Assessment of three mixed arrays dataset for subsurface cavities detection using resistivity tomography as inferred from numerical modelling

doi:10.21203/rs.3.rs-3229144/v1

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Assessment of three mixed arrays dataset for subsurface cavities detection using resistivity tomography as inferred from numerical modelling

https://doi.org/10.21203/rs.3.rs-3229144/v1

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A three mixed arrays dataset have been evaluated in term of their capability of detectability and enhanced the resolution of the resolved images obtained by the electrical resistivity tomography (ERT) technique. This study is based on numerical modelling for studying the detection of the subsurface cavities, where four cavity models were generated to simulate air-filled cavities embedded in limestone sets at different depths. The synthetic data were generated for the cavity models using three individual arrays. These arrays are dipole-dipole (DD), pole-dipole (PD), and Wenner- Schlumberger (W-S). Then the apparent resistivity data obtained from two different arrays were merged to form a high-resolution single model. Based on the obtained results, a combination between dipole-dipole- Wenner- Schlumberger (DD + WS) yields the highest resolution image regarding cavity detection among the other type of mixed arrays (e.g. pole-dipole, and Wenner- Schlumberger (PD + WS) or dipole-dipole and pole-dipole (DD + PD)). The inverted resistivity sections obtained from (DD and WS) arrays resolved the cavity models more accurately than other types of composite datasets or individual array data, as well as a significant resolution enhancement with depth, was observed. The recovered model’s parameters (e.g. resistivity and geometry) obtained from DD and WS composite data shows closer parameters to the true actual model.

Mixed arrays

Individual arrays

Numerical modelling

cavity detection

Comparison between three traditional arrays and mixed array datasets in delineation of the geometry of subsurface cavities using numerical simulation was made.
The resolution of the obtained resistivity model can be enhanced by using mixed array datasets.
The numerical simulations are considered an effective tool for predicting several scenarios for studying the electrical response of any subsurface structures.

The electrical resistivity tomography (ERT) technique has been developed rapidly and become a popular option for shallow subsurface investigations. Today, this technique has a wide range of applications, such as hydrological [1–3] ,environmental [4, 5], Structural mapping [6–8], geohazard [9, 10] investigations. Detection of subsurface cavities in Krastic rocks is considered one of the important applications of the ERT technique in the field of geohazard assessment. Many researchers have used the ERT technique for cavities identification [11–13]. However, accurate mapping of subsurface geological structures (e.g cavities) extremely depends on a proper selection of array for carrying the field ERT survey. There are many different types of electrode arrays used in resistivity surveys but the most commonly used ones are the Wenner (W), Wenner-Schlumberger (W-S), Dipole-Dipole (DD), Pole-Dipole (PD), Pole-Pole (PP) arrays [14–16]. Each array has particular merits for imagining a specific geological structure and thus is depending on a different factors such as depth of investigation, resolution, data coverage, and sensitivity of noise level [17].

Many authors have distinguished and compared the electrode arrays in order to determine their ability to detect different geological features such as cavities, faults, dykes, layers, and so on [18–21]. A lot of these studies depend on a numerical modelling approach. The construction of synthetic models for resistivity imaging studies is considered an effective tool for understanding the optimal resistivity response for a shallow target [12]. In this manner, [20] made a comparison between ten electrode arrays using five synthetic models. They reported that the DD array gave a better-resolution image than others. [22] has studied the response of three different electrode arrays (W, W-S, and DD) on resolving subsurface cavities using the numerical modelling of resistivity imagine technique. He concluded that the DD array yields a better resolution than W and WS arrays. [23] investigated the uncertainty of resistivity image survey on the detection of subsurface cavities. They revealed that the DD array is the best for cavity surveys and the PP gives the lower resolution for cavity anomaly while, PD and WS arrays can be considered adequate for cavity surveys.

Despite the efficiency of resistivity imagines survey in many applications, the (ERT) method often shows an exponential decrease in model resolution and resolving power with increasing the depth of investigation [24]. Decreasing the inter-electrode spacing of an array can increase the resolution. However, using a small electrode spacing will decrease the investigation depth [25]. To overcome this problem, two different array datasets can be merged to form one single composite model with high resolution compared to the use of individual array data. The advantages that stand behind using composite datasets are increasing the data point, increasing data levels, and overlapping data levels. Consequently, a better resolution of a particular model can be obtained [26].

The data obtained from the ERT survey using different electrode arrays to map a particular geological structure tend to obtain different resistivity models along the same profile. Thus due to the difference in data coverage, number of data points, depth of investigation, and data levels of each used array. Consequently, if the data of any two different arrays were merged to form composite datasets, it is expected to obtain a variance response of resistivity model to the subsurface target depending on which of arrays data type were merged.

Therefore, the main goal of the present study is to assess the performance of mixed array datasets technique in cavities detection using a numerical modelling approach in order to define the optimum arrays data types to be mixed for enhance the resolution of the obtained resistivity model with increased depth. In this work, three common arrays (DD, PD, and WS) were used to generate composite datasets along synthetic cavity models. Three possible combinations can be obtained from merging the data of the three above-mentioned arrays. The first one is the dipole-dipole and pole-dipole datasets (DD + PD), the second is pole-dipole and Wenner-Schlumberger (PD + WS), whereas the third one is a combination between dipole-dipole and Wenner-Schlumberger (DD + WS). The different composite datasets were modelled, and the obtained inverted resistivity section of each one was examined in terms of the resolution and ability power in the detection of the cavity models.

The ERT numerical modelling approach is used to predict the resistivity response of a well Known given model. It gives insight into the accuracy of the ERT method for resolving different scenarios of geological structures before a real costly field or laboratory investigations are carried out [27, 28]. In the present study, the ERT numerical modelling was used to examine the resistivity imaging accuracy for subsurface cavities resolving using mixed array datasets. The following procedures of the present work were achieved through three steps: forward modelling of the synthetic cavity models using three common individual arrays (DD, PD and WS), merging the synthetic data of the selected resistivity arrays and inverse modelling of both individual and mixed arrays synthetic data to reconstruct true resistivity distribution of the subsurface. Figure 1 illustrates a typical flow chart of the steps methodology which were employed in the current work. A detailed description of the steps methodology can be presented as follows:

2.1 Forward modelling

In the present study, four synthetic models were created to simulate air-filled cavities in a homogenous limestone as a host medium (Fig. 2). These models are more or less similar to those used by [23]. The model resistivity values were chosen to be 10,000 Ω.m for the air-filed cavities and 1000 Ω.m for the limestone [29, 12]. The air-filled cavity models have the same dimensions (16 m length x 4 m wide) which are located at different four depth levels coded as L1 (4.5 m), L2 (6.5 m), L3 (8.5 m), and L4 (10.5 m). For easy description, the cavity models were classified as shallow (L1 and L2), intermediate (L3) and deep (L4) based on the depth levels. The synthetic potential differences data for the selected three arrays (DD, PD, and WS) were calculated for each model using the RES2DMOD software [30]. The calculation of the potential differences data is based on the finite difference method [31] which determines the potentials at each node of the rectangular resistivity model discretization mesh. 51 electrodes with a 2-meter electrode spacing were used for all the created synthetic models.

2.2 Data merging

The performance of a resistivity survey with a different electrode array for a constant profile length yield to produce a different depth of investigations, different number of data points, and different number of data levels. For example, measurements were executed by using dipole-dipole and pole-dipole arrays with inter-electrode spacing equal to 2 m and the measurements were repeated along the survey line for n values equal to 1, 2, and 3. The number of datum points produced by such measurement will be 141 and 144 for dipole-dipole and pole-dipole arrays respectively. On the other hand, the median depth of investigation for dipole-dipole is about 0.83, 1.394, and 1.924 meters for n values of 1, 2, and 3 respectively. While the median depth of investigation for pole-dipole for the same variance of n values are about 1.038, 1.85, and 2.6 [32]. If the data of these two arrays were used, the data sets will have 285 data points and six data levels. This results in a pseudo section with overlapping data levels containing a higher number of data points and data levels, consequently the interpolation between data points can be reduced by reducing the spacing between data levels. The present study involved a merging of the calculated apparent resistivity data for every two individual arrays to produce composite datasets forming a single high-resolution resistivity model. As a result, three possible combinations of composite datasets can be obtained as follow: DD-PD, DD-WS, and PD-WS composite datasets. The total number of data points and data levels for each individual and composite arrays used in the present study are shown in Table 1.

Table 1

Number of data points and data levels for both individual and mixed arrays
Array	Number of data points	Number of data levels
DD	1283	45
PD	930	24
WS	978	35
DD-PD	2213	69
DD-WS	2261	80
PD-WS	1908	59

2.3 Inverse modelling

The synthetically apparent resistivity data were inverted for both the individual array types and the mixed one to obtain model parameters such as the true resistivity distribution of the subsurface. The inversion modelling was carried out using RES2DINV software [24]. The inversion process using this software can be accomplished through two types of inversion routines. The first one is the L1-norm optimization, otherwise called blocky or robust constrain inversion technique [33]. The robust constraint inversion technique attempts to minimize the absolute difference (Abs.) between the measured and the calculated apparent resistivity values. It can be a good choice when geological discontinuities are expected since it produces resistivity models characterized by sharp boundaries across the different resistivity layers. On the other hand, the second inversion routine is the L2- norm optimization (Gauss-Newton smoothness-constrained least-squares method) [34, 35]. The L2- norm optimization attempts to minimize the square of difference (RMS) between the measured and calculated apparent resistivity values [33]. In the present study, the robust inversion routine was chosen to carry out the inverse modelling process for all data to avoid the Smearing effect on the boundaries [33]. Table 2 displays the parameters used for the inversion process.

Table 2

The used parameters during the inversion process
Inversion parameters	Values
Initial damping factor Minimum damping factor Number of iterations Increase of the damping factor with depth Robust data inversion constraint is used with the cut off factor Robust model inversion constraint is used with the cut off factor Number of nodes between adjacent electrodes Extended model Reduce the effect of side blocks Type of mesh	0.25 0.015 5 1.05 0.05 0.005 4 Used None Normal

The inverted sections obtained from the inversion process for the three selected individual arrays are shown in Fig. 3, Fig. 4, and Fig. 5 for DD, PD, and WS respectively. These figures reflect that all the above mention arrays can resolve the cavity models more efficiently for the shallower depth level than the deeper one and the resolution of the inverted image decrease as the cavity depth increase because the measurement sensitivity is decreasing with survey depth [17]. The cavity model (L1) located at 4.5 m depth (Fig. 2a) was precisely recovered by the DD, PD, and WS arrays, as shown in Figs. 3a, 4a, and 5a. The top boundary of the cavity anomaly has coincided with the actual cavity model location however, the bottom boundary is misplaced and extended down the actual cavity model. The cavity model (L2) located at 6.5 m depth (Fig. 2b) was resolved by the three array types as a high resistivity anomaly zone surrounded by a lower resistivity background with a noticeable exaggeration in the anomaly size compared with the actual cavity model location (Fig. 3b, 4b, and 5b). There is a misplaced of the top and bottom boundaries of a model anomaly in the range of 1-2.5 m. The inverted resistivity sections for the cavity model (L3) were poorly resolved by all the selected three individual arrays (Fig. 3c, 4c, and 5c). The cavity anomalies zone were highly exaggerated in their size compared with the actual cavity model location and size. At a depth of 10.5 m the cavity models (L4) recovered poorly by both the DD and PD arrays, where the bottom of the resistivity anomaly zone extended down to the end of the inverted sections depth and the top boundaries of cavity anomaly misplaced by 2–4 m compared with the actual location of the modelled cavity (Fig. 3d, 4d,). On the other hand, the inverted resistivity section with the WS array (Fig. 5d) failed to reconstruct the deep cavity model.

Regarding the resolution of the obtained inverted resistivity section of the modelled cavities, the DD array shows a better-resolution image. In contrast, the WS array yields the lower resolution one. While the PD array produces a good resolution but is slightly lower than the DD array. By comparing the inverted resistivity anomaly of the modelled cavities obtained by the individual arrays with the true resistivity of the actual model as illustrated in Table 3, it is observed that the DD array reconstructed the cavity’s resistivity is better than PD and WS arrays. On the other hand, the WS array reconstructed the lowest cavity’s resistivity values. For a better comparison, the same color scale for resistivity values was used (Fig. 3, 4, and 5).

Table 3

Values of the inverted resistivity for synthetic cavity models using individual and mixed array
Models	True model resistivity (Ω·m)	Inverted maximum resistivity values (Ω·m)
Models	True model resistivity (Ω·m)	DD	PD	WS	DD-WS	PD-WS	DD-PD
Cavity model (L1)	10000	8097	8097	8097	8097	8097	8097
Cavity model (L2)	10000	5586	5586	4640	8097	8097	5586
Cavity model (L3)	10000	3853	3200	2208	6726	4640	4640
Cavity model (L4)	10000	2658	2208	1523	4640	2658	2208

The proposed composite datasets method of the three individual resistivity arrays was tested through the forward modelling approach. Firstly, the apparent resistivity data sets were calculated for each array (DD, PD, and WS) then, a composite dataset can be obtained by merging the calculated apparent resistivity data for every two arrays. As a result, three possible combinations of composite datasets can be obtained as follow: DD-PD, DD-WS, and PD-WS. Each one of these datasets is then used to generate the inverted sections as shown in Figs. 6 through 8.

The mixed array datasets of DD-WS (Fig. 6) show the best resolution inverted image for the cavity models compared with DD-PD and PD-WS composite datasets, where the actual shape and location for most of the cavity models are accurately resolved. Figures 6a and 6b show a good match between the inverted anomalies' location and shape with the true cavity models, where the top surface of inverted anomalies coincides with the actual top boundary of the actual cavity model, and the bottom boundary of the anomalies was overestimated only with 1 m relative to the true location of the actual cavity. The inverted resistivity model for the intermediate cavity (L3) located at 8.5 m depth (Fig. 6c) shows a good correlation with the actual model. The top and bottom resistivity anomaly was overestimated by about 1.3 m compared to the actual cavity location. Comparing the inverted resistivity model of composite datasets of DD-WS for the intermediate cavity (L3) with inverted resistivity sections of the DD and WS arrays (Fig. 3c and Fig. 5c) one can notice that, the anomaly cavity obtained by DD and WS is highly exaggerated and there are a misplaced of the top and bottom anomaly boundaries between 3–6 m. On the other hand, the inverted resistivity anomaly for the intermediate cavity (L3) shows maximum values of 3853 Ω.m, 2208 Ω.m, and 6726 Ω.m obtained by DD, WS, and composite DD-WS datasets respectively. Although the true resistivity of the cavity model is 10,000 Ω.m, the composite DD-WS datasets show a closer inverted resistivity value to the true model’s resistivity.

The inverted model of the deep cavity (L4) located at 10.5 m depth for the composite DD-WS datasets (Fig. 6d) shows a moderate resolution in regard to the actual cavity model. Although, it still does the best compared to other composite data sets (i.e, DD-PD, PD-WS) and the individual selected arrays. The inverted model of the composite DD-WS datasets (Fig. 6d) shows a maximum resistivity anomaly of about 4640 Ω.m, while maximum resistivity values of about 2208 Ω.m and 2658 Ω.m were reconstructed by DD-PD and PD-WS composite datasets respectively. Furthermore, the composite DD-WS datasets inverted model (Fig. 6d) shows adequate correlation regards to the location of the cavity anomaly related to the actual model, where the upper boundary of the anomaly shifted upward by 2 m and the lower boundary of the anomaly shifted downward by only 1 m.

The inverted models of the composite datasets of DD-PD ( Fig. 7) show the lowest resolution image for the cavity models recovered since neither the shape nor the location was resolved well. On the other hand, the inverted models of the composite datasets of PD -WS (Fig. 8) show a moderate resolution in between the inverted models obtained by DD-WS and DD-PD. It is clear that the use of composite datasets of DD and WS arrays could be given optimal information regarding cavity detection rather than using one single array or using composite datasets of DD-PD and PD –WS, since [36] had earlier mention that, the reliability of the resistivity image section obtained by an array restricted by getting maximum anomaly information.

Many previous studies compared the ability of different individual electrode arrays for subsurface cavity detection [13, 22, 23]. Some of these studies reported that the WS array can give a slightly better resolution capacity than DD for cavity detection [13]. On the other hand, the DD array has a priority in detecting subsurface cavities more accurately than the other arrays as reported by the literature [22, 23]. Unlike these previous studies, the present study revealed that the composited datasets between the DD array and the WS array provided more accurate detection of subsurface cavities than using the DD array or the WS array individually.

The outcome of this paper shows that the resolution of the subsurface geological structures (i.g cavity) can be improved by using mixed datasets of two arrays. The composite datasets improve the vertical resolution of the inverted sections by increasing the number of datum points as well as the number of data levels. This can significantly reduce the ambiguity and misinterpretation of the exponential decrease of resistivity resolution with depth. Also, the results of the present study illustrate the usefulness of the numerical modelling approach for testing the efficiency of resistivity images with different types of arrays and/or mixed arrays for resolving and obtaining optimal information about any subsurface structures before the actual field investigation.

Synthetic resistivity models were adopted to simulate subsurface cavities located at various depths in order to investigate the performance of composite datasets technique for cavity studies. The inverted images of the synthetic resistivity models using the individual arrays (DD, PD, and WS) show their capability in cavity detection especially when the cavities were located at shallow depths, but the resolution and detectability decrease rapidly with increasing depth. In contrast, by using the composite datasets the resolution and detectability were improved and the reliability of the inverted image was increased. The results show that a composite dataset from dipole-dipole and Wenner-Shlumberger arrays are better than using mixed data from pole-dipole and Wenner-Shlumberger or dipole-dipole and pole-dipole arrays. The composite datasets from the dipole-dipole and Wenner-Shlumberger arrays yield a single resistivity model, bringing out maximum information about the subsurface cavities. This study demonstrated the usefulness of the composite datasets approaches in the enhancement of the resolution of the 2D resistivity image model. So, this approach is recommended for cavity studies although the time and effort can be twice but the reliability of the obtained results is better.

Data availability

The datasets generated during the current study are available from the corresponding author on reasonable request.

Competing interests: The author declare that There are no known competing interests regarding this work.

Funding: No funding was received for conducting this study.

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Assessment of three mixed arrays dataset for subsurface cavities detection using resistivity tomography as inferred from numerical modelling

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Abstract

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Article Highlights

1 Introduction

2 Methodology

2.1 Forward modelling

2.2 Data merging

2.3 Inverse modelling

3 Results and discussion

4 Conclusions

Declarations

References

Additional Declarations

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