基于混合网格有限元的直流电阻率法三维正演研究

直流电阻率法因效率高、成本低等特点广泛应用于有色金属、煤田等矿产资源勘探和地质调查行业。但在井–地、地–井电阻率法勘探过程中,钻孔因素(井液电阻率和钻孔孔径)对不同探测模式下视电阻率响应的影响尚未明确,是否影响视电阻率资料的解释是值得探讨的一个问题。因此,提出采用混合网格有限元法实现直流电阻率三维正演。给出异常电位法满足的边值问题及有限元变分问题,应用三棱柱和四面体混合网格实现对计算区域的快速离散,并建立2种网格的线性插值基函数和单元系数矩阵;采用SSOR–PCG迭代算法求解异常电位满足的大型线性方程组,得到各观测点的响应。在保证计算精度的前提下,应用混合网格有效地离散钻孔地电模型,探讨钻孔因素对井–地、地–井观测方式视电阻率数据的影响特征。对于井–地观测方式:钻孔附近视电阻率受钻孔因素影响最大,严重影响视电阻率资料的合理解释,但随着测点收发距的增加,视电阻率响应逐渐趋于围岩电阻率;而且随着发射源深度的增加,钻孔对地表视电阻率响应的影响也逐渐减小。对于地–井观测方式:钻孔因素对浅部数据影响较大,对深部数据影响小,相比于井液电阻率,视电阻率响应更易受钻孔孔径的影响。直流电阻率法混合网格有限元三维正演算法的提出,对实际井–地、地–井电阻率法勘探具有理论指导意义,可结合钻孔信息进行正演模拟分析,选择合适的收发距,有效压制钻孔因素对实测资料的影响。      

视电阻率对模型电阻率的偏导数矩阵计算方法

按Tripp et al.(1984)提出的理论，给出了一种视电阻率对模型电阻率的偏导数矩阵简便计算方法，它的核心是互换定理。只要得到所有供电和测量电极节点分别供单位电流时各有限元网格节点上的电位，通过线性组合就可得到视电阻率对模型电阻率的偏导数。     

The use of vertical electrical sounding resistivity method for the location of low salinity groundwater for irrigation in Chaj and Rachna Doabs

A geoelectrical resistivity survey using vertical electrical sounding (VES) was conducted at Chaj Doab (land between rivers Jhelum and Chenab, Pakistan) and Rachna Doab (land between rivers Chenab and Ravi, Pakistan), with the objective of investigating groundwater conditions. A total of 90 sites were selected with 43 sites in Chaj and 47 sites in Rachna Doabs. The resistivity meter (ABEM Terrameter SAS 4000, Sweden) was used to collect the VES data by employing a Schlumberger electrode configuration, with half current electrode spacings (AB/2) ranging from 2 to 180 m and the potential electrode (MN) from 1 to 40 m. The field data were interpreted using the Interpex IX1D computer software and the resistivity versus depth models for each location was estimated. The outputs of subsurface layers with resistivities and thickness presented in contour maps and 3-D views by using SURFER software were created. A total of 102 groundwater samples from nearby hydrowells at different depths were collected to develop a correlation between the aquifer resistivity of VES and the electrical conductivity (EC) of the groundwater and to confirm the resulted geophysical resistivity models. From the correlation developed, it was observed that the groundwater salinity in the aquifer may be considered low and so safe for irrigation if resistivity >45 Ω m, and marginally fit for irrigation having resistivity between 25 and 45 Ω m. The study area has resistivities from 3.9 to 2,222 Ω m at the top of the unsaturated layer, between 1.21 and 171 Ω m, in the shallow aquifers, and 0.14–152 Ω m in the deep aquifers of the study area. The results indicate that the quality of groundwater is better near the rivers and in the shallow layers compared to the deep layers.     

Hydrogeophysical investigation and estimation of groundwater potentials of the Lower Palaeozoic to Precambrian crystalline basement rocks in Keffi area, north-central Nigeria, using resistivity methods

The use of resistivity sounding and two-dimensional (2-D) resistivity imaging was investigated with the aim of delineating and estimating the groundwater potential in Keffi area. Rock types identified are mainly gneisses and granites. Twenty-five resistivity soundings employing the Schlumberger electrode array were conducted across the area. Resistivity sounding data obtained were interpreted using partial curve matching approach and 1-D inversion algorithm, RESIST version 1.0. The 2-D resistivity imaging was also carried out along two traverses using dipole–dipole array, and the data obtained were subjected to finite element method modeling using DIPRO inversion algorithm to produce a two-dimensional subsurface geological model. Interpretation of results showed three to four geoelectrical layers. Layer thickness values were generally less than 2 m for collapsed zone, and ranged from 5 to 30 m for weathered bedrock (saprolite). Two major aquifer units, namely weathered bedrock (saprolite) aquifer and fractured bedrock (saprock) aquifer, have been delineated with the latter usually occurring beneath the former in most areas. Aquifer potentials in the area were estimated using simple schemes that involved the use of three geoelectrical parameters, namely: depth to fresh bedrock, weathered bedrock (saprolite) resistivity and fractured bedrock (saprock) resistivity. The assessment delineated the area into prospective high, medium and low groundwater potential zones.     

典型岩溶富水构造的多极距联合剖面曲线正演模拟研究

基于点电源电场微分方程以及电场满足的边界条件出发,结合目前高密度电法找水时常用的点线布设方式,对岩溶区常见的隐伏断层破碎带和溶洞两类低阻富水构造的多极距联合剖面曲线进行了二维正演模拟。模拟结果表明:联合剖面曲线对地下隐伏低阻体反应灵敏,曲线存在良好的分异性。对溶洞低阻富水构造来说,溶洞富水构造埋深约为1/2~2/3倍极距时,正交点异常最明显,随着联合剖面极距继续增大,同步低趋势逐渐显现;地下低阻溶洞空间范围越大,联合剖面曲线分异性越好,正交点异常越明显。对断层破碎带低阻富水构造来说,随着联合剖面极距的增大,正交点向断裂破碎带倾斜方向略为移动,但并不明显,正交点位置主要受浅部低阻的影响,随着极距的逐渐增大,同步低趋势逐渐显现,正交点左侧在断层倾斜方向上越来越多的测点呈现同步低异常,但曲线较平缓,而正交点右侧的曲线较陡,视电阻率在断层顶板的正上方处出现极小值。当联合剖面曲线正交点异常较明显时,随极距的增大正交点处视电阻率值逐渐降低,当联合剖面曲线异常形态以同步低为主时,随极距的增大正交点处视电阻率值趋于稳定。联合剖面曲线左右两支形态对于水平对称模型是对称的,对于倾斜模型是非对称的,倾斜低阻构造的倾向与联合剖面曲线正交点附近较陡一侧的曲线倾向一致。模拟结果可应用到岩溶地区高密度电法的多极距联合剖面曲线资料解释中。      

Identification and Correction for MT Static Shift Using TEM Inversion Technique

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Deformation of an elastic layer coupling in different ways to a base due to a very long vertical strike-slip dislocation

The closed-form analytic expressions for the displacement and stresses at any point of an elastic layer lying over a base due to a very long vertical strike-slip dislocation are obtained. The interface between the layer and the base is assumed to be either ‘smooth-rigid’ or ‘rough-rigid’ or ‘welded’. The variations of displacement and stresses with the horizontal distance from the fault for different types of coupling of the layer with the base have been studied. It is found that the displacement for ‘welded interface’ lies between the displacements due to ‘smooth rigid’ and ‘rough-rigid’ interfaces for different positions of the observer and different values of the ratio of rigidities of the layer and half-space.     

0.2 m高分辨率双侧向测井仪器仿真设计

为满足油田薄层及薄互层开发的需求,采用数值模拟与电路仿真联合的交互式仪器仿真设计方法,开发了高分辨率数字聚焦双侧向测井仪器。通过仪器仿真,形成了纵向分辨率为0.2 m、深浅侧向探测深度分别为1.09 m、0.38 m的双侧向测井电极系,并得到了不同地层条件下测量信号的幅度以及视电阻率测量误差。现场应用效果表明,所设计的双侧向测井仪器的纵向分辨率与探测深度达到了理论指标,曲线重复性满足质量要求。仪器仿真方法有效地沟通了理论设计与仪器实现,不仅有助于0.2 m高分辨率双侧向测井仪器开发,同样也适用于电极型测井仪器设计。     

Electrical resistivity investigation of potential cavities underlying a proposed ash disposal area

Measurements of electrical resistivity anomalies using a Wenner electrode array in a profiling mode were conducted over a 105-acre area near Crystal River, Florida Analyzed results of collected data were used to determine the likelihood of subsurface solution cavities beneath a proposed ash disposal area “Sounding” measurements with electrode spacing values extending up to 100 feet and Lee electrode measurements were used to identify and locate specific anomaly maxima identified anomalies on the order of 200 chms-feet contrasted with expected values of 300 to 400 ohms-feet and were attributed to lower resistivities inherent in water-filled solution cavities below a shallow water table Prominent cavity complexes at 5 to 15 feet depth were predicted in areas of low resistivity anomalies in the otherwise geoelectrically uniform, Eocene Ocala limestone Shallow test borings confirmed the presence of a significant concentration of shallow cavities in the predicted areas This study demonstrated the feasibility of electrical resistivity measurements as a reconnaissance tool to economically determine subsurface cavities and to aid in developmental and environmental planning     

井地-高密度电法联合数值模拟研究

从点源场的边值问题出发,利用有限元推导了井地电法和高密度电法2.5维的详细解法,并编制了相应的程序。利用均匀半空间的地电模型进行了正演计算,并与地下真实电阻率进行了对比分析,验证了算法的正确性。在此基础上对均匀介质中存在对称高阻体和边缘高阻体的模型,进行正演模拟,分别得到其井地电法的视电阻率断面图和高密度电法的视电阻率断面图。结果表明,结合两种方法可以对地下存在的高阻异常体进行有效精确地探测。     

含水采空区全空间瞬变电磁响应分析

针对含水采空区全空间瞬变电磁响应信号识别问题,采用有限元数值模拟及现场实测方法,基于电动势—视电阻率及对应时深转换关系,获取了全扇面视电阻率随深度变化的空间分布规律,提取了低阻异常区测点感应电动势衰减曲线,得出了测点随探测角度变化的电动势量化变化规律。基于上述研究,开展了井下钻探验证及钻孔窥视,并对现场钻孔出水水样进行了水质分析。结果表明:含水采空区的瞬变电磁响应横向角度对应一致性高于纵向深度;其感应电动势升幅与感应电动势差值变化趋势相反,呈现出在二次场观测初期急剧增大而后趋缓的特征,最大升幅可达10倍以上。钻探工程及化探分析进一步验证了物探成果。     

任意三维地电模型视电阻率异常的边界元法数值解

边界元法(BEM)是一种新的数值方法。由于该法可以降低所研究场问题的维数,因而边界元法较之域型法(FEM和FDM)具有应用简便、数据量少、计算快、精度高等优点。从而,用该法解决了域型法难以实现的三维地电模型视电阻率异常的计算问题。本文论述了用边界无法求解点源场地表水平和起伏下三维地电体位场问题的方法原理和数值处理技术,并给出了若干算例:导电球状矿体上视电阻率数值解与解析解结果;导电球状矿体上不同测线上视电阻率平剖曲线;三维山脊地形下导电椭球状矿体上视电阻率联剖曲线及其地形改正结果等。由本文内视电阻率的边界元法数值解与解析解结果对比的一致性和三维地形校正的显著效果,表明了边界元法是求解任意三维地电模型上位场问题的有效方法。由于用该法实现了对任意三线地质体上空间位场计算,必将推动三维电法勘探工作的开展与深入研究,无疑会对提高电法勘探的地质效果发挥重要作用。     

Some Results on the Spatial Breakdown Point of Robust Point Estimates of the Variogram

The effect of outliers on estimates of the variogram depends on how they are distributed in space. The ‘spatial breakdown point’ is the largest proportion of observations which can be drawn from some arbitrary contaminating process without destroying a robust variogram estimator, when they are arranged in the most damaging spatial pattern. A numerical method is presented to find the spatial breakdown point for any sample array in two dimensions or more. It is shown by means of some examples that such a numerical approach is needed to determine the spatial breakdown point for two or more dimensions, even on a regular square sample grid, since previous conjectures about the spatial breakdown point in two dimensions do not hold. The ‘average spatial breakdown point’ has been used as a basis for practical guidelines on the intensity of contaminating processes that can be tolerated by robust variogram estimators. It is the largest proportion of contaminating observations in a data set such that the breakdown point of the variance estimator used to obtain point estimates of the variogram is not exceeded by the expected proportion of contaminated pairs of observations over any lag. In this paper the behaviour of the average spatial breakdown point is investigated for cases where the contaminating process is spatially dependent. It is shown that in two dimensions the average spatial breakdown point is 0.25. Finally, the ‘empirical spatial breakdown point’, a tool for the exploratory analysis of spatial data thought to contain outliers, is introduced and demonstrated using data on metal content in the soils of Sheffield, England. The empirical spatial breakdown point of a particular data set can be used to indicate whether the distribution of possible contaminants is likely to undermine a robust variogram estimator.     

CSAMT电场y方向视电阻率的定义及研究

在准静态近似条件下,利用水平电偶源在均匀半空间表面激发电磁场的计算公式,讨论了可控源音频大地电磁法（CSAMT）水平电场y分量E_y的观测范围、特点和由其定义视电阻率的应用优势;E_y与常规标量CSAMT测量的E_x、H_y幅值范围不同,采集并利用E_y数据可以扩大CSAMT野外观测扇区,减少采集成本。依据电法及电磁法勘探中视电阻率定义的基本原则,提出了E_y视电阻率的定义,说明了其具备频率测深的意义;通过几种典型层状模型（均匀半空间,两层D、G,三层H、K以及四层KH、HK型）的数值计算,对比了E_y视电阻率和E_x、H_y、Z_xy、Re(Z_xy)等对应的波区视电阻率及E_x、Z_xy等对应的全区视电阻率对地电断面电性特征的反映效果。结果表明：E_y视电阻率的求取仅需测点的坐标和一个方向的电场值,计算方便、不必迭代,并且在曲线低频端收敛于一稳定值,可以明显改善非波区的畸变效应。     

Delineation of saltwater intrusion into the freshwater aquifer of Lekki Peninsula,Lagos, Nigeria

Recently, the deterioration of water quality in the coastal zones of Lekki Peninsula area of Lagos due to saltwater infiltration into the freshwater aquifer has become a major concern. With the aim of providing valuable information on the hydrogeologic system of the aquifers, the subsurface lithology and delineating the groundwater salinity, vertical electrical resistivity (VES) sounding survey was carried out utilizing surface Schlumberger electrode arrays, and electrode spacing varying between 1 and 150 m. The DC resistivity surveys revealed significant variations in subsurface resistivity. Also, the VES resistivity curves showed a dominant trend of decreasing resistivity with depth (thus increasing salinity). In general, the presence of four distinct resistivity zones were delineated viz.: the unconsolidated dry sand (A) having resistivity values ranging between 125 and 1,028 Ωm represent the first layer; the fresh water-saturated soil (zone B) having resistivity values which correspond to 32–256 Ωm is the second layer; the third layer (zone C) is interpreted as the mixing (transition) zone of fresh with brackish groundwater. The resistivity of this layer ranges from 4 to 32 Ωm; while layer four (zone D) is characterized with resistivities values generally below 4 Ωm reflecting an aquifer possibly containing brine. The rock matrix, salinity and water saturation are the major factors controlling the resistivity of the formation. Moreover, this investigation shows that saline water intrusion into the aquifers can be accurately mapped using surface DC resistivity method.     

线源直流电法有限元二维正演模拟

直流电法勘探中,三维点源正演计算复杂、计算量大,虽进行傅里叶变换可转化为二维点源,但相比二维线源计算还是复杂。基于Matlab编程,采用第一类边界条件,给出了线源直流电法二维有限元数值解法,通过与均匀半空间理论值比较,验证了计算结果的正确性;再建立高阻、低阻地电模型,并采用单边供电和双边供电分别对其响应进行比较和分析,得到了相应的视电阻率断面图。结果表明单边供电可以准确反映异常体在纵向上的位置,而双边供电更能准确反应异常体的横向位置和形态。论文研究为生产实际提供了理论依据。      

High-potassium intrusives from southeastern Papua

This paper presents petrographic, major element, and trace element data from high-potassium ‘shoshonitic’ rocks of Miocene age which intrude Eocene submarine basalts in southeastern Papua. The intrusives fall into two distinct but overlapping groups, a ‘near-saturated’ group ranging from gabbro to syenite with regular petrographic and chemical variations, which is either slightly nepheline normative or quartz normative, and a nepheline normative ‘undersaturated’ group which shows wide variations in texture, modal mineralogy, and chemistry. Biotite-bearing pyroxenites are associated with the intrusives but their genetic relationship to the intrusives is unknown. The intrusion of shoshonitic rocks at the beginning of a period of major tectonic activity in southeastern Papua shows that high-potassium magmas can be generated in areas of active tectonism and may form part of the island arc ‘magmatic’ association.     

点源二维有限元法在三电位电极系正演模拟中的应用

利用点源二维有限元法,针对二维地电模型,进行了三电位电极系视电阻率参数及比值参数的计算,对几种二维地电断面三电位电极系的视电阻率及比值参数的异常规律进行了探讨。这些研究结果,为实际勘探中复杂地电断面的异常解释打下了一定的理论基础,在利用比值参数进一步分辨复杂断面的电性异常方面作了有益的尝试。     

直流激电测深二维反演的若干问题研究

目前,激电数据的二维反演主要针对高密度激电数据,而对于常规的激电测深则很少涉及.据此,针对常规激电测深二维反演所涉及到的一些技术难点进行探讨.在正演过程中,根据实测数据实现有限元网格自动剖分,并采用双网格系统,用相邻节点电导率双线性连续进行有限元模拟,并对模拟的误差进行校正.在反演过程中,利用互换原理和Broyden的方法计算偏导数矩阵;采用与奇异值分解算法精度相当的共轭梯度算法求解偏导数矩阵方程.最后通过对模拟数据和实测数据进行反演试算,验证本计算方法是可行的.