Illuminating and optimising a three‐dimensional model of an oil shale seam and its volume distribution using the transient electromagnetic induction method,central part of Jordan

The oil shale exploration program in Jordan is undertaking great activity in the domain of applied geophysical methods to evaluate bitumen‐bearing rock. In the study area, the bituminous marl or oil shale exhibits a rock type dominated by lithofacies layers composed of chalky limestone, marls, clayey marls, and phosphatic marls. The study aims to present enhancements for oil shale seam detection using progressive interpretation from a one‐dimensional inversion to a three‐dimensional modelling and inversion of ground‐based transient electromagnetic data at an area of stressed geological layers. The geophysical survey combined 58 transient electromagnetic sites to produce geoelectrical structures at different depth slices, and cross sections were used to characterise the horizon of the most likely sites for mining oil shale. The results show valuable information on the thickness of the oil shale seam at 3.7 Ωm, which is correlated to the geoelectrical layer between 2‐ and 4 ms transient time delays, and at depths ranging between 85 and 105 m. The 300 m penetrated depth of the transient electromagnetic soundings allows the resolution of the main geological units at narrow resistivity contrast and the distinction of the main geological structures that constrain the detection of the oil shale seam. This geoelectrical layer at different depth slices illustrates a localised oil shale setting and can be spatially correlated with an area bounded by fold and fault systems. Also, three‐dimensional modelling and inversion for synthetic and experimental data are introduced at the faulted area. The results show the limitations of oil shale imaging at a depth exceeding 130 m, which depends on the near‐surface resistivity layer, the low resistivity contrast of the main lithological units, and the degree of geological detail achieved at a suitable model's misfit value.     

松辽盆地北部深层综合物探方法先导性研究

首先对岩石的速度、密度、磁化率、电阻率等物性资料进行统计分析 ,寻找它们之间的内在联系 ,在此基础上综合各种有用信息建立统一的物理 -地质模型。在统一的物理 -地质模型之上 ,进行重、磁、电、震单一方法的反演 ,分析各种物探方法反演结果的相容性与相背性 ,重新修改模型并进行重、磁、电、震的联合反演 ,最终确定深部地层的地质属性     

基于地质体空间位置优化约束的航空重力梯度数据三维物性反演

重力数据的物性反演面临着严重的多解性问题,降低多解性的有效手段是加入约束条件.而边界识别、深度估计及成像方法可获取地质体的水平位置、深度范围等几何参数信息,本文将基于数据本身挖掘的地质体几何参数信息约束到物性反演中,以降低反演的多解性.通过引入基于深度信息的深度加权函数及基于水平位置的水平梯度加权函数建立优化约束条件,有效地提高了反演结果的横向及纵向分辨率.重力梯度数据包含更多的地质体空间特征信息,将优化约束反演方法应用到全张量数据的反演中,模型试验表明本文方法反演结果与理论模型更加吻合.最后对美国路易斯安那州文顿盐丘实测航空重力梯度数据的应用表明,本文方法在其他地球物理、地质资料不足的情况下获得更可靠的反演结果.     

大地电磁、重力、磁法和地震初至波走时的交叉梯度二维联合反演研究

为了准确的探测和描绘地下复杂的地质结构,同时克服地球物理单一方法反演的多解性和单一参数反演模型的不一致性等问题,近年来基于交叉梯度联合反演的综合地球物理解释已经得到了广泛的关注和应用.本文首先研究了两种地球物理方法的交叉梯度联合反演算法,在此基础上,推导并实现了多种地球物理方法(大地电磁,重力,磁法,地震初至波走时)的多交叉梯度约束的二维联合反演算法;其次,我们设计了结构不一致模型和复杂模型,针对多物性联合反演算法的准确性和有效性进行了模拟试算,并对复杂模型的单独反演结果和联合反演结果进行了交叉梯度值和物性交会图的对比;最后,本文将成熟的卫星资料多光谱综合分析技术应用到联合反演中,将多物性参数反演模型结果图通过RGB(红-绿-蓝)模式进行合成,得到融合的RGB合成图.结果表明:通过对结构不一致模型和复杂模型的联合反演结果和单独反演结果的对比分析,可以得出联合反演得到的结果更接近真实模型,并从得到的交叉梯度值进一步证明了联合反演模型相似度高,也从物性交会图中得到联合反演的物性相关性更好的结论,反向证明了算法的正确性.最终从得到的RGB合成图像,我们可以更直观的分析反演结果,更有利于准确划分地下模型结构.     

部分区域约束下的交叉梯度多重地球物理数据联合反演

交叉梯度联合反演方法通过对多种地球物理模型实现结构耦合,在岩石物性关系不确定的情况下,既能提高反演结果的可靠性,又能减少反演的多解性,还能减少不同方法解释结果之间的矛盾.当不同的模型观测数据覆盖范围不一致时,交叉梯度联合反演通常需要取出重叠区域数据进行联合反演,并且建模时还要扩展一些模型范围.本文首先提出并实现了部分区域约束下的交叉梯度多重地球物理数据联合反演算法;接着进行了算法的模型试算;最后,我们将该反演算法用于本溪—集安深部地质调查重磁电综合地质地球物理解释中.结果表明:该算法不但能在重叠区域内很好地恢复结构相似的模型,而且在非重叠区域与重叠区域的边界处仍然可以得到平滑变化的模型;在本溪—集安10号剖面所获得的结构上相似的电阻率、密度及磁化率模型较好地反映了该区的深部地质结构,对于确定深部地质体的性质提供了有力的证据.     

南海海岛海山的重磁响应特征

南海的海岛、海山等地貌单元的地球物理研究对于南海成因、海岛利用、资源问题和我国海防建设均具有重要意义.过去我国的南海海洋实际测量资料覆盖面小,且多数为测线调查,海底地形测量精度和重磁等测量精度较低,因此,一直无法得到精度较高的研究成果.本文利用半个多世纪我国在南海历年的多波束、重力、磁力等船载海洋实际地球物理调查资料,加上少数卫星、航空测量成果,得到能够覆盖南海全部海域的多波束、重力、磁力实际测量的地球物理基础数据.追溯南海周边的地磁台站与当年调查时间匹配的日变数据,重新校正历年磁力测量成果,并利用"十一五"863国家海洋高科技计划的处理、拼合技术,获得了南海海底地形、重力、磁力三方互为印证的可靠地球物理成果,为海岛海山的地球物理研究奠定基础.研究发现,南海海岛海山按其地球物理性质并结合现有的岩石物性资料,可以分为三大类:1)南海大部分海岛海山为空间重力异常值高、正磁力ΔZ_⊥异常值也高的高密度高磁性的双高海山,以基性喷出岩(玄武岩)为主;2)空间重力异常值高、磁力ΔZ_⊥异常值低的海山,以花岗岩、变质岩为主;3)空间重力异常值高、部分磁力ΔZ_⊥异常值高部分低的海山,可能是花岗岩、变质岩海山的部分区域出现火山喷发形成的. 海山的分布有规律,与南海的成因与南海块体的分异状态有关.     

基于交叉梯度约束的重力、磁法和大地电磁三维联合反演

为了降低单一地球物理方法反演的多解性及受噪声的影响程度,本文围绕重力、磁法和大地电磁法开展了三维联合反演的研究.重、磁采用基于对数障碍法的正则化反演算法,大地电磁使用limited-memory BroydenFletcher-Goldfarb-Shanno(L-BFGS)反演算法,引入交叉梯度函数实现了三种物性结构的相互耦合,最终开发出一套重磁电三维联合反演算法,并实现MPI并行加速计算.通过理论模型算例验证了算法的准确性,结果表明:不论是单棱柱体模型还是组合棱柱体模型,联合反演结果相较单独反演对于异常体的空间形态刻画以及物性数值恢复具有较好的提升;单棱柱体模型算例使得异常体的物性参数(密度、磁化率和电阻率)更加接近于真实的物性参数;组合棱柱体模型的联合反演结果不仅仅消除了围岩物性参数的假异常,而且还增强了异常体边界结构的恢复程度.     

Structure of the Rambler Rhyolite, Baie Verte Peninsula, Newfoundland: Inversions using UBC-GIF Grav3D and Mag3D

Hosted within the Pacquet Harbour Group (PHG) on the Baie Verte Peninsula of north-central Newfoundland, the Rambler rhyolite is a 487 Ma unit of felsic tuffs, flows and subvolcanic intrusive rocks. The PHG has been affected by multiple phases of deformation with the youngest D₄ deformation event producing broad northeast plunging upright cross folds in the Rambler rhyolite. Fold culminations on the upper bounding surface of the rhyolite host Cu +/− Au volcanogenic massive sulfide deposits (e.g. Rambler and Ming mines). Geophysical inversions of recently acquired high resolution gravity and magnetic data have been implemented to determine the extent of the fold axis (dome) at depth. To direct the outcome of the inversion process towards a more geologically reasonable solution this study outlines a procedure which permits the inclusion of known geological and geophysical constraints into the input (reference) model for inversion using the MAG3D and GRAV3D algorithms provided by the University of British Columbia Geophysical Inversion Facility. Reference model constraints included surficial geological contacts as defined by aeromagnetic data, and subsurface distribution of physical property variations from a series of drill-hole logs. The output (computed) model images the surface of the rhyolite dome as dipping roughly 40° to the northeast as a series of voxels with density values ranging from 2.71 to 2.75 g/cm³. While previously published ore deposit models parallel this structure in the near surface, results from these inversions suggest deeper exploration may be favorable. Magnetic inversion modeling has not provided any insight into dome morphology however it outlines the distribution of gabbroic dykes surrounding the dome.     

The distribution of deep source rocks in the GS Sag: joint MT–gravity modeling and constrained inversion

The coal-bearing strata of the deep Upper Paleozoic in the GS Sag have high hydrocarbon potential. Because of the absence of seismic data, we use electromagnetic (MT) and gravity data jointly to delineate the distribution of deep targets based on well logging and geological data. First, a preliminary geological model is established by using three-dimensional (3D) MT inversion results. Second, using the formation density and gravity anomalies, the preliminary geological model is modified by interactive inversion of the gravity data. Then, we conduct MT-constrained inversion based on the modified model to obtain an optimal geological model until the deviations at all stations are minimized. Finally, the geological model and a seismic profile in the middle of the sag is analysed. We determine that the deep reflections of the seismic profile correspond to the Upper Paleozoic that reaches thickness up to 800 m. The processing of field data suggests that the joint MT–gravity modeling and constrained inversion can reduce the multiple solutions for single geophysical data and thus improve the recognition of deep formations. The MT-constrained inversion is consistent with the geological features in the seismic section. This suggests that the joint MT and gravity modeling and constrained inversion can be used to delineate deep targets in similar basins.     

Calibrating a Salt Water Intrusion Model with Time‐Domain Electromagnetic Data

Salt water intrusion models are commonly used to support groundwater resource management in coastal aquifers. Concentration data used for model calibration are often sparse and limited in spatial extent. With airborne and ground‐based electromagnetic surveys, electrical resistivity models can be obtained to provide high‐resolution three‐dimensional models of subsurface resistivity variations that can be related to geology and salt concentrations on a regional scale. Several previous studies have calibrated salt water intrusion models with geophysical data, but are typically limited to the use of the inverted electrical resistivity models without considering the measured geophysical data directly. This induces a number of errors related to inconsistent scales between the geophysical and hydrologic models and the applied regularization constraints in the geophysical inversion. To overcome these errors, we perform a coupled hydrogeophysical inversion (CHI) in which we use a salt water intrusion model to interpret the geophysical data and guide the geophysical inversion. We refer to this methodology as a Coupled Hydrogeophysical Inversion‐State (CHI‐S), in which simulated salt concentrations are transformed to an electrical resistivity model, after which a geophysical forward response is calculated and compared with the measured geophysical data. This approach was applied for a field site in Santa Cruz County, California, where a time‐domain electromagnetic (TDEM) dataset was collected. For this location, a simple two‐dimensional cross‐sectional salt water intrusion model was developed, for which we estimated five uniform aquifer properties, incorporating the porosity that was also part of the employed petrophysical relationship. In addition, one geophysical parameter was estimated. The six parameters could be resolved well by fitting more than 300 apparent resistivities that were comprised by the TDEM dataset. Except for three sounding locations, all the TDEM data could be fitted close to a root‐mean‐square error of 1. Possible explanations for the poor fit of these soundings are the assumption of spatial uniformity, fixed boundary conditions and the neglecting of 3D effects in the groundwater model and the TDEM forward responses.     

Grey wolf optimizer: a new strategy to invert geophysical data sets

There is no meta‐heuristic approach best suited for solving all optimization problems making this field of study highly active. This results in enhancing current approaches and proposing new meta‐heuristic algorithms. Out of all meta‐heuristic algorithms, swarm intelligence is preferred as it can preserve information about the search space over the course of iterations and usually has fewer tuning parameters. Grey Wolves, considered as apex predators, motivated us to simulate Grey Wolves in the optimization of geophysical data sets. The grey wolf optimizer is a swarm‐based meta‐heuristic algorithm, inspired by mimicking the social leadership hierarchy and hunting behaviour of Grey Wolves. The leadership hierarchy is simulated by alpha, beta, delta and omega types of wolves. The three main phases of hunting, that is searching, encircling and attacking prey, is implemented to perform the optimization. To evaluate the efficacy of the grey wolf optimizer, we performed inversion on the total gradient of magnetic, gravity and self‐potential anomalies. The results have been compared with the particle swarm optimization technique. Global minimum for all the examples from grey wolf optimizer was obtained with seven wolves in a pack and 2000 iterations. Inversion was initially performed on thin dykes for noise‐free and noise‐corrupted (up to 20% random noise) synthetic data sets. The inversion on a single thin dyke was performed with a different search space. The results demonstrate that, compared with particle swarm optimization, the grey wolf optimizer is less sensitive to search space variations. Inversion of noise‐corrupted data shows that grey wolf optimizer has a better capability in handling noisy data as compared to particle swarm optimization. Practical applicability of the grey wolf optimizer has been demonstrated by adopting four profiles (i.e. surface magnetic, airborne magnetic, gravity and self‐potential) from the published literature. The grey wolf optimizer results show better data fit than the particle swarm optimizer results and match well with borehole data.     

闽西南多金属成矿带地质地球物理特征综合研究——以永定大排多金属矿区为例

闽西南地区位于福建武夷山成矿带西南部,自远古宙以来经历了多期次的构造演化.该区地处东南沿海构造-岩浆-成矿带上,为环太平洋大陆边缘多金属成矿带与南岭多金属成矿带复合部位,是我国重要的多金属矿产地.永定大排多金属矿区作为近年来武夷山成矿带新发现的大型多金属矿,区内叠加作用和控矿作用相对复杂,现有的地质地球物理工作程度不足以满足对该区域成矿规律的深入认识,一些基础地质问题亟待解决.因此,本文在深入收集永定大排矿区地质地球物理资料基础上,综合分析区域成矿背景与成矿构造,在重点区域布设综合地球物理勘探工作,包括1：1万高精度磁测、可控源音频大地电磁剖面及反射地震剖面.基于上述工作：1）开展了研究区航磁数据三维磁化率反演与分布特征分析与大地电磁二维电阻率反演与分布特征分析,开展了地震资料真地表深度偏移成像,获得了更加准确的地震剖面成像结果.2）结合推覆体控矿特征,地震剖面和电阻率剖面、航磁反演结果相互验证和约束,勾画了地下构造形态.地表地质剖面延伸和标定了构造形态的地质内涵,获得了从地表到3000 m深度的构造解释结果.解释结果清晰地显示了与推覆相关的构造、控矿层位以及岩体信息,为三位一体的找矿思路提供了地球物理依据.     

Geophysical signatures of uranium mineralization and its subsurface validation at Beldih,Purulia District,West Bengal,India: a case study

The Beldih open cast mine of the South Purulia Shear Zone in Eastern India is well known for apatite deposits associated with Nb–rare‐earth‐element–uranium mineralization within steeply dipping, altered ferruginous kaolinite and quartz–magnetite–apatite rocks with E–W strikes at the contact of altered mafic–ultramafic and granite/quartzite rocks. A detailed geophysical study using gravity, magnetic, and gradient resistivity profiling surveys has been carried out over ～1 km² area surrounding the Beldih mine to investigate further the dip, depth, lateral extension, and associated geophysical signatures of the uranium mineralization in the environs of South Purulia Shear Zone. The high‐to‐low transition zone on the northern part and high‐to‐low anomaly patches on the southeastern and southwestern parts of the Bouguer, reduced‐to‐pole magnetic, and trend‐surface‐separated residual gravity–magnetic anomaly maps indicate the possibility of highly altered zone(s) on the northern, southeastern, and southwestern parts of the Beldih mine. The gradient resistivity survey on either side of the mine has also revealed the correlation of low‐resistivity anomalies with low‐gravity and moderately high magnetic anomalies. In particular, the anomalies and modeled subsurface features along profile P6 perfectly match with subsurface geology and uranium mineralization at depth. Two‐dimensional and three‐dimensional residual gravity models along P6 depict the presence of highly altered vertical sheet of low‐density material up to a depth of ～200 m. The drilling results along the same profile confirm the continuation of uranium mineralization zone for the low‐density material. This not only validates the findings of the gravity model but also establishes the geophysical signatures for uranium mineralization as low‐gravity, moderate‐to‐high magnetic, and low‐resistivity values in this region. This study enhances the scope of further integrated geophysical investigations along the South Purulia Shear Zone to delineate suitable target areas for uranium exploration.     

金平白马寨铜镍矿床地球物理成矿预测模式

通过对大量地质及物化探资料分析,运用地质学、矿床学以及地球物理勘探学的基本理论和方法,分析了金平白马寨铜镍矿床的地质与地球物理特征,从而提出了本区铜镍矿床为岩浆熔离脉冲贯入型矿床和“三高一低”,即重力高、磁力高、极化率高、电阻率低的地球物理成矿预测模式．     

Quantitative geophysical pore‐type characterization and its geological implication in carbonate reservoirs

This paper discusses and addresses two questions in carbonate reservoir characterization: how to characterize pore‐type distribution quantitatively from well observations and seismic data based on geologic understanding of the reservoir and what geological implications stand behind the pore‐type distribution in carbonate reservoirs. To answer these questions, three geophysical pore types (reference pores, stiff pores and cracks) are defined to represent the average elastic effective properties of complex pore structures. The variability of elastic properties in carbonates can be quantified using a rock physics scheme associated with different volume fractions of geophysical pore types. We also explore the likely geological processes in carbonates based on the proposed rock physics template. The pore‐type inversion result from well log data fits well with the pore geometry revealed by a FMI log and core information. Furthermore, the S‐wave prediction based on the pore‐type inversion result also shows better agreement than the Greensberg‐Castagna relationship, suggesting the potential of this rock physics scheme to characterize the porosity heterogeneity in carbonate reservoirs. We also apply an inversion technique to quantitatively map the geophysical pore‐type distribution from a 2D seismic data set in a carbonate reservoir offshore Brazil. The spatial distributions of the geophysical pore type contain clues about the geological history that overprinted these rocks. Therefore, we analyse how the likely geological processes redistribute pore space of the reservoir rock from the initial depositional porosity and in turn how they impact the reservoir quality.     

Electric field data in inductive source electromagnetic surveys

Measurement of the electric field data due to an inductive loop source in a controlled source electromagnetic survey is not common, because electric field data, usually involving grounded electrodes, are expensive to acquire and difficult to interpret. With the recently developed capability of versatile three‐dimensional inversion, we revisit the idea of measuring electric field in a large ground loop survey for mineral exploration. The three‐dimensional modelling and inversion approach helps us quantitatively understand the detectability and recoverability of the proposed survey configuration. Our detectability study using forward modelling shows that the relative anomaly (percentage difference) in electric field does not decay with a lower induction number, but the conventional magnetic field data (dB/dt) does. Our recoverability study examines how much and what kind of information can be extracted from electric field data for the reconstruction of a three‐dimensional model. Synthetic inversions show the following observations. (i) Electric field data are good at locating lateral discontinuity, whereas dB/dt has better depth resolution. (ii) Electric field is less sensitive to the background conductivity and, thus, is prone to misinterpretation because of a bad initial model in inversion. We recommend warm‐starting the electric field inversion with an initial model from a separate dB/dt inversion. (iii) Electric field data may be severely contaminated by near‐surface heterogeneity, but an inversion can recover the deep target concealed by the geologic noise. (iv) Even one line of single‐component electric field data can greatly improve the horizontal resolution in a dB/dt inversion. Finally, we investigate a field dataset of both electric field and dB/dt measurements at a uranium deposit. The field example confirms that the electric field and magnetic field data contain independent information that is crucial in the accurate recovery of subsurface conductivity. Our synthetic and field examples demonstrate the benefit of acquiring electric field data along with magnetic field data in an inductive source survey.     

综合地球物理方法对南海西北部-印支半岛地区中生界分布的研究

南海西北部是我国海洋油气的重要基地.为了研究该区前新生代尤其是中生代油气资源潜力,本文以岩石物性的差异为基础,建立地质界面与物性界面的联系,利用综合地球物理方法来分析目标物性界面的分布特征.在地震资料控制浅层沉积结构的约束下,根据重力资料,通过小波分析位场剥离等方法得到剩余场,由Parker界面反演法反演计算了研究区的重力基底,结合新生代沉积分布得出中生界分布特征并给出了中生代残留盆地的可能分布范围,为分析研究区中生代油气资源潜力提供参考.     

Large‐scale 3D inversion of potential field data

Inversion of gravity and/or magnetic data attempts to recover the density and/or magnetic susceptibility distribution in a 3D earth model for subsequent geological interpretation. This is a challenging problem for a number of reasons. First, airborne gravity and magnetic surveys are characterized by very large data volumes. Second, the 3D modelling of data from large‐scale surveys is a computationally challenging problem. Third, gravity and magnetic data are finite and noisy and their inversion is ill posed so regularization must be introduced for the recovery of the most geologically plausible solutions from an infinite number of mathematically equivalent solutions. These difficulties and how they can be addressed in terms of large‐scale 3D potential field inversion are discussed in this paper. Since potential fields are linear, they lend themselves to full parallelization with near‐linear scaling on modern parallel computers. Moreover, we exploit the fact that an instrument’s sensitivity (or footprint) is considerably smaller than the survey area. As multiple footprints superimpose themselves over the same 3D earth model, the sensitivity matrix for the entire earth model is constructed. We use the re‐weighted regularized conjugate gradient method for minimizing the objective functional and incorporate a wide variety of regularization options. We demonstrate our approach with the 3D inversion of 1743 line km of FALCON gravity gradiometry and magnetic data acquired over the Timmins district in Ontario, Canada. Our results are shown to be in good agreement with independent interpretations of the same data.     

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.     

New advances in regularized inversion of gravity and electromagnetic data

The interpretation of potential and electromagnetic fields observed over 3D geological structures remains one of the most challenging problems of exploration geophysics. In this paper I present an overview of novel methods of inversion and imaging of gravity and electromagnetic data, which are based on new advances in the regularization theory related to the application of special stabilizing functionals, which allow the reconstruction of both smooth images of the underground geological structures and models with sharp geological boundaries. I demonstrate that sharp-boundary geophysical inversion can improve the efficiency and resolution of the inverse problem solution. The methods are illustrated with synthetic and practical examples of the 3D inversion of potential and electromagnetic field data.