Euler deconvolution of the analytic signal and its application to magnetic interpretation

Euler deconvolution and the analytic signal are both used for semi‐automatic interpretation of magnetic data. They are used mostly to delineate contacts and obtain rapid source depth estimates. For Euler deconvolution, the quality of the depth estimation depends mainly on the choice of the proper structural index, which is a function of the geometry of the causative bodies. Euler deconvolution applies only to functions that are homogeneous. This is the case for the magnetic field due to contacts, thin dikes and poles. Fortunately, many complex geological structures can be approximated by these simple geometries. In practice, the Euler equation is also solved for a background regional field. For the analytic signal, the model used is generally a contact, although other models, such as a thin dike, can be considered. It can be shown that if a function is homogeneous, its analytic signal is also homogeneous. Deconvolution of the analytic signal is then equivalent to Euler deconvolution of the magnetic field with a background field. However, computation of the analytic signal effectively removes the background field from the data. Consequently, it is possible to solve for both the source location and structural index. Once these parameters are determined, the local dip and the susceptibility contrast can be determined from relationships between the analytic signal and the orthogonal gradients of the magnetic field. The major advantage of this technique is that it allows the automatic identification of the type of source. Implementation of this approach is demonstrated for recent high‐resolution survey data from an Archean granite‐greenstone terrane in northern Ontario, Canada.     

A different method for interpretation of magnetic anomalies due to 2-D dipping dikes

In this study a new method is presented to determine model parameters from magnetic anomalies caused by dipping dikes. The proposed method is applied by employing only the even component of the anomaly. First, the maximum of the even component is divided to its value at any distance x in order to obtain S1. Then, theoretical even component values are computed for the minimal depth (h) and half-width (b) values. S2 is obtained by dividing their maximum to the value computed for the same distance x. A set of S2 values is calculated by slowly increasing the half-width, and h and b for the S2 closest to S1 are determined. The same procedure is repeated by increasing the depth. The determined b values are plotted against the corresponding values of h. After repeating the process and plotting curves for different distances, it is possible to determine the actual depth and half-width values.     

A method for the interpretation of magnetic anomalies of dipping doublets

Summary A simple method for the interpretation of the vertical magnetic anomalies of dipping doublets is presented. In the first step, the line integrals of the anomalies along theX direction, which represent the anomalies of a vertical line double are utilised to obtain the depths to the two poles. In the second step, the profile alongY, through the point of intersection of the doublet with theX axis is used to determine the dip of the dipole.     

An analytic signal approach to the interpretation of total field magnetic anomalies1

The analytic signal (AS) is defined as the square root of the sum of the squares of the vertical and the two horizontal derivatives of the total magnetic field ΔT. This paper verifies theoretically that peaks of the AS correlate directly with their magnetic causative bodies and are positioned symmetrically over them, i.e. the main feature of the AS is that it is independent of the inclination of the magnetic field. This avoids the difficulties that are often faced in the conventional process of reduction to pole for ΔT, when the direction of magnetization of the causative bodies is not known. In addition, the AS has characteristics similar to the derivative features of the magnetic field, so that it is very sensitive to edge effects of the causative magnetic bodies. The theoretical derivations are tested by comparison with calculations on models, and, in a field example from Hunan Province, China, the AS is applied successfully to the interpretation of ΔT, whereas the conventional process of reduction to pole fails, due to the reverse magnetization of the causative body.     

重磁异常解释的归一化局部波数法

局部波数法是进行重磁数据解释的常用方法之一.本文提出归一化局部波数法,该方法在不需要任何关于地质体信息的前提下能有效地完成异常的反演工作,且给出了不同归一化方式的应用效果.理论模型试验表明归一化局部波数法能准确地完成异常的反演,且通过对比发现其他归一化方式（中值、几何平均和调和平均）的计算结果相对算术平均归一化结果具有更高的分辨率.将该方法应用于实测磁异常的解释,获得了未知地质体的空间位置.     

Depth and structural index from normalized local wavenumber of 2D magnetic anomalies

Recent improvements in the local wavenumber approach have made it possible to estimate both the depth and model type of buried bodies from magnetic data. However, these improvements require calculation of third‐order derivatives of the magnetic field, which greatly enhances noise. As a result, the improvements are restricted to data of high quality. We present an alternative method to estimate both the depth and model type using the first‐order local wavenumber approach without the need for third‐order derivatives of the field. Our method is based on normalization of the first‐order local wavenumber anomalies and provides a generalized equation to estimate the depth of some 2D magnetic sources regardless of the source structure. Information about the nature of the sources is obtained after the source location has been estimated. The method was tested using synthetic magnetic anomaly data with random noise and using three field examples.     

用最小二乘两步迭代法求解磁性球体几何与磁性参数

通过对常规最小二乘法在求解磁性球体参数过程中产生发散解的原因分析表明:非线性方程组中待定参数过多,特别是角度参数,是影响最小二乘法收敛性的主要因素.为此,提出将磁异常三分量作为观测值,用矢量磁矩作为待定参数,以替代磁化强度磁倾角和磁偏角,从而消除了非线性观测方程中的角度参数影响.根据观测值与磁矩的线性关系以及磁性球体中心位置的非线性关系,采用最小二乘两步迭代法对磁性球体几何与磁性参数进行分步求解,使得在利用最小二乘法时仅含有3个未知参数,大大减少了参数的维数.理论模型推导过程中,顾及了地磁背景场影响和多磁性体情况,给出了相应的数据处理方法.通过实测数据验证表明:提出的方法是收敛的,能达到很高的磁性体几何及磁性参数精度.     

A method to estimate the total magnetization direction from a distortion analysis of magnetic anomalies1

Knowledge of the declination and inclination of the total and induced magnetization vectors is normally required for the interpretation and analysis of magnetic anomalies. A new method of estimating the direction of the total magnetization vector of magnetized rocks from magnetic anomalies is proposed. The unknown declination and inclination (D*_T and I*_T) can be found by applying a reduction-to-the-pole operator to the measured anomalies for different couples of total magnetization direction parameters (D_T and I_T) and by observing the variation of the anomaly minimum as a function of both D_T and I*_T.and D*_T are estimated using the maximum of this function. Comparing our method to previous methods, one advantage is that our estimates are not zero-level dependent; furthermore, the method allows inclinations to be well estimated, with the same accuracy as declinations; finally declinations are not underestimated. Our method is applied to a real case and meaningful results are obtained; it is shown that the feasibility of the method is improved by removing the low-frequency components.     

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.     

基于重磁异常相关分析的场源位置及属性识别方法

针对传统的重磁对应分析在场源区域外趋于高相关度的缺点,本文提出了一种基于相关系数和垂向导数的重磁场源位置及属性识别方法,给出了一个新的重磁场源平面位置及属性判别参数（GMCP）,该参数能够有效地缩小重磁场源的识别范围.判别参数GMCP值非零分布范围反映了场源的规模.GMCP值的正负反映了场源属性,当GMCP大于零时为正相关,代表了该区域存在高磁高密度或低磁低密度的重磁同源地质体;当GMCP小于零时为负相关,代表了该区域存在高磁低密度或低磁高密度的重磁同源地质体;GMCP趋于零,则表示无重磁同源地质体.两组不同干扰水平的同源复杂组合模型实验、两组不同源组合模型试验以及南海中央海盆实际重磁数据处理结果均验证了该重磁场源位置及属性识别方法的正确性和有效性.

     

(T2,D)二维核磁共振测井混合反演方法与参数影响分析

一维核磁共振(1D NMR)测井技术在流体识别中具有一定的局限性.二维核磁共振(2D NMR)测井能同时测量到多孔介质中横向弛豫时间(T₂)和扩散系数(D)等信息,利用这两个参数区分流体性质,较一维核磁共振测井技术具有明显的优越性.针对梯度场下的2D NMR测井弛豫机理和数学模型,提出了适用于求解大型稀疏矩阵方程的反演方法-基于非负最小二乘法(LSQR)和截断奇异值分解(TSVD)法的混合算法.为验证方法的有效性,先根据多回波观测模式合成回波串数据,然后再用混合反演算法进行反演,反演得到横向弛豫时间(T₂)和扩散系数(D),并构建T₂-D二维谱图.结果对比表明,该混合反演算法得到的T₂-D二维谱与流体模型一致性好,计算精度均比单一反演方法有较大改善,表明该混合反演方法可用于油气储集层2D NMR测井的反演和流体识别.此外,分别对油水同层和气水同层模型进行了正演模拟和反演实验, 系统考察了不同磁场梯度、不同回波间隔组合对反演效果的影响,为2D NMR参数设计提供依据.     

Spectral method for estimating the quality of the medium from one source and two stations

Izvestiya, Physics of the Solid Earth - The method is suggested for estimating the quality (coefficient Q) of the medium from the longitudinal waves of the earthquakes in the regional zone (Q P )....     

A novel approach to the quantitative interpretation of petrophysical parameters using nano-CT: example of Paleozoic carbonates

The main goal was the analysis of parameters describing the structure of the pore space of carbonate rocks, based on tomographic images. The results of CT images interpretation, made for 17 samples of Paleozoic carbonate rocks were shown. The qualitative and quantitative analysis of a pore system was performed. Objects were clustered according to the pore size. Within the clusters, the geometry parameters were analysed. The following dependences were obtained for carbonate rocks, also for individual clusters (due to the volume): (1) a linear relationship (on a bilogarithmic scale) between the specific surface and the Feret diameter and (2) a strong linear relationship between specific surface area and Feret diameter and average diameter of the objects calculated for the sphere. The results were then combined with available results from standard laboratory tests, including NMR and MICP.     

A Fourier transform method for the interpretation of self-potential anomalies due to two-dimensional inclined sheets of finite depth extent

The self-potential anomaly due to a two-dimensional inclined sheets of finite depth extent has been analysed in the frequency domain using the Fourier transform. Expression for the Fourier amplitude and phase spectra are derived. The Fourier amplitude and phase spectra are analysed so as to evaluate the parameters of the sheet. Application of this method on two anomalies (synthetic and field data) has given good results.     

The R-approximation method and its application to the interpretation of detailed gravity and magnetic data

The application of the R-approximation method based on the use of the Radon integral transform within the framework of the method of linear integral representations to the interpretation of detailed gravity and magnetic data is considered in this paper. The results are presented for some research areas located in Russia and in the Crimea (Ukraine). The method determines the distribution of anomalous field elements, construction of the analytical continuation of fields, and their linear transformations with a sufficiently high degree of accuracy.     

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.     

Integrated interpretation of the magnetotelluric and magnetic data from Mahallat geothermal field,Iran

Magnetotelluric (MT) and ground magnetic surveys were conducted on the Mahallat geothermal field situated in Markazi province, central Iran, as a primary part of the explorations and developments of a geothermal energy investigation program in the region. Mahallat region has the greatest geothermal fields in Iran. MT survey was performed in November 2011 on an 8 km profile crossing the hot springs with a total of 17 stations. The 2D inversion of the determinant MT data was performed using a 2D inversion routine based on the Occam approach. The 2D resistivity model obtained from the determinant data shows a low resistivity zone at 800-2000 m depth and a higher resistivity zone above the low resistivity zone, interpreted as geothermal reservoir and cap rock, respectively. It also revealed two major concealed faults which are acting as preferential paths for the circulation of hydrothermal fluids. To obtain more geophysical evidence, a ground magnetic survey with 5000 stations was also performed over an area of 200 km² around the MT profile. Magnetic measurements show a main positive anomaly of about +1000 nT over the study area, which could be interpreted as an intrusive body with the high magnetic susceptibility (i.e. mafic and ultramafic rocks) into the sedimentary host rocks. We interpret the body as the heat source of the geothermal system. Structural index and depth estimation of the anomaly indicate that the intrusive body is similar to a cylinder extending from about one kilometer depth down to greater depths. The results of MT and magnetic investigations indicate a geothermal reservoir which proves the preliminary geological observations to a great extent.     

Modelling the effects of changes in the Earth's magnetic field from 1957 to 1997 on the ionospheric hmF2 and foF2 parameters

We have modelled the effects of changes in the Earth's magnetic field on the ionosphere as have occurred from 1957 to 1997 using the NCAR Thermosphere–Ionosphere–Electrodynamics General Circulation Model. Previous studies that attempted to quantify these effects used a constant wind field, so that any electro-dynamical coupling processes could not be accounted for. Using TIE-GCM we can account for these processes. We find substantial changes in the F2 layer peak height hmF2 (up to ±20 km) and critical frequency foF2 (up to ±0.5 MHz) over the Atlantic Ocean and South America, purely due to changes in the Earth's magnetic field (i.e. unrelated to greenhouse gas cooling effects, which are often held responsible for long-term trends in hmf2 and fof2). These would make up a significant contribution to observed long-term trends in these areas and therefore must be taken into account in their interpretation. Modelled trends of hmF2 and foF2 exhibit a strong seasonal and diurnal variation, highlighting the importance of separating data with respect to season and local time. Most of the modelled changes in hmF2 and foF2 can be related to changes in plasma transport up or down magnetic field lines driven by neutral winds, changes, which are mostly caused by changes in the inclination of the field, though changes in declination and neutral wind also play a role. Changes in the vertical component of the E×B drift seem to have little effect on hmF2 and foF2.     

Classification of near-surface anomalies in the seismic refraction method according to the shape of the time–distance graph: A theoretical approach

Results obtained by SASW and PS-logging (in-hole) seismic techniques are compared with the relatively new ReMi (Refraction microtremor) method at a common site with a well-known soil profile: a recently constructed high-speed railway embankment. PS-logging is the most accurate technique in identifying the soil profile of the embankment followed by Re-Mi and SASW. Mean shear wave velocity estimations are also higher for PS-logging, followed by SASW and ReMi, while mean deviation is similar in each technique. The ReMi technique has provided very accurate results in the study of the embankment profile, which in addition to its high operability and its fast data processing, makes it a very convenient technique for extensive geotechnical surveys.