Automatic 1D inversion of multifrequency airborne electromagnetic data with artificial neural networks: discussion and a case study

Artificial neural networks were used to implement an automatic inversion of frequency‐domain airborne electromagnetic (AEM) data that do not require a priori information about the survey area. Two classes of model, i.e. homogeneous half‐space models and horizontally layered half‐space models with two layers, are used in this 1D inversion, and for each data point the selection of the class of 1D model is performed prior to the inversion, also using an artificial neural network. The proposed inversion method was tested in a survey area situated in Austria, northwest of Vienna in the Bohemian Massif. The results of the inversion were compared with the geological setting, logging results, and seismic and gravimetric measurements. This comparison shows a good correlation between the AEM models and the known geological and geophysical data.     

基于主成分的时间域航空电磁数据神经网络反演仿真研究(英文)

传统上,时间域航空电磁数据通过拟合迭代反演计算得到大地模型,然而,由于航空电磁数据道间的较强相关性,导致病态反演,并引起超定问题;同时电磁数据的相关性使其与模型参数的映射关系复杂,增加了反演的复杂度。采用主成分分析法将航空电磁数据变换为正交的较少数量的主成分,不仅降低了数据道间的相关性,减小了数据量,同时压制了数据的不相关噪声。本文利用人工神经网络(ANN)逼近主成分与大地模型参数间的映射关系,避免了传统反演算法中雅克比矩阵的复杂计算。层状模型的主成分神经网络与数据神经网络的反演结果对比显示,主成分神经网络反演方法网络结构简单,训练步数少,反演结果好,特别是对于含噪数据。准二维模型的主成分ANN、数据ANN以及Zhody方法的反演结果显示了主成分神经网络具有更接近真实模型的反演效果,进一步证明了主成分神经网络反演方法适合海量航空电磁探测数据反演。     

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.     

基于PCA-RBF神经网络的航空飞行几何参数拟合

采用地面异常线圈对直升机时域航空电磁探测系统进行标定时,发射-接收线圈姿态的变化将导致实测数据产生误差,影响标定的精度.本文基于时间域航空电磁系统,计算了发射-接收线圈姿态任意变化时异常线圈的电磁响应,提出了主成分分析-径向基神经网络(PCA-RBF)的拟合算法,采用主成分分析法提取飞行几何参数的贡献率,利用径向基神经网络法对电磁响应进行了测线剖面的批量数据拟合,并对理论仿真和河南桐柏直升机飞行试验数据进行拟合分析,单一异常体理论数据的绝对误差平均值小于20nV·m-2,双异常体理论数据绝对误差平均值为160nV·m-2.野外实测数据在异常线圈中心位置的拟合相对误差小于1%,整条剖面测线的拟合相对误差小于±6%,平均值为2.5%.结果表明PCA-RBF拟合算法能够较好地实现航空电磁系统飞行参数的拟合,为航空电磁系统海量实测数据的快速处理提供了新方法.     

Geophysical monitoring and evaluation of coastal plain aquifers

We use time domain electromagnetic (TDEM) soundings to monitor ground water conditions beneath the coastal plain in eastern North Carolina. The TDEM method measures the earth's response to an induced electromagnetic field. The resulting signal is converted, through a complex inversion process, to apparent resistivity values, which can be directly correlated to borehole resistivity logs. TDEM soundings are used to map the interface between fresh and salt water within coastal aquifers, and estimate depth to basement when siting new monitoring wells. Focused TDEM surveys have identified areas of salt water encroachment caused by high volumes of discharge from local supply wells. Electromagnetic sounding, when used in tandem with the state's network of monitoring wells, is an accurate and inexpensive tool for evaluating fresh water/salt water relationships on both local and regional scales within coastal plain aquifers.     

A parallel,scalable and memory efficient inversion code for very large‐scale airborne electromagnetics surveys

Over the past decade the typical size of airborne electromagnetic data sets has been growing rapidly, along with an emerging need for highly accurate modelling. One‐dimensional approximate inversions or data transform techniques have previously been employed for very large‐scale studies of quasi‐layered settings but these techniques fail to provide the consistent accuracy needed by many modern applications such as aquifer and geological mapping, uranium exploration, oil sands and integrated modelling. In these cases the use of more time‐consuming 1D forward and inverse modelling provide the only acceptable solution that is also computationally feasible. When target structures are known to be quasi layered and spatially coherent it is beneficial to incorporate this assumption directly into the inversion. This implies inverting multiple soundings at a time in larger constrained problems, which allows for resolving geological layers that are undetectable using simple independent inversions. Ideally, entire surveys should be inverted at a time in huge constrained problems but poor scaling properties of the underlying algorithms typically make this challenging. Here, we document how we optimized an inversion code for very large‐scale constrained airborne electromagnetic problems. Most importantly, we describe how we solve linear systems using an iterative method that scales linearly with the size of the data set in terms of both solution time and memory consumption. We also describe how we parallelized the core region of the code, in order to obtain almost ideal strong parallel scaling on current 4‐socket shared memory computers. We further show how model parameter uncertainty estimates can be efficiently obtained in linear time and we demonstrate the capabilities of the full implementation by inverting a 3327 line km SkyTEM survey overnight. Performance and scaling properties are discussed based on the timings of the field example and we describe the criteria that must be fulfilled in order to adapt our methodology for similar type problems.     

3D joint inversion of magnetotelluric and airborne tipper data: a case study from the Morrison porphyry Cu–Au–Mo deposit,British Columbia,Canada

Z‐axis tipper electromagnetic and broadband magnetotelluric data were used to determine three‐dimensional electrical resistivity models of the Morrison porphyry Cu–Au–Mo deposit in British Columbia. Z‐axis tipper electromagnetic data are collected with a helicopter, thus allowing rapid surveys with uniform spatial sampling. Ground‐based magnetotelluric surveys can achieve a greater exploration depth than Z‐axis tipper electromagnetic surveys, but data collection is slower and can be limited by difficult terrain. The airborne Z‐axis tipper electromagnetic tipper data and the ground magnetotelluric tipper data show good agreement at the Morrison deposit despite differences in the data collection method, spatial sampling, and collection date. Resistivity models derived from individual inversions of the Z‐axis tipper electromagnetic tipper data and magnetotelluric impedance data contain some similar features, but the Z‐axis tipper electromagnetic model appears to lack resolution below a depth of 1 km, and the magnetotelluric model suffers from non‐uniform and relatively sparse spatial sampling. The joint Z‐axis tipper electromagnetic inversion solves these issues by combining the dense spatial sampling of the airborne Z‐axis tipper electromagnetic technique and the deeper penetration of the lower frequency magnetotelluric data. The resulting joint resistivity model correlates well with the known geology and distribution of alteration at the Morrison deposit. Higher resistivity is associated with the potassic alteration zone and volcanic country rocks, whereas areas of lower resistivity agree with known faults and sedimentary units. The pyrite halo and ≥0.3% Cu zone have the moderate resistivity that is expected of disseminated sulphides. The joint Z‐axis tipper electromagnetic inversion provides an improved resistivity model by enhancing the lateral and depth resolution of resistivity features compared with the individual Z‐axis tipper electromagnetic and magnetotelluric inversions. This case study shows that a joint Z‐axis tipper electromagnetic–magnetotelluric approach effectively images the interpreted mineralised zone at the Morrison deposit and could be beneficial in exploration for disseminated sulphides at other porphyry deposits.     

Slopes of an airborne electromagnetic resistivity model interpolated jointly with borehole data for 3D geological modelling

We investigate a novel way to introduce resistivity models deriving from airborne electromagnetic surveys into regional geological modelling. Standard geometrical geological modelling can be strengthened using geophysical data. Here, we propose to extract information contained in a resistivity model in the form of local slopes that constrain the modelling of geological interfaces. The proposed method is illustrated on an airborne electromagnetic survey conducted in the region of Courtenay in France. First, a resistivity contrast corresponding to the clay/chalk interface was interpreted confronting the electromagnetic soundings to boreholes. Slopes were then sampled on this geophysical model and jointly interpolated with the clay/chalk interface documented in boreholes using an implicit 3D potential‐field method. In order to evaluate this new joint geophysical–geological model, its accuracy was compared with that of both pure geological and pure geophysical models for various borehole configurations. The proposed joint modelling yields the most accurate clay/chalk interface whatever the number and location of boreholes taken into account for modelling and validation. Compared with standard geological modelling, the approach introduces in between boreholes geometrical information derived from geophysical results. Compared with conventional resistivity interpretation of the geophysical model, it reduces drift effects and honours the boreholes. The method therefore improves what is commonly obtained with geological or geophysical data separately, making it very attractive for robust 3D geological modelling of the subsurface.     

Singular value decomposition as a denoising tool for airborne time domain electromagnetic data

Airborne time domain electromagnetic (TDEM) surveys are increasingly carried out in anthropized areas as part of environmental studies. In such areas, noise arises mainly from either natural sources, such as spherics, or cultural sources, such as couplings with man-made installations. This results in various distortions on the measured decays, which make the EM noise spectrum complex and may lead to erroneous inversion and subsequent misinterpretations. Thresholding and stacking standard techniques, commonly used to filter TDEM data, are less efficient in such environment, requiring a time-consuming and subjective manual editing. The aim of this study was therefore to propose an alternative fast and efficient user-assisted filtering approach. This was achieved using the singular value decomposition (SVD). The SVD method uses the principal component analysis to extract into components the dominant shapes from a series of raw input curves. EM decays can then be reconstructed with particular components only. To do so, we had to adapt and implement the SVD, firstly, to separate clearly and so identify easily the components containing the geological signal, and then to denoise properly TDEM data.The reconstructed decays were used to detect noisy gates on their corresponding measured decays. This denoising step allowed rejecting efficiently mainly spikes and oscillations. Then, we focused on couplings with man-made installations, which may result in artifacts on the inverted models. An analysis of the map of weights of the selected “noisy components” highlighted high correlations with man-made installations localized by the flight video. We had therefore a tool to cull most likely decays biased by capacitive coupling noises. Finally, rejection of decays affected by galvanic coupling noises was also possible locating them through the analysis of specific SVD components. This SVD procedure was applied on airborne TDEM data surveyed by SkyTEM Aps. over an anthropized area, on behalf of the French geological survey (BRGM), near Courtenay in Région Centre, France. The established denoising procedure provides accurate denoising tools and makes, at least, the manual cleaning less time consuming and less subjective.     

A comparison of helicopter‐borne electromagnetic systems for hydrogeologic studies

The increased application of airborne electromagnetic surveys to hydrogeological studies is driving a demand for data that can consistently be inverted for accurate subsurface resistivity structure from the near surface to depths of several hundred metres. We present an evaluation of three commercial airborne electromagnetic systems over two test blocks in western Nebraska, USA. The selected test blocks are representative of shallow and deep alluvial aquifer systems with low groundwater salinity and an electrically conductive base of aquifer. The aquifer units show significant lithologic heterogeneity and include both modern and ancient river systems. We compared the various data sets to one another and inverted resistivity models to borehole lithology and to ground geophysical models. We find distinct differences among the airborne electromagnetic systems as regards the spatial resolution of models, the depth of investigation, and the ability to recover near‐surface resistivity variations. We further identify systematic biases in some data sets, which we attribute to incomplete or inexact calibration or compensation procedures.     

Reconstructing the gravity gradient anomaly field from surveys with wide line spacing using equivalent source processing: an error analysis

When anomalous gravity gradient signals provide a large signal‐to‐noise ratio, airborne and marine surveys can be considered with wide line spacing. In these cases, spatial resolution and sampling requirements become the limiting factors for specifying the line spacing, rather than anomaly detectability. This situation is analysed by generating known signals from a geological model and then sub‐sampling them using a simulated airborne gravity gradient survey with a line spacing much wider than the characteristic anomaly size. The data are processed using an equivalent source inversion, which is used subsequently to predict and grid the field in‐between the survey lines by means of forward calculations. Spatial and spectral error analysis is used to quantify the accuracy and resolution of the processed data and the advantages of acquiring multiple gravity gradient components are demonstrated. With measurements of the full tensor along survey lines spaced at 4 × 4 km, it is shown that the vertical gravity gradient can be reconstructed accurately over a bandwidth of 2 km with spatial root‐mean square errors less than 30%. A real airborne full‐tensor gravity gradient survey is presented to confirm the synthetic analysis in a practical situation.     

21世纪重力与磁法勘探的展望

对21世纪重力与磁法勘探的仪器，数据处理技术，解释理论与方法，应用领域等方面的发展方向进行了分析与展望，发展航空标量，矢量，梯度重力测量和航空全梯度磁力测量，三分量磁力测量，提高综合信息采集能力；开展卫星重磁测量，综合卫星，航空，地面重磁测量资料研究地球结构与构造；发展高精度数据处理技术；重磁异常弱信号的提取，不同深度重磁异常的划分，低纬底变倾角化磁极以及位场面延拓；发展复杂条件下三维重磁场多参数综合反演可视化技术以及快速自动反演技术；探索磁性多参数的应用新领域，充分发挥磁法在环境污染调查中的作用并开拓应用新领域。     

重力异常的BP神经网络三维物性反演

三维物性反演参数多,计算量巨大,传统的方法难以实现.本文使用BP神经网络实现重力三维物性反演,介绍了BP神经网络的基本原理及特性,并构造一个适用于重力位场反演的BP神经网络.并用其对模型进行反演计算,结果表明:BP网络具有较好的泛化能力和容错能力,反演速度快、准确,并且较好的反应了场源的分布情况.     

Effects of the sea floor topography on the 1D inversion of time‐domain marine controlled source electromagnetic data

Time‐domain marine controlled source electromagnetic methods have been used successfully for the detection of resistive targets such as hydrocarbons, gas hydrate, or marine groundwater aquifers. As the application of time‐domain marine controlled source electromagnetic methods increases, surveys in areas with a strong seabed topography are inevitable. In these cases, an important question is whether bathymetry information should be included in the interpretation of the measured electromagnetic field or not. Since multi‐dimensional inversion is still not common in time‐domain marine controlled source electromagnetic methods, bathymetry effects on the 1D inversion of single‐offset and multi‐offset joint inversions of time‐domain controlled source electromagnetic methods data are investigated. We firstly used an adaptive finite element algorithm to calculate the time‐domain controlled source electromagnetic methods responses of 2D resistivity models with seafloor topography. Then, 1D inversions are applied on the synthetic data derived from marine resistivity models, including the topography in order to study the possible topography effects on the 1D interpretation. To evaluate the effects of topography with various steepness, the slope angle of the seabed topography is varied in the synthetic modelling studies for deep water (air interaction is absent or very weak) and shallow water (air interaction is dominant), respectively. Several different patterns of measuring configurations are considered, such as the systems adopting nodal receivers and the bottom‐towed system. According to the modelling results for deep water when air interaction is absent, the 2D topography can distort the measured electric field. The distortion of the data increases gradually with the enlarging of the topography's slope angle. In our test, depending on the configuration, the seabed topography does not affect the 1D interpretation significantly if the slope angle is less or around 10°. However, if the slope angle increases to 30° or more, it is possible that significant artificial layers occur in inversion results and lead to a wrong interpretation. In a shallow water environment with seabed topography, where the air interaction dominates, it is possible to uncover the true subsurface resistivity structure if the water depth for the 1D inversion is properly chosen. In our synthetic modelling, this scheme can always present a satisfactory data fit in the 1D inversion if only one offset is used in the inversion process. However, the determination of the optimal water depth for a multi‐offset joint inversion is challenging due to the various air interaction for different offsets.     

Simple relative space–time scaling of electrical and electromagnetic depth sounding arrays: implications for electrical static shift removal and joint DC-TEM data inversion with the most-squares criterion

A simple scaling relationship is shown to facilitate comparison, correlation and integration of data recorded using the common experimental configurations in electrical and electromagnetic depth sounding. Applications of the scheme to field data from typical geological and landfill environments show that it is robust and, where transient electromagnetic (TEM) data are available, enables easy identification and quantification of electrical static shift (galvanic distortion) in magnetotelluric and direct current (DC) sounding curves. TEM‐based procedures are suggested for both the direct removal of static shift in DC sounding curves and effective joint data inversion with the most‐squares criterion in the presence of static shift. A case study of aquifer characterization using sounding data from borehole sites in the Vale of York in England shows that static shift is a common problem in this glacial‐covered terrain and demonstrates the effectiveness of the proposed joint DC‐TEM inversion strategy in handling distorted soundings.     

3D inversion of DC data using artificial neural networks

In this paper, we investigate the applicability of artificial neural networks in inverting three-dimensional DC resistivity imaging data. The model used to produce synthetic data for training the artificial neural network (ANN) system was a homogeneous medium of resistivity 100 Ωm with an embedded anomalous body of resistivity 1000 Ωm. The different sizes for anomalous body were selected and their location was changed to different positions within the homogeneous model mesh elements. The 3D data set was generated using a finite element forward modeling code through standard 3D modeling software. We investigated different learning paradigms in the training process of the neural network. Resilient propagation was more efficient than any other paradigm. We studied the effect of the data type used on neural network inversion and found that the use of location and the apparent resistivity of data points as the input and corresponding true resistivity as the output of networks produces satisfactory results. We also investigated the effect of the training data pool volume on the inversion properties. We created several synthetic data sets to study the interpolation and extrapolation properties of the ANN. The range of 100–1000 Ωm was divided into six resistivity values as the background resistivity and different resistivity values were also used for the anomalous body. Results from numerous neural network tests indicate that the neural network possesses sufficient interpolation and extrapolation abilities with the selected volume of training data. The trained network was also applied on a real field dataset, collected by a pole-pole array using a square grid (8 ×8) with a 2-m electrode spacing. The inversion results demonstrate that the trained network was able to invert three-dimensional electrical resistivity imaging data. The interpreted results of neural network also agree with the known information about the investigation area.     

Mapping Coastal Aquifers by Joint Inversion of DC and TEM Soundings-Three Case Histories

Electrical and electromagnetic methods are well suited for coastal aquifer studies because of the large contrast in resistivity between fresh water-bearing and salt water-bearing formations. Interpretation models for these aquifers typically contain four layers: a highly resistive unsaturated zone; a surficial fresh water aquifer of intermediate resistivity; an underlying conductive, salt water saturated aquifer; and resistive substratum. Additional layers may be added to allow for variations in lithology within the fresh water and salt water layers. Two methods are evaluated: direct current resistivity and time domain electromagnetic soundings. Use of each method alone produces nonunique solutions for resistivities and/or thicknesses of the different layers. We show that joint inversion of vertical electric and time domain electromagnetic soundings produces a more tightly constrained interpretation model at three test sites than is produced by inversion methods applied to each data set independently.     

Analysing two‐dimensional effects in central loop transient electromagnetic sounding data using a semi‐synthetic tipper approach

We present a simple and feasible approach to analyse and identify two‐dimensional effects in central loop transient electromagnetic sounding data and the correspondingly derived quasi two‐dimensional conductivity models. The proposed strategy is particularly useful in minimising interpretation errors. It is based on the calculation of a semi‐synthetic transient electromagnetic tipper at each sounding and for each observational transient time point. The semi‐synthetic transient electromagnetic tipper is derived from the measured vertical component of the induced voltage and the synthetically calculated horizontal component. The approach is computationally inexpensive and involves one two‐dimensional forward calculation of an obtained quasi two‐dimensional conductivity section. Based on a synthetic example, we demonstrate that the transient electromagnetic tipper approach is applicable in identifying which transient data points and which corresponding zones in a derived quasi two‐dimensional subsurface model are affected by two‐dimensional inhomogeneities. The one‐dimensional inversion of such data leads to false models. An application of the semi‐synthetic transient electromagnetic tipper to field data from the Azraq basin in Jordan reveals that, in total, eight of 80 investigated soundings are affected by two‐dimensional structures although the field data can be fitted optimally using one‐dimensional inversion techniques. The largest semi‐synthetic tipper response occurs in a 300 m‐wide region around a strong lateral resistivity contrast. The approach is useful for analysing structural features in derived quasi two‐dimensional sections and for qualitatively investigating how these features affect the transient response. To avoid misinterpretation, these identified zones corresponding to large tipper values are excluded from the interpretation of a quasi two‐dimensional conductivity model. Based on the semi‐synthetic study, we also demonstrate that a quantitative interpretation of the horizontal voltage response (e.g. by inversion) is usually not feasible as it requires the exact sensor position to be known. Although a tipper derived purely from field data is useful as a qualitative tool for identifying two‐dimensional distortion effects, it is only feasible if the sensor setup is sufficiently accurate. Our proposed semi‐synthetic transient electromagnetic tipper approach is particularly feasible as an a posteriori approach if no horizontal components are recorded or if the sensor setup in the field is not sufficiently accurate.     

Neural network inversion of data in classes of parametrized geoelectric sections

A method of approximate magnetotelluric sounding (MTS) data inversion is developed on the basis of the representation of the inverse operator by an artificial neural network in classes of geoelectric structures. A methodology of the neural network inversion of magnetotelluric data is proposed for a family of classes of geoelectric structures and the uncertainty of the inferred results is estimated. A neural network algorithm of MTS data inversion is tested using synthetic 2-D data.     

Inversion of band-limited TEM responses

It is shown that the electromagnetic (EM) spectrum is characterized by strong amplitude-modulated transmitters operating in the target bandwidth of transient electromagnetic (TEM) measurements. As these transmitters cause significant noise in TEM soundings, it is mandatory to band-limit the input signals to improve the signal-to-noise ratio and thereby the depth of exploration. Band-limitation will distort the TEM responses, which leads to erroneous inversion results if the applied low-pass filters are not accounted for in the inversion scheme. We incorporate the low-pass filters in the inversion scheme and test the inversion approach on theoretical and field data. Inversion of band-limited theoretical responses results in recovery of erroneous resistivity models if the filters are not included in the inversion scheme. By contrast, inversion of band-limited theoretical and field data, for which the applied low-pass filters are included in the inversion scheme, leads to recovery of similar resistivity models, independent of the applied cut-off frequencies.