The boundary integral calculations of the forward problem for D.C. sounding and MMR methods for a 3-D body near a vertical contact

Summary The paper presents comprehensive theory based on the boundary integral method for calculations of the electric potential, electric field and corresponding magnetic field due to a pair of D.C. source electrodes near a vertical resistivity contact in the halfspace, indlucing a 3-D disturbing body in the vicinity of the contact. Special attention is paid to the case when the disturbing body touches the vertical contact. Results of numerical calculations are presented in the form of sounding curves and a set of isoline graphs for potential, components of the electric and magnetic field (total and anomalous) on the surface of the Earth. It is shown that the presence of the disturbing body at the contact is most pronounced in the electrical characteristics. Anomalies in the magnetic field are small in comparison to the field due to the electric current in the electrode cable and primary currents flowing from the electrodes.     

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.     

Magnetotelluric response of a two-dimensional sloping contact by the finite element method

Summary The finite element method, with triangular elements, is used to study the effect of a two-dimensional sloping contact on the surface electromagnetic fields. It is found in the case ofH-polarization and small slopes that the electric field and the apparent resistivity near the contact, on the conductive side, are higher than their asymptotic values. In the case ofE-polarization the apparent resistivity and phase values on the conductive side fall off less rapidly to their asymptotic values with decreasing slope resulting in higher apparent resistivity and phase values on the conductive side, than those expected for a vertical contact. The peak in the amplitude and phase of the normalized vertical magnetic field shifts from the resistive side for a vertical contact to the conductive side for a sloping contact. Far from the sloping contact, on the conductive side, higher values are observed for the normalized vertical magnetic field than in the case of a vertical contact.     

1690～2000年地磁场能量的三维分布及其长期变化

利用Bloxham & Jackson 地磁场模型和国际参考地磁场模型(IGRF),研究了1690～2000年地磁总能量及其北向、东向和垂直向分量的能量以及非偶极子磁场的能量在地球内部的分布及长期变化.结果表明,地表和地核以外地磁场总能量及其北向和垂直向的能量是持续衰减的,垂直向的磁场能量占总能量的64％以上,对总能量的贡献起主要作用;东向分量的能量随时间的变化以增加为主.地磁场的能量变化率存在56年的周期,主要是由偶极子磁场产生的.地表以外的非偶极子磁能从减小到增大转折出现在1770年,比地核以外滞后40年.地球内部磁能随时间的变化显示,偶极子磁能逐渐减小,非偶极子磁能增加,越靠近核幔边界增加越快;偶极子和非偶极子磁能的变化量相等的分界面在距地心3780km处.从核幔边界到地表,磁能变化的衰减非偶极子比偶极子快,表明偶极子磁场比非偶极子磁场有更深的场源.     

磁总场异常垂直梯度三维相关成像

本文提出了磁总场异常垂直梯度三维相关成像方法,用于成像地下等效磁源分布.它首先将地下待成像空间划分为三维规则网格,然后直接计算每个网格节点磁偶板子在观测面理论磁总场异常垂直梯度与实测磁总场异常垂直梯度的互相关,其相关系数值表征等效磁偶极子分布(即磁偶极子发生的概率).理论长方体组合模型数据和实际某矿区磁测资料试验结果表明本文方法计算得到的相关系数值能基本反映地下的磁源分布,且分辨率明显高于磁总场异常三维相关成像的分辨率,也高于基于熵滤波分离异常的磁总场异常三维相关成像的分辨率.     

NUMERICAL MODELLING OF A NEW MULTI-FREQUENCY ELECTROMAGNETIC SYSTEM*

The amplitude of the horizontal magnetic field in the ground between two parallel wires, both carrying an alternating current in the same direction, is likely to have a saddle point if the separation between the wires is small and the frequency is low. The amplitude has a maximum in the vertical direction and a minimum in the horizontal. Rectangular geological structures in the ground which are centered between the wires have a varying effect on the magnetic fields at the surface. In general, the vertical magnetic field “crosses over” at the center of the structure. A shallow and flat lying conductor displays a broad flat type of profile when the horizontal magnetic field between the wires is measured. Changing the structure to a narrower but more conducting one at depth will provide a more pointed but still broad profile. The phase of the horizontal field is also increased. When the structure is a thin vertical dyke, the amplitude of the horizontal magnetic field anomaly due to the dyke rapidly decreases as the depth of the dyke is increased. The phase of the horizontal field is less sensitive to changes in depth of the dyke but is more sensitive to the conductivity ratio of the dyke and the half-space. The amplitude of the vertical magnetic field anomaly due to the dyke is only slightly influenced by conductivity contrast or the depth of the dyke. The phase of the vertical magnetic field, however, is strongly influenced by the conductivity contrast, particularly if the conductivity frequency product is greater than hundred. In essence, the field behaves like that of the conventional vertical loop source, but the fields are uniform over much larger areas. This suggests the possibility of using dip angle measurements for rapid reconnaissance.     

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.     

Stationary approximation of the magnetotelluric field in a halfspace with a vertical boundary and three-dimensional perturbing body

Summary Based on the generalized potential of a double layer, integral formulae have been derived for calculating the stationary approximation of the magnetotelluric field in a halfspace divided by a vertical boundary into two quarterspaces, one of which contains a three-dimensional perturbing body. The appropriate boundary integral equation and other surface integrals have been computed for a perturbing body in the shape of the three-dimensional prism located at the vertical boundary, or in contact with the said boundary. The exciting electrical field is assumed to be homogeneous and perpendicular to the vertical boundary. Isoline graphs of the electrical and magnetic fields on the surface of the halfspace have been plotted and their anomalies are discussed.     

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.     

Convective plan-form of two-scale dynamos in a plane layer

We study generation of magnetic fields, involving large spatial scales, by convective plan-forms in a horizontal layer. Magnetic modes and their growth rates are expanded in power series in the scale ratio, and the magnetic eddy diffusivity (MED) tensor is derived for flows, symmetric about the vertical axis in a layer. For convective rolls we demonstrate that MED is never below molecular magnetic diffusivity. For cell patterns possessing the symmetries of a rectangle, critical values of molecular magnetic diffusivity for the onset of small- and large-scale magnetic field generation are the same. No instances of negative MED in hexagonal cells have been detected. A family of plan-forms has been found numerically, where MED is negative for molecular magnetic diffusivity over the threshold for the onset of small-scale magnetic field generation. However, the region in the parameter space, where large-scale dynamo action is observed, is small.     

REMARKS ON THE USE OF THE MAGNETIC GRADIOMETER IN OIL EXPLORATION *

The principle of optical pumping allows the design of magnetometers with high sensitivity. When mapping the field of the total magnetic force, it is no longer possible to make full use of the accuracy of the instruments because the accuracy of the reduction of the diurnal variation is limited. By simultaneously recording with two instruments in different altitudes, the vertical gradient can be measured which doe's not depend on the time variation of the magnetic field. Therefore, the gradiometer seems to be a more adequate tool for oil exploration than the magnetometer. It is investigated in this article whether the results of this gradiometer or the measurements of the total magnetic field by the high sensitive magnetometer are more useful in oil exploration. The article comes to the conclusion that for most problems of oil exploration the total magnetic field is a more valuable unit than the vertical gradient measured directly by the gradiometer. The total magnetic field allows a better investigation of the tectonics than the vertical gradient. The apparent advantages of the gradiometer claimed by its supporters are mainly based on inconsistent mathematical concepts.     

Instability of a thin magnetic tube in the solar atmosphere

Abstract

The static equilibrium of a thin vertical magnetic tube embedded in the solar atmosphere is shown to be dynamically unstable against the fundamental mode of perturbation having no nodes in the vertical displacement. The instability has its origin in the convection zone, and the eigenfunction is extended further up in the stable upper layers by the magnetic field which guides the displacement mainly in the longitudinal direction. It is suggested that the downdraft observed in the solar network structure is a finite amplitude consequence of this instability. The overtone modes are found to be stable.     

A model for the coast-effect

A model for the coast-effect of geomagnetism is presented, in which the horizontal magnetic field induces currents in a circuit including a thin finite ocean. The currents flow horizontally across the ocean, vertically down into the earth, back through the deep interior of the earth, and vertically up to the ocean to complete the current loop. The upper layers of the earth are given non-zero conductivity, allowing the possibility of such current loops.A two-dimensional model involving such currents has been worked out analytically, and it is found that a significant induced magnetic field at the seafloor can be obtained with a reasonable conductivity in the earth's upper layers. A three-dimensional model has also been worked out numerically. It is found that the induced vertical component of magnetic field is of comparable magnitude to the horizontal component induced normal to the coast, whereas the horizontal component parallel to the coast is small. These relations are required to explain the observation of Parkinson arrows.     

Convection in a rotating magnetic system and Taylor's constraint

Abstract

A system is considered in which electrically conducting fluid is contained between two rigid horizontal planes and bounded laterally by a circular cylinder. The fluid is permeated by a strong azimuthal magnetic field. The strength of the field increases linearly with distance from the vertical axis of the cylinder, about which the entire system rotates rapidly. An unstable temperature gradient is maintained by heating the fluid from below and cooling from above. When viscosity and inertia are neglected, an arbitrary geostrophic velocity, which is aligned with the applied azimuthal magnetic field and independent of the axial coordinate, can be superimposed on the basic axisymmetric state. In this inviscid limit, the geostrophic velocity which occurs at the onset of convection is such that the net torque on geostrophic cylinders vanishes (Taylor's condition). The mathematical problem which describes the ensuing marginal convection is nonlinear, and was discussed previously for the planar case by Soward (1986). Here new features are isolated which result from the cylindrical geometry. New asymptotic solutions are derived valid when Taylor's condition is relaxed to include viscous effects.     

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。     

FREQUENCY ELECTROMAGNETIC SOUNDING USING A VERTICAL MAGNETIC DIPOLE*

A horizontal transmitter loop (vertical magnetic dipole) is used for frequency electromagnetic (FEM) soundings. The frequency ranges from approximately 6 Hz to about 4000 Hz. The vertical and radial magnetic field components are measured for 20 frequencies per decade several hundred meters from the transmitter loop. A very small bandwidth is selected for amplification using a reference signal. An Apple computer is used for data acquisition. A computer program for Marquardt inversion optimizes the parameters for the n-layer case: the resistivities and thicknesses of individual beds and a correction factor for the primary magnetic field. Interpretation of each component individually yields practically the same parameters. Examples from the field are given with interpretation; comparison with dc resistivity measurements is provided. The ratio of vertical/radial magnetic field components vs. frequency can be transformed simply into apparent resistivity vs. apparent depth. This can be done in the field to obtain an estimation of the depth of the layer boundaries. FEM results are compared with Schlumberger d.c. sounding obtained at the same site.     

A RECTANGULAR LOOP SOURCE OF CURRENT ON A TWO-LAYERED EARTH*

Using the concept of reciprocity and the known solution for the electric field of a vertical oscillating magnetic dipole source placed over a two-layered halfspace, an integral expression for the vertical magnetic field produced by a horizontal rectangular loop, carrying an oscillating current and placed on the surface of the same halfspace, is deduced. This expression is such that it can be evaluated by a combination of straightforward numerical integration and digital linear filter techniques. Displacement currents everywhere in space are neglected. Fields both inside and outside the loop are presented as sounding curves. A little over a decade of frequencies (100–3000 Hz) appears to be the minimum requirement and two decades (100–10000 Hz) are sufficient for most situations. Parametric and geometric sounding curves both show good resolution of subsurface layering. Phase shows better resolution than amplitude. Similarly, resolution is higher when conductivity increases with depth than when it decreases. Besides being useful for the electromagnetic depth sounding for layered earth structures, such computations can be applied to determine normal corrections to Turam observations, whenever a rectangular loop of finite size is used as a transmitter.     

ON THE COMPUTATION OF THE MAGNETIC FIELD DUE TO A D.C. POINT ELECTRODE AT THE VERTICAL BOUNDARY BETWEEN TWO QUARTER-SPACES1

New formulae are presented for the calculation of the horizontal magnetic field due to a point electrode situated at the vertical boundary between two quarter-spaces of different electrical conductivities. Previously the solution was obtained using a double Fourier transform of the expression for the vertical component of the magnetic field. The new formulae are given in the form of single integrals.     

The stabilizing effect of viscosity on magnetic wind flows from accretion discs

Magnetically channelled winds are believed to be a feature of most accretion discs. It has been shown that such flows can remove significant amounts of angular momentum from the disc and make a major contribution to driving the inflow. For a suitable range of poloidal magnetic field bending, only a small fraction of the disc mass is lost in the wind flow, so most material reaches the inner region of the disc. However, discs driven purely by such a process are prone to a field-bending instability which can lead to runaway mass loss. It is shown here that a small amount of disc viscosity can quench such an instability and allow steady disc-wind models to be constructed. The effects of perturbations to the coupling between the radial and vertical structures are allowed for, with the thermal balance having particular relevance. Runaway increases in field bending are prevented by increases in the disc temperature and magnetic diffusivity mainly caused by viscous dissipation.     

Experimental errors of measurements of vertical geomagnetic gradients in the stratosphere

The errors of measurements of vertical geomagnetic gradients at altitudes of 20–40 km, using a balloon magnetic gradiometer with a 6-km-long measuring base oriented along gravity, have been studied in the work. The errors related to the deviation of the measuring base position relative to the vertical have been studied during the real balloon flight with the help of the navigation GPS receivers. The deviations of the measuring base within 5°, which can sometimes reach 15°, have been obtained. This results in a decrease in the magnetic gradient measurement accuracy due to the errors introduced in the specification of the normal magnetic field used to detect magnetic anomalies. To eliminate this error, a GPS receiver was built in each magnetometer in order to observe magnetometers during synchronous measurements and to correct the measurements for the normal magnetic field. It has been indicated that the effect of deviations of the measuring base position on the results is not more than 2% of the measured value at such organization of a gradiometer.