Direct analytic signal (DAS) method in the interpretation of magnetic data

We presented a new method for interpreting 2D magnetic data, called direct analytic signal (DAS) method, which directly used the analytic signal of magnetic anomaly to compute the depth and the structural index of the source. The DAS method needs only the computation of the first order derivatives of magnetic anomaly, so that the inversion results are more stable than the results obtained by the other existing analytic signal methods. The DAS method is tested on synthetic magnetic data with and without noise, and the DAS method can successfully obtain the depth and the structural index of the source. We also applied the DAS method to interpret a real magnetic data over a shallow geological source whose source parameters are known from closely drilling information, and the inversion results are in accord with the true values.     

强剩磁强退磁条件下的二维井中磁测反演

强剩磁、强退磁改变了总磁化强度的大小和方向,给磁测资料解释带来困难.为此,本文利用二维井中磁测数据反演磁化强度矢量的二维分布.首先利用井中磁测的磁异常模量反演磁化强度大小的分布.然后,在已知磁化强度大小分布的前提下,拟合磁场分量,反演磁化强度方向的分布.其中,磁化强度大小和方向均用共轭梯度法求解,并通过预优矩阵改善磁化强度大小的反演效果.理论模拟说明,该方法能准确获得磁化强度矢量分布.磁化强度矢量反演结果包括感磁、剩磁及退磁的影响,这为研究强剩磁、高磁化率矿床提供了一种有效方法.     

黑蒙交界中强地震地磁异常特征分析

众所周知,在许多地震前可以观测到局部磁异常。选择位于中国最北部的国家级绝对地磁观测台内蒙古满洲里地磁台和黑龙江德都地磁台2008年的观测数据,采用差值法、响应比、能量比等分析方法,对2008年6月10日内蒙古阿荣旗M 5.2地震和7月7日黑龙江龙江县M 4.6地震前的局部空间磁场异常进行分析,并应用斜率分析和差分分析对差值法异常信息进行提取,发现在内蒙古阿荣旗M 5.2地震和黑龙江龙江县M 4.6地震前各方法均存在明显的异常,这些异常在一定程度上反映了台站周围小范围的震源区介质电性结构的变化。同时针对异常幅度、持续时间与地震强度间的关系进行了浅析。     

Interactive 3D forward modeling of total field surface and three-component borehole magnetic data for the Daye iron-ore deposit (Central China)

The ground magnetic response of deep ore bodies in the Daye iron-ore deposit is relatively weak, and sometimes concealed by the strong magnetic background of shallower sources. Apart from the low-quality ground magnetic data, another critical problem for reconstructing the deep skarn-type ore bodies is developing a versatile inversion scheme that can simultaneously resolve 3D sources with arbitrary shapes. In this case, we resort to interactive 3D forward modeling solution with the joint use of two data sets-total field surface and three-component borehole magnetic data. Joint inversion of the two data sets is expected to help resolve the ambiguity associated with either data set and greatly reduces the nonuniqueness of the magnetic inversion. Such nonuniqueness is especially severe when a 3-D distribution of magnetic susceptibility, instead of a simple body, is sought from the inversion.In this paper, we calculate the magnetic field on the surface and in the borehole caused by 3D arbitrarily-shaped bodies with the triple integral method. The complex 3D magnetic sources having arbitrary shapes are constructed with cross-sections, termination points and facets in our visualization technology. We specify, interactively and in a user-friendly environment, the outline of the sources in terms of geometric elements and their magnetic parameters. The method automatically fits the observations within a prescribed precision. If dissatisfied, the user can redefine the model parameters and proceed to a new inversion. The method's ability to interpret a complicated 3D geologic environment is demonstrated on synthetic models and real data profiles in the Daye iron-ore deposit in central China. The interactive forward modeling results in all tests demonstrate a good correlation of estimated magnetic sources with corresponding known geologic features.     

Fair function minimization for interpretation of magnetic anomalies due to thin dikes, spheres and faults

A new method is proposed to interpret magnetic anomalies due to a thin dike, a sphere, and a fault like structure, where depth, horizontal location, effective magnetization intensity and effective magnetization inclination of a buried structure are simultaneously obtained. The proposed method is based on Fair function minimization and also on stochastic optimization modeling. This new technique was firstly tested on a theoretical synthetic data randomly generated by a chosen statistical distribution from a known model with different random noises components. This mathematical simulation shows a very close agreement between the assumed and the estimated parameters. The applicability and validity of this method are thereafter applied to magnetic anomaly data taken from United States, Australia, India, and Brazil. The agreement between the results obtained by the new method and those obtained by other interpretative methods is good and comparable. Moreover, the depth obtained by such a method is found to be in high accordance with that obtained from drilling information.     

Modelling of magnetic data for scaling geology

Interpretation of magnetic data can be carried out either in the space or frequency domain. The interpretation in the frequency domain is computationally convenient because convolution becomes multiplication. The frequency domain approach assumes that the magnetic sources distribution has a random and uncorrelated distribution. This approach is modified to include random and fractal distribution of sources on the basis of borehole data. The physical properties of the rocks exhibit scaling behaviour which can be defined as P(k) = Ak^?β, where P(k) is the power spectrum as a function of wave number (k), and A and β are the constant and scaling exponent, respectively. A white noise distribution corresponds to β = 0. The high resolution methods of power spectral estimation e.g. maximum entropy method and multi‐taper method produce smooth spectra. Therefore, estimation of scaling exponents is more reliable. The values of β are found to be related to the lithology and heterogeneities in the crust. The modelling of magnetic data for scaling distribution of sources leads to an improved method of interpreting the magnetic data known as the scaling spectral method. The method has found applicability in estimating the basement depth, Curie depth and filtering of magnetic data.     

The secular geomagnetic variation. Statistical methods for paleomagnetic directions in sediments

Understanding the character of variations in the magnetic field of the Earth in the geological past requires a mathematically substantiated method for testing the statistical hypotheses against the real paleomagnetic data. As known, the paleomagnetic data from lava flows are sort of momentary snapshots of the state of the ancient magnetic field. Being quite fragmentary in time and space, these data compose what is referred to as a sample in statistics: on the close discrimination of the lava flows, the internal correlations in the data are absent. It is well known that the distributions of the paleomagnetic directions from the sedimentary data differ from the distributions in lavas, which is mainly due to the effect of averaging of the magnetization over the time interval corresponding to the accumulation of sedimentary layers represented in the rock specimen. Assuming the rate of sedimentation to be known for each specimen, one can suggest the method for the quantitative testing the statistical consistency of the paleomagnetic data in the sediments with the model variations of the magnetic field of the Earth in terms of the Giant Gaussian Process (GGP). It turned out that the averaging effect can well be allowed for by the coefficients of GGP, and the scheme of the further testing is in this case identical to the scheme of testing the paleomagnetic data obtained from lavas.     

CSAMT单分量数据解释方法

可控源音频大地电磁法(CSAMT)一直沿用大地电磁法(MT)的办法,通过计算电场分量与磁场分量的比值,求取卡尼亚视电阻率.而CSAMT场源已知,电场分量和磁场分量都与地下电阻率存在一定的关系,可以单独采用CSAMT电场分量或者磁场分量提取地下介质的视电阻率.本文通过分析电场分量与磁场分量的数据特性,提出利用CSAMT电场单分量数据进行视电阻率的计算,用改进的广义逆矩阵反演方法,使初始模型中的地电层数等于频道个数,克服了以往反演计算中层数较少的问题;实现全场区电场分量视电阻率曲线的拟合反演.同时对单分量视相位计算方法进行分析,结合山西大同地区积水采空区探测及数据解释结果,论证本文提出的单分量解释方法的有效性.     

Induction studies with satellite data

The natural variations of the Earth's magnetic field of periods spanning from milliseconds to decades can be used to infer the conductivity-depth profile of the Earth's interior. Satellites provide a good spatial coverage of magnetic measurements, and forthcoming missions will probably allow for observations lasting several years, which helps to reduce the statistical error of the estimated response functions.Two methods are used to study the electrical conductivity of the Earth's mantle in the period range from hours to months. In the first, known as the potential method, a spherical harmonic analysis of the geomagnetic field is performed, and the Q-response, which is the transfer function between the internal (induced) and the external (inducing) expansion coefficients is determined for a specific frequency. In the second approach, known as the geomagnetic depth sounding method, the C-response, which is the transfer function between the magnetic vertical component and the horizontal derivative of the horizontal components, is determined. If one of these transfer functions is known for several frequencies, models of the electrical conductivity in the Earth's interior can be constructed.This paper reviews and discusses the possibilities for induction studies using high-precision magnetic measurements from low-altitude satellites. The different methods and various transfer functions are presented, with special emphasis on the differences in analysing data from ground stations and from satellites. The results of several induction studies with scalar satellite data (from the POGO satellites) and with vector data (from the Magsat mission) demonstrate the ability to probe the Earth's conductivity from space. However, compared to the results obtained with ground data the satellite results are much noisier, which presumably is due to the shorter time series of the satellite studies.The results of a new analysis of data from the Magsat satellite indicate higher resistivity in oceanic areas than in continental areas. However, since this holds for the whole range of periods between 2 and 20 days, this difference probably is not caused purely by differences in mantle conductivity (for which one would expect less difference for the longer periods). Further studies with data from recently launched and future satellites are needed.     

井地磁异常模量联合反演

三维反演是磁测数据定量解释的重要方法,在金属矿勘探中扮演着重要的角色.但是在实际矿区的应用中,传统的磁总场异常反演方法依然存在两个问题：一是地面磁异常反演的深度分辨率较低,深部场源体的成像效果差;二是金属矿中可能包含强剩磁,反演结果可能是完全错误的.尽管前人对上述两个问题分别进行了广泛的研究,但尚未尝试同时解决这两个问题.本文在前人研究的基础上,提出了一种井地磁异常模量联合反演方法,该方法需要的控制参数少,无需加入额外的地质信息,且可用于多场源复杂磁异常的反演,具有较强的适用性.本文方法首先将地面和井中磁异常转化为模量数据,然后利用基于核函数或距离的加权函数将井地模量数据结合起来,使得该方法适用于联合反演.我们利用井地多种异常参量进行反演的模型试验表明,在强剩磁存在时,本文方法的效果优于其他方法,在减少剩磁影响的同时,也改善了深部成像效果,具有良好的应用前景.     

A New Best-Estimate Methodology for Determining Magnetic Parameters Related to Field Anomalies Produced by Buried Thin Dikes and Horizontal Cylinder-like Structures

A new best estimate methodology is proposed and oriented towards the determination of parameters related to a magnetic field anomaly produced by a simple geometric-shaped model or body such as a thin dike and horizontal cylinder. This approach is mainly based on solving a system of algebraic linear equations for estimating the three model parameters, e.g., the depth to the top (center) of the body (z), the index parameter or the effective magnetization angle (θ) and the amplitude coefficient or the effective magnetization intensity (k). The utility and validity of this method is demonstrated by analyzing two synthetic magnetic anomalies, using simulated data generated from a known model with different random errors components and a known statistical distribution. This approach was also examined and applied to two real field magnetic anomalies from the United States and Brazil. The agreement between the results obtained by the proposed method and those obtained by other interpretation methods is good and comparable. Moreover, the depth obtained by such an approach is found to be in high accordance with that obtained from drilling information. The advantages of such a proposed method over other existing interpretative techniques are clarified, where it can be generalized to be automatically applicable for interpreting other geological structures described by mathematical formulations.     

三维井地磁测联合约束反演

井中磁测在铁矿等磁性金属矿床勘查中具有举足轻重的作用.针对磁性金属矿床深部资源勘查中存在的有效信号弱、矿体形态复杂等技术难题,本文利用井中三分量磁测资料和地面磁测资料直接反演地下空间磁化率的分布情况,充分发挥纵、横向分辨率高的优势,通过磁化率的变化来确定矿（化）体的范围.分析了磁化率和磁场H_ax、H_ay、Z_a、ΔT各参量之间的关系,导出了磁化率反演方程;将钻孔编录、磁化率测井等结果作为约束条件构建了目标函数.以组合倾斜板状体模型为例,验证了方法的有效性,并在青海野马泉铁多金属矿区开展应用试验,试验结果与已有地质资料基本一致.该方法有效抑制了因反演数据源单一、缺乏约束条件而造成反演结果的多解性,实现了磁测资料的精细反演解释,为查明地下矿体空间位置、形态及规模,提高找矿效果,提供了一种新的解决方案.     

INTERPRETATION OF POTENTIAL FIELD DATA A GENERALIZED INVERSE APPROACH*

The interpretation of potential field data from two-dimensional structures with a single interface of density or susceptibility contrasts is solved in terms of generalized matrix inversion. The model equations are derived, and important features of generalized matrix inversion are treated. The method is subsequently used to solve two gravity problems, an artificial one where the solution is known, and a geophysical one related to the crust-mantle interface. The solution is shown to compare well with the FFT results of Oldenburg. The method is also used to solve two magnetic problems, an artificial one with the solution known, and a geophysical one from the continental shelf of Greenland. The advantages and limitations of the method are finally discussed.     

Application of the continuous wavelet transform of gravity and magnetic data to estimate sub‐basalt sediment thickness

The Continuous Wavelet Transform was recently proposed for the interpretation of gravity and magnetic potential data. We utilize the Continuous Wavelet Transform of gravity and magnetic data to address one of the most common issues in exploration geophysics: mapping of sub‐basaltic sedimentary strata. We observe that the magnetic response of the basaltic layer is dominant in a three‐layer case of a basalt‐sediment‐basement, whereas the gravity signal is dominated by the base of the sediment. Thus the Continuous Wavelet Transform of the magnetic data is related to the thickness of the basalt and the Continuous Wavelet Transform of the gravity data is related mostly to the bottom of the sediment. These observations are demonstrated with a synthetic model and a few field examples. Derived depths using Continuous Wavelet Transform are in good agreement with known vertical cross‐sections. Therefore, Continuous Wavelet Transform analysis of both gravity and magnetic data offers a possibility for primary information of sub‐basaltic sediment thickness, which can provide a basis for further detailed modelling.     

大庆外围盆地地球物理场与盆地基底特征

根据收集到的大庆外围盆地的布格重力异常和航磁异常数据,对外围盆地中的8个盆地进行了地球物理场特征的分析.对各盆地的重力异常进行了由下地壳与上地幔的密度差引起的重力效应的剥离,对磁力异常进行了由居里面起伏引起的磁力效应的剥离.在此基础上应用调和级数法和遗传算法分别反演计算了这8个盆地的重力基底和磁性顶界面,并分析了其基底特征. 各盆地重力基底在0.2~9.0 km之间变化,磁性顶界面在1.8~9.8 km之间变化,其特征反映了各盆地的基本现状.     

Electric circuits of the disturbed magnetosphere-ionosphere system and their generators

The simplest theory of electric circuits is applied to analysis of the observed large-scale electric field and currents in a disturbed magnetosphere-ionosphere system. Maps of distribution of field-aligned currents (FACs) obtained from ground-based magnetic measurements using the original magnetogram inversion method (MIT) and measurements by satellites were used. A method for circuit determination according to the data of such maps based on the detection of spatial R.N inhomogeneities in each of three Iijima and Potemra FAC zones is proposed. The results of the new method are used to describe some electric field and current generators not known before, new types of current systems in tail lobes and plasma sheet, and the formation and dynamics of new types of three-dimensional systems with auroral electrojets and meridional ionospheric Pedersen current, which have not been paid due attention in the literature.     

A magnetic polarity time scale for the Early Cretaceous and Late Jurassic

The ages of polarity chrons in previous M-sequence magnetic polarity time scales were interpolated using basal sediment ages in suitably drilled DSDP holes. This method is subject to several sources of error, including often large paleontological age ranges. Magnetostratigraphic results have now tied the Early Cretaceous and Late Jurassic paleontological stage boundaries to the M-sequence of magnetic polarity. The numeric ages of most of these boundaries are inadequately known and some have been determined largely by intuition. An examination of relevant data suggests that 114 Ma, 136 Ma and 146 Ma are optimum estimates for the ages of the Aptian/Barremian, Cretaceous/Jurassic and Kimmeridgian/Oxfordian stage boundaries, respectively. Each of these boundaries has a good correlation to the M-sequence of magnetic reversals. The magnetostratigraphic tie-level ages are linearly related to the spreading distance and have been used to calculate a new magnetic polarity time scale for the Early Cretaceous and Late Jurassic. All stage boundaries in this time interval were correlated by magnetic stratigraphy to the proposed new time scale which was then used to estimate their numeric ages. These are, with the approximate relative errors of placement within the M-sequence:The absolute errors of these interpolated stage boundary ages depend on the accuracy of the tie-level ages.     

Fast inversion of magnetic data using Lanczos bidiagonalization method

This paper describes application of a fast inversion method to recover a 3D susceptibility model from magnetic anomalies. For this purpose, the survey area is divided into a large number of rectangular prisms in a mesh with unknown susceptibilities. Solving the full set of equations is substantially time consuming, and applying an algorithm to solve it approximately can reduce the time significantly. It is shown that the Lanczos bidiagonalization method can be an appropriate algorithm to solve a Tikhonov cost function for this purpose. Running time of the inverse modeling significantly decreases by replacing the forward operator matrix with a matrix of lower dimension. A weighted generalized cross validation method is implemented to choose an optimum value of a regularization parameter. To avoid the natural tendency of magnetic structures to concentrate at shallow depth, a depth weighting is applied. This study assumes that there is no remanent magnetization. The method is applied on a noise-corrupted synthetic data to demonstrate its suitability for 3D inversion. A case study including ground based measurement of magnetic anomalies over a porphyry-Cu deposit located in Kerman providence of Iran, Now Chun deposit, is provided to show the performance of the new algorithm on real data. 3D distribution of Cu concentration is used to evaluate the obtained results. The intermediate susceptibility values in the constructed model coincide with the known location of copper mineralization.     

The Matachewan dyke swarm, Canada: an early Proterozoic magnetic field reversal

Consistent age relationships between oppositely magnetized dykes of the 2.45 Ga Matachewan dyke swarm suggest that only a single magnetic field reversal occurred during the period of igneous activity. The magnetic field throughout most of this time was characterized by a SSW declination and shallow negative inclination but reversed toward the waning stages of magmatism. The new paleomagnetic data provide the oldest known magnetic reversal for which the relative reversal sense is known.     

Interpretation of magnetic anomalies by horizontal and vertical derivatives of the analytic signal

Magnetic anomalies are often disturbed by the magnetization direction, so we can’t directly use the original magnetic anomaly to estimate the exact location and geometry of the source. The 2D analytic signal is insensitive to magnetization direction. In this paper, we present an automatic method based on the analytic signal horizontal and vertical derivatives to interpret the magnetic anomaly. We derive a linear equation using the analytic signal properties and we obtain the 2D magnetic body location parameters without giving a priori information. Then we compute the source structural index (expressing the geometry) by the estimated location parameters. The proposed method is demonstrated on synthetic magnetic anomalies with noise. For different models, the proposed technique can both successfully estimate the location parameters and the structural index of the sources and is insensitive to noise. Lastly, we apply it to real magnetic anomalies from China and obtain the distribution of unexploited iron ore. The inversion results are consistent with the parameters of known ore bodies.