Deep generative inversion of ERT data for electrical resistivity

Electrical resistivity tomography (ERT) is a non-destructive geophysical method that provides images of the soil electrical resistivity. In particular, this study focuses on small-scale soil subsurface areas (up to 1 m deep). Soil resistivity depends on several factors, particularly soil water content. Consequently, ERT has proven to be effective in detecting water flow pathways during infiltration tests. ERT has already been used for hydroecological and hydrogeological applications, but its use still requires further investigation and new developments, particularly for specific processes such as preferential flows. Indeed, water infiltration into the soil is all but homogeneous with the occurrence of preferential flows due to several factors (lithological heterogeneity, macropores, cracks, macrofauna galleries, and root channels). The presence of these preferential flows promotes the downward movement of water and solutes to deeper soil horizons. Thus, the detection of these flows using geophysical methods, such as ERT, should provide a better understanding of the dynamics of preferential flows. However, conventional ERT inversion methods have proven unable to provide insight into the processes at adequate scales (e.g., the macropore scale) and have shown difficulties in detecting sharp variations because of smoothing constraints. Information from apparent resistivity may be lost because of these constraints.To overcome these limitations, an inversion method based on Convolutional Neural Networks (CNNs) is proposed to detect small-scale resistivity heterogeneities. For the training step, we designed a specific generator to produce synthetic resistivity data for various 2D random electrical resistivity distributions mimicking different types of soil heterogeneity (earthworm and root induced macropore, layering, etc.) and for typical protocols for ERT acquisition. For each case, our database associates the true resistivity field with the apparent resistivity. This database contains a large number of training pairs that allow machine learning.The preliminary results show that while some predictions were able to predict properly the soil heterogeneities (shape and size), the values of the estimated true resistivity were far from the target values. To avoid unrealistic estimates, we added physical constraints during the training process. An additional forward calculation was performed based on the true resistivities predicted by the neural network, then the apparent resistivities corresponding to the predicted resistivities were compared to the apparent resistivities corresponding to the targeted true resistivities and a supplementary loss function was added to the initial loss function. At this stage, the neural networks were trained on heterogeneous resistivity distributions in the soil with neither time evolution nor link to hydrological processes. In the future, the resistivity generator will be coupled with hydrological models to simulate water infiltration dynamics and changes in soil water content over time. This perspective is essential for applying the proposed method to detect flow pathways during infiltration tests.

Landslides occur worldwide. Global damages range in billions of dollars and cost hundreds of lives each year; Sweden is not an exception. In this study, we have acquired radiomagnetotelluric (RMT), electrical resistivity tomography (ERT) and high-resolution reflection seismic along 4 profiles with the main aim of imaging the geometry of quick clays and associated unconsolidated sediments that have caused landslides in a pilot study area in southwest Sweden. Comparison between the electrical resistivity models from the 2D inversions of RMT and ERT data with the reflections observed in the seismic data suggests a good correlation between the small-scale structures and those observed in the RMT model. However, the ERT model better delineates the resistive bedrock than the RMT model. The resistivity models are also compared with the CPT-R data collected in two geotechnical boreholes and further confirm some of the layer boundaries imaged with the acquired surface geophysical data.

Málaga town presents a serious problem caused by the insufficient environmental offer of the superficial water resource to supply the dotation corresponding to the needs of the urban area. Although the geographic and geological location generates optimal conditions for the occurrence of groundwater, studies on the existence, location and availability are incomplete and fragmented, and in general, there is no information about the hidryc resource. The main objective of the present paper pretends to build through the applied geophysical prospection Vertical Electric Sounding (VES) and Electrical Resistivity Tomography (ERT) the 2D model of electrical resistivity of the subsurface, from the processing of synthetic data to the treatment of geoelectrical information with hydrogeological purposes. The data acquisition and processing allowed the interpretation, from the geoelectric point of view and the basic analysis of the 1D profiles and the 2D models developed; demonstrating the presence of highly fractured aquifers that can provide the municipal supply in the future; results that establish the first step in the evaluation of Málaga’s water resources

This paper integrates multichannel analysis of surface waves (MASW) and time-lapse electrical resistivity tomography (ERT) to define aquifer geometry and identify transient groundwater features of the Cascalheira Stream Basin Holocene alluvial aquifer (aquifer H), which contributes to the Santo André Lagoon, part of a coastal groundwater-dependent ecosystem (GDE), located in southwest Portugal. MASW measures shear-wave velocity (VS), allowing one to obtain steady geological models of the subsurface, and ERT measures subsurface electrical resistivity (ER), being subjected to ambient changes. MASW enables disambiguation of geological structures in low ER environments, such as coastal areas. This research covered one natural year and involved one MASW campaign, four ERT campaigns, and additional geological field surveys and groundwater monitoring to assist interpretation of results. In the area, the conjugate NW–SE and NE–SW strike-slip fault systems determine compartmentalization of geological structures and subsequent accommodation space for Holocene sedimentation. MASW and ERT surveys show how the NW–SE system deepens these structures toward the coast, whereas the NE–SW system generates small horsts and grabens, being one of these occupied by aquifer H. From upstream to downstream, aquifer H thickness and width increase from 10 m to 12 m and from 140 m to 240 m, respectively. Performance of VS and ER models was satisfactory, with a normalized error of the VR and ER models in the 0.01–0.09 range, meaning that a quantitative quota of uncertainty can be segregated from the overall uncertainty of groundwater models without substantially affecting its simulations accuracy. This methodology seeks to improve the design of shallow groundwater research in GDE preservation policies.

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 197573, “Asset Value Maximization Through a Novel Well-Completion System for 3D Time-Lapse Electromagnetic Tomography Supported by Machine Learning,” by Paolo Dell’Aversana, Raffaele Servodio, and Franco Bottazzi, Eni, et al., prepared for the 2019 Abu Dhabi International Petroleum Exhibition and Conference, Abu Dhabi, 11–14 November. The paper has not been peer reviewed. In this paper, the authors introduce a new technology installed permanently on the well completion and addressed to real-time reservoir fluid mapping through time-lapse electromagnetic tomography during production or injection. The variations of the electromagnetic fields caused by changes of the fluid distribution are measured in a wide range of distances from the well. The data are processed and interpreted through an integrated software platform that combines 3D and 4D geophysical data inversion with a machine-learning (ML) platform. The complete paper clarifies the details of the ML work flow applied to electrical resistivity tomography (ERT) models using an example based on synthetic data. Introduction An important question in well completions is how one may acquire data with sufficient accuracy for detecting the movements of the fluids in a wide range of distances in the space around the production well. One method that is applied in various Earth disciplines is time-lapse electrical resistivity. The operational effectiveness of ERT allows frequent acquisition of independent surveys and inversion of the data in a relatively short time. The final goal is to create dynamic models of the reservoir supporting important decisions in near-real-time regarding production and management operations. ML algorithms can support this decision-making process. Methodology In a time-lapse ERT survey [often referred to as a direct-current (DC) time-lapse survey], electrodes are installed at fixed locations during monitoring. First, a base resistivity data set is collected. The inversion of this initial data set produces a base resistivity model to be used as a reference model. Then, one or more monitor surveys are repeated during monitoring. The same acquisition parameters applied in the base survey must be used for each monitor survey. The objective is to detect any small change in resistivity, from one survey to another, inside the investigated medium. As a first approach, the eventual variations in resistivity can be retrieved through direct comparison between the different inverted resistivity models. A different approach is called difference inversion. Instead of inverting the base and monitor data sets separately, in difference inversion, the difference between the monitor and base data sets is inverted. In this way, all the coherent inversion artifacts may be canceled in the difference images resulting from this type of inversion. Repeating the measurements many times (through multiple monitor surveys) in the same area and inverting the differences between consecutive data sets results in deep insight about relevant variations of physical properties linked with variations of the electric resistivity.

This article presents a tutorial of the bases for, and problems encountered with, the resistivity and induced polarization methods in geotechnical and environmental applications. It commences with a discussion of aqueous electrolytic conduction in rocks including consideration of the effects of temperature, rock texture, rock type, geological processes, and of the presence of clay minerals. Both electrode and membrane polarization in soils and rocks are described. The elementary theory for the resistivity and induced polarization methods is introduced via formulas for electrodes on homogeneous and layered half-spaces. The notion of apparent resistivity is presented. Vertical electric sounding is described in relation to curve types, inversion, equivalence, anisotropy, and correlation. Profiling with resistivity is briefly treated while combined sounding-profiling is treated in more detail for both the resistivity and induced polarization methods. The parameters used to describe the induced polarization phenomena are introduced. A brief discourse follows on data acquisition and processing, including design considerations for transmitters and receivers, electrodes, and wire logistics. A section on arrays and the factors involved in selecting an array provokes the disclosure that while their application in geotechnical and environmental studies usually is straightforward much remains to be learned about the resistivity and induced polarization methods in general. Specific topics requiring study are comparative studies of various arrays in (a) depth of exploration in sounding and in profiling, (b) resolution of horizontal structures, (c) sensitivity to depth, (d) sensitivity to lateral effects, (e) sensitivity to buried and surface topography, and (f) the effectiveness of focused arrays. References to recent significant publications on one-, two-, and three-dimensional forward and inverse interpretation procedures follow. Problems encountered with these methods are initially treated under the section on arrays and are expanded with specific reference to geologic noise and negative induced polarization effects. The advantages of focused arrays are illustrated. The paper concludes with nine representative examples of applications.

Geophysical methods can characterize aquifer systems noninvasively and are particularly helpful to image the complex depositional architecture of the subsurface. Among these, ground-penetrating radar (GPR) is an effective tool for detailed investigations of shallow subsurface geometry, but it provides only limited information on hydraulic properties. Magnetic resonance tomography (MRT) provides parameters such as water content (porosity) and relaxation time/hydraulic conductivity, but it suffers from resolution limits. Furthermore, it requires knowledge of subsurface electrical resistivity, which can be obtained by electrical resistivity tomography (ERT) also suffering from resolution limits. To overcome the limitations in resolution, we have incorporated GPR reflectors as structural information into the ERT and MRT data inversion. We test the methodology on a synthetic example and find improved imaging properties compared to standard inversion, particularly at greater depths, where the resolution is limited. We apply the methodology to a test site that is characterized by a complex depositional architecture. The Quaternary deposits consist of interbedded meltwater deposits (aquifers) and till (aquitards), overlain by aeolian deposits. To image the subsurface depositional architecture in three dimensions, a 200×250 m area was surveyed by GPR. The use of GPR constraints clearly improves the resolution and zonation of the subsurface image, which is validated by drill-core analyses. We develop a workflow to combine GPR, MRT, and ERT, leading the way to high-resolution hydrogeologic models that can be used for groundwater studies.

The potable water system at Fort Knox is threatened by brine contamination from improperly abandoned natural gas exploration wells. The Fort Knox well field is located near the town of West Point, Kentucky, in the flood plain of the Ohio River. At the site, unconsolidated sediments approximately 30 – 40 m thick, overlie shale and porous limestone. Brine is believed to flow vertically from the underlying formations to the unconsolidated aquifer through damaged or leaky well casings under a high hydraulic gradient from the artificially pressurized porous limestone, which is utilized for natural gas storage by a regional energy company. Upon reaching the unconsolidated aquifer, brinecontaminated groundwater enters water supply production wells under the pumping‐induced gradient. As part of the Fort Knox remediation strategy to reduce the impact of brine contamination, electrical resistivity tomography (ERT) and borehole electromagnetic (EM) logs are being collected annually to detect gross changes in subsurface conductivity. The 2009 ERT data show areas of high conductivity on the western (contaminated) side of the site with conductivities more than an order of magnitude higher than on the eastern (uncontaminated) side of the site. The areas of high conductivity are interpreted as brine contamination, consistent with known regions of brine contamination. Conductivities from the EM logs are consistent with the results from the ERT inversions. The EM logs show little change between 2008 and 2009, except for some small changes in the brine distribution in well PZ1. Yearly ERT surveys will be continued to detect new areas of brine contamination and monitor the remediation effort.

Automated design synthesis has the potential to revolutionize the modern engineering design process and improve access to highly optimized and customized products across countless industries. Successfully adapting generative machine learning to design engineering may enable such automated design synthesis and is a research subject of great importance. We present a review and analysis of deep generative machine learning models in engineering design. Deep generative models (DGMs) typically leverage deep networks to learn from an input dataset and synthesize new designs. Recently, DGMs such as feedforward neural networks (NNs), generative adversarial networks (GANs), variational autoencoders (VAEs), and certain deep reinforcement learning (DRL) frameworks have shown promising results in design applications like structural optimization, materials design, and shape synthesis. The prevalence of DGMs in engineering design has skyrocketed since 2016. Anticipating the continued growth, we conduct a review of recent advances to benefit researchers interested in DGMs for design. We structure our review as an exposition of the algorithms, datasets, representation methods, and applications commonly used in the current literature. In particular, we discuss key works that have introduced new techniques and methods in DGMs, successfully applied DGMs to a design-related domain, or directly supported the development of DGMs through datasets or auxiliary methods. We further identify key challenges and limitations currently seen in DGMs across design fields, such as design creativity, handling constraints and objectives, and modeling both form and functional performance simultaneously. In our discussion, we identify possible solution pathways as key areas on which to target the future work.

Cross‐well electrical resistivity tomography (ERT) was used to monitor the migration of a saline tracer in a two‐well pumping‐injection experiment conducted at the Massachusetts Military Reservation in Cape Cod, Massachusetts. After injecting 2200 mg/L of sodium chloride for 9 hours, ERT data sets were collected from four wells every 6 hours for 20 days. More than 180,000 resistance measurements were collected during the tracer test. Each ERT data set was inverted to produce a sequence of 3‐D snapshot maps that track the plume. In addition to the ERT experiment a pumping test and an infiltration test were conducted to estimate horizontal and vertical hydraulic conductivity values. Using modified moment analysis of the electrical conductivity tomograms, the mass, center of mass, and spatial variance of the imaged tracer plume were estimated. Although the tomograms provide valuable insights into field‐scale tracer migration behavior and aquifer heterogeneity, standard tomographic inversion and application of Archie's law to convert electrical conductivities to solute concentration results in underestimation of tracer mass. Such underestimation is attributed to (1) reduced measurement sensitivity to electrical conductivity values with distance from the electrodes and (2) spatial smoothing (regularization) from tomographic inversion. The center of mass estimated from the ERT inversions coincided with that given by migration of the tracer plume using 3‐D advective‐dispersion simulation. The 3‐D plumes seen using ERT exhibit greater apparent dispersion than the simulated plumes and greater temporal spreading than observed in field data of concentration breakthrough at the pumping well.

Summary Electrical resistivity tomography (ERT) and time domain electromagnetic (TEM) are two widely adopted geophysical methods for near surface resistivity mapping. However, the results produced by the two may differ due to fundamental differences in physical principles, sensitivity, system geometry. The main objective of this paper is to provide a one-to-one comparison of ERT against a newly developed towed TEM system tTEM and comparison of tTEM against its airborne counterpart SkyTEM. We compare three methods using both synthetic as well as field data. Overall, we found that inversion results are comparable across the three methods. They all capture the prominent features of synthetic models. The ERT and tTEM inversion of field data show very comparable results even in the top 5 m where both can image thin resistive layers. However, the resistivity of the thin resistive layer is better resolved using ERT because of its high sensitivity close to the surface. In deeper part of the profile, tTEM tends to produce better resolved boundaries compared to the ERT method. Comparing the SkyTEM inversion results against the tTEM, shows that tTEM has a better vertical and horizontal resolution in the top 20 m.

Electromagnetic induction (EMI) systems measure the soil apparent electrical conductivity (ECa), which is related to the soil water content, texture, and salinity changes. Large‐scale EMI measurements often show relevant areal ECa patterns, but only few researchers have attempted to resolve vertical changes in electrical conductivity that in principle can be obtained using multiconfiguration EMI devices. In this work, we show that EMI measurements can be used to determine the lateral and vertical distribution of the electrical conductivity at the field scale and beyond. Processed ECa data for six coil configurations measured at the Selhausen (Germany) test site were calibrated using inverted electrical resistivity tomography (ERT) data from a short transect with a high ECa range, and regridded using a nearest neighbor interpolation. The quantitative ECa data at each grid node were inverted using a novel three‐layer inversion that uses the shuffled complex evolution (SCE) optimization and a Maxwell‐based electromagnetic forward model. The obtained 1‐D results were stitched together to form a 3‐D subsurface electrical conductivity model that showed smoothly varying electrical conductivities and layer thicknesses, indicating the stability of the inversion. The obtained electrical conductivity distributions were validated with low‐resolution grain size distribution maps and two 120 m long ERT transects that confirmed the obtained lateral and vertical large‐scale electrical conductivity patterns. Observed differences in the EMI and ERT inversion results were attributed to differences in soil water content between acquisition days. These findings indicate that EMI inversions can be used to infer hydrologically active layers.

Integrated electromagnetic (EM) and Electrical Resistivity Tomography (ERT) geophysical studies of environmental impact of Awotan dumpsite in Ibadan, southwestern Nigeria

Electrical resistivity as a binary classifier for bridge scour evaluation

ERT and salinity – A method to determine whether ERT-detected preferential pathways in brackish water-irrigated soils are water-induced or an artifact of salinity