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.     

Rapid least-squares inversion of apparent resistivity pseudosections by a quasi-Newton method1

A fast inversion technique for the interpretation of data from resistivity tomography surveys has been developed for operation on a microcomputer. This technique is based on the smoothness-constrained least-squares method and it produces a two-dimensional subsurface model from the apparent resistivity pseudosection. In the first iteration, a homogeneous earth model is used as the starting model for which the apparent resistivity partial derivative values can be calculated analytically. For subsequent iterations, a quasi-Newton method is used to estimate the partial derivatives which reduces the computer time and memory space required by about eight and twelve times, respectively, compared to the conventional least-squares method. Tests with a variety of computer models and data from field surveys show that this technique is insensitive to random noise and converges rapidly. This technique takes about one minute to invert a single data set on an 80486DX microcomputer.     

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.     

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.     

Combined straightforward inversion of resistivity and induced polarization (time-domain) sounding data

It is proposed that the Straightforward Inversion Scheme (SIS) developed by the authors for 1D inversion of resistivity sounding and magneto-telluric sounding data can also be used in similar fashion for time-domain induced polarization sounding data. The necessary formulations based on dynamic dipole theory are presented. It is shown that by using induced polarization potential, measured at the instant when steady state current is switched off, an equation can be developed for apparent ‘chargeability–resistivity’ which is similar to the one for apparent resistivity. The two data sets of apparent resistivity and apparent chargeability–resistivity can be inverted in a combined manner, using SIS for a common uniform thickness layer earth model to estimate the respective subsurface distributions of resistivity and chargeability–resistivity. The quotient of the two profiles will give the sought after chargeability profile. A brief outline of SIS is provided for completeness. Three theoretical models are included to confirm the efficacy of SIS software by inverting only the synthetic resistivity sounding data. Then one synthetic data set based on a geological model and three field data sets (combination of resistivity and IP soundings) from diverse geological and geographical regions are included as validation of the proposal. It is hoped that the proposed scheme would complement the resistivity interpretation with special reference to shaly sand formations.     

Deep geoelectrical models: geological and electromagnetic principles

An important result of recent years is the normal resistivity profile. It was obtained by interpretation of the combined apparent resistivity curve (magnetotelluric sounding and geomagnetic deep sounding) for the East European platform. This profile has no highly conducting layer and resistivity is greater than 100 ohm-m at asthenospheric depths. It corresponds well with geothermal indications of the absence of partial melting beneath the Precambrian plates. Nearly the same profiles have been obtained for the Canadian shield, and the Siberian and Australian platforms. Investigations carried out in many “hot” regions confirm the existence of a well-developed low-resistivity asthenosphere. Partially molten zones have conductances of about several thousand Siemens in the Eastern Pacific, Iceland and in the North American rift zone. Magnetotelluric soundings show that in many continental areas the lower part of the crust has low resistivity, in the range 10–20 ohm-m. Usually this crustal conductive layer is observed in regions of recent activity. Its total conductivity changes from several hundred to several thousand S. Many investigators propose that the most natural explanation of this conductivity is water solutions.It is necessary to note the distorting role of near-surface inhomogeneities. Local distortions can be eliminated by simple averaging of the experimental data. These average apparent resistivity curves are the starting point for the construction of deep geoelectrical models.     

MATRIX METHOD FOR THE TRANSFORMATION OF RESISTIVITY SOUNDING DATA OF ONE ELECTRODE CONFIGURATION TO THAT OF ANOTHER CONFIGURATION1

Matrix equations are derived to transform the resistivity sounding data obtained in one type of a four-electrode array to the corresponding resistivity sounding data that would be obtained using a different four-electrode array. These expressions are based primarily on recent work in which we have established a linear relation between the apparent resistivity and the kernel function by using a powerful exponential approximation for the kernel function. It is shown that the resistivity sounding data of two different four-electrode arrays have a linear relation through an essentially non-singular matrix operator and, as such, one is derivable from the other for a one-dimensional model and it can also be extended to two-dimensions. Some numerical examples considering synthetic data are presented which demonstrates the efficiency of the method in such transformations. Two published field examples are also considered for transformation giving a reliable interpretation.     

One-dimensional magnetotelluric inversion using an adaptation of Zohdy's resistivity method

An iterative refinement method for determining a layered resistivity model from a Schlumberger or Wenner sounding curve is adapted to determine a layered resistivity model by using apparent resistivity and phase derived from the magnetotelluric impedance. Magnetotelluric observations presented as a function of period are first converted to an approximate resistivity–depth profile using Schmucker's transformation and this is used to construct an initial guess (starting) model. A two-stage procedure is then invoked. Keeping resistivities constant, layer boundaries are first adjusted to give a minimum misfit between measured data and responses and this is followed by resistivity adjustments with fixed layer boundaries to reduce the misfit further. The method is illustrated by application to some synthetic data both exact and with added noise, to a real field data set and to some magnetotelluric profile data obtained in a survey over the Carnmenellis granites in south Cornwall. The method is validated by recovering conductivity models from the exact and noisy 1D synthetic data. For complicated three-dimensional data at a single site and along a profile of stations, the method is shown to produce acceptable solutions which may be used as starting models in further two- or three-dimensional studies.     

DEFINITION AND APPLICATION OF THE FREQUENCY -EFFECT TRANSFORM FUNCTION TO THE INTERPRETATION OF IP SOUNDINGS*

This paper deals with a new method of quantitative interpretation of induced polarization soundings in the frequency-domain. From the general expression of the apparent frequency-effect for soundings carried out on a multi-layered earth the application of Hankel's inversion theorem allows to introduce a new function, called here the “frequency-effect transform”. The new interpretation method consists of two steps: 1) the inversion of field data to obtain the frequency-effect transform graph and 2) the analysis of this graph to derive the layering parameters. The first step is performed by means of a slightly revised version of a simple numerical procedure, previously suggested by the author for the inversion of d.c. resistivity sounding data. The second step is carried out by a complete curve-matching procedure, applied directly on the transform graph. This implies suitable master curves, whose preparation doesn't meet all the mathematical difficulties which are present when preparing master curves of the apparent frequency-effect function.     

基于全区视电阻率的线源FCSEM二维正演模拟

频率域可控源电磁是在大地电磁测深的基础上发展起来的一种人工源电磁测深法,其二维电磁响应的计算须采用数值模拟方法.本文以Matlab为程序编译工具,采用双二次插值的有限单元法,推导出相应的计算公式.为了模拟无穷远边界及满足计算机的内存需求,在保证计算精度的情况下设计了非均匀网格剖分.在程序编制中,只存储有限元系数矩阵的非零元素,大大减少了正演计算的时间.针对频率域可控源电磁法中卡尼亚电阻率在过渡区和近区畸变的问题,给出了全区视电阻率的迭代公式,并对典型的一维层状模型以及简单二维模型进行了计算.过渡区和近区数据经过校正后,可以正确反映出模型的地电特征,证明了线源下近区勘探的可能性.     

垂向地电阻率观测装置系数的计算——以江宁地震台为例

井下地电阻率观测装置系数与电流的空间分布及电极位置有关,应针对不同的观测装置进行计算。本文以江苏省江宁地震台垂向观测为例,利用传统垂直观测装置系数方法、全空间及不完全全空间方式计算装置系数,比较不同装置系数对垂向观测的影响。研究结果表明,采用不完全全空间并考虑井距的装置系数计算方法适合江宁地震台垂向观测。     

北京市延庆地震台地电阻率长程观测数据研究

分析北京延庆台1988年以来地电阻率观测资料的可靠性,讨论归一化变化速率方法,用以处理该台地电阻率长程观测数据;结合北京及邻近地区近三十年来发生的7次中强地震,研究该台地电阻率异常与地震的对应关系。结果表明:延庆台地电阻率观测对附近的中等以上地震和远距离大震有一定的映震能力,可为今后该台附近及邻近地区的地震提供中、短期预测预报参考依据;同时该台在中国大陆及周边远距离大震前也观测到了时间上对应的地电阻率异常。     

江宁台多孔垂向地电阻率观测试验

为了提高地电阻率观测抑制地铁干扰的能力, 江宁台新建了多孔垂向地电阻率观测。 在观测中探讨完善了装置系数计算方法, 解决了缺数问题, 并通过比较同测区井下和垂向地电阻率观测数据, 得出如下结论: ① 垂向观测由于布极方式较为特殊, 其年变化幅度大于井下地电阻率观测同等极距; ② 与井下地电阻率观测相比, 垂向地电阻率观测信噪比更高, 具备更好的抗地铁干扰能力, 以期为地电观测抗干扰的方法和技术应用提供基础; ③ 垂向地电阻率观测建设中, 可能需要重视电极的位置固定。     

STUDYING THE INTERCONNECTION OF GROUND AND SURFACE WATERS IN REPRESENTATIVE BASINS UNDER THE PROGRAMME OF THE INTERNATIONAL HYDROLOGICAL DECADE

Abstract

Four geoelectrical soundings were measured with a combination of Schlumberger and azimuthal or equatorial dipole electrode arrays on a Carboniferous limestone basin of the Condroz area, Belgium. The measuring technique is briefly outlined as well as the interpretation procedure, which follows a closed-loop scheme with control of calculated model curves. Some general problems of interpretation of geoelectrical sounding curves are tackled, as far as they have a practical bearing on the treatment of Condroz soundings.

The problem of determining the very high resistivity of limestone is approached through ARCHIE's formula, an empirical relation between the bulk rock resistivity, the porosity and the electrolyte resistivity. An evaluation of the latter two parameters, combined with electrical horizontal conductance measurements directly made on resistivity sounding curves, offers a possibility for fast determination of the total water storage in a limestone aquifer. Such storage determinations could be applied whenever an aquifer shows up as a conductive layer interbedded between two highly resistant layers (e.g. nonsaturated limestone and compact, non-fractured limestone).     

A FAST METHOD FOR DETERMINING THE LAYER DISTRIBUTION FROM THE RAISED KERNEL FUNCTION IN GEOELEGTRICAL SOUNDING*

In a previous publication (Koefoed 1968) a function called the “raised kernel function” has been introduced as an intermediate function in the interpretation of resistivity sounding data, and methods have been described both for the determination of the raised kernel function from the apparent resistivity function, and for the determination of the layer distribution from the raised kernel function. In the present paper a procedure is described by which the second step in this interpretation method–i.e. the determination of the layer distribution from the raised kernel function–is considerably accelerated. This gain in interpretation speed is attained by the use of a standard graph for a function which defines the reduction of the raised kernel function to a lower boundary plane.     

EFFECT OF VERTICAL CONTACT ON WENNER RESISTIVITY SOUNDINGS*

The allowance for the influence of a vertical contact is evaluated on Wenner resistivity sounding curves, which are graphically constructed on bilogarithmic paper over simple composite earth models consisting of a vertical contact separating two- or three layered earth on one side and a homogeneous medium on the other side. The error incurred in the graphical constructions is explored. Finally, the use of these graphically constructed sounding curves is shown in the interpretation of two Wenner field soundings measured in a complex geologic area.     

ESTIMATION OF TEMPORAL CHANGES IN SOIL MOISTURE USING RESISTIVITY METHOD

The temporal variation in a soil moisture profile can be studied using resistivity sounding data acquired at different times. The layered earth model based estimation of soil moisture from apparent resistivity data is a two-step non-linear inversion. Firstly, the apparent resistivity data are inverted to derive the layer resistivity variations and thicknesses and, secondly, the moisture content is estimated from these layer resistivity variations using a calibration equation. The soil moisture–resistivity problem was studied using the one-dimensional formulation of resistivity problem. A generalized geoelectric earth model was considered to simulate the soil moisture distribution and its temporal variation in the unsaturated zone. An algorithm (RESMOS) for the interpretation of the apparent resistivity data in terms of soil moisture variations through this two-step inversion process is reported.     

DC resistivity methods for determining resistivity in the earth's crust

The use of Schlumberger and dipole arrays for crustal-scale resistivity soundings is considered. Advantages and disadvantages of the two methods are described. The depth to which resistivity may be determined from field measurements is discussed as well as the determination from the sounding curves of various parameters associated with layered structure. The interpretation of experimental data using reference curves as well as two approaches used in computer assisted interpretation are discussed.     

INTERPRETATION OF RESISTIVITY MEASUREMENTS OVER 2D STRUCTURES1

Resistivity measurements were carried out in a survey area in the south of Germany. This area is characterized by complicated subsurface geology. Schlumberger full-arrays and their respective half-arrays were recorded simultaneously. The results obtained by the one-dimensional (1D) interpretation of the full-array measurements were incorrect because of a resistivity discontinuity. This discontinuity, under a relatively thick overburden, could only be located by the half-array soundings. Its exact location and the resistivity distribution in the subsurface were ascertained by comparing the sounding curves with 2D model curves, which are calculated by a finite-difference method.     

A contribution to the self-potential method

To date, the interpretation of the self-potential anomalies, caused by the polarized spherical ore bodies, has usually been carried out based on the special graph along the profile passing through the extremes of these anomalies. This special graph could be identified only if we have at hand a map of self-potential distribution for which many profiles should be measured needing many man powers and time. To overcome this situation, in actual paper a new method of interpretation for the above mentioned self-potential anomalies is proposed for which sufficiency is provided by only two self-potential graphs along two parallel ordinary profiles oriented fortuitously.The theoretical basis of this new method of interpretation, together with several nomograms making comfortably its use as well as some testing results, were given.Until May 1986, Inst. of Hydrogeology and Eng. Geology, Warsaw University, 02-089 Warsaw, Poland.