The results of the simultaneous inversions can be seen in Fig. 3, 4, 5 and 6. In all sessions there is a predominance of low resistivity values, which suggests a strong influence of conductive materials in the composition of the landfill, probably associated with the leachate material from the decomposition of organic waste from the landfill.
All sessions have a large zone of low resistivity in the body of the landfill, between 5 to 50 Ω.m. This zone possibly corresponds to the waste package deposited over the years. Above this conductive zone, it is possible to observe, in the first meters of the sessions, an irregular layer of higher resistivity, between 40 to 180 Ω.m. The layer in question may correspond to the coverage of construction waste (CCW), deposited in more recent years of operation of the landfill. At higher depths, the sections have higher resistivity values in relation to the intermediate conductive portion of the landfill, between 100 and 200 Ω.m.
This can be associated with the natural geological substrate existing in the subsurface. The transition from low resistivity and higher resistivity values occurs gradually. The resistivity values calculated for the latosol in subsurface areas were much lower than the values expected for the latosol in the region (Cavalcanti et al., 2014; Seimetz et al., 2013). The reason for this fact may be related to the infiltration of the leachate material resulting from the decomposition of organic residues in the subsoil latosol.
When analyzing the images of the 4 arrays separately, Guedes et al. (2020) states that the DD arrangement is more coherent with the direct information extracted from the drillholes, and that the WN and WS arrangements highlighted the horizontal characteristic of the rock substrate in depth, although they do not correspond satisfactorily to the ground level in most of the lines. In the same paper, the authors point out that the PD sessions had the least correspondence with the information obtained from the drillholes.
The L1 sessions were correlated with the drill holes PG1, PG2, SP-04 at 2, 10 and 30 meters of distance between the line, respectively, and can be seen in Fig. 3. By correlating the resistivity values and the information through the holes, the most representative model of the landfill, which best defines the base of the waste package and that possesses the least absolute error, is the model generated by the simultaneous inversion WN-WS-DD, which in turn has a value of approximately 30 Ω.m to the base of the waste package.
In view of the low correspondence of the models after inversion with the PD arrangement with the expected configuration of the landfill subsurface, when observing the L1 simultaneous inversions, it is possible to notice that the images obtained with the simultaneou inversion that present data from the PD arrangement also had little correspondence with the drillhole information. The models obtained with the WN and WS arrangements together did not show major differences.
The L2 sessions (Fig. 4) were not correlated with any of the holes, due to the long distance between them. The sessions that most resemble the structural configuration of the landfill, that is, three striking horizontal layers, were the inversions with data from DD-PD. However, the absolute error associated with the model was greater in relation to the measurements of the other inversions.
The L3 sessions were correlated with the SP-07 drillhole, approximately 75 meters away from the line, and can be seen in Fig. 5. When correlating the resistivity values and the direct information of the holes, the image generated by the arrangement DD obtained the least correspondence with the base of the waste package, while the WN and WS arrangements show the greatest similarity. However, when performing the simultaneous inversion of the arrangements, the model generated by the simultaneous inversion WN-DD and WN-DD-PD presented itself as the most coherent, due to the correspondence with the drillhole and greater lateral investigation of the surface of the base of the waste package. The approximate apparent resistivity value for the waste package base is of 40 Ω.m.
The L4 sessions were correlated with the SP-07 drillhole, about 150 meters from the line, and can be seen in Fig. 6. The models generated by the DD, WN and WS arrays tend to tilt to the most resistive layer, and the base of the waste package, according to the direct information of the drillhole, points to lower values of resistivity (approximately 10 Ω.m). When these arrays are concatenated with each other, the slope pattern of the resistive layer and the value of resistivities in general are maintained. In contrast, the sessions after inversion with data from the PD arrangement predominate the pattern of more horizontal layers and higher resistivity values for the waste package base (above 150 Ω.m).
Comparison and validation of models
After analyzing the resistivity profiles of the ETR along the positioning of the drillholes, it was possible to observe the numerical behavior of the variation of the resistivity values in depth. In addition, for each multiple array, the resistivity contrast in the intervals of 5 meters above and below the CCW and Waste package (top of the waste package), and waste and soil (bottom of the waste package) were analyzed. The resistivity profiles of the resistivity model and the numerical model can be seen in Fig. 7.
Through statistical analysis, a ranking of the arrays combined with the best values of 𝛽1 and Range was created for all resistivity profiles. The combination of WN-PD, WN-DD-PD, DD-PD arrays obtained the best results, respectively (Fig. 7b). When observing the resistivity sessions of the WN-PD configuration as a whole and not just where the drillhole is located, it is possible to state that the sessions present the expected horizontality for the landfill layers, and the depth of investigation achieved by combining the WN-DD arrangement was greater in relation to the WN and DD arrangements separately. The absolute error between the observed model and the ETR decreased in relation to the DD arrangement, however, it remains one of the combinations of the arrangement with the most errors. Despite this, the images of the simultaneous inversion of WN-DD were chosen to generate the thickness model of the ACJC residue layer, considering the several positive factors that point out the combination of the WN-DD arrangement as adequate.
According to the ranking of the resistivity profile of the numerical analysis, the WN-DD, WN-DD-PD configurations also obtained the greatest variations in the waste package limits, which reaffirms the choice of the WN-DD arrangement for the elaboration of the waste thickness model, and validates the statistical analysis previously performed.
Waste thickness model
In Line 1, the approximate resistivity value used to extract the elevation from the base of the waste layer was 30 Ω.m. In L3 and L4, the surface of approximate values corresponded to 20 and 10 Ω.m, respectively. Bearing in mind that L2 does not present direct drillhole information, the values extracted from the profile correspond to the average of the resistivity values extracted from the other lines (20 Ω.m). The elevation values for the top of the waste package were extracted from the resistivity contrast in the initial meters of the sessions and based on direct information from PG1 and PG2. The lines of approximate resistivity values used for interpolation of the base and top of the waste package can be seen in Fig. 8a.
The interpolated model of the waste thickness has a greater thickness in the center of the waste package and decreases towards the limits of the investigated area. The layer of landfilled waste can reach up to a depth of 65 meters. In addition, it is estimated that the approximate volume of landfilled waste is approximately 23,340,429 m³, based on the cubic model generated.
The percentage error histogram of the top and bottom grids of the generated model is relatively symmetrical with a percentage average of approximately 0 and with little dispersion of the values, which points to the accuracy and precision of the interpolated grids. The statistical characteristics of Pearson's coefficient and RMSE for the grids have values close to 1 and 3 meters respectively, which indicates a strong direct correlation between the real and estimated values of the models, and a good accuracy of the estimated results. The thickness model of the waste layer, as well as the statistical characteristics of parameterization and validation of the interpolation of the top and bottom of the layer, can be seen in Fig. 8.