters is influenced by the variation of the dilution factor with frequency. Hence when estimating intrinsic parameters from the nomogram, based on constant (frequency-independent) dilution factors, particular care is required to correctly relate apparent parameters to intrinsic parameters.     

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.     

基于交叉梯度约束的时间域激发极化法二维同步反演

时间域激发极化法(Time-domain induced polarization method,简称为TDIP)已有的反演算法采用的是分步反演的思路,即先由视电阻率资料反演电阻率,固定电阻率再由视极化率资料反演极化率,这样就存在极化率结果严重依赖于电阻率反演结果的问题.为了有效解决这一问题,本文实现了TDIP二维数据空间分步反演算法,提出了基于交叉梯度约束的TDIP二维同步反演策略,实现了交叉梯度约束的电阻率和极化率二维同步反演算法.分别用电阻率和极化率结构一致和不一致的二维模型合成数据进行了分步和同步反演试算,对不同模型试算结果进行了对比分析.结果表明:对于电阻率和极化率结构一致和不一致模型,同步反演结果比分步反演结果能更好地确定异常体的空间分布范围,反演得到的电阻率和极化率值更接近真值.理论模型算例表明本文提出的同步反演算法有效解决了分步反演的问题,优于分步反演算法,具有更好的实用性.     

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.     

Two-dimensional inversion of spectral induced polarization data using MPI parallel algorithm in data space

Traditional two-dimensional (2D) complex resistivity forward modeling is based on Poisson’s equation but spectral induced polarization (SIP) data are the coproducts of the induced polarization (IP) and the electromagnetic induction (EMI) effects. This is especially true under high frequencies, where the EMI effect can exceed the IP effect. 2D inversion that only considers the IP effect reduces the reliability of the inversion data. In this paper, we derive differential equations using Maxwell’s equations. With the introduction of the Cole–Cole model, we use the finite-element method to conduct 2D SIP forward modeling that considers the EMI and IP effects simultaneously. The data-space Occam method, in which different constraints to the model smoothness and parametric boundaries are introduced, is then used to simultaneously obtain the four parameters of the Cole—Cole model using multi-array electric field data. This approach not only improves the stability of the inversion but also significantly reduces the solution ambiguity. To improve the computational efficiency, message passing interface programming was used to accelerate the 2D SIP forward modeling and inversion. Synthetic datasets were tested using both serial and parallel algorithms, and the tests suggest that the proposed parallel algorithm is robust and efficient.     

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.     

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.     

Parameter optimization of gravity density inversion based on correlation searching and the golden section algorithm

For density inversion of gravity anomaly data, once the inversion method is determined, the main factors affecting the inversion result are the inversion parameters and subdivision scheme. A set of reasonable inversion parameters and subdivision scheme can, not only improve the inversion process efficiency, but also ensure inversion result accuracy. The gravity inversion method based on correlation searching and the golden section algorithm is an effective potential field inversion method. It can be used to invert 2D and 3D physical properties with potential data observed on flat or rough surfaces. In this paper, we introduce in detail the density inversion principles based on correlation searching and the golden section algorithm. Considering that the gold section algorithm is not globally optimized, we present a heuristic method to ensure the inversion result is globally optimized. With a series of model tests, we systematically compare and analyze the inversion result efficiency and accuracy with different parameters. Based on the model test results, we conclude the selection principles for each inversion parameter with which the inversion accuracy can be obviously improved.