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.     

Remanence correction in magnetic interpretation with the infinitely deep plate model

Summary Conditions are given under which two thick plates, differing in dip, apparent susceptibility, and remanence, will produce similar magnetic anomalies. From these conditions correction formulae are developed. Using these formulae the dip and susceptibility of a plate with remanent magnetization can be obtained from those of non-remanent plate. An interpretation procedure is suggested where the magnetic anomaly is first interpreted by means of a plate without remanence, dip and apparent susceptibility are then estimated by using the correction formulae developed. Thickness, position and depth of the plate are unaffected by the remanence correction procedure. The procedure is independent of the field component measured.     

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.     

A NEW APPROACH TO MAGNETIC PROFILE INTERPRETATION*

By using two components of anomalous magnetic fields and a formulation including complex numbers it is possible to calculate the position parameters of thick plates and both magnetization and position of thin plates directly from any two or three points of anomaly profiles. The formulae (interpretation operators) allow automatic topographic corrections to be made. The new two-component operators give more reliable results than the conventional methods of interpretation. The variance of the parameter values obtained with subsequent points of an anomaly measures directly, the total error of interpretation. The application of infinite thin plate operators to a long profile results in characteristic patterns, from which the estimation of the number of plates and their approximate position is possible.     

A CONTRIBUTION TO THE QUANTITATIVE ERROR ANALYSIS IN MAGNETIC AND GRAVIMETRIC INTERPRETATION *

The paper discusses the smallest obtainable parameter errors (variances) in the interpretation with the least-squares method. Useful approximations of the sum of squares contained in the minimum error expressions are obtained using results of numerical integration. The approximations lead to especially simple results for long interpretation profiles, when the parameter errors are proportional to the square root of the point separation. Formulae are developed and examples shown for minimum error calculation in gravimetric interpretation with the cylindrical model and in magnetic interpretation with the two-dimensional plate model. Smallest errors are obtained when the interpretation profile is chosen around the anomaly maximum except for dip and depth extent interpretation of magnetic plates.     

Spherical earth gravity and magnetic anomaly analysis by equivalent point source inversion

To facilitate geologic interpretation of satellite elevation potential field data, analysis techniques are developed and verified in the spherical domain that are commensurate with conventional flat earth methods of potential field interpretation. A powerful approach to the spherical earth problem relates potential field anomalies to a distribution of equivalent point sources by least squares matrix inversion. Linear transformations of the equivalent source field lead to corresponding geoidal anomalies, pseudo-anomalies, vector anomaly components, spatial derivatives, continuations, and differential magnetic pole reductions. A number of examples using 1°-averaged surface free-air gravity anomalies and POGO satellite magnetometer data for the United States, Mexico and Central America illustrate the capabilities of the method.     

A CONTROL OF TWO-DIMENSIONAL MAGNETIC INTERPRETATION BY THREE-DIMENSIONAL MODEL BODY ANOMALIES*

In magnetic routine interpretation the comparison of two-dimensional model curves with measured magnetic anomalies is widely used for an approximate evaluation of the position and depth of magnetic models. Before starting an interpretation of a survey by means of two-dimensional models, it is very useful to have an idea of the shape of anomalies caused by extended but finite bodies, taking into account various strike directions: Three sets of anomalies of thin plates (horizontal length 19, downward length 9, width 1) dipping 30°, 60°, and 90° resp. for various strike directions and an inclination of 20° were computed. Some of these anomalies, e.g. those with nearly N-S strike direction look rather complicated, and at the first glance one would not expect that they are caused by such simple bodies. Several profiles crossing the computed anomalies perpendicularly were interpreted two-dimensionally. For less extended anomalies the depths determined for the top of the plates are 10-20% too small, the magnetization amounts to 50–75 % of the value of the finite bodies. The interpretation of the profiles covering more extended anomalies gave very accurately the same values for the position, depth and magnetization for the two-dimensional body as for the original three-dimensional model. Anomalies of vertical prisms with varying extensions in the y-direction were computed. Their differences in amplitude and in the distance maximum-minimum show that interpretation of short anomalies by two-dimensional methods yields depth errors of up to 20 percent. To see the possibilities of the separation of superimposed anomalies dike anomalies were added to the anomaly of a broad body in great depth and several attempts were made to interpret parts of the composite anomalies. The interpreted bodies lie too deep. In complicated cases the depth values can have large errors, but experienced interpreters should be able to keep the errors in the range of one third of the depth values.     

Virtual Pole from Magnetic Anomaly (VPMA): A procedure to estimate the age of a rock from its magnetic anomaly only

Virtual Pole from Magnetic Anomaly (VPMA) is a new multi-disciplinary methodology that estimates the age of a source rock from its magnetic anomaly, taken directly from available aeromagnetic data. The idea is to use those anomalies in which a strong remanent magnetic component is likely to occur. Once the total magnetization of the anomaly is computed through any of the currently available methods, the line that connects all virtual paleogeographic poles is related with the position, on a paleogeographic projection, of the appropriate age fragment of the APWP curve. We applied this procedure to five (5) well-known magnetic anomalies of the South American plate in SE Brazil, all of them associated to alkaline complexes of Mesozoic age. The apparent ages obtained from VPMA on three of the anomalies where the radiometric age of the source rock is known – Tapira, Araxá and Juquiá – were inside the error interval of the published ages. The VPMA apparent ages of the other two, where the age of the source rock is not known (Registro and Pariqueraçu magnetic anomalies) were geologically coherent. We expect that the application of the VPMA methodology as a reconnaissance geochronological tool may contribute to geological knowledge over continental areas, especially when the source rocks of the magnetic anomalies are unknown or buried below superficial sediments.     

Existence of the frequentistic estimate for power-law regression with a location parameter, with applications for making discharge rating curves

Practical application of the power-law regression model with an unknown location parameter can be plagued by non-finite least squares parameter estimates. This presents a serious problem in hydrology, since stream flow data is mainly obtained using an estimated stage–discharge power-law rating curve. This study provides a set of sufficient requirements for the data to ensure the existence of finite least squares parameter estimates for a power-law regression with an unknown location parameter. It is shown that in practice, these requirements act as necessary for having a finite least squares solution, in most cases. Furthermore, it is proved that there is a finite probability for the model to produce data having non-finite least squares parameter estimates. The implications of this result are discussed in the context of asymptotic predictions, inference and experimental design. A Bayesian approach to the actual regression problem is recommended.     

A NEW APPROXIMATE METHOD FOR DIRECTLY INTERPRETING GRAVITY ANOMALY PROFILES CAUSED BY SURFACE GEOLOGIC STRUCTURES*

For outcropping bodies an approximate direct interpretation of the associated gravity anomaly is generally obtained with the flat plate formula. Results can be significantly improved if the causative body is approximated by a bell shape instead of a flat plate. A set of parameter curves allows the conversion to depth data. The validity of the method is borne out by synthetic models and by field examples in a Nevada valley with Tertiary and in the Los Angeles Basin. The method provides structural definition more accurate than can be obtained with the flat plate formula, particularly in the case of narrow anomalies.     

Subducted slabs beneath the eastern Indonesia-Tonga region: insights from tomography

Tomographic images of mantle structure beneath the region north and northeast of Australia show a number of anomalously fast regions. These are interpreted using a recent plate tectonic reconstruction in terms of current and former subduction systems. Several strong anomalies are related to current subduction. The inferred slab lengths and positions are consistent with Neogene subduction beneath the New Britain and Halmahera arcs, and at the Tonga and the New Hebrides trenches where there has been rapid rollback of subduction hinges since about 10 Ma. There are several deeper flat-lying anomalies which are not related to present subduction and we interpret them as former subduction zones overridden by Australia since 25 Ma. Beneath the Bird’s Head and Arafura Sea is an anomaly interpreted to be due to north-dipping subduction beneath the Philippines-Halmahera arc between 45 and 25 Ma. A very large anomaly extending from the Papuan peninsula to the New Hebrides, and from the Solomon Islands to the east Australian margin, is interpreted to be the remnant of south-dipping subduction beneath the Melanesian arc between 45 and 25 Ma. This interpretation implies that a flat-lying slab can survive for many tens of millions of years at the bottom of the upper mantle. In the lower mantle there is a huge anomaly beneath the Gulf of Carpentaria and east Papua New Guinea. This is located above the position where the tectonic model interprets a change in polarity of subduction from north-dipping to south-dipping between 45 and 25 Ma. We suggest this deep anomaly may be a slab subducted beneath eastern Australian during the Cretaceous, or subducted north of Australia during the Cenozoic before 45 Ma. The tomography also supports the tectonic interpretation which suggests little Neogene subduction beneath western New Guinea since no slab is imaged south of the New Guinea trench. However, one subduction zone in the tectonic model and many others, that associated with the Trobriand trough east of Papua New Guinea and the Miocene Maramuni arc, is not seen in the tomographic images and may require reconsideration of currently accepted tectonic interpretations.     

Depth Estimates for Slingram Electromagnetic Anomalies from Dipping Sheet-like Bodies by the Normalized Full Gradient Method

The Normalized Full Gradient (NFG) method was proposed in the mid–1960s and was generally used for the downward continuation of the potential field data. The method eliminates the side oscillations which appeared on the continuation curves when passing through anomalous body depth. In this study, the NFG method was applied to Slingram electromagnetic anomalies to obtain the depth of the anomalous body. Some experiments were performed on the theoretical Slingram model anomalies in a free space environment using a perfectly conductive thin tabular conductor with an infinite depth extent. The theoretical Slingram responses were obtained for different depths, dip angles and coil separations, and it was observed from NFG fields of the theoretical anomalies that the NFG sections yield the depth information of top of the conductor at low harmonic numbers. The NFG sections consisted of two main local maxima located at both sides of the central negative Slingram anomalies. It is concluded that these two maxima also locate the maximum anomaly gradient points, which indicates the depth of the anomaly target directly. For both theoretical and field data, the depth of the maximum value on the NFG sections corresponds to the depth of the upper edge of the anomalous conductor. The NFG method was applied to the in-phase component and correct depth estimates were obtained even for the horizontal tabular conductor. Depth values could be estimated with a relatively small error percentage when the conductive model was near-vertical and/or the conductor depth was larger.     

On the interpretation of magnetic anomalies for strong remanent magnetizations

In this paper some aspects concerning the interpretation of magnetic anomalies are treated, particularly when the remanent magnetization intensity is strong. In this case, since total and induced magnetization vectors can have very different directions, a correct anomaly interpretation strictly depends on the knowledge of their declinations and inclinations.Thus, a specific procedure is described to determine such parameters from well-known semi-empirical techniques and vectorial relations.Furthermore, the classical definition of apparent susceptibility is shown to be inadequate to this problem and a more general formulation is suggested, which is not only related to the true susceptibility and to the Koenisberger ratio, but also to the declinations and inclinations of the induced and remanent magnetization vectors.The two apparent susceptibilities are then compared for some synthetic magnetic anomalies and significant differences are found.     

A direct method of interpreting gravity and magnetic anomalies: The case of a horizontal cylinder

Summary A new method of interpreting the gravity and magnetic anomalies is introduced with special reference to the magnetic anomalies of a horizontal cylinder. The method consists of calculating the functions of the anomaly and its distance from an arbitrary point. These form a simple linear equation with coefficients related to the parameters defining the body. Since each observation forms a separate linear equation, the required normal equations are formed by the method of least squares and solved for the coefficients and hence for the various parameters defining the target. The discussion here is confined to the vertical magnetic anomalies. The application of the method to horizontal and total field anomalies of two dimensional bodies is also outlined.     

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。     

解释重磁资料中最优化选择法的若干问题

本文中我们将拟牛顿法应用到磁力、重力资料的自动解释中来,通过计算对比说明,在收敛的稳定性上拟牛顿法比常用的阻尼最小二乘法大为优越。文中又讨论了最优化选择法的收敛性、多解性、模型体的选择、参量的选择和约束,以及解释三个矿区磁异常的实例。     

INTERPRETATION OF THE GRAVITY ANOMALY OVER A CAUSATIVE BODY WITH CIRCULAR SYMMETRY*

The interpretation of the gravity anomaly on a horizontal plane over a causative body having circular symmetry about a vertical axis is considered from a rather unconventional approach. As the analytical expression for the gravity effect of a circular body assumes a closed form only on the axis of symmetry, the interpretation in this approach is carried out with the anomaly profile along the axis—which leads to simpler and faster computation. A numerical method is developed for computation of the anomaly profile along the vertical axis from the horizontal radial profile of the symmetric anomaly by upward continuation. Provision is also made for an end correction when the radial profile has only a limited extension. Some simple geometrical shapes are assumed for the causative body. Its parameters are then determined from least squares fitting of its gravity effects to the observed (upward continued) vertical profile (i) by the steepest descent method and (ii) by the Newton-Raphson method. Some applications of these methods are demonstrated.     

EIN AUTOMATISCHES VERFAHREN ZUR INTERPRETATION MAGNETISCHER ANOMALIEN NACH DER METHODE DER KLEINSTEN QUADRATE*

The interpretation of magnetic anomalies on the basis of model bodies is preferably done by making use of “trial and error” methods. These manual methods are tedious and time consuming but they can be transferred to the computer by making the required adjustments by way of the method of least squares. The general principles of the method are described. Essential presumptions are the following:

• 1 the assumption of definite model bodies
• 2 the existence of approximation values of the unknown quantities (position, dip, magnetization, etc.)
• 3 a sufficiently large number of measuring values, so that the process of adjustment can be carried out.

The advantages of the method are the following:

• 1 substantial automatization and a quick procedure by using computers
• 2 determination of the errors of the unknown quantities.

The method was applied to the interpretation of two-dimensional ΔZ- and ΔT-anomalies. Three types of model bodies are taken as basis of the computer program, viz. the thin dyke, infinite resp. finite in its extension downward and the circular cylinder. Only the measuring values are given to the computer. The interpretation proceeds in the following steps:

• 1 calculation of approximation values
• 2 determination of the model body of best fit
• 3 iteration in the case of the model body of best fit.

The computer produces the end values of the unknown quantities, their mean errors, and the pertaining theoretical anomalies. These end results are given to a plotting machine, which draws the measured curve, the theoretical curve and the model bodies. Interpretation examples are given.     

应用远震有限频率层析成像反演中国东北地区上地幔P波三维速度结构

选取黑龙江、吉林、辽宁、内蒙古区域地震台网,以及NECESSArray流动台阵记录的223个远震事件的波形资料,采用多道互相关方法得到了22569个P波相对走时数据,并计算了相应的走时灵敏度核,应用有限频率层析成像反演得到中国东北地区上地幔600 km以上的P波三维速度结构模型,利用检测板评估了反演结果的分辨率。结果表明,松辽盆地下方80～200 km的深度上呈主体的低速异常,与这一地区上地幔浅部的高地温值和低密度的特征相互对应,可能暗示了部分熔融的地幔。南北重力梯度带两侧的速度结构明显不同,这一差异可以延伸到200 km以下,表明在中国东北地区南北重力梯度带有可能是一条上地幔内部结构的变化带,或是深部结构的分界线。长白山火山区下呈大范围的低速异常,并可从上地幔浅部延伸到地幔转换带中,推测此低速异常可能反映了地幔转换带内上涌的热物质,上涌的原因则主要是受到太平洋板块俯冲运动的作用。     

SIMPLIFIED EXPRESSIONS FOR THE MAGNETIC ANOMALIES DUE TO VERTICAL RECTANGULAR PRISMS*

The magnetic anomaly due to a uniformly magnetized vertical rectangular prism and that due to an arbitrary structure which can be divided into a number of such prisms are expressed in forms suitable for rapid computation. Both two-dimensional and three-dimensional cases are considered. The simplified expressions will find use in interpretation techniques where repeated computations have to be made of the anomaly due to prisms as in automated fitting of prism anomalies to observed magnetic anomalies using non-linear optimization techniques or related methods.