JOINT INTERPRETATION OF GRAVITY AND MAGNETIC DATA OVER AXIAL SYMMETRIC BODIES WITH APPLICATION TO THE DARNLEY BAY ANOMALY,NWT CANADA*

A method is presented for determining bounds of the properties of axial symmetric bodies from a finite number of gravity and magnetic observations based on Parker's theory of ideal bodies. Bounds on the density contrast and the intensity of magnetization are calculated as a function of depth to the top of the anomalous source, restricting the range of smallest possible solutions to fit the data. The model studied is approximated by an array of vertical annuli cylinders, each of uniform density and magnetization. Linear programming algorithms based on the ideal body theory were used to calculate the distribution of these parameters within the body. Simultaneous inversion of gravity and magnetic data is performed assuming a constant ratio between the density contrast and the intensity of magnetization and that a common body is responsible for both observed fields. The parameter k(|J|/δp) provides information about the rock type of the structure. Interpretation of gravity and aeromagnetic data from Darnley Bay, NWT, Canada, indicated the presence of a shallow ultrabasic intrusion.     

ESTIMATION OF THE MINIMUM DENSITY CONTRAST OF A HOMOGENEOUS BODY AS AN AID TO THE INTERPRETATION OF GRAVITY ANOMALIES*

Goodacre A.K. 1980, Estimation of the Minimum Density Contrast of a Homogenous Body as an Aid to the Interpretation of Gravity Anomalies, Geophysical Prospecting 28, 408–414. The minimum density contrast value for which a homogeneous body will accurately reproduce an observed gravity low can often be used to determine whether the causative body is a low-density granite batholith or a sedimentary basin. If the minimum density contrast value is large, the anomaly source is probably a sedimentary basin; if it is small, the source may be either a sedimentary basin or a granite batholith. The minimum density contrast method is tested on the Cheshire Basin and the Weardale Granite.     

THE USE OF COMPUTER GRAPHICS IN GRAVITY INTERPRETATION*

Computer-Graphics, the visual display of data in digital and analog form, allows immediate interaction between man and machine. This interaction facility is valuable when the user is engaged in model design. By using such a device in gravity interpretation, the geophysicist can overcome the slow process of model simulation constrained by the conventional input/output devices, also maximum control over running programmes can be exerted if needed.     

AUTOMATIC INTERPRETATION OF GRAVITY ANOMALIES ASSOCIATED WITH TWO-DIMENSIONAL MASS DISTRIBUTIONS*

Several new features are described which facilitate an automatic, more meaningful, and more accurate interpretation of gravity anomalies associated with approximately two-dimensional mass distributions. These include a provision for fixed points on the bounds of a distribution, outward dipping boundaries, calculation of the gravity effect at individual elevations of stations, smoothing of models and end-corrections for distributions of limited strike length. It is possible to obtain distributions about a median plane; these distributions are sensitive to shape and allow estimates of optimum depths and minimum density contrasts for the anomalous masses.     

ON THE APPLICATION OF INVERSE THEORY TO GRAVITY INTERPRETATION*

Numerical investigations have been carried out on suitable interpretation schemes for gravity, based upon Backus-Gilbert inverse theory. A two-dimensional linear model consisting of horizontal prisms (grid shape) has been adopted for interpretation of gravity profiles. An inversion technique, which uses a linear approach suitable for rapid computation, and studies with synthetic bodies have led to improvements in the method, mainly by applying weighting factors, which improve the solution in the final stages of computational work. Gravity data from the well-known Cyprus island positive anomaly were inverted to demonstrate the feasibility of the method.     

GRAVITY INTERPRETATION USING THE HANKEL TRANSFORM*

The Hankel transform theorem can be applied to the inversion of gravity data for the buried sphere, the horizontal cylinder, and the vertical rod. This new approach leads to exact solutions of the transforms for the assumed bodies. A comparison with the classical procedure by Fourier transform reveals that for the sphere and the vertical rod, the Hankel transform is preferable.     

太行山重力梯级带的密度结构及其地质解释

斜贯中国东部地区的大兴安岭 -太行山 -武陵山重力梯级带是一条地壳深部构造变异带。选择与其中段———太行山重力梯级带相垂直的阜平 -定州剖面 ,利用人工地震测深与布格重力异常资料 ,进行了地壳 -上地幔密度反演分析。结果表明 ,该剖面的地壳 -上地幔密度分布具有明显的不均匀性。总体特征是剖面西部密度较低 ,东部密度较高 ,地壳厚度的横向变化基本上决定了布格重力异常梯级带的形成。结合华北地区的中新生代构造演化 ,认为太行山重力梯级带是燕山期以后形成的 ,它与板块之间的相互作用及上地幔热物质的运动相关     

INTERPRETATION OF GRAVITY ANOMALIES BY NON-LINEAR OPTIMISATION*

The interpretation of a gravity anomaly in terms of the shape of the anomalous body is a non-linear problem and may, therefore, be carried out using non-linear optimisation techniques. The formulation is extended to include cases where the density contrast and the regional background are also unknown. For a given model the objective function is provided by the discrepancy between the observed anomaly and the calculated anomaly due to the model. Given an initial model, the optimisation procedure searches for a minimum of the objective function by an iterative adjustment of the parameters. A number of suitable objective functions is given. The behaviour of these functions in the parameter hyperspace is quite complex. Accordingly, direct search methods should be employed at the early stages of the search, changing to gradient methods at later stages. The use of constraints is also necessary to ensure the geological feasibility of the model. The required computer time may be largely reduced by careful programming. Two examples of interpretation by optimisation methods are given.     

A GENERAL TECHNIQUE FOR THE DIRECT INTERPRETATION OF RESISTIVITY DATA OVER TWO-DIMENSIONAL STRUCTURES*

The indirect method of interpreting resistivity data is capable only of limited success because of the difficulty of calculating type curves for complex structures. Consequently a need arises for a direct method of interpretation for complex generalized structures. Such a technique for the direct interpretation of apparent resistivity data, obtained by electrical soundings carried out over two-dimensional structures, has been developed from an examination of the Hankel transform of such data. The method is based on the observation that the asymptotic expansion of the Hankel transform is critically dependent upon the minimum distance between the measuring device and the surface of discontinuity in resistivity. The variation in the across strike direction may be mapped by a sequence of depth soundings made parallel to each other and separated in the across strike direction.     

重力潮汐观测资料的改正和异常背景值的显示问题

本文系统地研究了重力潮汐观测的改正和作为地震预报研究的异常背景值的显示问题.文章讨论了仪器弹性系统流变模型改正和惯性改正以及海洋潮汐等的资料精确化问题和气压、地下水等对重力潮汐观测的影响,并给出了相应的结果.文章还讨论了台站重力测量中非潮汐信息的提取问题,从理论上论证并对比了几种滤波器的实质.      

A STUDY ON THE DIRECT INTERPRETATION OF DIPOLE SOUNDING RESISTIVITY MEASUREMENTS OVER LAYERED EARTH *

Dipole sounding resistivity measurements over layered earth can be interpreted directly by adapting the procedure given by Koefoed (1968) for Schlumberger system. To carry out the first step of the interpretation leading to the determination of the raised kernel function, partial resistivity functions for the dipole method are derived and given in the form of standard curves. The second step involving the derivation of layering parameters from the kernel being independent of the electrode configurations remains unaltered. The applicability and limitations of the method are discussed.     

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.     

THE DIRECT INTERPRETATION OF RESISTIVITY OBSERVATIONS MADE WITH A WENNER ELECTRODE CONFIGURATION*

In a previous paper by the present author a method was developed for direct interpretation of resistivity observations made with a Schlumberger electrode configuration. This method consisted of two steps. The first of these was to derive the kernel function in the integral expression for the apparent resistivity from the observed data; the second step was to derive the resistivity stratification from this kernel function. The first of these two steps depends on the electrode configuration that has been used. In the present paper the above mentioned method is modified so as to make it apply to a Wenner electrode configuration. The procedure is indicated by which the method may be adapted to any other electrode configuration in which the distances between the electrodes are finite. The second step in the interpretation, i.e. the derivation of the resistivity stratification from the kernel function, is independent of the electrode configuration used, and therefore needs no further discussion in the present context.     

DIRECT INTERPRETATION OF RESISTIVITY DATA OVER TWO-DIMENSIONAL STRUCTURES*

A direct interpretation scheme is developed which is capable of determining most of the geological features of a ground which can be assumed to be two dimensional in structure. This scheme extends the earlier work of Pekeris (1940) and Koefoed (1968) to the case where the basal layer of a ground is undulating. It also has a limited use for finding the parameters of a dipping dyke in the lower medium. Though the top and dip of the dyke can be determined, this is not true for the thickness.     

NUMERICAL INTERPRETATION OF RESISTIVITY SOUNDINGS OVER HORIZONTAL BEDS*

The digital computer technique described for interpreting resistivity soundings over a horizontally stratified earth requires two steps. First, the kernel function is evaluated numerically from the inverse Hankel transform of the observed apparent resistivity curve. Special attention is given to the inversion of resistivity data recorded over a section with a resistant basement. The second step consists in the least-squares estimation of layer resistivities and thicknesses from the kernel function. For the case of S or T-equivalent beds only one layer-parameter can be obtained, either the longitudinal conductance, or the transverse resistance respectively. Two examples given in the paper show that a wide tolerance is permitted for Choosing the starting values of the layering parameters in the successive approximation procedure. Another important feature for practical applications is good convergence of the iterations. The method is probably best suited for interpreting profiles of electrical soundings with the purpose of mapping approximately horizontal interfaces at depth.     

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.     

A COMPARATIVE STUDY OF THE SHORTENING OPERATORS USED IN VARIOUS DATA PROCESSING TECHNIQUES IN GRAVITY INTERPRETATION*

Discrete Fourier transform analysis provides an infinite number of weight coefficients for filters like upward and downward continuation. For practical applicability, the lengths of such filters have been reduced to a manageable number by various shortening operators, viz. those by Peters, Martin, Mufti, v. Hann, Hamming, and the truncation operator. A comparative study for choosing an operator which approximates the theoretical filter response best has indicated that Martin's shortening operator and the truncation operator are best, respectively, for normalized and non-normalized sets of weight coefficients.     

QUANTITATIVE INTERPRETATION OF PULSE EM MEASUREMENTS OVER A WEATHERED KIMBERLITE DIATREME*

The application of pulse EM and MAXMIN II systems in search of a kimberlite diatremes under conducting cover has been demonstrated through a field example. The effectiveness of the PEM system in the search for conductive zones of economic importance and in discrimination against geologic noise such as overburden has been investigated. The transient observation has been transformed to equivalent half-space resistivities at various times. The feasibility of mapping thin conducting overburden using the PEM system has been studied by inverting the transient measurement to the thin infinite horizontal sheet conductance. The PEM measurement is shown to be an economic and effective tool for shallow geoelectric mapping.     

据断层附近布格重力异常分布反推地质时期断层运动的探讨

本文应用变形介质位移场产生的附加重力场的积分表达式,对麦克斯威尔介质半空间中断层长期活动引起的永久变形与现今布格重力异常分布的关系作了定量分析,并提出了由断层附近布格异常分布特征反推地质时期断层运动趋势的一般方法。其主要应用于平原地区断层运动(特别是扭动方式)的判别。文中以滦南断裂为实例,通过数值积分,计算了几种断层运动可能产生的地表重力异常。经理论计算与实测重力资料相对比,该断层曾发生过下盘上升的正倾滑运动,并具有顺扭走滑运动分量     

RESULTS OF GRAVITY SURVEY OVER RANIGANJ COALFIELD,INDIA*

Results of a gravity survey conducted over Raniganj coalfield, one of the Gondwana basins of Damodar Valley in north-eastern part of India, are presented. The gravity field was separated into regional and residual components. The residual Bouguer anomaly map shows that the coalfield is characterized by a gravity low of about—32 mGal associated with Gondwana sediments. The deepest part of basin is found to be located near Asansole (23° 40’N, 86° 55’E), where the maximum thickness of sediments is estimated to be about 1.3 miles (2.08 km). The faults along the northern as well as the southern boundaries are found to be normal. The Gondwana sediments appear to continue eastward beneath alluvium and laterite of Bengal basin as far as 87° 25’E.