An Approach for Interpretation of Self-Potential Anomalies due to Simple Geometrical Structures Using Fair Function Minimization

A quantitative interpretation method of self-potential field anomalies has been proposed. The method is designed and implemented for the estimation of center depth, electric dipole moment or magnitude of polarization, polarization angle, and geometric shape factor of a buried body from SP field data, related to simple geometric structures such as cylinders, spheres and sheet-like bodies. The proposed method is based on Fair function minimization and also on stochastic optimization modeling. This new technique was first tested on theoretical synthetic data randomly generated by a chosen statistical distribution from a known model with different random noise components. Such mathematical simulation shows a very close agreement between assumed and estimated model parameters. Being theoretically proven, it has been applied and tested on self-potential field data taken from the United States, Germany, India and Turkey. The agreement between results obtained by the suggested method and those obtained by other previous methods is good and comparable. Moreover, the depth obtained by this method is found to be in high accordance with that obtained from drilling information.     

Interpretation of ground VLF-EM data in terms of inclined sheet-like conductor models

The response of two-dimensional, inclined, sheet-like conductors with, low conductance values to plane wave electromagnetic fields in the very low frequency (VLF) range has been evaluated by using a numerical technique. The conductance values of the conductors considered are appropriate for those produced by water and/or clay-filled fracture and shear zones in the Precambrian crystalline rocks of the Canadian Shield. The surrounding host rock was assumed to be, resistive with resistivities in the 1–10 k.m range to reflect the high resistivities over the shield areas. No overburden was assumed in this analysis.The results of the computations are presented in the form of characteristic interpretation diagrams to interpret ground VLF data in the field, where facilities for direct numerical modelling may not be available. A method for interpreting ground VLF data using such characteristic diagrams has been proposed in this paper which requires a prior knowledge of the host rock resistivity and the inclination of the conductor. These two parameters may be derived from a VLF resistivity survey and from appropriate filtering of the VLF tilt angle response. The interpretation method was applied to a ground VLF anomaly obtained at a research site near Atikokan in NW Ontario, which yielded an interpretation compatible with information from geological mapping.Geological Survey of Canada Contribution No. 51888.     

应用加强解析信号倾斜角进行位场数据的边界检测

边界检测在地球物理位场数据解释中占有重要位置.现有的传统边界识别方法有的不能同时显示不同振幅的异常边界,有的虽然能均衡不同振幅的异常,但识别出来的边界信息中含有一些额外的错误的边界信息,尤其是当测量的异常中同时含有正异常和负异常时.目前已有的去除额外错误边界信息的方法存在着一定的人为主观性.为了解决这些问题,本文定义了加强解析信号倾斜角来进行地质体边界识别.通过模型试验证明了该方法不仅能同时清晰地识别深部和浅部地质体的边界,而且能有效地避免引入一些错误边界信息.最后将该方法应用到四川盆地的重力异常数据中,并取得了良好边界结果.     

GRADIENT ARRAY PROFILES OVER THIN RESISTIVE VEINS1

Furness , P. 1993. Gradient Array Profiles over thin resistive veins. Geophysical Prospecting 41 , 113–130. Gradient array geoelectric surveys are commonly used to explore for buried sheet-like targets. It is demonstrated that under certain circumstances the responses of such features can become practically equivalent for a range of models differing considerably in resistivity and thickness. This is the dual of the familiar equivalence phenomenon associated with thin beds in geoelectric sounding operations. Hence the geoelectric response profiles over thin dipping resistive veins are conveniently studied by considering equivalent forms with vanishing thickness and infinite resistivity but with the same resistivity-thickness product. The effects of varying the dip, depth of burial, depth extent and resistivity–thickness product of such features on the gradient array response profiles are investigated by means of a series of numerical experiments. These demonstrate several effects of significance to survey design and data interpretation. In particular it is found that while the resistivity–thickness product influences the amplitude of the response profiles it has little effect on their form. A similar behaviour is found to be exhibited by veins with extended depth extent when the dip is varied. A complete quantitative interpretation of gradient array profiles over thin dipping resistive veins is thus only possible for veins of limited depth extent. For veins with an extended depth dimension, the data is ambiguous (in a practical sense) in terms of the dip and the resistivity–thickness product. Here, the interpretation can only be expected to deduce the horizontal and vertical locations of the vein apex.     

核磁共振与瞬变电磁三维联合解释方法

传统核磁共振地下含水量解释多采用基于均匀半空间或层状导电模型的一维反演, 分层给出地下含水信息.然而, 这些方法忽略了地下复杂电阻率分布信息对结果的影响, 也不能很好地反映局部三维含水构造.本文从三维电介质中核磁共振响应的正演理论出发, 提出首先利用瞬变电磁数据进行基于等效导电平面法的快速电阻率成像, 然后将成像结果作为核磁共振三维反演的电性模型, 进行联合解释.激发磁场的分布采用有限元法直接求解, 通过引入伪δ源实现电流源的加载, 并强加散度条件排除了三维磁场模拟中"弱解"的影响.针对核磁共振灵敏度矩阵的病态性和数据中存在的干扰信号, 提出考虑罚项的非线性拟合目标函数, 利用线性化方法进行核磁共振反演.模型数据表明该方法能较准确反映地下三维含水构造, 实测算例进一步证明了方法的有效性.本研究将促使核磁共振方法在岩溶、裂隙水、孤立水体等复杂水文地质条件及隧道、矿井灾害水源探测等方面得到有效应用.     

Object-based model verification by a genetic algorithm approach: Application in archeological targets

A new target-oriented parameterization scheme, named the object-based model, is suggested to represent man-made or natural targets as regular shapes embedded in a two-dimensional resistivity background. The numerical values of the target parameters (size, depth, location and resistivity) are estimated in three steps consisting of conventional regularized inversion, exclusion of anomalous regions and delineation of target bodies. The method produces sharp edges and sharp variation in intrinsic resistivity between the targets and background.The number of target objects is decided by the visual inspection of the 2D resistivity section derived from the application of a conventional cell-based regularized inversion. The 2D background is also extracted from the same section. A genetic algorithm approach is used at the final stage to test a large number of distinct models. Each test model consists of the same number of objects buried in the 2D background. The size, depth, location and resistivity of the targets are estimated from a class of models generated by the application of biological rules. The derived images of buried bodies have sharp edges and can then be understood by engineers and archeologists. However, if the hypothesis about the ‘conceptual model’ is very different from the geometry of the subsurface, the proposed approach will not be able to produce satisfactory results.     

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.     

SOTEM数据一维OCCAM反演及其应用于三维模型的效果

本文基于垂直磁场分量研究了SOTEM数据的一维OCCAM反演方法,并将其应用于理论三维数据及野外实测数据的反演.对于大部分一维模型,OCCAM反演可取得较好的反演效果,且反演结果不依赖于偏移距;噪声对SOTEM数据的OCCAM反演具有较大影响,但当信号含噪水平不超过5%时,反演结果仍具有较好的准确性;若浅层存在较厚的低阻层,OCCAM反演结果对下部地层的分辨能力下降,仅能获得具有平均效应的电阻率.将一维算法应用于SOTEM三维数据的反演,会产生较大的误差,尤其是在异常体边缘地带影响最为严重.该影响程度与异常体和背景电阻率之间的差异有关,对于大多数电性近似呈连续变化的真实大地而言,一维OCCAM反演算法仍可获得较好的效果.最后通过陕西某煤田深部富水性调查的实测SOTEM数据反演验证了本文的研究成果.

     

Out‐of‐plane effects in 2D borehole‐to‐surface resistivity tomography and applications in mineral exploration

In this paper, we discuss the effects of anomalous out‐of‐plane bodies in two‐dimensional (2D) borehole‐to‐surface electrical resistivity tomography with numerical resistivity modelling and synthetic inversion tests. The results of the two groups of synthetic resistivity model tests illustrate that anomalous bodies out of the plane of interest have an effect on two‐dimensional inversion and that the degree of influence of out‐of‐plane body on inverted images varies. The different influences are derived from two cases. One case is different resistivity models with the same electrode array, and the other case is the same resistivity model with different electrode arrays. Qualitative interpretation based on the inversion tests shows that we cannot find a reasonable electrode array to determine the best inverse solution and reveal the subsurface resistivity distribution for all types of geoelectrical models. Because of the three‐dimensional effect arising from neighbouring anomalous bodies, the qualitative interpretation of inverted images from the two‐dimensional inversion of electrical resistivity tomography data without prior information can be misleading. Two‐dimensional inversion with drilling data can decrease the three‐dimensional effect. We employed two‐ and three‐dimensional borehole‐to‐surface electrical resistivity tomography methods with a pole–pole array and a bipole–bipole array for mineral exploration at Abag Banner and Hexigten Banner in Inner Mongolia, China. Different inverse schemes were carried out for different cases. The subsurface resistivity distribution obtained from the two‐dimensional inversion of the field electrical resistivity tomography data with sufficient prior information, such as drilling data and other non‐electrical data, can better describe the actual geological situation. When there is not enough prior information to carry out constrained two‐dimensional inversion, the three‐dimensional electrical resistivity tomography survey is the better choice.     

多同性源阵列电阻率法隧道超前探测方法与物理模拟试验研究

直流电阻率法以其对含水构造响应敏感且适应性强的特点,是隧道施工期超前地质预报的常用方法.针对目前定点源三极观测方式易受到测线附近旁侧异常干扰与聚焦观测方式探测距离过短无法三维成像的问题,提出了一种基于多同性源阵列电阻率的隧道超前探测新方法,利用环形布置的多同性源供电压制隧道掌子面后方的异常体的干扰,同时增强掌子面前方远处异常体的敏感度,阵列电极测量可为含水构造的三维反演成像提供三维数据.首先,开展了含水构造超前探测的数值正演模拟,发现多同性源方法的视电阻率纵向微分曲线极小值以及与横轴的交点位置可对异常体位置进行定性判断,探讨了多同性源方法对后方及侧向异常干扰的响应特征及识别方法.其次,将电阻率光滑约束与轨迹光滑策略引入蚁群反演算法,提出了一种最小二乘方法与改进蚁群算法相结合的混合反演算法,反演数值算例表明混合反演算法能够实现含水构造的三维成像,较好地反演出不同距离的含水构造位置,并使其边界较为清晰.为了验证多同性源探测方法的探测效果开展了物理模型试验,多同性源阵列电阻率法能较好的反映含水构造的存在,与实际含水构造的位置较为相符.     

基于水平方向解析信号的均衡重力位场边界识别方法

边界识别技术是位场数据解释中一项基本的工作,现有的边界识别方法多存在边界识别结果发散和不能均衡深浅地质体异常的缺点.目前一些均衡边界识别方法会因正负异常同时存在而引起额外的错误边界或者存在人为主观因素去除错误边界信息的缺点.本文充分利用重力位场张量梯度的多信息成分,提出利用水平方向解析信号及其垂向导数与传统的均衡边界识别方法做结合的方式定义新的探测边界的方法.通过理论模型试验证明新方法同传统方法相比,能够更加清晰、准确的圈定出深浅地质体的边界.最后将新的边界识别方法应用到实测重力异常数据解释中,取得了良好的边界识别结果并能够发现更多的构造细节.

     

复杂介质有限元法2.5维可控源音频大地电磁法数值模拟

利用有限元2.5维可控源音频大地电磁法（简称CSAMT）数值模拟方法,对100Ωm均匀半空间介质中有限长度的电偶极源产生的电场、磁场及视电阻率、相位特征进行了数值模拟,研究了场的空间变化规律. 在一个象限中,场的特征存在双叶现象,当收发距大于4个趋肤深度时,电阻率较接近介质真实的电阻率,这些结果为观测系统和收发距的选择提供了依据. 波数域场的特征表明,低波数对源的贡献占较大的比例. 有限元法2.5维CSAMT数值模拟的优势在于能较准确地获得复杂介质结构的波场特征. 本文结合直立异常体、倾斜异常体及断陷模型对CSAMT电阻率、相位剖面特征及频率曲线特征的可靠性进行了研究. 数值模拟结果直观地给出了异常体的剖面异常形态. 通过对比研究异常体的剖面异常形态和半空间场的特征进一步说明本文方法和软件在模拟复杂介质结构场特征时是可靠的. 这为认识观测数据,指导反演解释提供了较好的依据.     

Salt body detection from seismic data via sparse representation

In seismic interpretation and seismic data analysis, it is of critical importance to effectively identify certain geologic formations from very large seismic data sets. In particular, the problem of salt characterization from seismic data can lead to important savings in time during the interpretation process if solved efficiently and in an automatic manner. In this work, we present a novel numerical approach that is able to automatically segmenting or identifying salt structures from a post‐stack seismic data set with a minimum intervention from the interpreter. The proposed methodology is based on the recent theory of sparse representation and consists in three major steps: first, a supervised learning assisted by the user which is performed only once, second a segmentation process via unconstrained ?₁ optimization, and finally a post‐processing step based on signal separation. Furthermore, since the second step only depends upon local information at each time, the whole process greatly benefits from parallel computing platforms. We conduct numerical experiments in a synthetic 3D seismic data set demonstrating the viability of our method. More specifically, we found that the proposed approach matches up to 98.53% with respect to the corresponding 3D velocity model available in advance. Finally, in appendixes A and B, we present a convergence analysis providing theoretical guarantees for the proposed method.     

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处理实例,表明通过计算各向异性标准化方差,可以有效地确定重磁源边界,尤其对微弱异常能够实现较好的边界定位,计算的边界分辨率高且信息丰富,有利于资料的综合解释.     

基于多源地球物理数据的机器学习方法在地质体分类中的应用——以黑龙江多宝山矿集区为例

为适应多源地球物理大数据地质解释的需要,同时也为了在地质体物性存在交叠情况下快速有效地实现多源地球物理数据的地质解释,本文提出应用机器学习的支持向量机方法对多源地球物理数据进行地质解释的新思路,并给出了利用物性三体（密度、磁化率、电阻率）进行地质体圈定与分类方法.阐明了参数归一化、参数寻优对模型训练与学习及分类结果的影响与作用.本文将黑龙江多宝山矿集区物性三体与矿集区的区域地质、矿床地质及钻井资料相结合,利用所提出的方法对地下地质体进行了圈定与分类,对分类结果经过交叉检验,正确率达81.6%,表明了训练模型具有较高的可信度.经对预测模型填充已知物性参数正演的重磁异常与实测重磁异常对比,证明两者在整体和细节上均有高度的相似性,间接说明对地质体圈定与分类结果的可靠性,进一步表明利用多源地球物理数据,采用支持向量机方法圈定地质体及对地质体进行岩性识别方面的合理性与有效性.多源地球物理数据机器学习的支持向量机方法在多宝山矿集区地质体圈定与分类所取得较好的应用效果,为多源综合地球物理的地质解释提供了可借鉴的成功经验,也提供了多源地球物理资料地质解释的一种新型的技术手段,开辟了应用人工智能方法进行多源地球物理资料地质解释的新途径.

     

THE REDUCTION OF LATERAL EFFECTS IN RESISTIVITY PROBING*

To be able to make use of all existing probe interpretation techniques, it is desirable that field resistivity observations be conducted in such a way that it is possible to construct an equivalent curve for the surface variation of potential about a point source. Further, the usual parallel layer interpretation will only be justified in as much as the observed potential curve is compatible with such a subsurface geometry. Thus, whilst a potential curve may be constructed from suitable finite potential differences obtained using a Wenner configuration of electrodes, it can be shown, using the tri-potential technique of measurements, that these potential differences may arise partly from lateral resistivity variations. In this paper, a ladder network technique is employed to display these lateral effects and an adjustment method proposed to reduce them. The adjusted potential differences obtained form a consecutive series suitable for summation to give the potential function. These values are subject to further minimum adjustments required for them to comply with slope and curvature conditions for a layered medium. After forming the potential curve by summation, a final numerical smoothing process is carried out. From this smoothed potential curve, corresponding Wenner and Schlumberger curves can readily be derived for interpretation. The method proposed thus attempts to extract from the observed data the maximum part which can be reconciled with a purely depth variation of resistivity. A method is also proposed for compounding the ‘errors of closure’ of the network to provide a Lateral Inhomogeneity Index which gives a measure of the departure of the observed data from the basic interpretation requirements. The method involves no great labour, but can readily be programmed for a computer if desired. Examples are given of the application of the method to field observations. In the interest of objectivity, the final smoothing has been confined to a single stage but in certain very extreme examples a further stage may prove desirable.     

Discrete cosine transform for parameter space reduction in Bayesian electrical resistivity tomography

Electrical resistivity tomography is a non-linear and ill-posed geophysical inverse problem that is usually solved through gradient-descent methods. This strategy is computationally fast and easy to implement but impedes accurate uncertainty appraisals. We present a probabilistic approach to two-dimensional electrical resistivity tomography in which a Markov chain Monte Carlo algorithm is used to numerically evaluate the posterior probability density function that fully quantifies the uncertainty affecting the recovered solution. The main drawback of Markov chain Monte Carlo approaches is related to the considerable number of sampled models needed to achieve accurate posterior assessments in high-dimensional parameter spaces. Therefore, to reduce the computational burden of the inversion process, we employ the differential evolution Markov chain, a hybrid method between non-linear optimization and Markov chain Monte Carlo sampling, which exploits multiple and interactive chains to speed up the probabilistic sampling. Moreover, the discrete cosine transform reparameterization is employed to reduce the dimensionality of the parameter space removing the high-frequency components of the resistivity model which are not sensitive to data. In this framework, the unknown parameters become the series of coefficients associated with the retained discrete cosine transform basis functions. First, synthetic data inversions are used to validate the proposed method and to demonstrate the benefits provided by the discrete cosine transform compression. To this end, we compare the outcomes of the implemented approach with those provided by a differential evolution Markov chain algorithm running in the full, un-reduced model space. Then, we apply the method to invert field data acquired along a river embankment. The results yielded by the implemented approach are also benchmarked against a standard local inversion algorithm. The proposed Bayesian inversion provides posterior mean models in agreement with the predictions achieved by the gradient-based inversion, but it also provides model uncertainties, which can be used for penetration depth and resolution limit identification.     

改进的均衡滤波器在位场数据边界识别中的应用

边界识别是进行位场数据解释时一项必不可少的任务.现有的边界识别滤波器存在识别边界发散和深部地质体边界模糊的缺点.本文提出增强型均衡滤波器,可有效地改善上述缺点.该滤波器是利用不同阶导数之间的组合来进行地质体边界的识别,并在运算中引入一种计算高阶垂直导数的稳定算法.通过理论模型试验证明增强型均衡滤波器能使浅部与深部地质体的边界同时清晰地显示,且相对于其它边界识别滤波器能更加准确和清晰地识别出地质体的边界.最后将增强型均衡滤波器应用于实测位场数据的解释,根据其识别结果可容易地划分出断裂的水平位置及不同地层之间的界线,并能发现更多的细节信息.     

Adaptive hybrid diffusion model using variational mode decomposition for edge preserving noise attenuation

Preserving the structural and stratigraphic discontinuities or edges is essential in seismic data processing and interpretation. According to several numerical experiments, it is obvious that random noise has a constant spectral density, whereas the structural features vary significantly within different frequency bands, which means that the ratio between the densities of noise and structural features varies significantly in different frequency bands. Therefore, we propose a method called adaptive hybrid diffusion to attenuate random noise, which utilizes a novel adaptive frequency-based parameter. First, the adaptive hybrid diffusion method decomposes the seismic sections into several band-limited portions using variational mode decomposition. These portions are called intrinsic mode functions, in which noise and structural energy have distinct differences. Subsequently, utilizing the adaptive frequency-based parameter, each intrinsic mode function is divided into several monotonous portions that represent the noise or structural area. Afterwards, the total variation and L2 minimization algorithms are utilized separately to suppress the noise in different band-limited monotonous areas. The algorithms are chosen dynamically, as the portion changes with the change in the adaptive parameter. Finally, these denoised portions are combined to obtain the denoised seismic section. Experimental results on synthetic and field seismic data showed that seismic noise is effectively suppressed by the adaptive hybrid diffusion method, with the edge details of seismic events well preserved.     

An inversion of geomagnetic deep sounding data using simulated annealing

A maiden attempt on the use of the global optimization technique of Simulated Annealing (S.A.) inversion to model the conductivity structure derived from the geomagnetic deep sounding data of NW India is reported here. The location of the proposed model is now in agreement with the theory, since the conductive bodies are centered exactly below the center of the response function which was not feasible by the earlier linearized inversion. The central body is located at a depth of 19 km from the surface, suggesting thickness of 15 km and resistivity of 14 Ω m. The resistivity contrast of this ensemble of conductive bodies with the background is varying by a factor of 100 to 385. Existence of mid-crustal conductor (the conductivity estimate is marginally different) is clearly indicated which was also not detected in the earlier study. A likely explanation could be due to the presence of graphitic carbon at lower crustal depths, however, the role of electrolytic fluid present in the interconnected pore-spaces of rocks may be another explanation.