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.     

基于牛顿迭代法和遗传算法的CSAMT近场校正

由于可控源音频大地电磁法（CSAMT）采用人工场源在大大增加信号强度的同时也带来了在近区产生非平面波效应的问题,其表现特征为在双对数坐标中卡尼亚电阻率曲线呈45°上升,即所谓的近场效应.本文首先提出了基于牛顿迭代法求解视电阻率方程的近场效应校正方法,通过对二层、三层理论模型试算验证了该方法的有效性;为进一步增强对噪声的压制能力,本文进一步引入了遗传反演的思想,将全频段误差最小作为目标函数,采用自适应正则化方法引入模型参数梯度最小作为稳定因子,由遗传算法求解得到校正后视电阻率,通过对理论模拟数据加随机噪声的校正结果,表明该方法在实现近场校正的同时能剔除噪声干扰,得到的结果与理论模拟曲线吻合度较高.通过对内蒙古曹四夭钼矿区实测CSAMT数据处理结果表明,牛顿法和遗传算法均能明显校正CSAMT因近场效应引起的假高阻异常,能更好地反映地电结构特征.     

基于同步大地电磁时间序列依赖关系的噪声处理

本文从信号与系统的角度讨论了同步大地电磁时间序列信号之间的依赖关系,选取高信噪比的时间序列信号作为先验数据,用最小二乘法估算依赖关系;结合参考道的数据,合成本地道含噪声时段的数据,最后用合成数据替代噪声段数据,组成新数据,从而在时域中去除大地电磁噪声.西藏地区高信噪比实测数据的试算结果表明,无论电场还是磁场,信号之间的依赖关系是相对稳定的,只与先验数据的长度有关,与时间无关;虽然不同参考点之间的依赖关系不同,但都可以精确合成本地点数据,与参考点地下电性结构和参考距离无关.仿真实验显示,去噪后的信号与原始信号基本一致.实测数据处理结果表明,该方法可以有效去除强噪声干扰,抑制中高频段的近场源效应,同时保留了微弱的有效信号,保证了处理结果的正确性.最后针对方差比方法无法识别的方波噪声,提出了一种简单的平移方法,成功去除了持续时间大于窗口长度的方波噪声;将该方法与远参考技术结合,可以有效抑制近场源噪声干扰,获得光滑连续并且可信的测深资料.     

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.     

用有限元法正演京津唐地区二维构造的大地电磁测深资料

本文阐述在大地电磁测深工作中,用有限单元法,模拟计算京津唐地区二维地质构造的大地电磁响应。 文章前部分,论述了用有限单元法正演二维大地电磁测深曲线的原理及其数学公式推导。文章后部分,根据两条测线实测的大地电磁测深结果并结合其它地球物理探测资料,给出了两个二维剖面模型,并计算了两种极化的视电阻率曲线。两条实测剖面分别是横切唐山地震带的马兰峪—柏各庄剖面及横过北京地区北北东构造走向的文化营—王辛庄剖面     

含噪声数据反演的概率描述

根据贝叶斯理论给出了对含噪声地球物理数据处理的具体流程和方法,主要包括似然函数估计和后验概率计算.我们将数据向量的概念扩展为数据向量的集合,通过引入数据空间内的信赖度,把数据噪声转移到模型空间的概率密度函数上,即获得了反映数据本身的不确定性的似然函数.该方法由于避免了处理阶段数据空间内的人工干预,因而可以保证模型空间中的概率密度单纯反映数据噪声,具有信息保真度高、保留可行解的优点.为了得到加入先验信息的后验分布,本文提出了使用加权矩阵的概率分析法,该方法在模型空间直接引入地质信息,对噪声引起的反演多解性有很强的约束效果.整个处理流程均以大地电磁反演为例进行了展示.     

Joint inversion of Rayleigh‐wave dispersion data and vertical electric sounding data: synthetic tests on characteristic sub‐surface models

In the traditional inversion of the Rayleigh dispersion curve, layer thickness, which is the second most sensitive parameter of modelling the Rayleigh dispersion curve, is usually assumed as correct and is used as fixed a priori information. Because the knowledge of the layer thickness is typically not precise, the use of such a priori information may result in the traditional Rayleigh dispersion curve inversions getting trapped in some local minima and may show results that are far from the real solution. In this study, we try to avoid this issue by using a joint inversion of the Rayleigh dispersion curve data with vertical electric sounding data, where we use the common‐layer thickness to couple the two methods. The key idea of the proposed joint inversion scheme is to combine methods in one joint Jacobian matrix and to invert for layer S‐wave velocity, resistivity, and layer thickness as an additional parameter, in contrast with a traditional Rayleigh dispersion curve inversion. The proposed joint inversion approach is tested with noise‐free and Gaussian noise data on six characteristic, synthetic sub‐surface models: a model with a typical dispersion; a low‐velocity, half‐space model; a model with particularly stiff and soft layers, respectively; and a model reproduced from the stiff and soft layers for different layer‐resistivity propagation. In the joint inversion process, the non‐linear damped least squares method is used together with the singular value decomposition approach to find a proper damping value for each iteration. The proposed joint inversion scheme tests many damping values, and it chooses the one that best approximates the observed data in the current iteration. The quality of the joint inversion is checked with the relative distance measure. In addition, a sensitivity analysis is performed for the typical dispersive sub‐surface model to illustrate the benefits of the proposed joint scheme. The results of synthetic models revealed that the combination of the Rayleigh dispersion curve and vertical electric sounding methods in a joint scheme allows to provide reliable sub‐surface models even in complex and challenging situations and without using any a priori information.     

PROGRESS IN THE DIRECT INTERPRETATION OF RESISTIVITY SOUNDINGS: AN ALGORITHM*

An algorithm is presented for the direct interpretation of resistivity sounding data. The algorithm is based on the method of successive reductions to lower boundary plane of the resistivity transform function. A novel aspect of the algorithm is that error limits are assigned to the initial values of the resistivity transform, and these error limits are carried through in all the subsequent computations. The width of the error range is then used as the basis for assigning weight factors in the final computation of thicknesses and resistivities of the layers. The errors in the resistivity transform derived from the solution given by the algorithm are usually not more than twice as large as those in the original data.     

大地电磁全张量响应的一维各向异性反演

目前大地电磁(MT)测深资料反演主要基于各向同性介质,但随着MT实际应用的需要,各向异性研究已逐渐引起关注.我们采用广泛应用的广义逆法对一维MT水平层状各向异性介质模型反演进行了探索性研究,并实现了MT全张量响应(即所有的阻抗张量的视电阻率和相位)的一维各向异性反演.理论模型试验表明,无论理论观测值中是否含有噪声,这种方法都能够较好地恢复真实模型,验证了其正确性和有效性.将此方法用于MT实测资料时,能够同时拟合4对视电阻率和阻抗相位曲线,说明本方法可以用于实测资料的处理解释,具有一定的实用价值.     

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.     

FAST AUTOMATIC PROCESSING OF RESISTIVITY SOUNDINGS*

The difficulty to use master curves as well as classical techniques for the determination of layer distribution (e_i, ρ_i) from a resistivity sounding arises when the presumed number of layers exceeds five or six. The principle of the method proposed here is based on the identification of the resistivity transform. This principle was recently underlined by many authors. The resistivity transform can be easily derived from the experimental data by the application of Ghosh's linear filter, and another method for deriving the filter coefficientes is suggested. For a given theoretical resistivity transform corresponding to a given distribution of layers (thicknesses and resistivities) various criteria that measure the difference between this theoretical resistivity transform and an experimental one derived by the application of Ghosh's filter are given. A discussion of these criteria from a physical as well as a mathematical point of view follows. The proposed method is then exposed; it is based on a gradient method. The type of gradient method used is defined and justified physically as well as with numerical examples of identified master curves. The practical use for the method and experimental confrontation of identified field curves with drill holes are given. The cost as well as memory occupation and time of execution of the program on CDC 7600 computer is estimated.     

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.     

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.     

Joint parameter estimation from magnetic resonance and vertical electric soundings using a multi‐objective genetic algorithm

Magnetic resonance sounding (MRS) has increasingly become an important method in hydrogeophysics because it allows for estimations of essential hydraulic properties such as porosity and hydraulic conductivity. A resistivity model is required for magnetic resonance sounding modelling and inversion. Therefore, joint interpretation or inversion is favourable to reduce the ambiguities that arise in separate magnetic resonance sounding and vertical electrical sounding (VES) inversions. A new method is suggested for the joint inversion of magnetic resonance sounding and vertical electrical sounding data. A one‐dimensional blocky model with varying layer thicknesses is used for the subsurface discretization. Instead of conventional derivative‐based inversion schemes that are strongly dependent on initial models, a global multi‐objective optimization scheme (a genetic algorithm [GA] in this case) is preferred to examine a set of possible solutions in a predefined search space. Multi‐objective joint optimization avoids the domination of one objective over the other without applying a weighting scheme. The outcome is a group of non‐dominated optimal solutions referred to as the Pareto‐optimal set. Tests conducted using synthetic data show that the multi‐objective joint optimization approximates the joint model parameters within the experimental error level and illustrates the range of trade‐off solutions, which is useful for understanding the consistency and conflicts between two models and objectives. Overall, the Levenberg‐Marquardt inversion of field data measured during a survey on a North Sea island presents similar solutions. However, the multi‐objective genetic algorithm method presents an efficient method for exploring the search space by producing a set of non‐dominated solutions. Borehole data were used to provide a verification of the inversion outcomes and indicate that the suggested genetic algorithm method is complementary for derivative‐based inversions.     

AN INTERPRETATION SYSTEM FOR GEO-ELECTRICAL SOUNDING GRAPHS *

For the two and three layer cases geo-electrical sounding graphs can be rapidly and accurately evaluated by comparing them with an adequate set of standard model graphs. The variety of model graphs required is reasonably limited and the use of a computer is unnecessary for this type of interpretation. For more than three layers a compilation of model graphs is not possible, because the variety of curves required in practice increases immensely. To evaluate a measured graph under these conditions, a model graph is calculated by computer for an approximately calculated resistivity profile which is determined, for example, by means of the auxiliary point methods. This model graph is then compared with the measured curve, and from the deviation between the curves a new resistivity profile is derived, the model graph of which is calculated for another comparison procedure, etc. This type of interpretation, although exact, is very inconvenient and time-consuming, because there is no simple method by which an improved resistivity profile can be derived from the deviations between a model graph and a measured graph. The aim of this paper is, on the one hand, to give a simple interpretation method, suitable for use during field work, for multi-layer geo-electrical sounding graphs, and, on the other hand, to indicate an automatic evaluation procedure based on these principles, suitable for use by digital computer. This interpretation system is based on the resolution of the kernel function of Stefanescu's integral into partial fractions. The system consists of a calculation method for an arbitrary multi-layer case and a highly accurate approximation method for determining those partial fractions which are important for interpretation. The partial fractions are found by fitting three-layer graphs to a measured curve. Using the roots and coefficients of these partial fractions and simple equations derived from the kernel function of Stefanescu's integral, the thicknesses and resistivities of layers may be directly calculated for successively increasing depths. The system also provides a simple method for the approximative construction of model graphs.     

电测深曲线的遗传算法反演

电测深曲线作为地下介质电阻率和深度的非线性函数，其解具有高度的非唯一性．常规的基于局部线性化的最优化反演方法易使解估计陷入局部极大值中，而且严重地依赖初始模型的选择．遗传算法作为一种全局最优化方法，对初始模型的依赖性大为减弱，且不易陷人局部极大值之中，从而能有效地解决这类非线性最优化问题．本文首次将遗传算法用于电测深解释并对实测曲线进行反演，效果很好，显示了遗传算法独特的优越性．     

电测深曲线的遗传算法反演

电测深曲线作为地下介质电阻率和深度的非线性函数，其解具有高度的非唯一性．常规的基于局部线性化的最优化反演方法易使解估计陷入局部极大值中，而且严重地依赖初始模型的选择．遗传算法作为一种全局最优化方法，对初始模型的依赖性大为减弱，且不易陷人局部极大值之中，从而能有效地解决这类非线性最优化问题．本文首次将遗传算法用于电测深解释并对实测曲线进行反演，效果很好，显示了遗传算法独特的优越性．     

GEOELECTRIC AXIAL DIPOLE SOUNDING CURVES FOR A CLASS OF TWO-DIMENSIONAL EARTH STRUCTURES*

With the aim of studying the behaviour of geoelectric axial dipole vertical soundings over complex geology, a systematic theoretical approach is presented for a class of earth structures characterized by horizontal and vertical parallel boundary planes. The two-dimensional cylindrical bodies of infinite length and rectangular cross-section are constrained to have resistivities satisfying Alfano's condition at every intersection line of the graticule, in order to adopt the image-point theory. A detailed analysis is performed for models with any number of horizontal boundaries and two vertical discontinuities. The apparent resistivity formulas are obtained and selected apparent resistivity curves are drawn for different parameter combinations and various directions of the sounding expansion axis. The class under consideration contains as a particular case the HVC model elaborated in Alpin's monograph, where only a small collection of master curves is available for the axial array. The reconstruction of those curves by the present formulation shows the existence of large discrepancies. A test based on the transformation to equivalent half-Schlumberger sounding curves supports the conclusion that an unidentified error must exist in some part of the theoretical approach of the Russian researchers. Finally, some field sounding curves based on geothermal and volcanological surveys are presented and interpreted by complete curve matching, essentially to show the applicability of the theoretical solutions.     

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.     

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.