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.     

3D resistivity inversion using 2D measurements of the electric field

Field and 'noisy' synthetic measurements of electric-field components have been inverted into 3D resistivities by smoothness-constrained inversion. Values of electrical field can incorporate changes in polarity of the measured potential differences seen when 2D electrode arrays are used with heterogeneous 'geology', without utilizing negative apparent resistivities or singular geometrical factors. Using both the X - and Y -components of the electric field as measurements resulted in faster convergence of the smoothness-constrained inversion compared with using one component alone. Geological structure and resistivity were reconstructed as well as, or better than, comparable published examples based on traditional measurement types. A 2D electrode grid (20 × 10), incorporating 12 current-source electrodes, was used for both the practical and numerical experiments; this resulted in 366 measurements being made for each current-electrode configuration. Consequently, when using this array for practical field surveys, 366 measurements could be acquired simultaneously, making the upper limit on the speed of acquisition an order of magnitude faster than a comparable conventional pole–dipole survey. Other practical advantages accrue from the closely spaced potential dipoles being insensitive to common-mode noise (e.g. telluric) and only 7% of the electrodes (i.e. those used as current sources) being susceptible to recently reported electrode charge-up effects.     

Definitions of apparent resistivity for the presentation of magnetotelluric sounding data1

A new definition of apparent resistivity for the presentation of magnetotelluric sounding data is proposed. The new definition is based on the frequency-normalized impedance function. Both the existing and proposed definitions of apparent resistivity are analysed theoretically and are compared using model curves computed for a 1D earth model. Apparent resistivity curves computed using the proposed definition are a better approximation to the true resistivity values of the subsurface layers. In addition, the layers are more noticeable on the apparent resistivity curves, which is an advantage, especially for the ascending and descending type of apparent resistivity curve.     

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.     

考虑电流型畸变的大地电磁三维反演

大地电磁测深(MT)的观测数据易受到由近地表小尺度非均匀体或地形起伏引起的电流型畸变干扰,消除或压制这种干扰对获取可靠的深部电性结构至关重要.当区域结构为二维时,电流型畸变可采用张量分解等方法予以消除或压制.当区域结构为三维时,畸变问题更加复杂和严重,传统张量分解方法往往效果不佳或无效,严重地制约了MT三维反演技术的实用性.对此,本文提出一种考虑电流型畸变的MT三维反演算法,将完整的电流型畸变参数引入到目标函数,并采用非线性共轭梯度法与电阻率参数同时反演,从而达到压制畸变的目的.该算法有两个关键点:一是通过分析实测数据所遭受畸变的分布特征,在目标函数中对其进行有效约束;二是在迭代过程中,通过自适应地调整双正则化因子保障算法的稳定和效率.理论模型测试结果显示,常规三维反演算法不能合理解释数据中的畸变成分,而只能通过引入虚假异常体强制地拟合受畸变数据,从而造成电阻率模型严重失真.与之相比,本文算法能够在反演中自动求解各测点所受到的畸变,获得更接近真实的电阻率模型.     

Estimation of clay content in soil based on resistivity modelling and laboratory measurements

The determination of clay content in near‐surface formations is crucial for geotechnical, hydrogeological and oil‐contamination studies. We have developed a technique for estimating clay content that consists of the minimization of the difference between the theoretically calculated and measured soil resistivities as a function of water salinity. To calculate the resistivity, we used a model that takes into account the electrochemical processes in the clay micropores. The experimental measurements of soil resistivity were performed on soil samples, completely saturated by brines at different concentrations of NaCl salt in the range 0.6–100 g/l, to obtain the resistivity versus salinity curve. The parameters obtained with this curve inversion are the clay content, the total porosity and the cation exchange capacity. To verify the new technique, we determined clay concentrations of artificial mixtures of calibrated sand and clay. The relative mean error in the clay content does not exceed 20% for a 5% fitting error of the resistivity versus salinity curves. Such evaluations allow the correct separation of the main lithological groups (sand, sandy loam, loam, and light, medium and heavy clay). We applied this technique to estimate the petrophysical parameters of soils (clay content, porosity and cation exchange capacity) at various sites in Mexico. The results improved the interpretation of the vertical electrical soundings, the lithological soil characterization and the delineation of oil‐contaminated areas.     

基于印模法的地面磁电阻率数据三维非线性共轭梯度反演

本文提出了能提高异常体分辨能力,同时得到绝对电导率的地面磁电阻率数据三维反演方法.磁电阻率响应用准直流的低频磁场代替;数值模拟由频率域电场满足的Helmholtz方程出发,采用三维交错网格有限差分法;长直导线源作为发射源,其中源的计算包含在背景场中;结合地面磁电阻率数据各分量的特点,选择y分量进行反演研究;反演采用三维非线性共轭梯度反演技术,为了提高异常体的深度分辨能力,进行迭代重构反演;用印模法对初始模型进行重构,采用的是辅模型在浅部,元模型在深部的组合方式.从合成数据和实际数据的反演结果可以得到以下的认识：（1）由频率域麦克斯韦方程组出发,低频磁场数据反演可以直接得到电导率,而不是相对电导率之比;（2）采用印模法组合初始模型,进行迭代重构反演,可以提高地面磁电阻率数据反演对异常体的分辨能力,确定埋深位置,同时不会丧失对于浅部异常体的分辨能力;（3）在结合印模法的地面磁电阻率数据三维反演中,深部异常体的分辨能力受地表不均匀导电体影响较小;（4）确定印模深度可以采用上一次重构反演结束时的模型变化量,通过相邻两次重构反演结束时的模型变化量之差来确定迭代重构是否终止.因为静磁场与重力场在数学上的相似性,本文的反演方法可以被运用到重力场等位场的地面数据的反演中.

     

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.     

A portable magnetic susceptibility meter for measurements on rocks in situ and in laboratory

Summary An instrument for the measurement of the magnetic susceptibility of rocks in situ or in the laboratory has been described. The instrument is a completely portable and transistorised unit having a range from 5 to 50000×10^–6 CGS units of volume susceptibility. The accuracy of measurements is ±5%. It is rapid and simple in operation.This paper is published by the kind permission of the Director General, Geological Survey of India.     

Quasi-one-dimensional method for solving the inverse magnetotelluric problem

We consider the iterative numerical method for solving two-dimensional (2D) inverse problems of magnetotelluric sounding, which significantly reduces the computational burden of the inverse problem solution in the class of quasi-layered models. The idea of the method is to replace the operator of the direct 2D problem of calculating the low-frequency electromagnetic field in a quasi-layered medium by a quasi-one dimensional operator at each observation point. The method is applicable for solving the inverse problems of magnetotellurics with either the E- and H-polarized fields and in the case when the inverse problem is simultaneously solved using the impedance values for the fields with both polarizations. We describe the numerical method and present the examples of its application to the numerical solution of a number of model inverse problems of magnetotelluric sounding.     

Heat production data from airborne and laboratory measurements of gamma-ray activity of rocks

Summary The paper discusses the obvious experimental relation between the laboratory determinations of total gamma-ray activity, expressed in equilibrium uranium concentration, and heat production due to radioactive decay. The heat production data were calculated by means of the concentrations of uranium, thorium and potassium determined spectrometrically, together with the conversion factors into the rate of heat generation. The obtained relation may help define the typical heat production for characteristic surface rocks and estimate their contribution in heat flow study. Between the gamma-ray activity recorded during aeroradiometric mapping and the laboratory radiometric measurements of surface rock samples, there is also an experimental relation, which can be used further in estimating the value of surface heat production at a chosen locality.     

电阻率横向剖面法在倾斜断层精确探测中的应用研究

在横向剖面法研究的基础上,选取30度和60度倾斜良导体模型,利用有限元三维数值模拟方法,对比研究横向剖面法和常规剖面法的异常特征.研究结果表明：两方法对断层的倾向都有较好反映,对倾角难以判定.为研究倾角定量化判定,本文提出了横向剖面电阻率成像方法与常规的电阻率层析成像方法对比研究,结果表明：两者均较准确的反映出断层的倾角变化,前者效果略优于后者.     

The effect of screening of the magnetotelluric field by high resistivity layers: Three-dimensional numerical modeling constraints

A 3-D numerical modeling approach is applied to the effect of screening of the magnetotelluric (MT) field by high resistance (≥10⁶ Ω m²) layers, which up to now has mainly been studied in terms of 2-D heterogeneous models of geological sections [Berdichevsky and Yakovlev, 1990]. Three-layer models above a poorly conducting basement (ρ=10⁴ Ω m) are used. The resistance of the screening layer was generally taken equal to 2×10⁶ Ω m² and its thickness was varied from 200 to 2000 m. The resistivity of the host medium was set at 10 Ω m. Heterogeneities of a low and a high resistivity (ρ=10^?3 and 10⁴ Ω m, respectively) ranging in horizontal size from 4 to 40 km and having a height of 1–2.8 km (a protrusion on the basement) were examined. Based on calculations of these models, 2-D and 3-D screening effects were compared. The 3-D modeling determined values of model parameters at which the screening properties are preserved both in the case of a screen of limited horizontal dimensions and in the presence of a rupture in the screen comparable in horizontal size with the 3-D heterogeneity. As follows from the modeling results, the screening effect of the high resistivity model layers seriously complicates the use of MT soundings for the identification of a local heterogeneity of both a low and a high resistivity (ρ=10^?3 and 10⁴ Ω m, respectively) if its lateral size is smaller than the 4-km thickness of the studied three-layer section in question and its height is 1–1.5 km. The regular patterns of the screening effect revealed in this work are of interest in electromagnetic sounding applications.     

低阻油层成因机理及测井评价方法综述

为了提高低阻油层测井识别评价的精度,本文基于大量的文献调研,通过对前人研究成果的吸收继承,梳理了国内外关于低阻油层的定义,归纳总结了低阻油层一般成因机理,研究了低阻油层的常规测井响应特征及其一般识别评价方法,进而探讨了低阻油层识别评价测井新技术和新思路.研究表明,低阻油层一般成因和影响因素包括十个方面;低阻油层常规测井响应呈现为高自然伽马、较高声波时差及高中子测井值、自然电位异常幅度低和密度测井值低等特征,低阻油层常规测井响应特征随其成因机理而异;低阻油层一般识别评价方法有九种之多;核磁共振测井、阵列感应测井及MDT等测井新技术可有效识别评价低阻油层;非线性数学方法为低阻油层识别评价提供了新思路.     

A new method for evaluating errors in high‐frequency ADV measurements

The acoustic Doppler velocimeter (ADV) measures three‐dimensional velocities in a small, remote sampling volume at high frequencies, however, these measurements incorporate errors that are intrinsic to the measurement technique. This paper demonstrates a new method for calculating the total measurement errors, including sampling errors, Doppler noise and errors due to velocity shear in the sampling volume associated with single‐point ADV measurements. This procedure incorporates both the effects of instrument configuration and the distribution of errors between velocity components for any probe orientation. It is shown that the ADV can characterize turbulent velocity fluctuations at frequencies up to the maximum sampling rate and that Reynolds shear stress errors are very small. Copyright © 2000 John Wiley & Sons, Ltd.     

Two-level magnetovariational measurements for the determination of underground resistivity distributions1

We investigate, from a theoretical point of view, the possibility of performing marine two-level magnetovariational measurements. An apparent resistivity function is denned and calculated after solving the differential equation governing the behaviour of the natural magnetic field variations inside a one-dimensional earth. In order to generalize the problem, a frequency-dependent resistivity is assumed to characterize the layers and the distortions caused by the polarization effects are carefully analysed. The computation of three-layer amplitude and phase diagrams for the apparent resistivity function shows that, in the case of an intermediate polarizable layer, sandwiched between a non-dispersive overburden and substratum, the H-type sequence results are the most affected by the dispersion phenomenon as it occurs in magnetotellurics. Finally we consider the problem of the sensitivity of the method, since, in practice, it requires top and bottom sensors separated by a vertical finite distance. It is found that in the higher-frequency range, due to the strong attenuation of the relative components of the field, the depth of the bottom sensor must be small enough to guarantee detectable signals, well above the full-scale resolution of the acquisition system. Conversely, in the lower-frequency range such a depth must be large enough to allow the difference between the top and bottom signals to be above the same recording sensitivity threshold.     

The use of invariant MTS curves in deep magnetotelluric studies

Invariant amplitude curves of the phase tensor are shown to be applicable to the geoelectric model reconstruction in the lower part of the section even if its upper part includes geoelectric heterogeneities described by the tensor of galvanic distortions. The use of other types of invariant curves provides reliable constraints on the deep structure of the section only if the upper part of the section does not contain contrasting geoelectric heterogeneities.     

Inversion of relative changes in the magnetotelluric apparent resistivity into the relative changes in the resistivity of the elements of a geoelectric structure

The earlier proposed method for inversion of the observed changes in the magnetotelluric apparent resistivity ρ_a into the relative changes in the resistivity of the elements of a well-studied geoelectric structure is tested on a 2D model representing one of the geodynamic research areas of Kamchatka. The possibilities are demonstrated for choosing the most effective observation conditions of the study, and for the determination of the source of the observed variations in γ_a. It is concluded that, if a number of conditions are met, it is possible to estimate the amplitude of relative changes in the electrical resistivity of rocks with sufficient accuracy for monitoring these changes with the aforementioned changes used as a prognostic parameter.