南大西洋洋中脊板块构造运动过程:古地磁的约束

海底磁异常的形态与洋中脊两侧板块的微运动或变形密切相关.因此,这方面的研究可为确定板块运动的演化历史、小尺度的动力学过程以及洋中脊分段的机制等提供重要约束.本文对南大西洋一段洋中脊(31°S—34.5°S)两侧的磁异常的偏度进行了系统研究.结果表明研究区域内扩张方向并不总是垂直于洋中脊走向,并且研究区域不同剖面的扩张方向也不一致,具体表现为从北向南,平均扩张方向逐渐增加,依次为33.6°±5.3°、62.8°±13.0°以及94.3°±8.0°.这表明洋中脊的倾斜扩张机制具有复杂性,初步解释应该与转换断层的剪切应力增加有关.深部辉长岩层倾斜和扩张速率不对称性对海底磁异常偏度的影响值得深入研究.另外,由北向南确定的欧拉极向东移动,表明洋中脊两侧的板块在6.5 Ma期间存在剧烈形变.     

三度体（物性随深度变化模型）位场波谱的正演计算

本文将均质的任意二维、三维物体位场的波谱解析表达式的研究成果推广到变密度、变磁化强度的更一般的情形。对密度差随深度呈指数函数衰减或线性变化的模型,获得了任意倾斜多边形质量面、斜平行六面体以及一般的多面体等形体的重力谱的解析表达式。它们的结构与均质体相应表达式一样简单,易于计算。以上结果表明,在很一般的条件下,位场波谱具有指数函数和的形式。     

Magnetic studies on Kilauea Iki lava lake,Hawaii

Ground surveys made during August, 1961, show large vertical magnetic intensity anomalies associated with the partly lava filled crater of Kilauea Iki. A vertical magnetic variation of 11,600 gammas occurs along a north-south profile across the crater, the maximum being on the north rim of the crater and the minimum on the south edge of the encrusted lava lake below the south rim. An east-west profile shows less vertical magnetic variation, with lake-surface measurements 1500 to 2500 gammas lower than measurements on the east rim of the crater. Computed anomalies using two-dimensional potential field graticules are in good agreement with the observed anomalies and support the following conclusions: 1) Average measured values of remanent magnetization of 10^?2 cgs units and susceptibilities of 10^?3 cgs units give reasonable magnitudes to the computed anomalies. 2) The remanent magnetization is parallel to the earth’s present magnetic field. 3) The maximum vertical magnetic field value in the north-south profile is the result of reinforcement of the positive terrain effect of the north rim of the crater and the positive edge effect of the north side of the lava lake. 4) The minimum value in the same profile is the result of reinforcement of the negative terrain effect at the base of the south rim of the crater and the negative edge effect of the south side of the lava lake. 5) Variation in the east-west magnetic profile is less because the terrain and edge effects of the horizontal components of the earth’s magnetic field and remanent magnetization approach zero. Changes in vertical magnetic field values as the lake solidifies will be maximum at the north edge of the lava lake, but more consistent changes of the opposite sign will occur on the south side of the lava lake. Total change will be approximately + 2300 gammas between the August 1961 measurement at station S6 and the value at that point when the entire lava lake has cooled below 400° C. The maximum rate of change at station S6 will occur when the 500° C isotherm is 35 to 65 meters below the surface and will be about 28 gammas per meter of lowering of the 500°C surface. Because of the steep magnetic anomalies associated with the lava lake and crater rims, the permanent magnetization presently forming in the cooling lake crust will have inclinations as much as 12° less than the average 37.5° inclination in the Kilauea area.     

有限长圆柱体磁异常场全空间正演方法

在经典位场理论中,许多简单形体位场异常难以通过积分得到全空间的解析式.圆柱体是一类很重要的理论模型体,常用于模拟圆柱状地质体或非地质体(如管线),但目前还不能用解析公式正演有限长圆柱体在三维空间里的磁异常,而多是采用近似简化为有限长磁偶极子或线模型代替.对于有限长圆柱体,特别是半径相对于上顶埋深较大时,这种近似的误差不可忽略.本文利用共轭复数变量替换法,推导出有限长圆柱体在全空间的引力位一阶、二阶导数,利用Poisson关系得到磁异常正演公式,进而利用有限长圆柱体磁异常正演公式求解管状体的磁异常,得到不同磁化方向、不同大小的管线产生的磁场的特征,并将其推广到截面为椭圆的情况.最后通过模拟计算定量给出了将圆柱体近似为线模型的条件.     

基于离散余弦变换（DCT）的化磁极方法

针对提高磁异常化磁极的质量问题,提出基于离散余弦变换(DCT)的化磁极方法.以位场余弦变换谱分析为基础,从理论上推导了基于DCT的二度和三度体总场磁异常化磁极转换公式.在倾斜板状体模型实验中,化磁极误差小于0.001 nT,具有较高的精度;在单球体及多球体模型实验中,采用基于DCT的化磁极方法在5.倾斜磁化时就可以取得较好的化磁极结果,15°时化磁极的效果更加明显,其等值线的形态、幅值以及所反映的磁性体的水平位置都得到较好的恢复,这说明,采用本文方法进行化磁极时,可以取得较好的效果.     

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.     

A GYRO-ORIENTED 3-COMPONENT BOREHOLE MAGNETOMETER FOR MINERAL PROSPECTING,WITH EXAMPLES OF ITS APPLICATION1

A triple axis borehole magnetometer is described that consists of a Förster-probe (fluxgate) triplet (sensitivity 1 n T), a Förster-probe gradiometer (sensitivity 2 nT/40 cm), a gyro unit (mean angular drift approx. 0.5°/h) which is equipped with accelerometers (sensitivity 1/100°), and a data transmission unit (with multiplexer and 16-bit AD converter). The sensitive fluxgate-magnetometer can detect weakly magnetic or small source bodies. Data from the gyro and the accelerometers allow the 3-component magnetic field values to be transformed to north, east and vertical components. Since they do not rely on magnetically-determined directional data, the results are not disturbed by local anomalies of the magnetic declination. Furthermore, the magnetometer can also be used in vertical boreholes. 3-component measurements are carried out at discrete points in the neighbourhood of a source body to locate its position, and within the source body to determine the direction of magnetization. The strength of magnetization and information on magnetic classification are obtained by continuous measurement of one or more components within the source body. Calculation algorithms and computer programs are available to simplify data processing and interpretation. Survey examples are discussed.     

Magnetic anomalies — India and Antarctica

Magnetic anomalies over the continental shelf off the east coast of India (Orissa) suggest the presence of a highly magnetic rock type magnetized with an intensity of 900 nT in a direction, azimuth(A) = 150° and inclination(I) = +65°. This suggest the occurrence of igneous volcanic rocks which is confirmed from samples found below Tertiary sediments from a few boreholes in this region. The depth of this rock type as estimated from magnetic anomalies varies from approximately 1–2 km near the coast to 4–4.5 km towards the shelf margin. This direction of magnetization is the reverse of the reported direction of magnetization for the Rajmahal Traps of the Cretaceous period (100–110 m.y). A small strip of the body near the continental shelf margin appears, however, to possess normal magnetization suggesting the occurrence of normal and reversed polarities side by side, a characteristic typical for oceanic magnetic anomalies. The reversed polarity of the rocks on the continental shelf suggests that they correspond probably to the MO reversal (115 m.y.) on world magnetostratigraphic scale and provide a paleolatitude of 47°S for the land mass of India which agrees with the palaeoreconstruction of India and Antarctica. In this reconstruction, the Mahanadi Gondwana graben on the Indian subcontinent falls into line with the Lambert Rift in Antarctica, suggesting a probable common ancestry. The volcanic rocks on the continental shelf off the east coast of India might represent a missing link, that is, rocks formed between India and Antarctica at the time of the break-up of Gondwanaland. Satellite magnetic anomalies (MAGSAT) recorded over the Indian shield and interpreted in terms of variations in the Curie point geotherm provide a direction of magnetization which also places this continent close to Antarctica. As such MAGSAT anomalies recorded over eastern Antarctica are found compatible with those recorded over the Indian shield.     

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.     

Interpretation of Magnetic Anomalies and Estimation of Depth of Magnetic Crust in Slovakia

The magnetic map of Slovakia used in the paper was compiled as part of a project titled Atlas of Geophysical maps and profiles in 2001. The residual magnetic data were analyzed to produce Curie point estimates. To remove distortion of magnetic anomalies caused by the Earth’s magnetic field, reduction to pole transformation was applied to the magnetic anomalies using the magnetization angle of the induced magnetization. Anomalies reduced to the pole tend to be better correlated with tectonic structures. We applied a 3-km upward continuation to the residually compiled magnetic anomalies in order to remove effects of topography. The depth of magnetic dipoles was calculated by an azimuthally averaged power spectrum method for the entire area. Such estimates can be indicative of temperatures in the crust, since magnetic minerals lose their spontaneous magnetization according to Curie temperature of the dominant magnetic minerals in the rocks. The computed Curie point depths in the Slovakia region vary between 15.2 km and 20.9 km. Heat flow higher than 100 mWm⁻² occurs at the central volcanics and eastern part of Slovakia, where the Curie point depths values are shallow. The correlation between Curie point depths, heat flow and crust depth was investigated for two E-W cross sections. Heat flow and Curie point depth values are correlated with each other however, these values could not be correlated with crust depth. The Curie point isotherm, which separates magnetic and non-magnetic parts of the crust, is represented in two cross sections.     

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.     

A geophysical approach to the granite batholith under the eastern Southern Uplands,Scotland

From our interpretation of the Bouguer gravity and aeromagnetic anomalies in south-east Scotland, we conclude that a massive granite batholith underlies the greater part of the eastern Southern Uplands. The granite model which we computed earlier from gravity anomalies in the Tweeddale area fits the observed magnetic anomalies closely, if a normal magnetization of 0.095 A m^–1 is assigned, similar to values found for exposed local granites. Further gravity modelling shows that, apart from the Tweeddale boss, the granite shallows to less than 1 km near Lammer Law in East Lothian and extends north of the Lammermuir Fault. A model for the East Lothian volcanics was computed from their aeromagnetic anomalies, then their gravitational effect was combined with that estimated for the Devonian and Carboniferous sediments and the result stripped off the observed gravity field. The residual gravity anomalies were used to generate a two-dimensional model for the granite north of the Lammermuir Fault. The expected tectonic consequences of a massive granite batholith in the eastern Southern Uplands are compared with the known development of faults and sedimentary basins around its margins.     

强磁性体ΔT异常计算的误差分析研究

本文主要针对当前磁法勘探中高精度处理解释的需求,对强磁性体ΔT异常计算存在的误差进行分析研究.我们首先通过理论模型计算试验,证明常规计算采用的投影关系的ΔT与实际测量的模量差ΔT之间的误差E在磁异常幅值大时是明显存在的,其影响不容忽视.其次,当磁性强且剩磁存在时,投影ΔT曲线及其误差曲线在磁化方向与地磁场方向改变时具有一定的对称性;地磁场T0、磁性体形态(如二度水平圆柱体模型的半径r、柱体埋深R)和磁性参数(如磁化率κ)等参数确定的情况下,最大误差值出现在磁性体正上方,且其大小与磁性参数(κ)和模型体规模(如r/R)之间皆是指数关系;另外,研究还发现ΔT的计算误差曲线的一些其他规律特点,如在各纬度带上,ΔT计算误差的最大值Emax曲线的极值主要分布在中纬度地区;磁异常矢量Ta与地磁场T0的夹角θ逐渐变化时,随θ变化Emax曲线的极值分布在θ=90°~120°范围内;当磁异常幅值小于10000nT时,最大误差近似为磁异常矢量垂直于地磁场方向的测点附近的误差值;另外,磁性体(圆柱体为例)的半径(即尺度)与埋深的比值r/R超过0.5,且磁化率超过0.1SI时误差已达到3.9nT,磁化率增大与对应的Emax的值呈指数增长特点.因此,我们的研究表明,在强磁性体、磁异常幅值大的数据处理、反演及解释时,现有方法会产生较大的误差,应该基于严格的模量差ΔT,完善相应的处理以及反演方法.     

A magnetic model for deep plutonic bodies beneath the central Taupo Volcanic Zone, North Island, New Zealand

The central Taupo Volcanic Zone (TVZ) is a region of intense Quaternary rhyolitic volcanism and geothermal activity in the North Island of New Zealand from which about 14,000 km³ of pyroclastics and lavas have been erupted during the last 1.6 Ma. Analysis of aeromagnetic surveys over the TVZ showed the presence of long-wavelength (10 to 25 km) magnetic anomalies which roughly follow the trend of the currently active eastern TVZ, from the north of Lake Taupo to the east of Lake Rotorua. An interpretation of the long-wavelength magnetic anomalies using 3-D magnetic modelling suggests that these anomalies are caused by the magnetic effects of < 3 km thick sequence of volcanic rocks and deeper magnetised bodies within the non-magnetic upper crust (4–7 km depth) beneath the young (age < 0.7 Ma), currently active eastern TVZ. The deep magnetised bodies are interpreted as solidified rhyolitic sub-volcanic plutons that have cooled down to below their Curie temperature.Although the existence of plutonic bodies beneath the TVZ has been postulated prior to this study, this magnetic interpretation result appears to be the first geophysical model of such bodies.     

Asymmetric spreading across the Juan de Fuca and Gorda rises as obtained from a detailed magnetic survey

Marine magnetic data collected along 37 east-west lines off the Washington and Oregon coast between 42°N and 48°N westward to 144°W have been interpreted. Our interpretation shows that decrease in the offsets of the anomalies across the Surveyor fracture zone and the presence of undisturbed north-south lineations east of it are the result of continuous asymmetric spreading along the Surveyor fracture zone. The survey has delineated the extension of the Blanco fracture zone north-westward to about 133°W. Movement along the Blanco fracture zone was initiated about 15 million years ago. The undisturbed north-south trend of the magnetic anomalies between latitudes 42°N and 48°N and longitudes 133°W and 136°W is interpreted as the interval (22 to 15 my) during which the Juan de Fuca and Gorda rises were one continuous structure. West of 137° the Surveyor, Sedna and three minor fracture zones are mapped.     

Estimation of depth and magnetization of magnetic sources from magnetic data: The linearized continuous inverse problem for 21/2D structures

The estimation of the depth to the top and bottom of a magnetic source from magnetic data defines a nonlinear inverse problem, while the evaluation of the distribution of magnetization determines a linear inverse problem. In this paper, these interpretation problems are resolved in the continuous case of 2_1/2D magnetized bodies with lateral magnetization variations. A formulation of the magnetic problem accounting for different directions of remanent and total magnetization vectors and including a more general definition of apparent susceptibility is presented. Differences between 2D and 2_1/2D formulations are stressed, as regards the anomaly amplitude, shape and zero-level.In order to utilize well-known continuous linear inverse methods, Fréchet derivatives of the data functionals with respect to the depth of the source top and bottom, are analytically described. Thus, using the spectral expansion inverse method (Parker, 1977) and linearizing the problem at several steps of an iterative process, the source depth is obtained within a few iterations, although the starting model is distant from the final solution. The interpretation of an anomaly in the Italian region shows the usefulness of the method.     

Estimating the magnetization direction of sources from southeast Bulgaria through correlation between reduced-to-the-pole and total magnitude anomalies

We present a new method to estimate the direction of the magnetization vector of geological bodies based upon the correlation between the reduced-to-the-pole field for tentative values of the magnetization direction and the total magnitude anomaly, obtained by a transform of the measured magnetic field. The reduced-to-the-pole and the total magnitude anomaly are centred over the sources in the case of 2D anomalies or well-centred in the case of compact 3D sources and have similar patterns for the same source. The method has several important advantages over similar transform-correlation methods for estimation of the magnetization direction. It calculates only one transform for many tentative values of the magnetization direction. The method does not use derivatives of any order and relies on confident isolation of the target anomalies based on one of the compared transforms, the total magnitude anomaly. We studied the performance of the method on five 2.5D and compact 3D sources. We analysed possible inherent to the method errors, as well as errors due to interference from neighbouring sources. Finally, we estimated the magnetization-vector direction of the main sources causing the magnetic field in the Burgas region and the adjoining southeast Bulgarian Black Sea shelf. The sources in the Black Sea shelf show prevalently reverse magnetization, while the sources on land have normal or reverse magnetization.     

3D Inversion of magnetic data of grouped anomalies — Study applied to São José intrusions in Mato Grosso,Brazil

The southwest border of the Parecis Basin (central Brazil) presents several occurrences of gold, copper and zinc. Parallel to this border, there is an alignment of magnetic anomalies with varied size and polarities. In particular, five magnetic anomalies are referred to, in this study, as SJ1 to SJ5. The proximity of these anomalies to each other makes it hard to isolate the magnetic component associated with each source. Furthermore, these anomalies have different magnetization directions, which require the use of a technique which is slightly or not affected by the presence of a remanent magnetization, as the amplitude of the anomalous magnetic field. Considering that, in these intrusions no outcrops are observed, the enhanced horizontal derivative technique was used to estimate the edges location and the depth of these sources. The geological context, allied to the results from the magnetic techniques, allowed to establish binds to restrain the interpretation of the results of the 3D inversion. This procedure permitted to compose three hypothesis to explain the magnetic behavior of the region, from which can be conclusively determined with a borehole analysis.     

磁张量梯度数据方向解析信号比值的边界识别和空间位置反演方法

磁张量梯度测量具有高分辨率、多参量的优点,能更准确地描述磁源体的分布特征,在矿产资源勘探中具有广阔的用途.磁异常解析信号具有受倾斜磁化干扰小的特点,且为了增强深部地质体的分辨能力,本文提出磁张量梯度数据的解析信号比值的均衡边界识别及空间位置反演技术.磁张量梯度数据的均衡边界识别方法为不同方向解析信号比值的反正切函数,在降低倾斜磁化干扰的同时能有效地均衡不同深度地质体的响应,提高了对较深地质体的分辨率;空间位置反演技术是建立解析信号比值与地质体位置参数的对应方程,利用解析信号比值与地质体的对应关系作为约束条件来反演获得地质体的水平位置和深度信息,具有无需已知任何先验信息的优势.通过磁性体张量异常试验表明解析信号比值的边界识别方法能清晰和准确地获得不同深度地质体的边界,所建立的反演方程能准确地计算出地质体的范围和深度,具有较高的水平分辨率和精度.将本文方法应用于实测磁张量梯度数据的解释,获得了地下铁矿的分布特征,为区域矿产资源潜力评价提供了翔实的基础资料.     

The effects of anisotropy of marine magnetic anomalies on the Curie point depth estimates from spectral analysis

Azimuthally averaged power spectra are widely used in the Curie point depth (CPD) estimation with the implicit assumption that the magnetization distribution is random and uncorrelated. However, the marine magnetic anomalies are caused by bands of normal and reverse magnetization and show obvious trends. To investigate the effects of the anisotropy of marine magnetic anomalies on the CPD estimates, we develop 3D fractal striped magnetization models to produce lineated marine magnetic anomalies for the first time. We analyze the spectra anisotropy of the lineated magnetic anomalies of the synthetic fractal striped magnetization models and investigate its effects on the CPD estimates. The synthetic models and actual data show that the spectra of the lineated marine magnetic anomalies are directionally anisotropic. The amplitude response is strong and the slope of the logarithmic spectrum is large in a direction perpendicular to the stripes of magnetic anomalies, whereas the amplitude response is weak and the slope of the logarithmic spectrum is small in a direction parallel to the stripes of magnetic anomalies. The depth estimates in the perpendicular direction are close to the actual values, whereas the depths estimates in the parallel direction are significantly lower than the actual values. The actual marine magnetic anomalies of the South China Sea exhibit an anisotropic power spectrum that is consistent with the spectral anisotropy of magnetic anomalies of the synthetic fractal striped magnetization models.