NUMERICAL MODELLING OF STANDARD AND CONTINUOUS VERTICAL ELECTRICAL SOUNDINGS1

Analytical solutions of vertical electrical soundings (VES) have mostly been applied to groundwater exploration and monitoring groundwater quality on terrains of fairly simple geology and geomorphology on which the electrode arrays are symmetrical (e.g. Schlumberger or Wenner configurations). The sounding interpretation assumes flat topography and horizontally stratified layers. Any deviations from these simple situations may be impossible to interpret analytically. The recently developed GEA-58 geoelectrical instrument can make continuous soundings along a profile with any colinear electrode configuration. This paper describes the use of finite-difference and finite-element methods to model complex earth resistivity distributions in 2D, in order to calculate apparent resistivity responses to any colinear current electrode distribution in terrains in which the earth resistivities do not vary along the strike. The numerical model results for simple situations are compared with the analytical solutions. In addition, a pseudo-depth section of apparent resistivities measured in the field with the GEA-58 is compared with the numerical solution of a real complex resistivity distribution along a cross-section. The model results show excellent agreement with the corresponding analytical and experimental data.     

电位双二次变化二维地电断面电阻率测深有限元数值模拟

以异常电位为研究对象,给出了一种新的二维地电断面电阻率测深的有限元数值模拟方法.该方法与以往这类方法的主要区别在于,网格单元中的电导率采用双线性插值,电位则用二次函数进行双二次插值,从而使得电位的正演结果以及由电位导出的视电阻率更加符合实际地电场的变化规律;另外,有限元网格单元数也大为减少.对几例模型的试算结果表明,文中提出的计算方法是行之有效的.     

用正向供电技术提高视电阻率观测精度

定量地实验研究了在采用不同观测方法相同干扰对视电阻率测量的影响。结果表明，采用正反向供电方法可大幅度提高视电阻率的观测测精度。同时还在ＺＤ８地电仪上实现了这种观测方法，试验结果与理论推算值基本相符。     

起伏地形条件下层状介质的视电阻率计算及其在地电前兆分析中的应用

本文以二维层状介质模型为基础利用边界单元法,对地形起伏所引起的视电阻率变化进行了数值模拟,探讨了水平层状介质表层存在不规则地形条件下地电阻率的理论计算方法,并讨论了地形对地电前兆复杂性的影响。结果表明,起伏较大的地形变化对视电阻率相对变化量中的深层电阻率变化有减小作用,这就降低了地电观测资料中包含的深层电性信息的比例,因而对突出地电观测资料中孕震变化的成份是不利的。     

二维各向异性地电断面大地电磁场的有限元法解法

假定各向异性主轴之一与层面垂直,另一主轴与构造走向平行,本文给出这种条件下,二维各向异性地电断面的大地电磁场的变分方程。用有限单元法解变分方程。对区域进行三角单元剖分,在单元内进行二次函数插值,将变分方程转变为线性代数方程组。解方程组得各节点的场值,并可计算场的导数。由这些值可计算地表的视电阻率。 算例表明,对于H_x型波(x平行构造走向),各向异性体与各向同性体的大地电磁场有很大区别。      

THE INTERPRETATION OF THE VERTICAL FAULT PROBLEM IN GEOELECTRICS USING HANKEL INTEGRAL*

It is shown how to interpret, without curve-matching, Schlumberger resistivity soundings carried out with the array parallel to the surface trace of a vertical boundary plane separating two media with different resistivities (the vertical fault problem). To this end, it is demonstrated that the apparent resistivity function can be expressed as an Hankel-transformable integral that allows to invert the apparent resistivity curve into an associated resistivity transform curve. The study of the asymptotical properties of this function and of some mathematical properties of a related reduced transform function allows to realize a simple procedure for deriving the parameters of the model. In practice, this procedure consists in fitting a straight-line to a semi-logarithmic plot of the reduced transform function and in evaluating the intercept along the vertical axis and the slope.     

THE APPLICATION OF LINEAR FILTER THEORY TO THE DIRECT INTERPRETATION OF GEOELECTRICAL RESISTIVITY SOUNDING MEASUREMENTS*

Koefoed has given practical procedures of obtaining the layer parameters directly from the apparent resistivity sounding measurements by using the raised kernel function H(λ) as the intermediate step. However, it is felt that the first step of his method—namely the derivation of the H curve from the apparent resistivity curve—is relatively lengthy. In this paper a method is proposed of determining the resistivity transform T(λ), a function directly related to H(λ), from the resistivity field curve. It is shown that the apparent resistivity and the resistivity transform functions are linearily related to each other such that the principle of linear electric filter theory could be applied to obtain the latter from the former. Separate sets of filter coefficients have been worked out for the Schlumberger and the Wenner form of field procedures. The practical process of deriving the T curve simply amounts to running a weighted average of the sampled apparent resistivity field data with the pre-determined coefficients. The whole process could be graphically performed within an quarter of an hour with an accuracy of about 2%.     

二维层状介质点电源边界单元解

本文用付氏变换将点源二维地电断面的三维边值问题变成二维边值问题,然后讨论了边界元法在解决层状介质中存在二维柱体时点源场视电阻率计算问题中的应用。由于选取的基本解避免了对水平层状界面的积分计算,从而大大减少了边界剖分节点数。在计算中设法略去了对边界上位场法向导数的求解,使未知量大为减少,从而便利了求解二维边值问题,并由付氏反变换求得三维空间中的位。本方法所需计算机内存少,原始数据的输入简单,且有较高的计算精度。     

Real-Time Geoelectric Monitoring of Seepage into Sand and Clay Layer

The migration of groundwater in rock and soil can appear as abnormalities in geoelectric fields. It is therefore important to study the characteristics of seepage in porous media by measuring the geoelectric field signatures. In this study, a physical model with layers of sand and clay was constructed and an electrical resistivity meter was used to examine the changes in the geoelectric field parameters during the infiltration process. The results show that the infiltration could be detected based on the geoelectric signatures including temporal changes through the spontaneous potential, excitation currents, and apparent resistivity. Specifically, the spontaneous potential was reduced by 100 to 200 mV when the water reaches an electrode. During the second water injection in the experiment, the measured spontaneous potential of all the electrodes recovered to the previous extreme values that range from −200 to −550 mV, thus indicating a “memory” effect. With stepwise changes in the excitation current, it was possible to determine the seepage velocity in sand and clay layer. The apparent resistivity is reduced to less than 400 Ωm when the infiltration reaches the electrodes. These results indicate the potential for real-time monitoring of water flow.     

含激电效应的CSAMT一维正演研究

地电体对频率域电磁波激发源的响应为电磁感应和激电效应的综合响应.传统CSAMT法进行数据正反演时认为大地介质电阻率是与频率无关的实数,而实际上因为激电效应,地下可极化体的电阻率是一个与频率相关的复数.为推进二者总体响应研究,并扩展激电法的应用范围,同时提高电磁法勘探的精度,本文基于Dias模型,以复电阻率代替不考虑地电体极化效应的直流电阻率,对CSAMT场源一维层状模型进行了正演模拟,为提取CSAMT信号中所含激电信息提供理论基础.结果表明,考虑激电参数后,视电阻率及相位响应曲线出现明显异常（包括远场、过渡场、近场）;极化前后振幅比值异常峰值、相位差值异常峰值可直观体现激电异常;异常峰值与极化层层厚、埋深以及电阻率变化有连续的对应关系.认为从频率域电磁法信号中提取激电信息有乐观的前景.     

A NUMERICAL METHOD OF CALCULATING THE KERNEL FUNCTION FROM SCHLUMBERGER APPARENT RESISTIVITY DATA*

A method to calculate the resistivity transform of Schlumberger VES curves has been developed. It consists in approximating the field apparent resistivity data by utilizing a linear combination of simple functions, which must satisfy the following requirements: (i) they must be suitable for fitting the resistivity data; (ii) once the fitting function has been obtained they allow the kernel to be determined in an analytic way. The fitting operation is carried out by the least mean squares method, which also accomplishes a useful smoothing of the field curve (and therefore a partial noise filtering). It gives the possibility of assigning different weights to the apparent resistivity values to be approximated according to their different reliability. For several examples (theoretical resistivity curves in order to estimate the precision of the method and with field data to verify the practicality) yield good results with short execution time independent of shape the apparent resistivity curve.     

GEOELECTRIC DETERMINATION OF QUALITY CHANGES AND TECTONIC DISTURBANCES IN COAL DEPOSITS*

A new underground geoelectric method is presented for the determination of small tectonic disturbances and barrenings in coal seams. The distribution of the apparent resistivity can be mapped from the measured apparent resistance data by using a recently developed geoelectric imaging method. The applicability of the methods are proved by in situ measurements and by a model experiment.     

Results of the monitoring of geomagnetic field variations in the Kamchatka region

The transfer function between the vertical and horizontal components of geomagnetic field variations is studied and the frequency responses of its parameters are presented. The relation to geoelectric heterogeneities of the medium is analyzed. The coast effect is considered and a deep curve of the apparent electrical resistivity constructed on its basis is used for estimating the depth to the asthenospheric conducting layer. The behavior of the induction vectors in the frequency-time domain is studied. Specific features of the behavior of the real and imaginary parts of the induction vector related to geoelectric heterogeneities of the medium are determined. Monitoring results are compared with time moments of earthquakes of K = 13?14 at epicentral distances of up to 150 km.     

甘肃张掖MS5.0地震前山丹地电异常探讨

2019年9月16日在甘肃省张掖市甘州区发生M_S5.0地震,震前山丹地电阻率和地电场观测资料出现了较为明显的短临异常,震中距63 km。本文对该异常进行分析总结,排除周围观测环境,观测系统,自然环境,磁暴等因素外,认为该异常是较为可信的地震前兆异常。地电阻率观测资料异常形态NS测道表现为转折快速上升-缓慢下降,EW测道为转折缓慢上升,N45°W测道为缓慢下降-转折缓慢上升。地电场观测资料异常形态长极距NS道、长极距N45°E道、短极距NS道表现为转折同步缓慢上升,长极距EW道和短极距EW道转折同步缓慢下降,短极距N45°E道异常不明显。地震在异常持续过程中出现转折变化或上升(下降)速率发生改变时发生。     

Monitoring of relative changes in the electrical conductivity of rocks from observations of the magnetotelluric apparent resistivity (numerical modeling)

A method for direct conversion of observed variations in the magnetotelluric (MT) apparent resistivity ρ_a into relative variations in the resistivity of elements of a well-studied geoelectric structure is proposed. The method is tested on a 1-D model structure consisting of seven horizontal layers in three of which the conductivity can vary within certain limits. It is inferred that the frequency range and the accuracy of methods of magnetotelluric sounding presently applied to the construction of transfer operators are sufficient for determining relative changes in the resistivity of rocks; the latter, as distinct from ρ_a, can serve as an effective prognostic parameter. The method can be extended to more complex geoelectric structures.     

小波方法在地电场干扰处理中的分析研究

该文在对地电场信号及地电阻率人工供电干扰信号的时频特征进行分析的基础上, 提出了小波域阈值滤波方法, 对地电场秒采样信号中叠加地电阻率人工供电干扰信号进行了分析和处理, 处理产生的误差在地电场观测的允许误差范围之内。     

Method for Constructing a Model of a Geoelectric Section Taking into Account Seasonal Variations Based on Data from Long-Term Vertical Electric Sounding Monitoring in Search of Earthquake Precursors

The study analyzes data from high-precision measurements of the apparent resistivity by a stationary multielectrode vertical electric sounding (VES) system including 12 current and 4 potential lines spaced 2–650 m apart. Observations had been being carried out at the Garm test area on a daily basis for 12 years in an earthquake prediction experiment. The use of special technical methods during measurements ensured an instrumental error of about 0.01%. The virtual error of each individual measurement of apparent resistivity (taking into account all possible noise) was 0.1–0.2%. The availability of more than 3000 VES curves measured in different seasons allows us to propose a new approach to constructing a geoelectric section model. To solve the inverse VES problem, a set of 36 averaged 10-day VES curves was analyzed, each of which was obtained by averaging approximately 100 individual VES curves accumulated in the same 10-day period of the annual (seasonal) cycle in different years. Comparative analysis of these curves made it possible to calculate and include corrections for stationary geological noise in the model. As a result, it was possible to substantially reduce (by an order of magnitude) the discrepancies in fitting the curves and dramatically narrow the equivalence domain. Based on the results of our analysis, we have constructed a model of a four-layer horizontally layered geoelectric section of the Khazor-Chashma depression to adequately describe not only the averaged section, but also its seasonal variations throughout the year. The stability in estimating the model parameters is studied. To further reduce the equivalence domain, we propose that the layer thicknesses be fixed. This model can be used not only to study the aforementioned characteristics of the section, but also to monitor time variations of resistivity in individual layers of the section. This will significantly improve the resolving power of systems for detecting time variations in geoelectric sections, including when searching for earthquake precursors.     

A new method for geoelectrical investigations underwater1

A new electrical method is proposed for determining the apparent resistivity of multi-earth layers located underwater. The method is based on direct current geoelectric sounding principles. A layered earth model is used to simulate the stratigraphic target. The measurement array is of pole-pole type; it is located underwater and is orientated vertically. This particular electrode configuration is very useful when conventional electrical methods cannot be used, especially if the water depth becomes very important. The calculated apparent resistivity shows a substantial quality increase in the measured signal caused by the underwater targets, from which little or no response is measured using conventional surface electrode methods. In practice, however, different factors such as water stratification, underwater streams or meteorological conditions complicate the interpretation of the field results. A case study is presented, where field surveys carried out on Lake Geneva were interpreted using the calculated apparent resistivity master-curves.     

Automated 1D interpretation of resistivity soundings by simultaneous use of the direct and iterative methods*

Noise contamination of measured data greatly affects the final results of inversion. Three types of noise source — random and systematic errors and the uncertainties due to the inadequacy of the mathematical model in representing the actual physical conditions — are discussed in the framework of resistivity sounding data. Two methods are proposed for describing these uncertainties. The first possibility is to smooth the measured data by a combination of simple fitting functions that satisfies the ‘1D smoothness’ criteria and consequently simulates the behaviour of a 1D Schlumberger apparent resistivity curve. The second method is to derive weight coefficients from the differences between the measured and the smoothed data sets. Both methods are carried out under the control of the interpreter. The relative merits and drawbacks of the direct and iterative interpretation methods used for the estimation of the parameters of the layered earth model are summarized. Two variants of the combination of these methods are presented to obtain more powerful and automatic interpretation schemes. In the sequential interpretation, an initial guess supplied by the direct method is improved by the iterative method to obtain a reasonable fit between the measured data and the model response. In the simultaneous interpretation, the successive application of the direct and iterative methods is carried out, starting from the first branch of the apparent resistivity curve. The operation is then shifted to subsequent branches that represent the deeper parts of the geoelectric section. This is similar to the data acquisition applied in direct current sounding in which the depth penetration is increased by expanding the current electrode spacings. The proposed sequential and simultaneous interpretation algorithms require minimum aids and efforts of the interpreter.     

地电场观测过程中的干扰因素分析

本文主要利用榆树地震台2000年以来的地电场资料,对观测中常见的干扰因素进行了详细的识别与归类。研究结果表明：在地电场观测过程中存在地电阻率同场观测干扰、雷电干扰、地电暴干扰、电极长期稳定性问题引起的数据漂移及数据传输错误等。