Interpretation of VLF Resistivity Data for Ground Water Contamination Surveys

Very low frequency (VLF) military communications systems provide a primary field that can be used for shallow geophysical surveys to locate ground water contamination and vertical geologic contacts. Useful properties that can be easily obtained from the interaction of the earth and the primary field are the magnitude of the vertical secondary magnetic field, the surface impedence, and the phase angle between the electrical and magnetic horizontal components. The variations in the secondary magnetic field can be related to vertical geologic contacts, such as the edges of landfill trenches. The surface impedence yields an apparent terrain conductivity, which can be used to locate low-resistivity anomalies often associated with contaminated ground water. The phase angle gives information on vertical variations in resistivity, phase angles less than 45° indicating increasing resistivity with depth. The depth of penetration of the VLF field is about one skin depth. For a frequency of 20 kHz, the skin depth in meters is approximately equal to 3.67 where p is terrain resistivity in ohmmeters.     

Analysis of magnetic anomalies due to some two-dimensional bodies using the Mellin transform

An interpretation technique using the Mellin transform is suggested for the analysis of magnetic anomalies due to some two-dimensional structures namely (i) a vertical sheet of both finite and infinite depth extent, (ii) a thick dyke and (iii) a horizontal circular cylinder. The Mellin transformed magnetic anomalies resemble gamma functions which are amenable to an easy interpretation. This procedure is illustrated with a small number of synthetic examples in each case. The practicality of the method is exemplified with the well-known vertical magnetic anomalies of Kursk (USSR) in the case of an infinite sheet model and Karimnagar magnetic anomaly (India) in the case of a horizontal circular cylinder. The results are compared with the techniques already available and found to be reliable.     

位场解析信号振幅极值位置空间变化规律研究

通过对单一边界、双边界、多边界以及点(线)质量模型重力异常解析信号振幅和重力异常垂向导数解析信号振幅的极值位置空间变化规律研究表明,重力异常垂向导数解析信号振幅和化极磁力异常解析信号振幅的极值位置相同,且与重力异常解析信号振幅的极值位置空间变化规律相似.利用位场解析信号振幅极大值位置能够准确识别单一直立边界地质体的边缘位置,但不能准确识别其它任何形体的边缘位置,其识别结果的偏移量大小随地质体的埋深、水平尺寸以及倾斜程度等变化.虽然重力异常垂向导数解析信号振幅比重力异常解析信号振幅的峰值更加尖锐、横向识别能力更强,其极大值位置更靠近地质体上顶面边缘位置,但均受地质体埋深的影响较大;随着埋深的增加,位场解析信号振幅的极大值位置会快速收敛到形体的"中心位置",其轨迹类似"叉子状";且对多边界模型会出现"极大值位置盲区"而无法识别其边缘位置.通过这些理论研究表明,位场解析信号振幅只能识别单一边界地质体的边缘位置;而不宜用来识别多边界地质体的边缘位置,但可以用来识别多边界地质体的"中心位置".     

Magnetic interpretation of long horizontal cylinders using correlation factors between successive least-squares residual anomaly profiles

Procedures are formulated using the correlation factors between successive least-squares residual magnetic anomaly profiles due to long horizontal cylinders for interpreting the three principal anomalies (vertical, horizontal, and total). It is demonstrated that correlation values can be used to determine the depth to the center of the buried structure and the index parameter. Procedures are also formulated to estimate the amplitude coefficient. Two worked examples using theoretical data show the effectiveness of the present method.     

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.     

Applying the tilt‐depth and contact‐depth methods to the magnetic anomalies of thin dykes

A new method for the calculation of the depth, location, and dip of thin dykes from pole‐reduced magnetic data is introduced. The depth can be obtained by measuring the distance between chosen values of a tilt angle that is based upon the ratio of the magnetic field and its Hilbert transform over the dyke. Alternatively, it can be obtained from the horizontal derivative of the ratio of the Hilbert transform of the field to the field itself, over the dyke. The latter method also allows the dip of the dyke to be estimated from the gradient of the depth estimates.     

RESPONSE OF A TWO-LAYER GROUND TO AN INFINITE CABLE CARRYING ALTERNATING CURRENT WITH REFERENCE TO TURAM ANOMALIES *

A formula is developed for the vertical magnetic field due to an alternating current passing through a long horizontal cable placed on a two-layer ground. The variations of the phase and amplitude ratio of the vertical field, along profiles perpendicular to the cable line are investigated. Within the limits encountered in practice, it is found that if the upper layer is conductive, as compared to the lower layer, the phase may vary appreciably whereas the amplitude ratio changes as in the case of vacuum.     

给定观测精度下的点(线)源模型重力与磁力垂向识别能力研究

重、磁勘探具有效率高、成本低、工作范围广等优点,已在地球物理勘探中得到了广泛应用.前人大多在不考虑重、磁勘探观测精度的条件下进行了垂向识别能力的研究,但在考虑重、磁观测精度条件下,重力（重力异常、重力张量）与磁力（磁力异常、磁力三分量、磁力张量）对孤立异常的垂向识别能力如何则需要进行深入的理论研究.本文从重、磁场正演理论出发,以球体（点源模型）和无限延伸水平圆柱体（线源模型）为例,考虑给定观测精度条件下,以重力和磁力幅值大小与观测精度的关系来研究垂向识别能力,从而消除了背景场的影响,提高了研究结果的可靠度.通过研究表明,对于孤立异常,重力张量在浅部一定深度内比重力异常的垂向识别能力强,该深度与重力异常和重力张量观测精度的比值成正比;垂直磁化磁力张量在浅部一定深度内比化极磁力异常的垂向识别能力强,该深度与磁力异常与磁力张量观测精度的比值成正比;磁力在浅部一定深度内比重力的垂向识别能力强,该深度与地质体的磁化强度和剩余密度比值、重力观测精度和磁力观测精度比值成正比.通过重力和磁力垂向识别能力的研究将为重、磁勘探的实际应用起到指导作用.     

On the use of the autocorrelation method for estimating the depth to the magnetic basement

The depth to the top of magnetic dykes can be estimated from total field aeromagnetic data using the relation between the depth to magnetic sources and the autocorrelation function of magnetic data. By using synthetic anomalies we show that in the ideal case, depth can be determined to an accuracy of 10% or better, when the anomaly sources are two-dimensional dykes. However, the estimated depths depend on the width of the dykes. The estimated depth is about 0.6 times the actual depth to the top of thin dykes, and around the true depth for thick dykes having width-to-depth ratio around 3. The depth is considerably overestimated for very thick dykes (e.g., contacts, which is a special case of the thick dyke). Thus, the autocorrelation method requires that the width-to-depth ratio of the dyke is estimated independently to correctly estimate the depths. Alternatively, it must be assumed that the width-to-depth ratio for the two-dimensional source body is between 1.5 and 4.     

ELECTROMAGNETIC FIELD OF SOURCES AT THE SURFACE OF A HOMOGENEOUS CONDUCTING HALFSPACE WITH HORIZONTAL ANISOTROPY: APPLICATION TO FISSURED MEDIA*

The electric and magnetic fields generated by horizontal electric and vertical magnetic dipoles lying on the surface of a conducting medium with horizontal anisotropy are investigated. Full expressions of their Fourier transforms are given, and the fields for a vertical magnetic dipole are calculated numerically. The radial and vertical magnetic components are found to be independent of the receiver-transmitter direction, whereas the other magnetic and electric components strongly vary with this direction. These results give useful criteria for defining the direction and amplitude of anisotropy from ground data; a ground experiment on fissured limestone was found to confirm the expected variations of the various field components. It is believed that this electromagnetic method can be used in order to provide information about the direction and amplitude of electric anisotropy.     

CONSTRUCTION OF COMPONENT MAPS FROM AEROMAGNETIC TOTAL FIELD ANOMALY MAPS1

Total field anomalies as defined from normal aeromagnetic surveys give good approximations of the anomalous components along the direction of the main geomagnetic field, which is generally much larger than the anomalous field. Using the relations between vertical and horizontal components of the field, the total field anomaly is related to any vertical or horizontal component and the corresponding horizontal and vertical derivatives. An example from the Siljan impact structure indicates that such directional filters may be applied to extract useful information from magnetic maps.     

层状介质中水平磁偶极子电磁场空间分布特征

针对岩层中介电常数和磁导率随深度变化的情况,给出水平磁偶极子源电磁场的水平或垂直空间分布特征及相应的变化规律。采用Kong给出的汉克尔（Hankel）J0变换线性滤波器（241点）和汉克尔J1变换线性滤波器（241点）算法,选用均匀大地和两层地电模型,讨论介质的介电常数和磁导率变化时的水平磁偶极子电磁场空间分布特征。计算结果表明,磁场的峨分量幅值与磁导率反相关;磁场H2和电场Ey分量随着磁导率的增大而增大;低频电磁测深中介电常数变化时对电磁场基本没有影响。     

QUANTITATIVE INTERPRETATION OF TRANSIENT ELECTROMAGNETIC FIELDS OVER A LAYERED HALF SPACE*

The transient fields from a finite horizontal loop excited by a half sine wave current pulse have been computed numerically for a particular source receiver configuration at a height of 100 meters above a layered ground. The amplitude of the vertical component of the magnetic field has been chosen for the interpretation. Curves of apparent conductivity vs. time, plotted during the off-time of the signal, show that layering is easily resolved, that resonance effects are present and that polarization effects are detectable for certain types of polarization.     

Electromagnetic induction in spherical cap current layers under lunar and terrestrial conditions

We present the theory of electromagnetic induction in spherical cap current sheets of arbitrary angular size, with arbitrary axisymmetric integrated electrical conductivity variations and located at any radial position with respect to the surface of observation. The external time-varying magnetic field may be arbitrarily oriented with respect to the current layer cap and the induced fields are derived for vacuum boundary conditions appropriate to terrestrial induction and plasma confinement boundary conditions relevant to lunar induction in the solar wind or magnetosheath plasmas. Numerical evaluations show the induced magnetic field as a function of position over the current sheet cap, depth to the current layer, size of the cap, integrated electrical conductivity of the current sheet, and frequency of the fluctuating external field. The local vertical magnetic field component and the horizontal field component which is normal to the periphery of the cap exhibit peak inductive responses above the edge of the current sheet for external magnetic fields perpendicular to the axis of the cap. Thus, induced magnetic field fluctuations observed over the edge of a conductivity anomaly may exhibit a highly directional, or polarized behavior. This may provide an explanation for the asymmetric character of induced magnetic field fluctuations observed on the lunar surface.     

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.     

玉树地震的地磁预测研究

利用玉树地震前玉树周围500 km范围内的地磁观测数据,采用地磁垂直分量加卸载响应比、地磁垂直分量日变化幅度逐日比、地磁垂直分量日变化空间相关、低点位移等方法讨论了震源区地磁场变化与地震的相关性,并发现它们之间有较好的对应关系。     

Electric field variations measured continuously in free air over a conductive thin zone in the tilted Lias-epsilon black shales near Osnabrück,Northwest Germany

Common studies on the static electric field distribution over a conductivity anomaly use the self-potential method. However, this method is time consuming and requires nonpolarizable electrodes to be placed in the ground. Moreover, the information gained by this method is restricted to the horizontal variations of the electric field. To overcome the limitation in the self-potential technique, we conducted a field experiment using a non conventional technique to assess the static electric field over a conductivity anomaly. We use two metallic potential probes arranged on an insulated boom with a separation of 126 cm. When placed into the electric field of the free air, a surface charge will be induced on each probe trying to equalize with the potential of the surrounding atmosphere. The use of a plasma source at both probes facilitated continuous and quicker measurement of the electric field in the air. The present study shows first experimental measurements with a modified potential probe technique (MPP) along a 600-meter-long transect to demonstrate the general feasibility of this method for studying the static electric field distribution over shallow conductivity anomalies.Field measurements were carried out on a test site on top of the Bramsche Massif near Osnabrück (Northwest Germany) to benefit from a variety of available near surface data over an almost vertical conductivity anomaly. High resolution self-potential data served in a numerical analysis to estimate the expected individual components of the electric field vector.During the experiment we found more anomalies in the vertical and horizontal components of the electric field than self-potential anomalies. These contrasting findings are successfully cross-validated with conventional near surface geophysical methods. Among these methods, we used self-potential, radiomagnetotelluric, electric resistivity tomography and induced polarization data to derive 2D conductivity models of the subsurface in order to infer the geometrical properties and the origin of the conductivity anomaly in the survey area. The presented study demonstrates the feasibility of electric field measurements in free air to detect and study near surface conductivity anomalies. Variations in Ez correlate well with the conductivity distribution obtained from resistivity methods. Compared to the self-potential technique, continuously free air measurements of the electric field are more rapid and of better lateral resolution combined with the unique ability to analyze vertical components of the electric field which are of particular importance to detect lateral conductivity contrasts. Mapping Ez in free air is a good tool to precisely map lateral changes of the electric field distribution in areas where SP generation fails. MPP offers interesting application in other geophysical techniques e.g. in time domain electromagnetics, DC and IP.With this method we were able to reveal a ca. 150 m broad zone of enhanced electric field strength.     

ON THE POSSIBILITIES OF DETERMINING DIP IN MAGNETIC INTERPRETATION WITH THE INFINITELY DEEP PLATE MODEL*

Dip and magnetic susceptibility of very deep magnetic plates can be estimated approximately from either vertical, horizontal or total field measurements. A general accuracy of 2–5 degrees is easily obtained, if the other plate parameters, most notably horizontal position of the plate, are precisely determined. For reliable interpretation, measurements around the anomaly maximum or on the dip-side flank of the anomaly should be preferred. The depth extent of the plates must be great, some ten times the plate width at least. The method is best suited to form a part of a plate interpretation scheme, where the other plate parameters are found by some other suitable means. The method can be applied to a simultaneous determination of dips of several plates, but because of its error sensitivity an iterative formulation should then be preferred.     

Geomagnetic sounding of conductivity anomalies in the lower crust and uppermost mantle

Knowledge of the structure of the lower crust and uppermost mantle is of special importance in understanding plate tectonics. Electrical conductivity of this region has been measured recently in various parts of the world. Transfer functions are still the most widely used quantity in data analysis and model fitting. Anomalies in the horizontal magnetic components in combination with anomalies in the vertical component have been found very useful in locating conductivity contrasts. With these, when the cause of the anomaly is a concentrated line current, both the position of the line current and its depth can be directly located. The method of hypothetical event analysis is another new technique and this is highly suited for areas having complex subsurface geology or areas under non-uniform source fields or both. The anomaly is more suitable for modelling geophysical structures when it is separated into regional and local components. Model calculations still are not very satisfactory and the importance of one dimensional calculations must be emphasized for they give direct information on the variation of conductivity with depth, which is the purpose of GDS. We need more results, especially from tectonically active areas, before the underlying physical processes can be completely understood.     

CARACTERES DE ĽONDE ELECTROMAGNETIQUE DE SURFACE ENGENDREE PAR UN DIPOLE MAGNETIQUE *

The electromagnetic field radiated from a magnetic dipole lying on the ground is considered, in the extremely low frequency range (DC to 20 000 Hertz). Theoretical and experimental data are given on the characteristics of the surface wave (vanishing wave) generated at the air-ground interface, in the case of an homogeneous subsurface. The case of a subsurface with electrical resistivity varying with depth is considered. It is shown how the above-mentioned characteristics may be applied in the quantitative investigation of the electrical resistivity of the subsurface as a function of depth, in a method using the measurements on the ground of all the components of the radiated field: horizontal electrical components, vertical and horizontal magnetic components.