Interpretation of Gravity Anomalies with the Normalized Full Gradient (NFG) Method and an Example

The Normalized Full Gradient (NFG) method which was put forward about 50 years ago has been used for downward continuation of gravity potential data, especially in the former Union of Soviet Socialist Republics. This method nullifies perturbations due to the passage of mass depth during downward continuation. The method depends on the downwards analytical continuation of normalized full gradient values of gravity data. Analytical continuation discriminates certain structural anomalies which cannot be distinguished in the observed gravity field. This method has been used in various petroleum and tectonic studies. The Trapeze method was used for the determination of Fourier coefficients during the application of this method. No other techniques for calculating these coefficients have been used. However, the Filon method was used for the determination of Fourier coefficients during the application of the NFG method in this work. This method, rather than the Trapeze method, should be preferred for indicating abnormal mass resources at the lower harmonics. In this study, the NFG method using the Filon method has been applied the first time to theoretical models of gravity profiles as example field at the Hasankale-Horasan petroleum exploration province where successful results were achieved. Hydrocarbon presence was shown on the NFG sections by the application of NFG downward continuation operations on theoretical models. Important signs of hydrocarbon structure on the NFG section for field and model data at low harmonics are obtained more effectively using this method.     

Application of Normalized Full Gradient Method to Self Potential (SP) Data

Recently, Normalized Full Gradient (NFG) method has widespread applications to natural potential fields, especially in gravity and magnetic. In this study, usage of NFG in Self-Potential (SP) data evaluation is tested. Results are compared to other SP interpretation methods. The NFG method is applied to synthetic and field SP data. As a consequence of application of the method to the anomalies of spherical, cylindrical and vertical sheet models, whose theoretical structures are explicit, the structures were found very close to their actual locations. In order to see the capability of the method in detecting the number of sources, NFG method was applied to different spherical models at different depths and locations. The least-squares inverse solution was applied to the same models and NFG method was found more powerful in detecting model structure. Sensitivity of NFG method for application to noisy data is also tested. An anomaly is generated by adding a random noise to two close sphere SP anomalies. The method seems to work for the two close spheres at high S/N ratio. Then, NFG method was applied to two field examples. The first one is the cross section taken from the SP anomaly map of the Ergani-Süleymanköy (Turkey) copper mine. The depth of the mineral deposit at that site was found about 38 m from the ground level. This result is well matched to previous studies. NFG was also applied to SP data from Seferihisar Izmir (Western Turkey) geothermal field and the location of the point source was determined. The field data of this site have already been modeled by the thermoelectric source (coupling) solution method. When these two methods are compared, they seem to support each other. It is concluded that the NFG method works perfectly when the structure model is simple. It is observed that natural potential sources close to earth’s surface are identified by the method more accurately at greater harmonics, while deep sources are identified at lesser harmonics. It produces reasonable results for noisy multi-source models than the other parameter identification methods (inverse solution, power spectrum, etc.).     

INTERPRETATION OF PULSE EM ANOMALIES OVER GANI CONDUCTORS,KURNOOL, INDIA*

A survey using Crone pulse electromagnetic (PEM) equipment was conducted near the village of Gani in Andhra Pradesh, India. The anomalies obtained had a shape typical for an inclined sheet conductor. From the multichannel TEM response, the multifrequency Slingram response was calculated. A comparison of the Slingram response of the Gani conductors with the free-air model response of a thin sheet conductor shows phase rotation and attenuation of the anomaly vector, thereby confirming the presence of a conductive overburden. Interpretation of the Gani results using free-air phasor diagrams causes an overestimation of depth and conductance of the target conductor unless data obtained at a sufficiently low frequency are used for the interpretation. For areas like Gani this frequency can be as high as 336 Hz.     

Detection of High-Potential Oil and Gas Fields Using Normalized Full Gradient of Gravity Anomalies: A Case Study in the Tabas Basin,Eastern Iran

The normalized full gradient (NFG) represents the full gradient of the gravity anomaly at a point divided by the average of the full gradient at the same point. The NFG minimum between two maxima in an NFG section or a closed minimum surrounded by closed maxima on an NFG map may indicate density-deficient anomalies closely related to possible oil–gas reservoirs. On a cross-section, closed minima can be used to estimate the depth to centers of possible hydrocarbon reservoirs. The NFG map can also be used to locate oil–gas exploratory wells for estimation of the depth of possible reservoirs. The objective of this paper is to use two and three-dimensional (2D and 3D) NFG on gravity data of the Tabas basin in Yazd province, eastern Iran. A hypothetical model is first considered to explore the NFG characteristics and their relationship with the geometry of the model. The physical properties of the model are then studied to simplify the interpretation of real data. Finally 2D and 3D NFG models are developed for real gravity data to predict the location of any possible high potential oil–gas reservoirs. The results obtained indicate two zones in the northern and central parts of the Tabas basin suitable for hydrocarbon prospecting. However, the favorable zone located in the middle of the basin in which anticline E is detected at a depth of 5–7 km is more important for the purpose of hydrocarbon exploration.     

QUANTITATIVE INTERPRETATION OF HORIZONTAL-LOOP EM MEASUREMENTS USING A PERMEABLE SPHERE MODEL*

An interpretation scheme for horizontal-loop EM measurements is presented for a permeable sphere model. The induced multipole moments are found to contribute significantly even at very low frequencies for a permeable conductor. The anomaly profiles are computed considering multipole excitation (up to 20) to study the effect of depth of burial and permeability of conductor. The anomaly half-width along with the inphase and quadrature anomaly amplitudes allow direct interpretation of the parameters of the sphere. The above scheme is suitable for results of Dighem II (coplanar configuration), Slingram and Max Min II measurements.     

Research Note: A simple method of image solution for a sphere of constant electrical potential in a conducting half‐space: implications for the applied potential method

The applied potential, or mise‐à‐la‐masse, method is used in mineral exploration and environmental applications to constrain the shape and extent of conductive anomalies. However, few simple calculations exist to help gain understanding and intuition regarding the pattern of measured electrical potential at the ground surface. While it makes intuitive sense that the conductor must come close to the ground surface in order for the lateral extent of the potential anomaly to be affected by the dimensions of the conductor rather than simply by the depth, no simple calculation exists to quantify this effect. In this contribution, a simple method of images solution for the case of a sphere of constant electrical potential in a conducting half‐space is presented. The solution consists of an infinite series where the first term is the same as the method of images solution for a point current source in an infinite half‐space. The higher order terms result from the interaction of the constant potential sphere with the no‐flux boundary condition representing the ground surface and cause the change in the shape of the potential anomaly that is of interest in the applied potential method. The calculation is relevant to applied potentials when the conductive anomaly is limited in all three space dimensions and is highly conductive. Using the derived formula, it is shown that, while the electrical potential at the ground surface caused by the sphere is affected even when the sphere is quite deep, the ratio of the potential to the current, a quantity that is more relevant to the applied potential method, is not affected until the centre of the sphere is within two radii of the ground surface. An expression for the contact resistance of the sphere as a function of depth is also given, and the contact resistance is shown to increase by roughly 45% as the sphere is moved from great depth to the ground surface.     

重力场向下延拓Milne法

重力场向下延拓能够突出局部和浅部的异常信息,分离叠加的异常特征.但是向下延拓通常具有过程不稳定、下延深度小、结果不准确等问题.针对向下延拓所存在的不足,本文利用重力场及其垂向一阶导数,基于辛普森(Simpson)求积公式,推导出重力场向下延拓米尔尼(Milne)公式.将本文向下延拓方法应用于模型数据,向下延拓模型结果及误差曲线表明,相对于向下延拓快速傅里叶变换(FFT)法和积分迭代法,向下延拓Milne法的深度更大,相对误差更小;相对模型值,向下延拓Milne法能够获得稳定且准确的结果.对加拿大乃查科(Nechako)盆地地区实测航空重力数据进行本文方法向下延拓验证,处理结果表明,相对于实测异常,本文方法向下延拓结果能够很好还原实测数据,并且在进一步向下延拓中反映原始异常的趋势,增强局部和细小异常信息.     

小波极大值方法及其在电磁异常信号提取中的应用

小波极大值法作为一种数据挖掘技术已经受到关注,并在地震科学研究领域开始进行应用研究。它能在长时间的观测数据中快速提取出不同时间、不同频率的有关异常信息。文中介绍了如何应用小波极大值法提取电磁场异常信息,即利用连续小波变换计算小波系数,计算各尺度小波系数的极大值,结合表征信号奇异性的Lipschitz指数分析异常的真实性,进而研究极大值在时间分布上的特点或规律,捕捉有关的电磁异常现象。利用该方法对2013年4月20日四川芦山7.0级地震后35d的连续观测的电磁场数据进行了分析,发现存在3次电磁场异常,探讨了这些异常可能与地震活动性之间存在的关系。尽管用这种方法尚不能确定发现的电磁场异常现象与地震有某种特定的关系,但是证明了小波极大值方法在连续观测数据中提取电磁异常现象的有效性。     

VLF ANOMALIES FROM A PERFECTLY CONDUCTING HALF PLANE BELOW AN OVERBURDEN*

A theoretical solution to the electromagnetic problem of a perfectly conducting half plane below a conducting overburden has been obtained. The VLF anomalies have been computed for different overburden conductivity and thickness and also for different dip angles of the half plane. In the computations the contribution to the secondary magnetic field from the electric Hertz potential has been neglected. The anomaly curves which are displayed as EM 16 readings, show a fairly complicated behaviour. This is mainly due to the phase shift and attenuation of the field caused by the conductivity of the overburden and the host rock. From the anomaly curves it is possible to define the apparent depth to the top of the conductor as the distance between the peak value and the cross-over of the real component. The apparent depth is usually larger than the actual depth, but it is possible to determine the actual depth to the conductor from the relation between the peak-to-peak anomaly and the apparent depth. When the peak-to-peak anomaly is fairly large, it is also possible to make estimates of the dip angle. However, a complete set of master curves will be a necessary tool for interpretation of VLF data when there is need to obtain more accurate estimates of the half plane parameters. In a specific case the theoretical calculations are shown to be in good agreement with measured data.     

瞬变电磁法对存在山谷地形时的多个异常体的探测能力研究

以层状地层中的2个三维导电薄板为例,考虑了山谷地形存在时,瞬变电磁法(TEM)分辨地下多个三维异常体的能力。模型计算的结果表明,当有山谷地形存在时,总的异常场由薄板的异常和地形的异常叠加在一起,表明异常场在空间上具有可加性质。在地形平坦时,TEM方法对相同尺寸的近源异常体的分辨能力要优于远源,而且离源越远的异常体异常越小,最后直到无法分辨。但是当存在山谷地形并且把源放在其中时,它们的总异常场叠加后会“放大”远源异常体的异常场,在一定意义上说,这对于分辨远处的异常体更加有利。当异常体在接收器下方埋深不是太大时,不论山谷地形在源处还是接收器处,TEM法对这些异常体的探测能力都是比较好的。2个异常体相距太近时,其异常会叠加在一起,给TEM的分辨增加一些困难。总体表明,在有山谷地形存在时,TEM方法对多个异常体仍具有较好的探测能力     

FIELD CONTINUATION AND THE STEP MODEL IN AEROMAGNETIC INTERPRETATION*

Downward continuation of the field in the neighborhood of a singularity of a magnetic anomaly is used to render the anomaly more two-dimensional, to make the bottom of the causal body more remote, and to obtain an auxiliary function, φ (O, z), by means of which the anomaly may be interpreted in terms of an equivalent vertical contact or step model. The concept of “apparent depth” is introduced and used in studying depth extent and susceptibility. The methods are illustrated with theoretical and practical examples.     

FIELD CONTINUATION AND THE STEP MODEL IN AEROMAGNETIC INTERPRETATION*

Downward continuation of the field in the neighborhood of a singularity of a magnetic anomaly is used to render the anomaly more two-dimensional, to make the bottom of the causal body more remote, and to obtain an auxiliary function, φ (O.z), by means of which the anomaly may be interpreted in terms of an equivalent vertical contact or step model. The concept of “apparent depth” is introduced and used in studying depth extent and susceptibility. The methods are illustrated with theoretical and practical examples.     

Nomograms for rapid evaluation of magnetic anomalies over long tabular bodies

The magnetic anomaly due to a long tabular body usually consists of a maximum and a minimum. The distances and the amplitudes of the maximum and the minimum, when defined in dimensionless quantities, may be used as characteristics of the source. In this paper, a method based on the positions of the maximum and the minimum on the magnetic anomaly due to a long tabular body has been presented. Characteristic ratios,D andA involving the distances and amplitudes of the maximum and the minimum points on the anomaly curve are defined. Nomograms showing the variations ofD andA with the parameters of (1) the dike and (2) the vertical fault models are presented. The parameters of the causative source are evaluated from the two ratiosD andA and the nomograms, using some simple analytical relations presented here. From the nomograms, it is observed that (a) for a thick dike,A is always greater thanD, (b)A=D for a thin sheet and (c) for a vertical fault,A is always less thanD. Thus from the characteristic ratiosD andA it is possible to evaluate the source parameters and also to distinguish whether the source is a dike, sheet or a vertical fault. The method is fast and is applicable for the magnetic anomalies either in total, vertical or horizontal component. The method has been applied on two field examples and the results are found to be in close agreement with those obtained by using other methods. A simple method of locating the origin on the anomaly curve is included. The limitations of the method are also discussed.     

Numerical modelling of airborne electromagnetic anomalies originating from low-conductivity 3D bodies1

Responses of a multifrequency, multicoil airborne electromagnetic (AEM) system were modelled numerically for 3D electrical conductors embedded in a resistive bedrock and overlain by an overburden of low to moderate conductivity. The results cover a horizontal coplanar coil configuration and two frequencies, 7837 Hz and 51 250 Hz. The models studied are single or multiple, poor conductors (conductance lower than 0.1 S) embedded in a host rock of high but finite resistivity (5000 Ωm) and overlain by a layer of overburden with finite thickness and low to moderate conductivity (conductance up to 2 S). On the basis of the modelling results, limits of detectability for poor conductors have been studied for the various model structures. The results indicate that the anomaly from a steeply dipping, plate-like conductor will decrease significantly when the conductor is embedded in a weakly conductive host rock and is overlain by a conductive overburden. However, an anomaly is obtained, and its magnitude can even increase with increasing overburden conductivity or frequency. The plate anomaly remains practically constant when only the overburden thickness is varied. Changes in overburden conductivity will cause the plate-anomaly values to change markedly. If the plate conductance is less than that of the overburden, a local anomaly opposite in sign to the normal type of anomaly will be recorded. Another major consequence is that conductors interpreted with free-space models will be heavily overestimated in depth or underestimated in conductance, if in reality induction and current channelling in the host rock and overburden make even a slight contribution to the anomalous EM field. The lateral resolution for the horizontal coplanar coil system was found to be about 1.7 times the sensor altitude. Similarly, the lateral extension of a horizontal conductive ribbon, required to reach the semi-infinite (half-space) behaviour, is more than three times the sensor altitude. Finally, screening of a steeply dipping plate, caused by a small, conductive horizontal ribbon, is much more severe than screening of the same plate by an extensive horizontal layer.     

INTERPRETATION OF VLF-EM IN-PHASE DATA USING CURRENT DENSITY PSEUDOSECTIONS1

The interpretation of VLF-EM surveys in terms of buried conductors can be assisted by the application of a linear filter to the observed in-phase component of the vertical magnetic field. One such scheme is examined critically by using the calculated response from a variety of synthetic models to compute theoretical current density pseudosections. The results confirm that this filter technique provides a useful complementary tool for studying the third (i.e. depth) dimension. For single, steeply dipping plates (> 45°) diagnostic information may be derived concerning the depth, size, lateral location, and direction of dip, since the current density maxima seems always to occur within the conductor or at least within one data interval. However, there are some limitations which do not appear to be widely recognized. For single plates the angle of dip cannot be resolved by the current density transformation. Pattern distortions can occur where targets are in close proximity, where the cross-sectional form of the conductor is complex or where the dip is shallow (< 45°). In these latter cases the current density maxima may not occur within the conductive structure and therefore cannot be used to infer depth of burial and/or conductor shape with the same degree of confidence.     

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.     

Downward continuation of (Vs)L profile in 1P (time-domain) with linear excitation using point electrodes. A short notet1

It is seen that the apparent chargeability (M_a)_L anomaly over a 2D graphite body splits into two distinct (V_s)_L anomalies which closely follow the apparent resistivity profile. This suggests that the electric field amplitude is distorted due to a superficial inhomogeneity creating a (V_s)_L anomaly, which bears no relation to the polarized body. The target depth obtained by continuation of such a profile is therefore, not acceptable.     

CURRENT CHANNELLING IN SQUARE PLATES WITH APPLICATIONS TO MAGNETOMETRIC RESISTIVITY1

The magnetometric resistivity (MMR) method uses a sensitive magnetometer to measure the low-level, low-frequency magnetic fields associated with the galvanic current flow between a pair of electrodes. While the MMR anomalies of simple structures such as dikes and vertical contacts have been determined analytically, there is a lack of systematic information on the expected responses from simple three-dimensional bodies. We determine the characteristic anomalies associated with square, plate-like conductors, which are excellent models of many base metal mineral deposits. The anomalies of plates of finite size are determined numerically using an integral equation method. A plate is subdivided into many sections and the current flow within each section is solved by equating the electrical field within each section to the tangential electrical field just outside it. When the plate size is small in relation to either the depth or the transmitter spacing, the shape and amplitude of the anomaly produced is closely approximated by a current dipole model of the same length and depth. At the other extreme, a large plate is represented by a half-plane. The dipole and half-plane models are used to bracket the behaviour of plates of finite size. The form of a plate anomaly is principally dependent on the shape, depth and orientation of the plate. A large, dipping plate near the surface produces a skewed anomaly highly indicative of its dip, but the amount of skew rapidly diminishes with increased depth or decreased size. Changes in plate conductivity affect the amplitude of the anomaly, but have little effect on anomaly shape. A current channelling parameter, determined from the conductivity contrast, can thus be used to scale the amplitude of an anomaly whose basic shape has been determined from geometrical considerations. The separation into geometrical and electrical factors greatly simplifies both the interpretation and modelling of MMR anomalies, particularly in situations with multiple plates. An empirical formula, using this separation, predicts the anomaly of two or more parallel plates with different conductances. In addition, the relation between the resolution of two vertical, parallel plates of equal conductance and their separation is determined. The ability of the integral equation method to model plate-like structures is demonstrated with the interpretation of an MMR anomaly in a survey conducted at Cork Tree Well in Western Australia. The buried conductor, a mineralized graphitic zone, is modelled with a vertical, bent plate. The depth to the top of the plate, and the plate conductance, is adjusted to fit the anomaly amplitude as closely as possible. From the modelling it would appear that this zone is not solely responsible for the observed anomaly.     

论被动源磁电勘探理论

本文从麦氏方程出发,运用电流磁场的等效理论阐明了在磁电勘探中,当矿体的二次极化电流具有垂直对称轴分布时,在地表面及以上空间中任一点的磁异常场（H）均等于零。因而,具有任何垂直对称状电化学矿产模式（石油、天然气、地下水及金属矿床等）的磁电勘探法异常场线积分均不存在。此外,由于对各种形状和任何极化倾角的矿体情况,地表面上均无电流密度垂直分量（i_n）存在,故地表面上异常场线积分均为零（∮_L H·dL=0）。因此,磁电勘探法不具备在地面上寻找此种矿产的物理前提。 本文还对倾斜极化球体和柱体的磁电勘探异常进行了计算,给出了主剖面上理论曲线的异常分布规律,指出了磁电异常的数量级。同时,还对井中磁电异常的分布规律给出了计算资料。为了对比,也对相应条件下的自然电场异常做了计算,指出了电场异常与磁场异常之间的不同特点及其对实际找矿的意义。     

CORRECTIONS FOR CONDUCTIVITY ESTIMATES IN INDUCTION PROSPECTING OF SULPHIDE DYKES IN A LAYERED ENVIRONMENT*

In a weathered environment estimates of depth and conductance of metallic sulphide dykes from conventional anomaly index diagrams for a vertical half-plane in air have to be corrected, besides the usual corrections, for: 1. moderate conductivity of the host rocks, and 2. finiteness of strike length S and depth extent D. Model experiments have been carried out to evaluate the response variation of a vertical planar conductor with varying depth extent and strike length for both insulating and conductive surroundings. The results indicate: 1. A conductor with finite depth extent (D/L < 2.5) or strike length (S/L < 5.0) in an insulating medium yields a lower estimate of conductance (mineralization) and a greater depth. 2. A moderately-conductive host rock enhances the anomaly and rotates the phase so that the conductor appears to be more resistive (less mineralized) and shallower. The results have practical significance since in weathered surroundings a highly-mineralized body of finite size could be missed, or misjudged, because of low estimates of conductivity and depth.