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.     

Electrical resistivity investigations for guiding and controlling fresh water well drilling in semi-arid region in Khanasser Valley,Northern Syria

Electrical resistivity survey is conducted in the Khanasser Valley, considered as a semi-arid region in Northern Syria, to guide and control fresh water well drilling. Vertical Electrical Soundings (VES) are carried out near the existing wells, which were also used to measure salinity and conductivity of water samplings. Resistivity and hydrogeological data combination made it possible to establish empirical relationships between earth resistivity, water resistivity, and the amount of total dissolved solids (TDS). These relationships are used in the present research in order to follow the TDS salinity variations, both in lateral and depth directions, along the longitudinal profile LP3, located in Khanasser Valley. Apparent salinity map under this profile is established for Quaternary and Paleogene deposits, and boundaries of suitable areas for fresh water well drilling in the totality of the Khanasser Valley are drawn. It was shown that excessive fresh-water depletion may affect the groundwater quality by upward seepage of saline water. Therefore, it is important to keep the fresh-salt water interface in a stationary situation. The geoelectrical methods widely contribute in determining the position of such interface, and can be easily applied in similar arid areas.     

On the question of the interrelation between variations in crustal electrical conductivity and geodynamical processes

The behavior of the variations in the crustal electrical conductivity in a wide range of periods is studied from the data of magnetotelluric soundings (MTS) during the Kambarata experiment (a strong industrial explosion to construct the blast-fill dam on the Naryn river), as well as at Aksu, a stationary geophysical monitoring point. The concept of the interrelation between the stress-strain state of the medium and the change in the apparent electrical resistivity, which is based on the idea of the redistribution of mineralized solutions between the crack networks, is confirmed experimentally. A procedure of azimuthal monitoring is developed, which allowed us not only to identify the anomalous changes in the module and phase of apparent resistivity but also to establish the directions of their maximum increases and decreases (the axes of compression and tension). For 34 points of deep MTS in the territory of Central Tien Shan, the depth intervals in the upper crust that are most sensitive to the changes in the stress-strain state of the medium are established. The variations in the electrical conductivity are compared with the solar-lunar tidal impacts. It is shown that by analyzing the recorded time series, it is possible to recognize the characteristic signs of the changes in the stress-strain state of the medium that are caused by seismic events.     

POTENTIAL FIELD OF A STATIONARY ELECTRIC CURRENT USING FREDHOLM'S INTEGRAL EQUATIONS OF THE SECOND KIND*

An integral equation method is described for solving the potential problem of a stationary electric current in a medium that is linear, isotropic and piecewise homogeneous in terms of electrical conductivity. The integral equations are Fredholm's equations of the ‘second kind’ developed for the potential of the electric field. In this method the discontinuity-surfaces of electrical conductivity are divided into ‘sub-areas’ that are so small that the value of their potential can be regarded as constant. The equations are applied to 3-D galvanic modeling. In the numerical examples the convergence is examined. The results are also compared with solutions derived with other integral equations. Examples are given of anomalies of apparent resistivity and mise-a-la-masse methods, assuming finite conductivity contrast. We show that the numerical solutions converge more rapidly than compared to solutions published earlier for the electric field. This results from the fact that the potential (as a function of the location coordinate) behaves more regularly than the electric field. The equations are applicable to all cases where conductivity contrast is finite.     

视电阻率变化与地下水位定量关系的探讨

本文以三层电剖面模型计算出由于电剖面参数变化而引起的视电阻率变化,进而说明因地下水位变化所引起的视电阻率变化是可能估计的。根据这个结果能够确定出由于地下水干扰所引起的视电阻率异常幅度,这将有利于视电阻率变化与地震关系的定性、定量分析研究。实际工作表明,视电阻率变化很复杂,许多因素都会使视电阻率发生变化,但水的影响很重要,因此,研究这个问题有重要意义。      

基于非结构网格的电阻率三维带地形反演

地表起伏地形在野外矿产资源勘察中不可避免,其对直流电阻率法勘探影响巨大.近年来,电阻率三维正演取得诸多进展,特别是应用非结构网格我们能够进行任意复杂地形和几何模型的电阻率三维数值模拟,但面向实际应用的起伏地形下电阻率三维反演依然困难.本文基于非结构化四面体网格,并考虑到应用GPS/GNSS时,区域地球物理调查中可非规则布设测网的实际特点,实现了任意地形(平坦或起伏)条件下、任意布设的偶极-偶极视电阻率数据的不完全Gauss-Newton三维反演.合成数据的反演结果表明了方法的有效性,可应用于复杂野外环境下的三维电法勘探.     

Shallow fault location in coal measures using offset Wenner resistivity profiling1

The five-electrode resistivity configuration of Barker, who introduced the concept of offset resistivity measurements, is used in a profiling mode in the search for lateral variations of resistivity down to depths of a few tens of metres. Theoretical computations show that plotting simple pseudosections of offset measurements over faults is sufficient to reveal the fault position. The method is subsequently applied in the field for locating a buried fault in coal measures. Although offset pseudosections are often all that is required, apparent resistivity pseudosections are examined and compared to collations of 1D inversions of the sounding profile data and to computations over 2D models. It is shown that apparent restivity pseudosections may present a rather misleading picture.     

压制空间非平稳地震勘探随机噪声的ROAD径向时频峰值滤波算法

径向时频峰值滤波算法是一种有效保持低信噪比地震勘探记录中反射同相轴的随机噪声压制方法,但该算法对空间非平稳地震勘探随机噪声压制效果不理想.本文研究空间非平稳地震勘探随机噪声,即各道噪声功率不同的地震勘探随机噪声,其在径向滤波轨线上表征近似脉冲噪声,在径向时频峰值滤波过程中干扰相邻道滤波结果.为了减小空间非平稳随机噪声的影响,本文提出一种基于绝对级差统计量(ROAD)的径向时频峰值滤波随机噪声压制方法.该方法首先根据径向轨线上信号的绝对级差统计量检测空间非平稳地震勘探随机噪声,然后结合局部时频峰值滤波和径向时频峰值滤波压制地震勘探记录中的随机噪声.将ROAD径向时频峰值滤波方法应用于合成记录和实际共炮点地震记录,结果表明ROAD径向时频峰值滤波方法可以压制空间非平稳地震勘探随机噪声且不损害有效信号,有效抑制随机噪声空间非平稳对滤波结果的影响.与径向时频峰值滤波相比,ROAD径向时频峰值滤波方法更适用于空间非平稳地震勘探随机噪声压制.     

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.     

The application of electromagnetic techniques to groundwater recharge investigations

The use of electrical methods for estimating spatial patterns of groundwater recharge was evaluated at a field site in southeastern Australia. Here, recharge increased from less than 0.2 mm year⁻¹ under native Eucalyptus vegetation, to between 1 and 14 mm year⁻¹ under dryland agriculture. This increase in recharge results in progressive leaching of salts in the soil profile. Differences in recharge can be estimated from differences in depth of leaching. The estimated recharge rates are correlated with soil texture, with higher recharge rates generally occurring through sandier soils. The relationships of recharge to salt content and soil texture both contribute to lower apparent electrical conductivities for higher recharge rates.

The effect of recharge rate on measured apparent electrical conductivities was modelled for various geophysical devices (including frequency-domain (FEM) and time-domain (TEM) electromagnetic instruments and direct current resistivity). The soil-texture effect was shown to have a greater effect than the solute leaching effect in determining the correlation between recharge and apparent electrical conductivity. Analysis of sensitivity to geological noise showed that variations in soil type below 2 m could disguise any correlation.

Correlations between recharge rate, measured at core sites from chloride tracer techniques, and apparent electrical conductivity, measured with FEM electromagnetic devices, supported the conclusions of the model. For DC resistivity and TEM methods, correlations between recharge and apparent electrical conductivity were not significant, although for resistivity this may be due partly to the small number of measurements made. The FEM device most sensitive to variations in recharge had an operating frequency of 9.8 kHz. At lower frequencies the sensitivity is reduced, as the instruments are sensing too deeply. The poor correlations for TEM, as compared with FEM, are due probably to the relatively deeper penetration of the TEM instrument used in the study, rather than any inherent differences between the techniques.

Because the major reason for the correlation between recharge and apparent electrical conductivity is soil texture, in this area the geophysical devices are mostly mapping soil type.     

A class of non-stationary covariance functions with compact support

This article describes the use of non-stationary covariance functions with compact support to estimate and simulate a random function. Based on the kernel convolution theory, the functions are derived by convolving hyperspheres in \(\mathbb{R}^n\) followed by a Radon transform. The order of the Radon transform controls the differentiability of the covariance functions. By varying spatially the hyperspheres radius one defines non-stationary isotropic versions of the spherical, the cubic and the penta-spherical models. Closed-form expressions for the non-stationary covariances are derived for the isotropic spherical, cubic, and penta-spherical models. Simulation of the different non-stationary models is easily obtained by weighted average of independent standard Gaussian variates in both the isotropic and the anisotropic case. The non-stationary spherical covariance model is applied to estimate the overburden thickness over an area composed of two different geological domains. The results are compared to the estimation with a single stationary model and the estimation with two stationary models, one for each geological domain. It is shown that the non-stationary model enables a reduction of the mean square error and a more realistic transition between the two geological domains.     

A stochastic approach to nonlinear unconfined flow subject to multiple random fields

In this study, the KLME approach, a moment-equation approach based on the Karhunen–Loeve decomposition developed by Zhang and Lu (Comput Phys 194(2):773–794, 2004), is applied to unconfined flow with multiple random inputs. The log-transformed hydraulic conductivity F, the recharge R, the Dirichlet boundary condition H, and the Neumann boundary condition Q are assumed to be Gaussian random fields with known means and covariance functions. The F, R, H and Q are first decomposed into finite series in terms of Gaussian standard random variables by the Karhunen–Loeve expansion. The hydraulic head h is then represented by a perturbation expansion, and each term in the perturbation expansion is written as the products of unknown coefficients and Gaussian standard random variables obtained from the Karhunen–Loeve expansions. A series of deterministic partial differential equations are derived from the stochastic partial differential equations. The resulting equations for uncorrelated and perfectly correlated cases are developed. The equations can be solved sequentially from low to high order by the finite element method. We examine the accuracy of the KLME approach for the groundwater flow subject to uncorrelated or perfectly correlated random inputs and study the capability of the KLME method for predicting the head variance in the presence of various spatially variable parameters. It is shown that the proposed numerical model gives accurate results at a much smaller computational cost than the Monte Carlo simulation.     

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.     

Apparent resistivity over a three layer earth with an inhomogeneous interstratum

Summary The theory of resistivity sounding on a three layer earth comprising an inhomogeneous interstratum has been presented. The electrical conductivity in the intermediate layer, embedded between two layers of uniform conductivity, is assumed to follow either generalised power law or exponential variation. A point source of current is placed on the surface. The electric potential functions on the ground surface have been obtained. The expressions for apparent resistivity over the above models for the Wenner and Schlumberger electrode configurations have been derived.     

Low induction number, ground conductivity meters: A correction procedure in the absence of magnetic effects

Ground conductivity meters, comprising a variety of coil–coil configurations, are intended to operate within the limits provided by a low induction number (LIN), electromagnetic condition. They are now routinely used across a wide range of application areas and the measured apparent conductivity data may be spatially assembled and examined/correlated alongside information obtained from many other earth science, environmental, soil and land use assessments. The theoretical behaviour of the common systems is examined in relation to both the prevailing level of subsurface conductivity and the instrument elevation. It is demonstrated that, given the inherent high level of accuracy of modern instruments, the prevailing LIN condition may require operation in environments restricted to very low (< 12 mS/m) conductivities. Beyond this limit, non-linear departures from the apparent conductivity that would be associated with a LIN condition occur and are a function of the coil configuration, the instrument height and the prevailing conductivity. Using both theory and experimental data, it is demonstrated that this has the potential to provide biased and spatially distorted measurements. A simple correction procedure that can be applied to the measured data obtained from any of the LIN instruments is developed. The correction procedure would, in the limit of a uniform subsurface, return the same (correct) conductivity, irrespective of the ground conductivity meter used, the prevailing conductivity or the measurement height.     

Stochastic analysis of groundwater flow in aquifers with leakage

 Stochastic analysis of one- and two-dimensional flow through a shallow semi-confined aquifer with spatially variable hydraulic conductivity K represented by a stationary (statistically homogeneous) random process is carried out by using the spectral technique. The hydraulic head covariance functions for flows in a semi-confined aquifer bounded by a leaky layer above and an impervious stratum below are derived by assuming that the randomness forcing the head variation to originate from the hydraulic conductivity field of the aquifer. The head covariance functions are studied using two convenient forms of the logarithmic hydraulic conductivity process. The results demonstrate the significant reduction in the head variances and covariances due to the presence of a leaky layer. The hydraulic head correlation distance is also reduced greatly due to the presence of the leaky layer.     

RESISTIVITY SOUNDING ON A MULTILAYERED EARTH CONTAINING TRANSITION LAYERS*

For curves over a horizontally stratified earth where any of the layers has a conductivity variation proportional to (1 +β·z)^N, where β and N are arbitrary constants and z is the depth to the layer, expressions for apparent resistivity for Wenner and Schlumberger sounding are derived. No assumption has been made about the continuity of conductivity at the interface. It is shown that most of the previous investigations in this connection can be regarded as particular cases of the present study.     

ON THE COMPLETENESS OF DATA SETS WITH MULTIELECTRODE SYSTEMS FOR ELECTRICAL RESISTIVITY SURVEY

This paper describes how, using a surface linear array of equally spaced electrodes, potential data can be obtained for use in electrical resistivity imaging. The aim is to collect a complete data set which contains all linearly independent measurements of apparent resistivity on such an array using two-, three- or four-electrode configurations. From this primary data set, it is shown that any other value for apparent resistivity on the array can be synthesized through a process of superposition. Numerical tests show that such transformations are exact within the machine error for calculated data but that their use with real field data may lead to noise amplification.     

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