基于不等式约束的三维电阻率探测混合反演方法

三维电阻率探测的线性反演和非线性反演中均存在着多解性的固有难题.电阻率线性反演方法的效率较高,但反演结果对初始模型的依赖性较强,易陷入局部极小;而非线性反演方法不依赖初始模型,但搜索效率极低,尚未见到关于三维电阻率非线性反演的文献.针对上述问题,融合线性与非线性反演方法的互补优势,提出了最小二乘法（线性方法）与改进遗传算法（非线性方法）相结合的混合反演方法的概念和思想.首先,提出了将介质电阻率变化范围作为不等式约束引入反演方程的思路,以实现压制多解性、提高可靠性的目标.提出了宽松不等式约束和基于钻孔推断的局部严格不等式约束的获取及定义方法.在此基础上,分别提出了基于不等式约束的最小二乘线性反演方法和遗传算法非线性反演方法.其次,对于遗传算法在变异搜索方向控制、初始群体产生等方面进行了改进,优化了其搜索方向和初始群体多样性.然后,提出了混合反演方法及其实现方案,利用改进遗传算法进行第一阶段反演,发挥其对初始模型的依赖程度低的优势,搜索到最优解附近的空间,输出当前最优个体;利用最小二乘法进行第二阶段反演,将遗传算法得到的当前最优个体作为初始模型,在最优解附近空间执行高效率的局部线性搜索,最终实现地电结构的三维成像.最后,开展了合成数据与实际工程算例验证,与传统最小二乘方法进行了对比,发现混合反演方法在压制多解性、摆脱初始模型依赖和提高反演效果方面有较好效果.

     

An algorithm for fast 3D inversion of surface electrical resistivity tomography data: application on imaging buried antiquities

In this work a new algorithm for the fast and efficient 3D inversion of conventional 2D surface electrical resistivity tomography lines is presented. The proposed approach lies on the assumption that for every surface measurement there is a large number of 3D parameters with very small absolute Jacobian matrix values, which can be excluded in advance from the Jacobian matrix calculation, as they do not contribute significant information in the inversion procedure. A sensitivity analysis for both homogeneous and inhomogeneous earth models showed that each measurement has a specific region of influence, which can be limited to parameters in a critical rectangular prism volume. Application of the proposed algorithm accelerated almost three times the Jacobian (sensitivity) matrix calculation for the data sets tested in this work. Moreover, application of the least squares regression iterative inversion technique, resulted in a new 3D resistivity inversion algorithm more than 2.7 times faster and with computer memory requirements less than half compared to the original algorithm. The efficiency and accuracy of the algorithm was verified using synthetic models representing typical archaeological structures, as well as field data collected from two archaeological sites in Greece, employing different electrode configurations. The applicability of the presented approach is demonstrated for archaeological investigations and the basic idea of the proposed algorithm can be easily extended for the inversion of other geophysical data.     

Advances in interpretation of subsurface processes with time‐lapse electrical imaging

Electrical geophysical methods, including electrical resistivity, time‐domain induced polarization, and complex resistivity, have become commonly used to image the near subsurface. Here, we outline their utility for time‐lapse imaging of hydrological, geochemical, and biogeochemical processes, focusing on new instrumentation, processing, and analysis techniques specific to monitoring. We review data collection procedures, parameters measured, and petrophysical relationships and then outline the state of the science with respect to inversion methodologies, including coupled inversion. We conclude by highlighting recent research focused on innovative applications of time‐lapse imaging in hydrology, biology, ecology, and geochemistry, among other areas of interest. Copyright © 2014 John Wiley & Sons, Ltd.     

Electrical resistivity imaging and hydrochemical analysis for groundwater investigation in Kuala Langat,Malaysia

ABSTRACT

Integrated two-dimensional electrical resistivity imaging (ERI) and hydrochemical surveys were used to investigate the groundwater alluvial aquifer in Kuala Langat, Malaysia. The study in the Langat basin considered the thickness of the aquifer, the depth of the bedrock, the regions influenced by seawater intrusion, and the monitoring of water levels. The resistivity imaging results show that the upper layer consists of clay, while the second layer is an aquifer whose thickness varies mostly in the range of 10–30 m, and in some cases extends to 40 m. The bedrock depth varies from 30 to 65 m. The chemical analyses were carried out on groundwater samples from nine boreholes collected between 2008 and 2012. The analyses indicate that the total dissolved solids (TDS) exceed 1000 mg L^-1 near the coastal area and are often less than 500 mg L^-1 further inland. The ERI and hydrochemical analyses reveal that groundwater in the study area, especially towards the coast, is a mixture of brackish and fresh waters.

EDITOR D. Koutsoyiannis; ASSOCIATE EDITOR M.D. Fidelibus     

三维高密度电法在底板水探测中应用

针对目前采用二维高密度探测矿井底板水, 只能获得巷道底板的富水性特征, 而不能获得工作面内部的底板富水性情况的现状,研制出了通过在工作面周边铺设电缆,采集工作面底板三维数据体的设备及数据处理软件,并结合三维成像技术,实现了工作面底板富水性采前三维探测、三维数据体垂直及水平切割技术.结合新汶煤田协庄煤矿71504W工作面应用实例,介绍了三维高密度电法技术在底板水探测中的应用, 实现了对工作面底板富水性采前三维数据体的采集、采场底板含水性三维电阻率成像, 可方便地进行水平及垂直切片, 将工作面底板富水状态直观地表现出来,说明了该技术的实用性和有效性.     

电阻率层析成像非线性反演

本文通过概率成像法、α中心法、遗传算法的有机结合, 实现了2-D电阻率层析成像非线性反演.首先,根据概率成像结果指示出的2-D地质异常体的相对电性和大致分布范围,合理地确定出α中心的位置与强度系数的变化范围.其次,以α中心法作为2-D地电结构的正演手段,采用遗传算法反演出各α中心的强度系数.在此基础上, 应用α中心法重新构建出地下介质电阻率的分布.通过对均匀半空间中赋存2-D地质异常体模型的反演试验, 获得了令人满意的结果.     

Detection of sinkholes using 2D electrical resistivity imaging

Sinkholes in dolomitic areas are notoriously difficult geophysical targets, and selecting an appropriate geophysical solution is not straightforward. Electrical resistivity imaging, or tomography (RESTOM) is well suited to mapping sinkholes because of the ability of the technique for detecting resistive features and discriminating subtle resistivity variations. RESTOM surveys were conducted at two sinkhole sites near Pretoria, South Africa. The survey areas are located in the dolomites of the Lyttelton Formation, which forms part of the Malamani Subgroup and Chuniespoort Group of the Transvaal Supergroup. The survey results suggest that RESTOM is an ideal geophysical tool to aid in the detection and monitoring of sinkholes and other subsurface cavities.     

Time‐lapse electrical resistivity imaging of solute transport in a karst conduit

The use of electrical resistivity surveys to locate karst conduits has shown mixed success. However, time‐lapse electrical resistivity imaging combined with salt injection improves conduit detection and can yield valuable insight into solute transport behaviour. We present a proof of concept above a known karst conduit in the Kentucky Horse Park (Lexington, Kentucky). A salt tracer solution was injected into a karst window over a 45‐min interval, and repeat resistivity surveys were collected every 20 min along a 125‐m transect near a monitoring well approximately 750 m downgradient from the injection site. In situ fluid conductivity measurements in the well peaked at approximately 25% of the initial value about 3 h after salt injection. Time‐lapse electrical resistivity inversions show two broad zones at the approximate conduit depth where resistivity decreased and then recovered in general agreement with in situ measurements. Combined salt injection and electrical resistivity imaging are a promising tool for locating karst conduits. The method is also useful for gaining insight into conduit geometry and could be expanded to include multiple electrical resistivity transects. Copyright © 2015 John Wiley & Sons, Ltd.     

Resolution of 2D Wenner resistivity imaging as assessed by numerical modelling

Modelling of 2D resistivity imaging was done in order to understand the principle resolution of the technique in different geological situations, and for assessing the behaviour of the interpretation methods under controlled circumstances. The Wenner array was used throughout. The results show that the 1D approximation only provides reasonable results in environments with very gradual lateral resistivity changes, otherwise the result may be strongly misleading. Inversion using the 2D quasi-Newton technique results in adequate resolution of the structures in moderately complex environments, but the Gauss–Newton method holds a significant advantage in some complicated cases. The data density can also be of crucial importance for the resolution capability, notably of narrow structures.     

电阻率成像及浅层地震勘探在控盆构造探测中的应用——以万全断裂为例

万全断裂是洋河盆地北缘断裂带组成断裂之一,控制沿线构造活动及地貌发育。断裂走向NE,倾向SE,在沟口处隐伏于第四纪覆盖层,采用电阻率成像和浅层地震联合勘探方法,获得该断裂隐伏段落综合物探异常,结合地质地貌调查,判定隐伏段落展布的具体位置、产状、活动特征及地下结构特征等。研究结果表明,万全断裂隐伏段落走向NE,倾向SE,倾角约75°,上断点埋深约20 m,20—240 m深度可见断裂破碎带（宽约10—20 m）物探异常特征及断裂两侧地层结构差异。该联合探测模式可有效探测复杂地质构造条件下的隐伏活动断裂,具有较强实用性,值得推广。     

青藏高原岩石圈三维电性结构

本文报道通过综合大地电磁调查数据研究青藏高原岩石圈三维电阻率模型的初步成果.大地电磁法调查区域已经覆盖了高原大部分面积,为全区三维电阻率成像研究打下了可靠的基础.对多个测区大地电磁数据进行精细的同化处理和反演成像,取得了青藏高原可靠的岩石圈三维电阻率结构图像.成像的区域为28°N—35°N,80°E—104°E.三维反演计算时采用的网格尺寸为20 km×20 km,垂直方向不等间距剖分为26层.结果表明,青藏高原现今岩石圈电阻率扰动主要反映印度克拉通对亚欧大陆板块俯冲引起的热流体运动和大陆碰撞和拆离产生的构造.在岩石圈地幔,察隅地块、喜马拉雅地块和拉萨地块东部联成统一的高电阻率地块,它们反映了向北东俯冲的印度克拉通.雅鲁藏布江、班公—怒江和金沙江缝合带都有明显的低电阻率异常,表明岩石圈深处有热流体活动.雅鲁藏布江、班公—怒江和金沙江缝合带都有明显的低电阻率异常,也表明它们的岩石圈还有流体活动.青藏高原东部的低阻区沿100°E向地幔下方扩大,反映了金沙江断裂带有切穿岩石圈的趋势.地幔电阻率平面扰动的模式显示,青藏高原东西部的地体碰撞拼合形式和方向是不同的.在青藏高原西部,羌塘、拉萨和喜马拉雅等地体从北到南碰撞拼合.在青藏高原东部,羌塘—拉萨、察隅、印支、雅安和扬子等地体多方向拆离拼合,在地壳造成不正交的拆离带和压扭构造系.从高阻-低阻区的分布看,东部的地体拼合有地幔的根源,今后还会进一步发展.察隅地块岩石圈对青藏高原东部的楔入,使其北部和东部地块的岩石圈发生拆离撕裂,也造成热流体上涌的低电阻率异常.

     

基于不等式约束的最小二乘法三维电阻率反演及其算法优化

基于光滑约束的最小二乘法是三维电阻率反演的主要方法,但该方法在某些情况下存在着多解性较强的问题,且普遍耗时较长,严重制约了三维反演方法的推广与发展.为改善上述问题,将表征模型参数变化范围的不等式约束作为先验信息引入最小二乘线性反演方法中,有效地改善了反演结果的精度,降低了反演的多解性问题.为了解决耗时较长的问题,基于预条件共轭梯度(PCG)算法和Cholesky分解法的特点提出了一套优化三维电阻率反演计算效率的计算方案.在该方案中,Cholesky分解法被用来求解敏感度矩阵计算中的多个点源场的正演问题,Cholesky分解法只需对总体系数矩阵进行一次分解,然后对不同的右端向量进行回代即可.将预条件共轭梯度法引入到三维电阻率反演方程的求解中,将雅可比迭代中的对角阵作为预处理矩阵,其具有求逆方便、无需内存空间的特点,有效地加快了收敛速度.对合成数据以及实测数据的反演算例表明,借助不等式约束和反演效率优化方案,最小二乘反演方法可得到较为精确的反演结果,有效地提高了反演计算效率,具有良好的推广前景.     

不同土壤中含油污水污染区的电性变化研究及污染区探测

本文利用室内电阻率测试的方法研究了研究了饱和土和不饱和土两类土中含油污水的侵入量对其导电性的影响.测试结果表明,对于不饱和土,含油污水的侵入会改变土的饱和度从而引起其电阻率的降低,侵入量越大其电阻率越低;而饱和土的电阻率随含油污水侵入量的增大而增大直到趋于稳定.基于此,通过室内模拟土层污染和野外实地观测污染土层的方式研究了含油污水污染不同饱和度土层的电剖面异常特征,在不饱和土层中污染区域表现为相对低阻异常区而在饱和土层中表现为相对高阻异常区.通过对比不同时期的监测结果显示异常区的范围随污染区的变化而变化,并可反映出污染区的实际分布.文章分析了利用电阻率法进行含油污水污染地下介质调查的几个模糊点,对提高探测效果具有指导意义.     

Delineating coastal groundwater discharge processes in a wetland area by means of electrical resistivity imaging, 224Ra and 222Rn

Coastal groundwater discharge (CGD) plays an important role in coastal hydrogeological systems as they are a water resource that needs to be managed, particularly in wetland areas. Despite its importance, identifying and monitoring CGD often presents physical and logistical constraints, restraining the application of more traditional submarine groundwater discharge surveying techniques. Here we investigate the capability of electrical resistivity imaging (ERI) in the Peníscola wetland (Mediterranean coast, Spain). ERI surveying made it possible to identify and delineate an ascending regional groundwater flow of thermal and Ra‐enriched groundwater converging with local flows and seawater intrusion. The continuous inputs of Ra‐rich groundwater have induced high activities of Ra isotopes and ²²²Rn into the marsh area, becoming among the highest previously reported in wetlands and coastal lagoons. Geoelectrical imaging enabled inferring focused upward discharging areas, leaking from the aquifer roof through a confining unit and culminating as spring pools nourishing the wetland system. Forward modelling over idealized subsurface configurations, borehole datasets, potentiometric records from standpipe piezometers, petrophysical analysis, and four natural and independent tracers (²²⁴Ra, ²²²Rn, temperature and salinity) permitted assessing the geoelectrical model and a derived hydrogeological pattern. The research highlights the potential of ERI to improve hydrogeological characterization of subsurface processes in complex contexts, with different converging flows. Additionally, a hydrogeological conceptual model for a groundwater‐fed coastal wetland was proposed, based on the integration of surveying datasets. Copyright © 2013 John Wiley & Sons, Ltd.     

垃圾填埋场渗滤液污染地下含水层及修复过程的三维动态监测实验

为实现垃圾填埋场渗滤液在地下含水层中动态扩散及污染层修复过程的实时监测,利用自行设计的三维电学观测系统开展了室内相关监测实验.实验表明渗滤液在含水层中的扩散过程会引起不同时期实测电剖面上低阻异常区的动态变化.对比分析这种变化特征可确定渗滤液扩散区的污染程度、扩散速度及扩散方向.在注水修复过程中,扩散区污染物含量的降低会引起对应区域实测视电阻率值的升高和异常区范围的变化.实验结果对于实现垃圾渗滤液污染地下含水层现状调查及动态监测具有重要意义.     

土壤—地下水系统非水相液体污染区的电性特征及电阻率法探测

从土壤-地下水系统被非水相液体污染后引起的导电性变化、污染区地电模型演化、电阻率异常认识及量化解释等方面分析了国内外利用电阻率法探测这一问题的研究现状.已有研究表明,污染区电性随污染程度、污染时间变化显示一定的动态性;污染区地电模型建立是个复杂过程,不仅反映污染物的扩散过程,还要考虑地质、地下水、土层含水量等影响因素,并随外部条件和时间变化显示一定的动态性;这也决定了实测电剖面异常特征的复杂性.由于基于电测数据的真电阻率获取及污染土电性基本模型建立都尚未解决,利用电性探测结果进行污染量化分析的研究还没有形成统一的认识和结论,这也是未来很长时间内需要攻克的难题.     

坑（井）-地电阻率成像技术数据处理方法研究

开发坑（井）一地电阻率成像技术数据处理软件包,对分布式地面一坑道电磁信号接收仪记录的时间序列进行分析处理,最终得到相应的视电阻率和相位参数。实际资料处理结果表明,在远区情况下,需考虑信噪比水平,选择合适的计算方法。当信噪比很低或较高时,可选择根据卡尼亚电阻率定义式直接比值的方法,该方法计算简便、效率高;当信噪比一般时,采用最小二乘或Robust等估算方法,能在一定程度上改善数据处理质量。     

Subsurface architecture of the Boulder Creek Critical Zone Observatory from electrical resistivity tomography

The architecture of the critical zone includes the distribution, thickness, and contacts of various types of slope deposits and weathering products such as saprolite and weathered bedrock resting on solid bedrock. A quantitative analysis of architecture is necessary for many model‐driven approaches used by pedologic, geomorphic, hydrologic or biologic studies. We have used electrical resistivity tomography, a well‐established geophysical technique causing minimum surficial disturbance, to portray the subsurface electrical resistivity differences at three study sites (Green Lakes Valley; Gordon Gulch; Betasso) at the Boulder Creek Critical Zone Observatory (BcCZO). Possible limitations of the technique are discussed. Interpretation of the specific resistivity values using natural outcrops, pits, roadcuts and drilling data as ground truth information allows us to image the critical zone architecture of each site. Green Lakes Valley (3700 MASL), a glacially eroded alpine basin, shows a rather simple, split configuration with coarse blockfields and sediments, partly containing permafrost above bedrock. The critical zone in Gordon Gulch (2650 MASL), a montane basin with rolling hills, and Betasso (1925 MASL), a lower montane basin with v‐shaped valleys, is more variable due to a complex Quaternary geomorphic history. Boundaries between overlying stratified slope deposits and saprolite were identified at mean depths of 3.0 ± 2.2 m and 4.1 ± 3.6 m in the respective sites. The boundary between saprolite and weathered bedrock is deeper in Betasso at 5.8 ± 3.7 m, compared with 4.3 ± 3.0 m in Gordon Gulch. In general, the data are consistent with results from seismic studies, but electrical resistivity tomography documents a 0.5–1.5 m shallower critical zone above the weathered bedrock on average. Additionally, we document high lateral variability, which results from the weathering and sedimentation history and seems to be a consistent aspect of critical zone architecture within the BcCZO. Copyright © 2013 John Wiley & Sons, Ltd.     

Tracing solute infiltration using a combined method of dye tracer test and electrical resistivity tomography in an undisturbed forest soil profile

An accurate prediction of solute infiltration in a soil profile is important in the area of environmental science, groundwater and civil engineering. We examined the infiltration pattern and monitored the infiltration process using a combined method of dye tracer test and electrical resistivity tomography (ERT) in an undisturbed field soil (1 m × 1 m). A homogeneous matrix flow was observed in the surface soil (A horizon), but a preferential flow along macropores and residual rock structure was the dominant infiltration pattern in the subsurface soil. Saturated interflow along the slopping boundaries of A and C1 horizons and of an upper sandy layer and a lower thin clay layer in the C horizon was also observed. The result of ERT showed that matrix flow started first in A horizon and then the infiltration was followed by the preferential flows along the sloping interfaces and macropores. The ERT did not show as much detail as the dye‐stained image for the preferential flow. However, the area with the higher staining density where preferential flow was dominant showed a relatively lower electrical resistivity. The result of this study indicates that ERT can be applied for the monitoring of solute transportation in the vadose zone. Copyright © 2010 John Wiley & Sons, Ltd.     

地-空瞬变电磁法电阻率成像研究与应用

地-空瞬变电磁法（Semi-airborne transient electromagnetic,SATEM）凭借适应能力强、探测深度大、实时性强等特点,适用于湖泊、沼泽、山区等地形复杂地区观测.SATEM接收数据量大、精度要求高,传统成像方法基于地面视电阻率计算未考虑飞行高度,开展SATEM的高精度快速成像研究对实际运用有重要作用.针对SATEM中电性源发射装置感应电流分布,接收装置设置于空中以及两者不在相同平面的特点,本文考虑横向、纵向感应电流差异,飞行高度对视电阻率影响等因素,提出电性源SATEM电阻率成像方法.首先,基于电性源瞬变电磁场感应电流分布特征及各分量空间分布、扩散特性分析,推导出基于均匀半空间磁场与感应电压解析解,然后定义了电性源地-空瞬变电磁法早期、晚期、全期视电阻率;最后根据对感应电流分布分析定义了横向分量和纵向分量的成像深度,并研究了成像深度受飞行高度、发射磁矩、偏移距、偏移角度的影响;对煤炭采空区的实测结果表明,利用本文提出的电阻率成像方法可以更加精确定位目标体位置.