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.     

VERTICAL PROFILING OVER A MEDIUM OF CONTINUOUSLY VARYING RESISTIVITY*

An interpretation method is suggested for apparent resistivity profiles over a medium of continuously varying resistivity. The medium is replaced by an equivalent laminated system of constant resistivity in each layer and evaluated by superposition. The approximation facilitates detailed subsurface profiling as required for underground storage projects or water infiltration schemes.     

多辐射场源地空瞬变电磁法多分量全域视电阻率定义

本文针对多辐射场源地空瞬变电磁法理论,建立了相应的多分量全域视电阻率定义方法.分析了利用磁场强度进行多辐射场源地空系统全域视电阻率定义的优点,针对磁场强度的各个分量,提出了各自的全域视电阻率算法,实现了多分量、全时域、全空域视电阻率计算,并分析了偏移距对全域视电阻率的影响.通过调整源的相对位置及电流方向等参数,多辐射源瞬变电磁地空系统不仅可以加强不同分量信号强度,削弱随机干扰,还可更好地分辨地下异常体的位置.通过对所设计模型的处理,证实了多辐射场源地空系统多分量全域视电阻率算法的有效性,也验证了多辐射场源地空系统的优势.     

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.     

Increased resolution of subsurface parameters from 1D magnetotelluric modeling

In electric and electromagnetic techniques, it is well known that the principle of equivalence poses a problem in the interpretation of subsurface layers. This means the inversion problem can provide the conductivity-thickness product more confidently than the individual parameters — conductivity and thickness — separately. The principle of equivalence corresponds to the middle layer in a three-layer earth structure. In order to resolve this problem, we have touched upon the different formulae of apparent resistivity proposed by earlier workers considering the real and imaginary parts of the impedance tensor and designed a new formula to compute apparent resistivity for different models. We observed that the application of our new formula for apparent resistivity using the combination of real and imaginary parts of the impedance has a better resolution as compared to earlier conventional formulae of apparent resistivity. These results have been demonstrated through both forward and inverse modeling schemes.     

Fast imaging of subsurface conductors using very low‐frequency electromagnetic data

The study presents a fast imaging technique for the very low‐frequency data interpretation. First, an analytical expression was derived to compute the vertical component of the magnetic field at any point on the Earth's surface for a given current density distribution in a rectangular block on the subsurface. Current density is considered as exponentially decreasing with depth, according to the skin depth rule in a particular block. Subsequently, the vertical component of the magnetic field due to the entire subsurface was computed as the sum of the vertical component of the magnetic field due to an individual block. Since the vertical component of the magnetic field is proportional to the real part of very low‐frequency anomaly, an inversion program was developed for imaging of the subsurface conductors using the real very low‐frequency anomaly in terms of apparent current density distribution in the subsurface. Imaging results from the presented formulation were compared with other imaging techniques in terms of apparent current density and resistivity distribution using a standard numerical forward modelling and inversion technique. Efficacy of the developed approach was demonstrated for the interpretation of synthetic and field very low‐frequency data. The presented imaging technique shows improvement with respect to the filtering approaches in depicting subsurface conductors. Further, results obtained using the presented approach are closer to the results of rigorous resistivity inversion. Since the presented approach uses only the real anomaly, which is not sensitive to very small isolated near‐surface conducting features, it depicts prominent conducting features in the subsurface.     

ELECTRICAL SOUNDING OF A HALF-SPACE WITH A MONOTONIC CONTINUOUS VARIATION OF THE RESISTIVITY WITH DEPTH*

The interpretation of electrical sounding data for a subsurface with monotonic continuous variation of the resistivity with depth is becoming increasingly necessary. The contribution of this article is the derivation of the solution for the Wenner and the Schlumberger apparent resistivity functions for a resistivity varying as a real power of a linear positive function of the depth. The interpretation of sounding data in these cases can be used to estimate the variation of the porosity or the salt content of the pore water with depth.     

THE QUANTITATIVE INTERPRETATION OF DIPOLE SOUNDINGS BY MEANS OF THE RESISTIVITY TRANSFORM FUNCTION*

In this paper a theorem is demonstrated which allows—after the introduction of a suitable dipole kernel function or dipole resistivity transform function—to write the apparent resistivity function as an Hankel transformable integral expression. As a practical application of the theorem a procedure of quantitative interpretation of dipole soundings is suggested in which the dipole resistivity transform function obtained after inversion of the original dipole apparent resistivity data is used to control the goodness of the set of layering parameters which have been derived with our previous method of transformation of dipole sounding curves into equivalent Schlumberger diagrams.     

Advances in the combined interpretation of seismics with magnetotellurics1

Five examples, obtained during exploration for hydrocarbons in the Pannonian Basin of Hungary, are used to show how the interpretation of seismic sections can be usefully complemented by results from MT surveys. Selection of the most appropriate MT quantities, considered to be proper ‘MT attributes’ for the purpose of visualization as well as recognition of the subsurface structures and the different inversions of MT data is essential for practical integration of seismic and MT surveys. A new technique providing a semiquantitive MT-attribute pseudosection for the purpose of visualization of the subsurface structures is proposed. The procedure utilizes derivative functions of the phase of MT impedance for visualization and derives estimated depths from the Bostick transformation of Cagniard apparent resistivities. On the basis of the MT-attribute pseudosections, constructed from the phase derivatives and transformed resistivity data, depths are estimated for interfaces between geological formations with significant resistivity contrast. In particular examples, the interface between the Tertiary sediments and the older basement rocks as well as tectonic fracture zones with decreased resistivity can be resolved.     

Two-dimensional resistivity imaging and modelling in areas of complex geology

A system is described for the automatic measurement of electrical resistivity pseudo-sections. This comprises a linear array of up to 32 electrodes connected through a multicore cable to a computer controlled switching module and a resistivity meter. The processing of the measured sections to produce two-dimensional true resistivity images of the subsurface is briefly described. Some account is given of the capabilities and limitations of the technique. This is illustrated by a series of computed constant separation traverses for models of simple subsurface structures. Examples of processed images derived from sections measured in areas of relatively complex geology follow, a comparison being made of the interpretations obtained using an automatic imaging method and a manual iterative approach. It is concluded that with the equipment and software so far developed, in areas of modest subsurface geological complexity where some control is available and where the structures are essentially two-dimensional, then good approximations to the true geoelectric sections can be obtained down to depths of between 100 and 200 m.     

Two-dimensional, regularised inversion of VLF data

Very low frequency electromagnetic (EM) methods using VLF transmitters have found many applications in subsurface geophysical investigations. Surface measurements involving both the vertical component of the magnetic field (VLF-EM or VLF-Z) and of the apparent resistivity (VLF-R) are increasingly common. Although extensive VLF data sets have been successfully used for mapping purposes, modelling and interpretation techniques which asess the third (i.e. depth) dimension appear limited.Given a profile of VLF-R measurements the main purpose of the present study is to demonstrate an automatic method for the construction of a resistivity cross-section. The technique used is one of a new generation of regularised inversion methods. These techniques attempt to overcome the problem of equivalence/non-uniqueness in EM sounding data by constructing the resistivity distribution with the minimum amount of structure that fits the data.VLF data represent a special case of plane-wave EM sounding in that they conform, in practice, to a single-frequency technique. This fact imposes a limitation in the amount of vertical resolution that we can expect using such data. In the case of two-dimensional modelling and inversion, resolution through the cross-section is a resultant attribute from both vertical and lateral resistivity gradients within the subsurface. In order to provide insight into the practical application of regularised inversion techniques to VLF data, both synthetic and field examples are considered. Both sets of examples are primarily concerned with VLF data applied to near-surface fault mapping where the main aim is to assess the location, dip and depth extent of conductive subsurface features.     

An apparent-resistivity concept for low-frequency electromagnetic sounding techniques

Apparent resistivity is a useful concept for initial quickscan interpretation and quality checks in the field, because it represents the resistivity properties of the subsurface better than the raw data. For frequency‐domain soundings several apparent‐resistivity definitions exist. One definition uses an asymptote for the field of a magnetic dipole in a homogeneous half‐space and is useful only for low induction numbers. Another definition uses only the amplitude information of the total magnetic field, although this results in a non‐unique apparent resistivity. To overcome this non‐uniqueness, a complex derivation using two different source–receiver configurations and several magnetic field values for different frequencies or different offsets is derived in another definition. Using the latter theory, in practice, this means that a wide range of measurements have to be carried out, while commercial systems are not able to measure this wide range. In this paper, an apparent‐resistivity concept is applied beyond the low‐induction zone, for which the use of different source–receiver configurations is not needed. This apparent‐resistivity concept was formerly used to interpret the electromagnetic transients that are associated with the turn‐off of the transmitter current. The concept uses both amplitude and phase information and can be applied for a wide range of frequencies and offsets, resulting in a unique apparent resistivity for each individual (offset, frequency) combination. It is based on the projection of the electromagnetic field data on to the curve of the field of a magnetic dipole on a homogeneous half‐space and implemented using a non‐linear optimization scheme. This results in a fast and efficient estimation of apparent resistivity versus frequency or offset for electromagnetic sounding, and also gives a new perspective on electromagnetic profiling. Numerical results and two case studies are presented. In each case study the results are found to be comparable with those from other existing exploration systems, such as EM31 and EM34. They are obtained with a slight increase of effort in the field but contain more information, especially about the vertical resistivity distribution of the subsurface.     

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.     

A TUNNEL RESOLUTION INVESTIGATION USING AN AUTOMATED RESISTIVITY TANK ANALOG*

The examination of apparent resistivity space sections over two-dimensional targets requires the accumulation of large amounts of data, if the resistivity field is to be adequately described. Whilst such data may be obtained from an intensive sounding traverse in the field, it is desirable for interpretation purposes to be able to generate such space sections for a range of model variations. Within their limitations, tank analogs can be used to provide such interpretation material, but the collection of data can itself be time-consuming. In this paper, an account is given of the development of an automated tank analog, where an entire space section can be scanned and the output obtained in paper tape format for later processing on a digital computer. The resistance measurement accuracy attained is comparable with normal field measurement accuracy. A practical example of the use of this analog in investigating the problem of resolving and discriminating between two horizontal cylindrical tunnels is given. This problem is basic to an understanding of the minimum size and disposition of targets which can be observed on a space section. The square array has been used in this example because of its good resolution properties in general prospecting rather than its particular suitability for the targets investigated. The directional response of the array is also illustrated and discussed.     

CSAMT单分量数据解释方法

可控源音频大地电磁法(CSAMT)一直沿用大地电磁法(MT)的办法,通过计算电场分量与磁场分量的比值,求取卡尼亚视电阻率.而CSAMT场源已知,电场分量和磁场分量都与地下电阻率存在一定的关系,可以单独采用CSAMT电场分量或者磁场分量提取地下介质的视电阻率.本文通过分析电场分量与磁场分量的数据特性,提出利用CSAMT电场单分量数据进行视电阻率的计算,用改进的广义逆矩阵反演方法,使初始模型中的地电层数等于频道个数,克服了以往反演计算中层数较少的问题;实现全场区电场分量视电阻率曲线的拟合反演.同时对单分量视相位计算方法进行分析,结合山西大同地区积水采空区探测及数据解释结果,论证本文提出的单分量解释方法的有效性.     

AN EXAMPLE OF THE APPLICATION OF THE RULES OF COMPOSITION IN RESISTIVITY INTERPRETATION*

The application of approximate rules, whereby apparent resistivity space sections for two dimensional structures can be composited from spaces derived for elementary features is extended to a complex example drawn from a field survey over a fluorite mineral vein. A quantitative solution for the observed resistivity space is presented and the computational sequence involved in matching the observed space is given in detail. The interpreted results are examined in relation to the known geology, supplemented by the results of excavation, and to model tests conducted using a tank analogue. The example also illustrates how successive compositions can be employed in estimating the form of resistivity space in a relatively complex situation.     

宁夏海原大震区西安州—韦州剖面大地电磁探测与研究

对穿过宁夏海原大震区西安州(N36.5°,E105.5°)北至同心县韦州(N37.28°,E106.48°)的大地电磁测深剖面，采用远参考道大地电磁方法进行测量和资料处理，得到高精度的数据如视电阻率、阻抗相位、二维偏离度、最佳主轴方位角等. 依据这些数据，对测区的电性结构进行了定性分析和二维定量反演解释. 结果表明，沿剖面可以分成5个电性区块，与西、南华山隆起(Ⅰ)、兴仁堡—海原盆地(Ⅱ)、中卫—清水河盆地(Ⅲ)、中宁—红寺堡盆地(Ⅳ)和鄂尔多斯西缘带(Ⅴ)对应，各区块的边界由大断裂构成. 地表到深度10km左右，西、南华山隆起和鄂尔多斯西缘带呈高阻特性，兴仁堡—海原、中卫—清水河、中宁—红寺堡三个盆地的电阻率较低且呈盆地凹陷形状，盆地基底显示为西南深东北浅的簸箕状起伏形态，基底最深约为8km. 西、南华山隆起、中卫—清水河盆地和鄂尔多斯西缘带的下地壳为“正常”电阻率结构. 兴仁堡—海原和中宁—红寺堡盆地的下地壳上部为“异常”低电阻率带. 1920年的海原大震区存在明显的电性结构差异，震区西南侧和上部区域为相对高阻，东北侧和下部区域为相对低阻.     

A SIMPLE METHOD OF INTERPRETATION OF RESISTIVITY SOUNDING DATA USING EXPONENTIAL APPROXIMATION OF THE KERNEL FUNCTION*

A simple unified equation of apparent resistivity for a general four-electrode array is developed. The main idea is the analytical integration of the Stefanescu expression for potential over a layered earth by writing an exponential approximation for the kernel function. Finally a matrix equation is developed to estimate the kernel function from observed apparent resistivity values. The general equation automatically reduces to the particular configuration once the electrode separations are modified suitably. Examples for Schlumberger and Wenner configurations are numerically calculated to estimate the precision of the method. Good results in a short execution time are obtained, irrespective of the shape of the apparent resistivity curve. Finally, the full interpretation of one theoretical resistivity curve and two field resistivity curves is demonstrated. The more stable ridge-regression estimation method is used in the identification of layer parameters from the kernel function.     

Laterally constrained inversion of helicopter-borne frequency-domain electromagnetic data

Helicopter-borne frequency-domain electromagnetic (HEM) surveys are used for fast high-resolution, three-dimensional resistivity mapping. Standard interpretation tools are often based on layered earth inversion procedures which, in general, explain the HEM data sufficiently. As a HEM system is moved while measuring, noise on the data is a common problem. Generally, noisy data will be smoothed prior to inversion using appropriate low-pass filters and consequently information may be lost.For the first time the laterally constrained inversion (LCI) technique has been applied to HEM data combined with the automatic generation of dynamic starting models. The latter is important because it takes the penetration depth of the electromagnetic fields, which can heavily vary in survey areas with different geological settings, into account. The LCI technique, which has been applied to diverse airborne and ground geophysical data sets, has proven to be able to improve the HEM inversion results of layered earth structures. Although single-site 1-D inversion is generally faster and — in case of strong lateral resistivity variations — more flexible, LCI produces resistivity — depth sections which are nearly identical to those derived from noise-free data.The LCI results are compared with standard single-site Marquardt–Levenberg inversion procedures on the basis of synthetic data as well as field data. The model chosen for the generation of synthetic data represents a layered earth structure having an inhomogeneous top layer in order to study the influence of shallow resistivity variations on the resolution of deep horizontal conductors in one-dimensional inversion results. The field data example comprises a wide resistivity range in a sedimentary as well as hard-rock environment.If a sufficient resistivity contrast between air and subsurface exists, the LCI technique is also very useful in correcting for incorrect system altitude measurements by using the altitude as a constrained inversion parameter.