Direct interpretation of 2D potential fields for deep structures by means of the quasi-singular points method

The founder of the Russian school of direct interpretation of potential fields (with minimal prior geological‐geophysical information) was V.M. Berezkin, who introduced the operator of total normalized gradient for the 2D interpretation of profile gravity data sets. This operator was successfully applied in searches of hydrocarbon reservoirs. The further development of this approach (the so‐called quasi‐singular points method) has allowed solution also to various structural problems, using mathematical criteria for the transition from extremes of total normalized gradient fields to coordinates of anomalous sources. The main numerical evaluation strategy is based on stabilized downward continuation of field derivatives and specific use of the filtration properties of Fourier series approximation. The characteristic properties of the quasi‐singular points method are: 1) presentation of a more general total normalized gradient function through additional parameters (derivative order m, form of smoothing function Q, number of Fourier coefficients N* with maximal N), optimum values being chosen during a peak‐spectrum analysis of the interpreted function; 2) calculation of the set of total normalized gradient fields for various values of N*/N, representing coordinate systems {x,N*/N} as an ‘axes tree’ of extrema, where each 2D total normalized gradient field is representationally compressed in a 1D line, permitting a) immediate overview of the positions of the axes in all variants of the calculated fields and b) reduction of the retained information, as required in subsequent interpretation; 3) development of two criteria for transition from extrema of total normalized gradient fields to the coordinates of anomaly sources. The quasi‐singular points method is intended for tracing limiting gently‐sloping boundaries, if their micro‐relief features are sources of the interpreted anomaly but sub‐vertical contacts may also be traced. The method has been tested in delineating various geological structures. One of the most challenging, successfully achieved, was tracing of the Moho discontinuity and study of the upper mantle, using only Bouguer anomaly data along interpretation profiles. This is attested in an example of two regional profiles intersecting the European part of Russia. The central part of one of them coincides with the results from a deep seismic profile.     

Location and depth estimation of point-dipole and line of dipoles using analytic signals of the magnetic gradient tensor and magnitude of vector components

The magnetic gradient tensor (MGT) provides gradient components of potential fields with mathematical properties which allow processing techniques e.g. analytic signal techniques. With MGT emerging as a new tool for geophysical exploration, the mathematical modelling of gradient tensor fields is necessary for interpretation of magnetic field measurements. The point-dipole and line of dipoles are used to approximate various magnetic objects. I investigate the maxima of the magnitude of magnetic vector components (MMVC) and analytic signals of magnetic gradient tensor (ASMGT) resulting from point-dipole and line of dipoles sources in determining horizontal locations. I also present a method in which depths of these sources are estimated from the ratio of the maximum of MMVC to the maximum of ASMGT. Theoretical examples have been carried out to test the feasibility of the method in obtaining source locations and depths. The method has been applied to the MMVC and ASMGT computed from the total field data over a basic/ultrabasic body at the emerald deposit of Socoto´, Bahia, Brazil and buried water supply pipe near Jadaguda Township, India. In both field examples, the method produces good correlations with previous interpretations.     

Edge Detection in Potential-Field Data by Enhanced Mathematical Morphology Filter

Enhancement on the edges of the causative source is an indispensable tool in the interpretation of potential-field data. There are a number of methods for recognizing the edges, most of which involve high-pass filters based on derivatives of potential-field data. A new edge-detection method is presented, called the enhanced mathematical morphology (EMM) filter. The EMM filter uses the ratio of the erosion of the total horizontal derivative to the dilation of total horizontal derivative to recognize the edges of the sources, and can display the edges of the shallow and deep bodies simultaneously. The EMM filter does not require the computation of vertical derivatives, which makes this method computationally stable. The EMM filter is tested on synthetic and real potential field data in China. Compared to other edge-detection filters, the new method is able to recognize the source edges more clearly, and the outputs are more insensitive to noise.     

Interpretation of magnetic and gravity gradient tensor data using normalized source strength – A case study from McFaulds Lake,Northern Ontario,Canada

In this paper, we present a case study on the use of the normalized source strength (NSS) for interpretation of magnetic and gravity gradient tensors data. This application arises in exploration of nickel, copper and platinum group element (Ni‐Cu‐PGE) deposits in the McFaulds Lake area, Northern Ontario, Canada. In this study, we have used the normalized source strength function derived from recent high resolution aeromagnetic and gravity gradiometry data for locating geological bodies. In our algorithm, we use maxima of the normalized source strength for estimating the horizontal location of the causative body. Then we estimate depth to the source and structural index at that point using the ratio between the normalized source strength and its vertical derivative calculated at two levels; the measurement level and a height h above the measurement level. To discriminate more reliable solutions from spurious ones, we reject solutions with unreasonable estimated structural indices. This method uses an upward continuation filter which reduces the effect of high frequency noise. In the magnetic case, the advantage is that, in general, the normalized magnetic source strength is relatively insensitive to magnetization direction, thus it provides more reliable information than standard techniques when geologic bodies carry remanent magnetization. For dipping gravity sources, the calculated normalized source strength yields a reliable estimate of the source location by peaking right above the top surface. Application of the method on aeromagnetic and gravity gradient tensor data sets from McFaulds Lake area indicates that most of the gravity and magnetic sources are located just beneath a 20 m thick (on average) overburden and delineated magnetic and gravity sources which can be probably approximated by geological contacts and thin dikes, come up to the overburden.     

ON THE PROPERTIES OF THE RECIPROCAL GEOELECTRIC SECTION*

The interpretation of vertical electrical sounding data can be facilitated by the application of the reciprocal geoelectric section. If an apparent resistivity field curve has a descending right end, the apparent resistivity curve of the reciprocal geoelectric section can be obtained by the application of linear filter theory; from this the total transverse resistance of the geoelectric section can be calculated without having to interpret the field curve. In addition, Orellana's auxiliary point method can now be extended to interpret three and four layer apparent resistivity curves of all types. This paper summarizes the properties of the resistivity transform curve, the apparent resistivity curve, and the apparent resistivity curve of the reciprocal geoelectric section, with several new applications.     

重力异常视深度滤波及应用

为了解观测面以下位场场源体产生的异常,设计了一种波数域的滤波器,该滤波器可在无需岩石物性资料的前提下用于位场数据的反演．对位场资料用解析法和差分法上、下延拓,以消除浅表干扰源的影响,并最后下延至观测面以下,根据下延后场的极值确定场源的质心深度．理论模型的试算和实际资料的处理均获得了令人满意的效果．     

地震波衰减规律及其恢复方法

针对地面地震分辨率低,不能有效识别薄层储层、薄层地层等问题,本文通过地震波衰减规律的分析,提出了一种恢复地震波高频衰减获得宽频带地震剖面的方法,从而大幅度地提高了地震分辨率.应用双井微地震测井资料对松辽盆地地震波动力学特征研究表明,地震波衰减规律是在近地表低速层和近地表低速层的近震源区地震波高频衰减巨大,而在高速层地震波高频衰减很小.药量大近震源区地震波高频衰减大,药量小近震源区地震波高频衰减小.那么,近震源区和近地表低速层对地震波的衰减是地面地震资料频带窄、分辨率低的主要原因.据此提出了如下确定性反褶积方法,用双井微地震测井资料求取近震源区、近地表低速层和虚反射等滤波因子,用其对地面地震资料作确定性反褶积处理,从而恢复近震源区、近地表低速层等几种因素的地震波衰减,将大药量激发地表接收的地面地震延拓成小药量激发高速层接收的宽频带地震.应用该方法对松辽盆地优势频带宽5~90 Hz,视主频50 Hz的地面地震资料处理后,地震剖面优势频带宽达5~360 Hz,视主频达180 Hz,使常规地震剖面分辨率提高2倍.具体的说松辽盆地中部含油组合的地面地震分辨能力由9~15 m提高到3~5 m.宽频带地震剖面与160 Hz的人工合成地震记录对比符合的很好,表明其处理结果是正确.该成果在油气勘探开发中的油气储层预测、构造学研究、沉积学研究等方面有重要的意义.     

位场数据网格化的反插值法

位场不规则分布数据的网格化是位场数据分析处理的首要问题.本文借鉴反插值法的原理，提出利用基于预条件共轭梯度的反插值法实现位场数据的网格化.其中，插值算子采用高斯权系数，滤波算子采用Laplacian算子，预条件算子采用滤波算子的逆.通过理论模型和实际航磁数据的网格化试验分析，验证了本文的反插值法适合地球物理位场特征，网格化速度快，精度高，效果好.     

归一化总水平导数法在位场数据解释中的应用

本文提出归一化总水平导数法,通过对总水平导数进行空间归一化计算实现了异常体水平位置和深度的估计,此外还推导出基于归一化总水平导数的欧拉反褶积法来估算地下地质体的空间位置,两种方法反演结果的相互验证可有效地提高反演结果的可信度.理论模型试验证明空间归一化总水平导数法和归一化总水平导数欧拉反褶积法均能有效地完成异常体的水平位置和深度的估计,所获得的位置参数与理论值相一致.在利用归一化总水平导数法进行磁异常解释时,对数据进行化磁极计算可得到更加准确的结果.将其应用于实际航磁数据的解释,获得了岩脉的大致分布特征.     

利用加强水平方向总水平导数对位场全张量数据进行边界识别

位场全张量梯度数据以其信息量大、含有更高频的信号成分,能更好地描述小的异常特征等优点在地球物理领域中得到广泛应用.边界检测是位场解释中不可缺少的任务,需要新的边界探测器来处理位场梯度张量数据.为了充分利用位场梯度张量数据的多信息成分,本文定义了方向总水平导数和加强方向总水平导数,并利用其定义新的边界检测器.为了能同时显示不同振幅大小异常的边界,本文对其进行了归一化处理.通过模型试验,证明了归一化方法能更加清晰准确地显示浅部和深部的地质体边界信息.最后将该边界检测方法用于加拿大圣乔治湾实际测得全张量重力梯度数据和中国朱日和地区的磁异常数据中,并得到了较好的边界检测结果.     

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.     

磁总场异常垂直梯度三维相关成像

本文提出了磁总场异常垂直梯度三维相关成像方法,用于成像地下等效磁源分布.它首先将地下待成像空间划分为三维规则网格,然后直接计算每个网格节点磁偶板子在观测面理论磁总场异常垂直梯度与实测磁总场异常垂直梯度的互相关,其相关系数值表征等效磁偶极子分布(即磁偶极子发生的概率).理论长方体组合模型数据和实际某矿区磁测资料试验结果表明本文方法计算得到的相关系数值能基本反映地下的磁源分布,且分辨率明显高于磁总场异常三维相关成像的分辨率,也高于基于熵滤波分离异常的磁总场异常三维相关成像的分辨率.     

各向异性标准化方差计算重磁源边界

在重磁源边界定位方法中,传统的梯度方法易受干扰的影响使计算的边界混乱,而且在弱异常处由于叠加异常的影响很难识别场源边界.本文首先利用坐标旋转构造了各向异性高斯函数,提出了各向异性标准化方差计算重磁源边界的方法.理论分析与模型实验详细阐明了该方法的数学含义,并通过干扰分析验证了方法的稳定性与有效性,结合中扬子地区航磁异常...     

DOWNHOLE SYNTHETIC SEISMIC PROFILES IN ELASTIC MEDIA1

A multichannel lattice filter structure is utilized to represent seismic waves propagating in adjacent layers in an elastic medium. Using this model, an explicit time-domain solution for arbitrary source and receiver locations is obtained as an ARMA (AutoRegressive and Moving-Average) process. The lattice and ARMA structures have given rise to an effective algorithm for the calculation of offset/downhole synthetic seismograms. A large range of recently developed offset/downhole seismic survey geometries, such as the ‘Yo-Yo’ arrangement, can thus be simulated. In addition, the explicit solutions for upgoing and downgoing waves provide new insight into the properties of general downhole seismic signals, including wave-mode conversion effects and multiple reflections. Furthermore, offset/downhole seismograms generated by a line source (i.e. 2D point source) can also be constructed by superposition of plane waves with different incidence angles. Synthetic seismograms generated using a different source-receiver arrangement indicate that the properties especially associated with offset/downhole seismic signals can be predicted by this modelling method. These properties include arrival times, amplitude attenuation and wave-mode conversion effects. Finally, utilizing this numerical modelling method to a real downhole survey with Yo-Yo geometry may lead to a proper data acquisition and processing procedure, and improves the interpretation confidence of the field section.     

Processing And Interpretation Of Electromagnetic Induction Array Data

The simultaneous nature of array data can be exploitedin electromagnetic induction studiesfor three general purposes.First, one or more reference sites can be usedto reduce bias, improve signal-to-noise ratios, and provide bettercontrol over source complications and coherent noisein estimates of MT impedances and otherEM transfer functions (TFs).Although a single good reference site can dramatically improveTF estimates, improvements due to multiple sites are often rather modest, because local noise is the limiting factor.Secondly, arrays allow for estimation of inter-station transfer functions, and maps of anomalous horizontal field variations. Relatively straightforward modifications to inversion codes wouldallow quantitative interpretation of these additionalconstraints on resistivity variations.Finally, with arrays it is possible to estimate the response of theEarth to a richer spectrum of external source excitations. In particular,the natural extension to the usual uniform source assumption implicit inthe MT method allows for three curl-free magnetic gradient sources.Quantitative interpretation of the response of a three-dimensionalEarth to these sources could provide additionalconstraints on large scale variations in crustal and uppermantle resistivity, and might help to overcome problemsdue to aliasing of near surface distortion in widely spaced MT data.     

Toward a full multiscale approach to interpret potential fields

The way potential fields convey source information depends on the scale at which the field is analysed. In this sense a multiscale analysis is a useful method to study potential fields particularly when the main field contributions are caused by sources with different depths and extents. Our multiscale approach is built with a stable transformation, such as depth from extreme points. Its stability results from mixing, in a single operator, the wavenumber low‐pass behaviour of the upward continuation transformation of the field with the enhancement high‐pass properties of n‐order derivative transformations. So, the complex reciprocal interference of several field components may be efficiently faced at several scales of the analysis and the depth to the sources may be estimated together with the homogeneity degrees of the field. In order to estimate the source boundaries we use another multiscale method, the multiscale derivative analysis, which utilizes a generalized concept of horizontal derivative and produces a set of boundary maps at different scales. We show through synthetic examples and application to the gravity field of Southern Italy that this multiscale behaviour makes this technique quite different from other source boundary estimators. The main result obtained by integrating multiscale derivative analysis with depth from extreme points is the retrieval of rather effective information of the field sources (horizontal boundaries, depth, structural index). This interpretative approach has been used along a specific transect for the analysis of the Bouguer anomaly field of Southern Apennines. It was set at such scales, so to emphasize either regional or local features along the transect. Two different classes of sources were individuated. The first one includes a broad, deep source with lateral size of 45∼50 km, at a depth of 13 km and having a 0.5 structural index. The second class includes several narrower sources located at shallowest depths, ranging from 3–6 km, with lateral size not larger than 5 km and structural indexes ranging from 1–1.5. Within a large‐scale geological framework, these results could help to outline the mean structural features at crustal depths.     

Interpretation of regional aeromagnetic data by the scaling function method: the case of Southern Apennines (Italy)

A complex aeromagnetic anomaly in Southern Apennines (Italy) is analysed and interpreted by a multiscale method based on the scaling function. We use multiscale methods allowing analysis of a potential field along ridges, which are lines defined by the position of the extrema of the field at the considered scales. The method developed and applied in this paper is based on the study of the scaling function of the total magnetic field. It allows recovering of source parameters such as depth and structural index. The studied area includes a Pleistocene volcanic structure (Mt. Vulture) whose intense dipolar anomaly is superimposed on a longer wavelength regional anomaly. The interpretation of ridges of the modulus of the analytic signal at different altitude ranges allows recognition of at least three distinct sources between about 5 km and 20 km depth. Their interpretation is discussed in light of borehole data and other geophysical constraints. A reasonable geological model for these sources indicates the presence of intrusions, probably linked to the past activity of Mt. Vulture.     

The theory of the continuous wavelet transform in the interpretation of potential fields: a review

We consider the use of the continuous wavelet transform in the interpretation of potential field data. We report its development since the publication of the first paper by Moreau et al . in 1997. Basically, it consists in the interpretation in the upward continued domain since dilation of the wavelet transform is the upward continuation altitude. Thus within a range of altitudes, the wavelet transform of the noise is decreased faster than the wavelet transform of the potential field caused by underground sources; this means that the signal-to-noise ratio is much better than those involved in other enhancing methods (e.g., Euler deconvolution, gradient analysis, or the analytic signals). Similarly to the Euler deconvolution, its first target parameters were the source positions and shape. The method has then been developed to estimate size and directions of extended sources (e.g., faults and dikes of finite dimensions) and also the magnetization direction in the case of magnetic data. Latest developments show that when combined with a Radon transform, the continuous wavelet transform can help in the automatic detection of elongated structures in 3D, simultaneously to the estimation of their strike direction, shape and depth. Several applications to real case studies have been shown before; however for clarity's sake in the present paper, only synthetic cases have been reproduced to clearly sum up the development of the methodology.     

点源二维电场中纵剖面上电位的计算

将总电位ν分解为正常电位．ｕｏ和异常电位ｕ·本文绘出点源二维电场中，异常电位ｕ的傅氏变换Ｕ的变分方程，以及点源二维电场地形影响的异常电位ｕ的傅氏变换Ｕ的积分方程，前者可用有限单元法求解，后者可用边界单元法求解．根据电源点的Ｕ的傅氏反交换，解决了前人尚未解决的直接计算点源二维电场中纵剖面（通过电源点、平行走向的剖面）的电位问题．     

Depth from extreme points method for gravity gradient tensor data

The ‘depth from extreme points’ method is an important tool to estimate the depth of sources of gravity and magnetic data. In order to interpret gravity gradient tensor data conveniently, formulas for the tensor data form regarding depth from the extreme points method were calculated in this paper. Then, all of the gradient tensor components were directly used to interpret the causative source. Beyond the g_zz component, also the g_xx and g_yy components can be used to obtain depth information. In addition, the total horizontal derivative of the depth from extreme points of the gradient tensor can be used to describe the edge information of geologic sources. In this paper, we investigated the consistency of the homogeneity degree calculated by using the different components, which leads to the calculated depth being confirmed. Therefore, a more integrated interpretation can be obtained by using the gradient tensor components. Different synthetic models were used with and without noise to test the new approach, showing stability, accuracy and speed. The proposed method proved to be a useful tool for gradient tensor data interpretation. Finally, the proposed method was applied to full tensor gradient data acquired over the Vinton Salt Dome, Louisiana, USA, and the results are in agreement with those obtained in previous research studies.