Processing of electrical resistivity tomography data using convolutional neural network in ERT-NET architectures

Electrical resistivity tomography (ERT) inversion has emerged as an effective method for predicting resistivity in complex geological structures. In most cases, traditional ERT inversion problems are posed as nonlinear optimization problems. Solving distribution resistivity inversion can be computationally challenging for two reasons: one is the significant cost of software and the other is the issue of local minima. The ERT-NET architecture was developed in this study to learn the parameter regression relationship between geophysical ERT datasets and subsurface models. We developed a novel convolutional neural network (CNN) technique that comprised of a fully connected network (ERT-INET) and a fully convolutional network (ERT-UNET); both train ambiguity information of the inverted resistivity based on processing ERT datasets. We also output our network segmentation of pixel-wise prediction for ERT-INET and structured prediction segmentation. The noise assessments of our network inversion were managed by employing depth of investigation (DOI) and statistical analysis for evaluation performance. The DOI appeared to be effective in conveying the breadth of possibility within our networks. Moreover, the performances are either the synthetic resistivity model or the field resistivity data, both of which have an average of greater than 95%. The inversion results of both architectures are precisely and accurately expressed, containing approximately the ground truth models and thereby also the field observation models. We conclude that these ERT-NET architectures could be one approach to ERT interpretation handling, and we strongly suggest alternatives that promote the geoelectrical method of interpretation.


Introduction
Geoelectric data are distinguished by apparent resistivity profiling data or main pseudo-sections depicting vertical or horizontal variations in the near-surface Earth.Geoelectric inverse problems are more difficult to resolve because they are nonlinear and ill-posed (Rucker and Gunther 2011;Tabbagh et al. 2007).The resolution capability structures and inverted models provide a guide to resistivity beneath the surface and true geometry resistivity (Dahlin and Zhou 2004).However, acquisition data might pose some challenges in terms of computations or interpretations (Loke et al. 2010;Rucker et al. 2010).
Geophysicists have handled geoelectric data through resistivity investigation both practically and in laboratories, which involved inverse problem-solving (Park et al. 2014).The emergence of resistivity imaging from the inverse problem continues to confound geoscience experts.Geoelectric inverse concerns have been continuously developing.For instance, a numerical study of electrical resistivity imaging (ERI) and the advancement of high-efficiency resistivity models and optimization techniques for geoelectrical measurements (Loke et al. 2015;Pan and Tang 2014;Wilkinson et al. 2012).Yuan et al. (2016) attempted to reduce the numerical error in the resistivity images by using 2.5-D Responsible Editor: Narasimman Sundararajan This research employed convolutional neural network techniques to comprehend the ERT-NET architecture techniques within the ERT data approach processing, in addition to providing an alternative approach for interpreting ERT results.Meanwhile, we prove that these ERT-NET architectures can be used to supplement existing geophysical software on Earth's subsurface interpretations.
direct-current resistivity forward modeling.These efforts, however, are occasionally unexpected among geoscientists due to a lack of documentation.
Geoelectric data are derived from a subsurface's pseudoresistivity, for which the tomography image is challenging to interpret due to its interpretations.As a result, resistivity inversion is used to overcome the preceding problems.Furthermore, neural network techniques are employed for the subsequent inversion of the geoelectric data (El-Qady and Ushijima 2001; Naeh et al. 2018;Xu et al. 2006).In regards to image processing, neural networks have started to receive numerous advancements (Kim and Nakata 2018;Russell 2019), causing geosciences to promote the use of these techniques in other geophysical fields (Bergen et al. 2019;Reichstein et al. 2019).
Deep learning is advancing in engineering and science, particularly in geophysical fields.This provided assessments and approaches for image visualization and interpretation based on structural datasets (Yu et al 2020).The majority of geophysical branches support convolutional neural networks (CNNs) because they can be applied to computer vision applications.Morales and colleagues (Morales et al. 2020) had been using CNNs to recognize gravitational wave patterns.Geng and Wang (2020) were using CNNs as they included topological modules capable of classifying seismic data, which aided their interpretations.Zhang et al. (2018) were successful at predicting uncertain lithology using deep learning frameworks and continuous wavelet transform data.Hydrocarbon exploration is required to investigate the formation of a velocity seismic model, and thereafter, Araya-Polo et al. (2018) discussed a deep learning method for solving hydrocarbon prospecting problems.A CNN can also detect earthquake locations (Perol et al. 2018).Tong et al. (2020) used ground penetrating radar (GPR) datasets for civil engineering examinations using advanced deep learning applications.Puzyrev (2019) demonstrated the EM model by considering electromagnetic inversion using a deep learning CNN technique, and Liu et al. (2020) performed deep learning inversion depending on the electrical resistivity data that were employed to produce the apparent resistivity data mapping.
CNN techniques are primarily used in network implementations for geophysical prospecting cases.To achieve deep predictions, the geophysical dataset ought to have slightly elevated image resolution and satisfactory images (Simonyan and Zisserman 2015).Distribution resistivity mapping images are affected by uncertain images and successive discrepancies.The learning mechanism of the CNN algorithm for data reorganization has limitations.These issues may be resolved by designing modules within CNN's encoder.In range predictions, especially, this can achieve the best estimate targets (Lecun et al. 2015).
In this paper, we propose ERT-Net architectures, which are a fully dataset-propagated method for learning ERT surveying mappings from input to output using a synthetic resistivity model and CNN subsurface depictions.As research progresses, the input emerges from the observed (V/I) data and is constituted in the pixel-segment datasets referred to as "sample pairs."Fig. 1 represents the presence of bodies in the resistivity model, which needs to serve as feedback in the observed resistivity dataset.Aside from that, the figure illustrates the feedback of observed data, which was additionally verified by contrasting resistivity anomalies to display specific patterns.The patterns represent physical body correlations to resistivity bodies in the synthetic resistivity model.The distribution of resistivity data encapsulates portions of regions, revealing that they exist locally and that the input and output for resistivity inversion have two characteristics: (1) they have a particular spatial distribution and (2) they have local existing distributions.As a consequence, the input and output can be presumed to be the original images, and the task can be considered the common mapping between images.In this case, the techniques of the DNN variants of CNN are preferred because they are considerably powerful at extracting local distributions and exhibit better effectiveness in regards to the number of parameters, and previous remote sensing research has widely used CNNs (Cheng et al. 2020;Maggiori et al. 2017;Zhang et al. 2018).
The inverted resistivity pseudo-sections tend to imitate the original resistivity model; nevertheless, the inverted resistivity data have distinct characteristics.Figure 2 presents that the two similar physical bodies are located up and down in a vertical position; the two models have contrasting resistivity values.Furthermore, the inverted resistivity pseudo-sections have a similar distribution for the topmost body compared to the lower body.They described vertical patterns that seemed to be spatially invariant.Meanwhile, CNN techniques have been using local and weight-sharing convolutional kernels to generate a particular responsive field and effective regions.In this paper, we face the challenge of applying CNN techniques to the inverted resistivity sections, where the techniques are expected to produce results that differ from the inverted resistivity distribution and depict acceptable resistivity distributions similar to the resistivity model.This condition poses a significant obstacle to CNN techniques and will result in mismatching CNN outputs.Notwithstanding, we realized that they may be the foremost complication for applying prevalently used CNN techniques to inverse electrical resistivity data.The next section will discuss the precise details of CNN techniques.
We employ the two most prevalent CNN-based architectures: fully connected networks and fully convolutional networks.The latter is referred to in this work as the ERT-UNET architecture, whereas the ERT-INET of the first architecture is employed to design our networks (Loginov Page 3 of 14 581 and Petrov 2019; Ozturk et al. 2020).The global resistivity patterns will be depicted using segmentation prediction outputs.Furthermore, segmentation is one of the most widely employed classification techniques that still includes a semantic label, in this case, the inverted resistivity section.As a necessary consequence, the technique can assist in minimizing potential ambiguity caused by the vertically varying characteristic of inverted resistivity data pseudosection.Furthermore, the proposed ERT-NET consistently achieves promising results in terms of fast inference speed and excellent inversion accuracy, based on comprehensive qualitative analysis and quantitative comparison.This objective is to investigate whether the ERT-NET architecture can be used for natural interpretation of the Earth's subsurface while also ensuring that geoscience experts can decide on appropriate subsurface information.

Design of ERT-NET architectures and implementations
We designed our ERT-NET with a convolutional neural network (CNN) architecture, which is a type of network that processes data in a grid-like topology (LeCun et al. 1989).CNNs have played a significant role in the history of deep learning (DL) and are going to lead to a recent series of advancements in image classification (Singstad and Tronstad 2020).CNN techniques are a foremost example of a successful application of knowledge gained from brain research, which has been inspired in part by the structure of the mammalian visual system (Gatys et al. 2019).Convolutional networks, as even the term suggests, use a convolution operation, which is filtering by a feature map or kernel, in place of general matrix multiplication in fully connected networks (in fact, convolution corresponds to a product by a sparse matrix).While in a fully connected network, each neuron is connected to all the others in the previous layer, and each connection has its own weight, in a convolutional layer, each neuron is connected only to a few neurons in the previous layer (i.e., a much smaller sensitive field), and the same set of weights is shared.Almost all CNNs employ a technique known as "pooling" to make the representation approximately invariant to small translations of the input.The max pooling operation, which returns the maximum within a rectangular neighborhood, is frequently used.Pooling with down sampling reduces the representation size, relieving the computational and statistical burden on the next layer.
Figure 3a depicts the ERT-INET, which is made up of a variety of layers, each with several filters for detecting various features in the input or the sample pairs of the synthetic models.This most common CNN architecture has been created for classification (predicting a class label) and regression (outputting a real value) tasks, and it contains a fully connected layer at the end to build pixel-wise prediction segmentation.All the same, CNNs can be used to produce a high-dimensional segmentation of a structured object (Fig. 3b), and this network has several additional layers on a fully convolutional architecture (ERT-UNET).
The fundamental surveys of ERT are built by injecting current into the ground through two current electrodes and calculating the potential difference between the other pairs of electrodes.The potential difference data are captured as observed data at the Earth's subsurface in an ERT common scheme.Problem inversion involves summarizing a set of variables in model from a set of data, and it generally seems to take the equitable function into consideration.In this study, we determine the mapping function F using apparent resistivity datasets (d) and resistivity model (m), which can be expressed as: ERT-NET works directly to obtain an approximation of F −1 , mapping from d to m.Most inverse problems are solved using least-squares approaches with some regularizing constraints to improve stability and convergence.
We accomplish resistivity inversion by designing the mapping from observed data to the resistivity model directly through the CNN model.The methods are divided into two categories: trained and predicted.Due to the issues with inverted resistivity distribution, we nourished a significant number of apparent resistivity pseudo-section datasets into the system and tested them to predict the appropriate resistivity models (He et al. 2016;Shelhamer et al. 2017).The mapping from the apparent resistivity ( 1) image to the resistivity model can be correctly learned since the dimension of the training datasets is sufficiently large.Once the training process is complete, the optimized CNN can predict and update the inverted resistivity section from the matching resistivity model.Meanwhile, in this study, the inversion software for EarthImager2D by AGI (Advanced Geosciences 2009) and Res2DInv by Geotomo (Loke 2015) are employed as validation inversions since both will have a good fitting position and appropriate appearance within the natural model.
The universal convolution approximation theorem (Cuevas and Galvez 2019) states that deep neural network can theoretically approximate any continuous function if several hidden parameters are massive enough.This approximator is based on CNN techniques.Convolution can be defined for shapes of every size (Shelhamer et al. 2017).The discrete convolution operation for two-dimensional (2-D) datasets is defined as: where X i,j ′ expresses the value of the (i, j) location of the output data of the network, and X states the input data.ꞵ represents the bias, and α is the activation function.The p and q are the sizes of the convolutional kernel in the column and row directions, respectively.We have W ∈ R p×q denotes the trainable kernel, and s represents the strides between each movement of the kernel.
(2) In this architecture, we use an activation function that further contains a non-linear function that sets some of the input values to zero or a value close to zero.The activation constituent is the Rectified Linear Unit (ReLU), which has been used continuously in the CNN process, and there must be smaller numbers of overfitting risks to accomplish linearity (Xu et al. 2014).Convolutional layers used in this can be considered a set of layers, and deconvolutional layers (also known as transposed convolutional layers) can be figured out as a subcategory of convolutional layers (Gatys et al. 2019).It tends to generate outputs that are larger or similar to the input, which can be gained by padding the input feature map to zeros (Sonoda and Murata 2017).
The predictive outputs are the effects of convolutional neural network learning that was capable of analyzing the input datasets.The Adam optimizer with a 10 −4 learning rate was implemented to optimize the architecture.We executed 500 epochs of optimization during training and one-time validation after each training epoch to verify the training effect (Kingma and Ba 2015).
The CNN evaluation regression exhibits the performance of the final prediction model, which has 16 channels either for the ERT-INET or ERT-UNET architectures.We slide a 1 × 1 × 128 × 1 kernel over the feature map to lessen the resistivity value for each location.The inverted resistivity distribution is evaluated using a streamline with an iteration parameter for the values to display information in the same quantity as an inferential image error function (Rücker et al. 2006).A mean square error (MSE) is the prediction segmentation value for CNN evaluation of the inverted resistivity model.A root mean square relative error (RMSRE) is considered the CNN sensitivity of a meaningful predictive resistivity value.These are expressed as: where m n and mn are the vectorized proper and forecast model values, respectively, and w n is the vectorized weight, which is created to make the domain far from anomalies in the resistivity model that has enormous weight.These are false predictions far from true predictions, which are not preferred, whereas false predictions close to true predictions are usually preferred in connection with the amount of the dataset (n).N is the number of sample pairs.The lower the MSE and RMSRE values, the better they are, especially when they are < 10%.The coefficient of determination for the Pearson correlation coefficient (R 2 ) measures the statistical relationship between the input and output prediction segmentations.The larger the value, the better it is (Jordi et al. 2018), which is defined as: We use mn and mn to denote the average values and to show the analysis for all the observations.

Datasets used in the works
ERT inversion processing employs a CNN technique in which the dataset achieves adequate and warranted diversity within geoelectrical data distributions.As a result, we × 100 %.III: the double side-by-side rectangular bodies (10,674 sample pairs), which directly exemplify the presence of such a free aquifer above an igneous material; Type IV: two declining adjacent rectangular bodies (10,674 sample pairs), which depict an aquifer heavily influenced by an igneous material; and Type V: three rectangular bodies (9243 sample pairs), which further depict an aquifer block above surrounding igneous materials.The anomalous bodies for each type may have different resistivity values; in our dataset, the background resistivity is 100 m, the low resistivity anomaly is 10 m for higher positions, and the high resistivity anomaly is 1000 m for subordinate positions.As an outcome, we had five distinct types of resistivity models, and the corresponding apparent resistivity data were generated using forward modeling.The selection of inversion software for ERT forward modeling is essential to gaining the response of the ERT interpretation because different iterations have different both horizontal and vertical resolutions (Rucker et al. 2010).
The observed field data were collected in the vicinity of dominant clay soils and sandstone rock structures.The field observations were based on a project report for a reservoir leakage investigation at Liyutan Reservoir between latitudes from 24° 20′ 23.9″ to 24° 20′ 31.2″N and longitudes from 120° 46′ 29.4″ to 120° 46′ 53.3″ E. The field survey configuration is deployed using Wenner γ-configuration or CPCP arrays (130 m length and 2 m spacing), which are automated existing arrays from the multichannel geoelectrical device (Szalai et al. 2008).The reason for the chosen configuration is the availability of the choice arrays in the setting device, and this array, among other configurations on the device, is very similar to the Wenner-Schlumberger arrays, notably in terms of sensitivities and depth coverages (Szalai et al. 2014).Meanwhile, this study concentrated on the processing of ERT datasets rather than the discrepancies in configurations utilized by these architectures.In the future, we will begin research to investigate the influences and impacts on intensity, sensitivity, and resolution using the same arrays dealing with synthetic and field datasets within our networks.
We collected 51,644 sample pairs for the field observation and observed approximately 4300 sample pairs every hour for 12 h (from 6 a.m. to 6 p.m. for the observed day).The sample pairs for the field datasets were derived from several observed quantity datasets every hour.We also took the observed datasets at noon explicitly as a land-use validation measurement and then inverted them utilizing EarthImager2D, which has the purpose of commonly representing the resistivity field model.As a result, these outcomes were used to validate datasets within this network.
In this work, we used two field datasets based on in situ precipitation conditions, retrieved on May 13, 2019, and May 19, 2019, respectively.The first condition was that there had been no rainfall for 2 days before and after, so we can refer to the land as dry.The second condition was that there had been pouring rain for 3 days in advance, and it was drizzly when the measurement was collected, so the land became wet.We will be capable of describing and understanding their natural subsurface using our ERT-NET architectures for both two-land and subsurface interpretation.
All of the synthetic and field datasets in the study were randomly divided into training and validation or test sets in an 80:20 (percent) ratio, after which they will have accomplished an appropriate performance on the original model for the synthetic model data and the natural subsurface for the field data.We used Python 3.6 and Tensorflow 1.13.1 to take advantage of CUDA 10.0 and cu-DNN 7.5.We have been running the hardware apparatus for governance and consistency on an i7-5960X @ 3.00 GHz 8 CPU and a GTX 1080Ti*2 GPU, with memory and storage capacities of DDR4 2666 MHZ 8 GB * 8 and SATA 1 TB, respectively.
Four observations were adjusted to confirm the suggested ERT-NET: Observation I: ERT-NET performance analysis for the results of the synthetic apparent resistivity model; Observation 2: a comparison of the resistivity model for synthetic datasets among architecture schemes; Observation 3: network performance analysis for the results of the field inverted apparent resistivity pseudo section; Observation 4: contrasting resistivity inverse results from both land architectures within the target locations.All experiments were carried out on test, validation, or training sets.
Observational noise exists in all measured datasets, synthetic or field.In general, the greater the depth of the anomalous body and the land-use condition, the stronger the impact of noise on our network inversion results.The noise discovered in this research was caused by convolutional block sequences within both networks.We were able to figure out the noise differences of convolutional neural network inversion using previously reported observations from the depth of investigation (DOI) and statistical analysis of performance evaluations.We will also use transfer learning in the future to establish network training stability for anti-noise functionality (Pan and Yang 2010).

Results and discussion
Several of the main practical limitations of ERT traditional deterministic inversion are the computational complexity costs caused by a large number of forward modeling operations for multiple source positions and minima intensity local (Günther and Rücker 2012).All of this encourages the development and application of alternative inversion methods with low computational requirements while remaining robust and efficient.We are now at the start of a new era in computational geosciences, with deep CNN methods capable of taking simulations of geophysical processes to a novel stage of processing (Shahriari et al 2020).Segmentation regularizations are required by the method's common-sense meaning (Badrinarayanan et al 2017).Alternatively, the network is trained on a data set containing realistic models and natural field sections, learning how to reconstruct a similar model that fits the datasets well.The deep CNN-based inversion's main advantage is its high computational efficiency (Dong et al. 2016).The networks used in this study have a  Figure 4 illustrates all of the inversion results for the five model types of the ERT-NET architectures' synthetic resistivity model distribution works that depict our architectures' loss learning curves on the test and training sets when performed on I-(Fig.4a) and U-(Fig.4b) architectures.As the number of epochs increased, both loss learning curves gradually decreased.This indicates how efficiently the overfitted classification quality was implemented during training.When the epochs had been reached 500 times, the loss segmentations were reduced from 0.3% to below 0.2%, and the accuracy (ACC) segmentations were above 90% for both of the evaluation model networks.Eventually, the evaluation performances reveal the training effectiveness of both techniques as well as the ways in which they are appropriate for use in this work (Grandini et al. 2020).The images in Fig. 5 are comparable to the synthetic resistivity model as a ground-truth model, the inverted resistivity section from the inverse process using conventional geophysical software (EarthImager 2D and Res2DInv), and the inverted resistivity pseudo-section formed by the ERT-INET and ERT-UNET architectures, respectively.In general, the synthetic resistivity model types can successfully forecast model attributes and match actual body localization, implying a promising inversion ability.However, focusing on the fourth and fifth columns, the network findings indicated the appropriate physical body resistivity model rather than the geophysical software's inverted resistivity pseudo-section data (the second and third columns).They demonstrated that the network results successfully overcome the software inversion's shortage of the lower physical body location.Nevertheless, the profiles demonstrate the coherence of the placements of the anomaly forms in relation to the resistivity models.As a consequence, while both architectures indicated tangible precision on the synthetic resistivity models, the U-network results are clearer than those of another network.The I-network results, on the other hand, benefit from less time spent on data processing.Fundamentally, the ERT-NET results closely match the majority of the resistivity models.
The issues arise from comparing the DOI (depth of investigation) for vertical positions and validating the resistivity profile models for horizontal positions in the previous observation.Figure 6 needs to be compared with ERT architecture models, ground truth models, and resistivity models (the first column in Fig. 5).In terms of vertical position, the first line is comparable to the DOI; however, the horizontal position for the resistivity profiles expresses the blue line as smoothly as possible in contrasting to the red line, which revealed some surges The second line (type II) revealed the DOI qualities of the U-network were indeed narrower than others, especially for the blue one, or low resistivity; meanwhile, the resistivity graph is depicted as a sinusoidal curve, and the blue line's skewness is slimmer, denoting that the U-architecture compiled data linearly.The resistivity curves of type III exhibit a few similarities in horizontal position among the architectures, but the UNET is better at attaining higher linearity in the datasets.Meanwhile, we noticed from the DOI lines of the results that the INET reproduced much deeper than the ERT-UNET, notably in the top body.Type IV includes resistivity profiles that look like sinusoidal curves, and the I-technique skewness on the right side was broader than on the left, implying that the U-method has updated ERT processing data.The U-network results' DOI (type V) unambiguously revealed the correct placements and palpable relationship to the ground truth for the third rectangular body.The DOI positions for both networks were productive in separating the bodies; however, the U-NET depth analyses were more precise than other techniques.In addition, the UNET resistivity graph shows a significantly different profile vertically from another (Dumoulin and Visin 2016).In conclusion, all of the ERT-NET resistivity findings for the synthetic resistivity models, especially This field observation demonstrates the performance of the suggested ERT structures, as seen in Fig. 7.In terms of the graph, we choose all of the network results that correspond to the misfit quality of locations and dimensions of resistivity patterns; therefore, resistivity levels are the most essential parameters during learning, regardless in the test or training sets (Tan et al. 2019).The graphs (Fig. 7a  was less than 0.30, and continuing, while the ACC segmentation must have been much higher than 80%, and the sounds tended to remain steady (Pires de Lima et al 2019).To summarize, the learning curves for both learning curves are similar; as a result, the learning can be convinced for use in field observations of ERT processing data.The field sections were based on land conditions.There are dry-land and wet-land conditions.Figure 8 portrays borehole sections observed in the field at which four boreholes were drilled at depths of 40 m, 60 m, 80 m, and 100 m.Boreholes had been examined after there had been no rain in the areas for about a week.We observed that the dominating structures in situ are clay soils (10-100 m) and sand rocks (10-1000 m).As a result, the geological formations are sandy clay (40-35 m), silty sand (40-80 m), silty clay (25-35 m), and clayey (10-25 m).Water channels formed between 100 and 200 m beneath the surface.As a consequence of the dominance of flowing water, land formations degrade quickly, particularly at shallower depths (Chen et al. 2015).
Figure 9 presents a pseudo-section of the ERT inversion results to demonstrate the impact of rainfall on field observations of geological structures with the objective to represent the two experimental land conditions.As mentioned in the previous section, in drylands (Fig. 9a) and wetlands (Fig. 9d), inverted resistivity was assessed using Earth Imager 2D.The results of the inverted resistivity inversion have divergent DOI positions and were directly superimposed with boreholes.Figures 9b and c depict the outcomes of the dryland inversion.Based on drill sections with the existing clayey structure on the bottom surface, they discovered that the UNET inverted resistivity section is substantially more accurate.Meanwhile, ERT-INET data suggested that silty sand predominated near the subsoil's top.The inverted images of the wetland between INET (Fig. 9e) and UNET (Fig. 9f) might indicate whether reservoir leakage occurs as a result of heavy or continuous rainfall.As a result of both designs demonstrating acceptable efficiency and inversion results for the appropriate ERT interpretation.Regardless, the DOI distributions show that the U-architecture inversion result is marginally superior to another architecture inversion result.The water channel in these figures can show spreading rainfall-water flow from the right to the left and down to satisfy the subsurface, inferring that the silty clay and clayey soil are easily saving the water and the subsurface has an impact with lower resistivity.The ERT-NET architectures for field investigation achieved satisfactory structured prediction segmentation field section performance, as shown in Table 3.The MSE and RSMSRE scores for all outputs, including the Pearson evaluation, met their requirements (R 2 ).Both architectures scored over 97%, indicating that the results are satisfactory and reliable (Studer et al 2011).As an outcome, the regression profile can be used to appropriately interpret the subsurface resistivity pseudo-section and depict the origin inversion.Meanwhile, the ERT-UNET network's performance enhancement has proved the network's robustness by obtaining smooth constraints and depth weighting (Luo et al. 2016).Notwithstanding, owing to the stability and intensity of portraying subsurface, these ERT-NET results were not as satisfactory as the conventional software results; consequently, this research has the potential to be optimized and expanded in the future.
The precision and accuracy of both the inversion yields and the ERT-INET can be deduced for preliminary ERT interpretation, whereas the ERT-UNET can be employed for advanced ERT interpretation.Regrettably, the ERT-NET can only be utilized as an alternative approach to ERT interpretations and is unable to replace geophysical software because the ERT-NET requires substantially more computational time, sophisticated algorithm steps, and also numerous datasets for geophysical ERT processing data (Osinowo and Falufosi 2018).Consequently, synthetic models must be developed more complexly to mimic natural phenomena closely.Following that, we confirmed that the study area had a possibility of Liyutan DAM reservoir leakage during heavy rain and continuous rainfall; thus, based on the investigated results, the land conditions should be improved with the soil reinforcement method (Archie 2003), and the best time to do so should be during the dry season.

Conclusions
We created a procedure for processing ERT data in the ERT-NET architecture for a unique CNN-based technique.This method is unique for resolving subsurface resistivity inversion while doing electrical resistivity imaging.Our network is made up of two parts: ERT-INET, a fully linked network, and ERT-UNET, a completely convolutional network.The ambiguous interpretations occurred when employing the inverted resistivity section of geophysical software, notably for the lower physical body.To address this issue, the I-network inversion result demonstrates a few further improvements in pixel-wise prediction segmentation, despite the slight lack of body.Nonetheless, the U-network produced excellent inversion results for all models evaluated.The comparative datasets, which contain around 50,000 sample pairs, are comparable to either synthetic resistivity models or field observation data.Because of structured prediction segmentation, the U-architecture performs well when applied to the synthetic resistivity model and field resistivity data; however, this network takes significantly longer to run the algorithm.Meanwhile, the I-architecture appeared to have the advantage of quicker algorithm operation and results, leading to an effective outcome, despite a few disparities in vertical and horizontal positions.Finally, ERT-NET architectures are proposed as an alternative technique for ERT interpretation, and the networks should always be managed to develop and reinforce so that they can challenge the processing of geophysical ERT approaches.Nonetheless, the techniques should not be utilized to substitute or move the fundamental electrical resistivity tomography interpretation from geophysical advanced software.

Fig. 1
Fig. 1 Task explanation.The distinct resistivity patterns in the inverted resistivity section were generated by recognized data in the synthetic resistivity model, and the matching patterns show plausible physical body correlations involving resistivity bodies

Fig. 2
Fig.2Two pairs of synthetic resistivity models and inverted resistivity pseudo-sections.In the vertical position, the two models have the same size bodies but opposing resistivity values.The response match-

Fig. 3
Fig. 3 Proposed ERT-NET: a top panel is fully connected network architecture, which is ERT-INET with fully connected layers at the end, and the output represents pixel-wise prediction segmentation.All while, b the bottom panel is a deep convolution network architecture that is addressed ERT-UNET, displaying some convolutional layers till the reaching flattened block toward segmentation of structured prediction as the output created the ERT-NET dataset, which includes 53,507 sample pairs.The sample pair for the synthetic model referred to several observed quantity datasets for each single-size variety.Each pair of samples contains one resistivity model (with spatial size[30 × 130]) and one model that deals with apparent resistivity image data[30 × 130].The resistivity models are created with real 2-D ERT schemes and executed with the Wenner-Schlumberger configuration, which has the required vertical and horizontal resolution for this observation.We produced a composite dataset by pre-defining a few anomalous bodies with vastly differing resistivity values and incorporating them in different positions.Table1depicts the schematic and parameters of anomalous bodies.The resistivity anomalous bodies are divided into five sections, which are as follows: Type I: the lower resistivity in a single rectangular body (12,242 sample pairs), representing the occurrence of a free aquifer in the subsurface; Type II: a trapped aquifer close to the igneous material explained by double up-and-down rectangular bodies (10,674 sample pairs); Type

Fig. 4
Fig. 4 ERT-NET loss learning curves for composite apparent resistivity datasets under different test and training learning circumstances.a ERT-INET and b ERT-UNET

Fig. 5
Fig. 5The inversion results of the synthetic resistivity model and the inverted resistivity section data (from left to right).The resistivity model (first column) is the ground-truth model, the inverted resistivity pseudo-section results from EarthImager2D inversion (second col-

Fig. 6
Fig. 6 Vertical and horizontal positions of the synthetic resistivity models are indicated by depth comparisons using DOI (dotted line) between the ERT-INET (first column) and ERT-UNET (second column), as well as the truncation line of the resistivity graphs shown

Fig. 7
Fig. 7 ERT-NET loss learning curves for field observations of ERT geophysical processing datasets under various tests and training learning requirements.a ERT-INET and b) ERT-UNET

Fig. 8
Fig. 8 Observations of borehole sections in the field.Sandy clay, silty sand, silty clay, and clayey are geological structures.A water channel runs between 110 and 120 m from the top surface Fig. 9 The resistivity pseudo-section of the inverted field observation results: a EarthImager2D, b ERT-INET, and c ERT-UNET describing the dry-land condition, d EarthImager2D, e ERT-INET, and f ERT-

Table 1
Schematic and parameters of the synthetic resistivity models

Table 2
Evaluation of pixel-wise prediction segmentation for synthetic resistivity learning.(↑) demonstrates that the larger value achieves better performance, while still (↓) proves that the smaller values achieve better results

Table 3
Evaluation of structured prediction segmentation for field resistivity learning comparison.The (↑) suggests that higher values result in better performance, whereas (↓) indicates that smaller values result in better results