Giorgio De Donno1*, Michele Cercato1 and Davide Melegari1 present an application of a global inversion approach based on the Very Fast Simulated Annealing (VFSA) algorithm to ERT and IP datasets acquired on a municipal solid waste (MSW) landfill located in Central Italy.

Abstract

Electrical Resistivity Tomography (ERT) and induced polarisation (IP) methods are widely employed in the characterisation of urban landfills due to their sensitivity to subsurface moisture and electrochemical properties of waste. Traditional local inversion techniques, typically based on smoothness-constrained Occamtype methods, can fail to resolve the high spatial variability of leachate accumulation areas. Additionally, these techniques do not provide an assessment of the uncertainty associated with the detection of accumulation areas, which is pivotal for informing quantitatively the landfill management. In this study, we apply a global inversion approach based on the Very Fast Simulated Annealing (VFSA) algorithm to ERT and IP datasets acquired on a municipal solid waste (MSW) landfill located in Central Italy. This site, characterised by a steep slope and high risk of leachate-induced instability, is currently monitored with time along multiple profiles. The global inversion process was implemented on a selected line where also piezometric level logged in wells are available. Posterior model ensembles were also analysed to derive uncertainty estimates, and petrophysical transformations were applied to extract water content and Cation Exchange Capacity (CEC) from the geoelectrical parameters. The results demonstrate the effectiveness of the VFSA method in detecting highly variable leachate zones, as confirmed by the good agreement with leachate levels logged in wells. The uncertainty assessment highlighting areas of higher and lower reliability of the geophysical model can further support the landfill monitoring, with implications for risk assessment and long-term management.

Introduction

Urban waste landfills present complex, dynamic subsurface environments characterised by heterogeneity in both composition and hydro-chemical conditions. Among the key concerns in landfill management is the formation and accumulation of leachate, a liquid produced by the percolation of water through solid waste (Mukherjee et al., 2015). A leachate flow outside the landfill site may cause serious environmental issues to groundwater, while in the case of landfills located on slopes leachate accumulation can

1’Sapienza’ University of Rome

* Corresponding author, E-mail: giorgio.dedonno@uniroma1.it

DOI: 10.3997/1365-2397.fb2025063 also trigger instability. Therefore, in the latter case, detecting and monitoring the accumulation zones is critical not only for environmental protection but also for geotechnical risk mitigation.

Geophysical methods have proven effective in supporting non-invasive characterisation of Municipal Solid Waste (MSW) landfills. Electrical Resistivity Tomography (ERT) and induced polarisation (IP) techniques have been extensively applied due to their sensitivity to changes in moisture content, salinity, and electrochemical properties of the waste mass (see De Donno et al., 2024 for a review). ERT provides information on the bulk resistivity of the subsurface, which mainly correlates with saturation levels and waste composition, while the IP effect is primarily caused by microbial activity in the waste mass (e.g. Flores-Orozco et al., 2020). These attributes make ERT and IP complementary tools in the identification of zones saturated by leachate.

Conventionally, inversion of geoelectrical data has been conducted using local and deterministic approaches employing Occam’s-like smoothness-constrained inversion algorithms (de Groot-Hedlin and Constable, 1990). While computationally efficient, such methods may obscure sharp boundaries or localised anomalies such as leachate pockets, as well as the solution may remain trapped in local minima. Additionally, they fail to provide a statistical assessment of uncertainty associated with the inverted models, which can be of paramount importance in heterogeneous media such as landfills.

In contrast, global inversion techniques, exploring the entire model space offer a promising alternative, even though they require a higher computational effort. Among the global inversion algorithm, the Very Fast Simulated Annealing (VFSA) algorithm (Ingber, 1989) has gained attention due to its capability to navigate high-dimensional and non-linear inverse problems (e.g. Cercato, 2011). Unlike Monte-Carlo or genetic algorithms, VFSA is a cost-effective algorithm, balancing the capability to properly sample the whole model space and the speed of convergence (Sen and Stoffa, 2013). Despite its potential, VFSA and other global inversion methods have had limited practical application in ERT/IP data inversion due to the high computational demand required by the ERT/IP forward solver and the large number of evaluations needed to achieve convergence. However, recent works have begun to incorporate probabilistic frameworks and ensemble analysis to assess model uncertainty, further enhancing the interpretative power of global inversion schemes (e.g. Aleardi et al., 2021; Isunza Manrique et al., 2023).

This study builds on these developments by applying a global VFSA-based inversion algorithm to jointly invert ERT and IP data acquired on a MSW landfill located in Central Italy. The site, situated on a steep slope, is subject to potential leachate-induced instability, making accurate and reliable detection of leachate pockets a priority for both environmental monitoring and structural safety. The survey targeted a specific area within the landfill known from previous local inversions to exhibit high variability in moisture conditions (De Donno et al., 2025).

Our implementation leverages an extended version of the VEMI inversion software (De Donno and Cardarelli, 2017), customised to perform forward modelling of resistivity and integral chargeability using the finite-element method on structured meshes. The global inversion, carried out using VFSA, enables both resistivity and chargeability model ensembles to be generated. These models are then post-processed to derive petrophysical properties, such as volumetric water content and cation exchange capacity (CEC), using empirical relationships established by Revil et al. (2020) and site-specific calibration data, including leachate levels and conductivity logged in wells. Then, the quantification of model uncertainty and correlation is addressed through a statistical analysis of the model ensembles. By computing posterior covariance and correlation matrices, we assess the spatial variability of confidence in the inversion results, which informs both the reliability of interpretations and future monitoring strategies.

The goal of this paper is threefold:

• To demonstrate the applicability and advantages of VFSAbased global inversion in resolving complex resistivity and IP patterns associated with leachate accumulation in a real landfill environment;

• To provide petrophysical interpretations of the inverted models through derived water content and CEC, offering insights into waste moisture and composition;

• To evaluate the uncertainty and reliability of the inversion results using statistical descriptors from the ensemble of accepted models.

Methods

Study area and data acquisition

The study was conducted at a large municipal solid waste landfill located in Central Italy (Figure 1), situated on a steep natural slope, where the risk of leachate accumulation triggering slope instability is a major concern. The site has been active for several years, and the waste mass composition reflects a wide range of waste types and degradation stages. The landfill stratigraphy can be summarised as a three-layer model: i) a top thin cover of compacted soil, ii) the heterogeneous waste mass with variable leachate saturation levels, and iii) a bottom high-density polyethylene (HDPE) liner, acting as an insulator due to its very high resistivity (> 107 Ωm). Since leachate accu- mulation zones are expected to be highly variable within the waste mass, a high-resolution geophysical survey is essential for their detection.

To this aim, four ERT/IP profiles (L1–L4) were acquired across the landfill (see Figure 1 for location), using a SyscalPro48 multi-channel resistivity-meter (IRIS Instruments), equipped with 48 stainless steel electrodes spaced 5 m apart, using a dipole-dipole array configuration in a roll-along mode. The current injection cycle was performed using a pulse duration of 2 s with 2 stacks (50% duty cycle), while the IP decay curve was sampled with 20 logarithmically spaced gates (first gated centred at 30 ms, last at 1.78 s), with a delay time of 20 ms after the current switch-off. Apparent resistivity (ρₐ) and integral chargeability (mₐ) were then derived from the recorded voltage data, removing poor-quality readings (negative data/decay curves, data with experimental standard deviations higher than 10%).

Firstly, the acquired dataset was locally inverted only for resistivity, to have a preliminary screening of the landfill to select the most suitable line for global inversion. The resistivity models (Figure 2) clearly show a main accumulation zone (conductive intermediate layer), located in the natural impluvium of the landfill (old topographic surface), which can contribute to the slope instability. Conversely, the resistive zones are related to the unsaturated waste and covering soil (top layer) and to the presence of the HDPE liner (bottom layer), acting as an insulator.

However, these results leave room for ambiguous interpretation of the leachate-saturated zones, as the definition of a resistivity threshold for delineating fully saturated areas is not straightforward. Conversely, an accurate assessment of the fully saturated zones is pivotal to ensure that the drainage interventions will be effective for landfill management (Mukherjee et al., 2015). We selected the final part of the L2 profile (20 electrodes starting from x = 205 m, dotted black line in Figure 1) for applying global inversion to the combined ERT/ IP dataset, with the aim of improving resolution in detection of leachate accumulation areas, providing petrophysical models and evaluating the uncertainty and reliability of the inversion results. The choice of L2 is also motivated by the availability of two piezometers (P1 and P2 in Figure 1), installed for logging leachate levels and conductivity, which were later used for petrophysical calibration. To speed up the global inversion process, we downgraded the electrode spacing to 10 m as well as the mesh size in the profile direction, which was fixed to be equal to the electrode spacing.

Global inversion algorithm

Our global inversion approach is based on the Very Fast Simulated Annealing (VFSA) algorithm (Ingber, 1989), due to its robustness and its use of a small number of inversion parameters. The VFSA algorithm draws random models from a Cauchylike distribution, which is dependent on temperature. Models that lower the energy are always accepted, while models that increase energy are accepted with a probability that is finite and temperature-dependent (Sen and Stoffa, 2013). This acceptance criterion, coupled with an adequate cooling schedule and an adequate number of random samples, ensures that the inversion process converges to the global minimum of the energy function, making it virtually independent of the initial model (Cercato, 2011). In this study, the energy function E is defined, for the model of resistivity (ρ) and chargeability (m) under consideration, as:

(1) being the dataset with and apparent resistivity and chargeability vectors and N the number of measurements (doubling the number of quadrupoles). A log-10 conversion of parameters was used because it is better suited for electrical data, usually spanning several orders of magnitude (Kim and Kim, 2011).

To improve the stability of the solution, after each simulation step, the randomly altered resistivity values are smoothed using a 5-point cross-median filter and the random search is constrained within closed resistivity and chargeability intervals ([0.2-105 Ωm] and [1-500 mV/V]), reflecting the expected ranges of parameters in urban landfills. After a preliminary trial-and-error stage, where we explored different temperature ranges, we set the initial and final temperature values to 1 and 10-9, while the total number of random walks is set to 2·106. Since one run of the VFSA algorithm is often not enough to find the global solution (Sen and Stoffa, 2013), we performed 10 independent runs using parallel calculations (10 cores/20 threads CPU).

Petrophysical transformation and uncertainty analysis

To derive petrophysical parameters after inversion, we convert the resistivity and chargeability minimum misfit models into water content (θ) and cation exchange capacity (CEC) models, using the equations after Revil et al. (2020). We assumed the cementation exponent in the Archie’s equation equal to 2, the waste grain density equal to 1500 kg/m3 (Steiner et al. 2022) with a leachate conductivity of 1300 mS/m as directly measured in the wells. The resulting θ and CEC models allowed for hydro-geophysical interpretation of the subsurface, offering insights into waste saturation patterns and degradation zones with high biological or electrochemical activity.

Uncertainty on model parameters is estimated via the posterior covariance matrix: where NM is the number of accepted models lying within a one-standard deviation threshold (68.2%) and is the mean model. The square root of the diagonal elements of C are the standard deviations (σ ρ and σ m). Then the a posteriori correlation matrix, which indicates the inter-dependence between the parameters, can be calculated: where Cij is a generic element (i-th row and j-th column) of the covariance matrix C defined in equation (2).

Results

Inverted models

The results of the global inversion using the VFSA algorithm are presented in Figures 3 (models) and 4 (uncertainty analysis), as linearised 2D profiles. The impact of the linearisation of curvilinear acquisition on the geophysical model is marginal almost everywhere, and we can use the linearisation of the profiles in the inversion procedure (De Donno et al., 2025). The interpretation of the models is supported by independent well measurements (piezometers P1 and P2), which serve as ground truth for leachate level validation.

The results are shown in Figure 3 in terms of observed data (Figures 3a,b), mean (Figures 3c,e) and minimum misfit (Figures 3d,f) models, water content and CEC sections (Figures 3g,h), where the position of the bottom liner acting as an insulator (solid black line) and the well levels (white-filled area) are superposed Figures 3a and 3b display the input apparent resistivity and chargeability datasets, while Figures 3c–3f illustrate the resulting models after VFSA inversion, where Figures 3c and 3e present the mean models derived from all accepted models of the 10 runs, and Figures 3d and 3f the minimum misfit models, considered the best-fitting realisations. In both resistivity and chargeability sections, we detected three different layers:

• Top layer (from surface to 8-10 m), displaying high resistivity values (> 10 Ωm) and low chargeability (< 10 mV/V). This layer probably represents the compacted soil cover and the unsaturated waste, with limited moisture content and minimal leachate presence;

Figure 3 Results of VFSA inversion: (a) apparent resistivity and (b) chargeability datasets; mean and minimum misfit models of resistivity (c,d) and integral chargeability (e,f), water content (g) and CEC (h)cross-sections. The position of the bottom liner is marked with a solid black line and the leachate accumulations in wells with a white-filled area (black-filled areas indicate dry zones).

• Intermediate layer (10–30 m depth), exhibiting low resistivity (<10 Ωm) and moderate to high chargeability values (>10 mV/V) due to the partially/fully saturated waste mass. The inversion reveals significant lateral variability, with zones of very low resistivity interpreted as leachate-rich pockets, while the high chargeability areas are mainly a proxy for an increase of biogeochemical activity in the waste mass (Flores-Orozco et al., 2020);

• Bottom layer (>35-40 m depth), marked by a sharp increase in resistivity and a drop in chargeability due to the HDPE liner, which acts as an insulator. The location of this interface is also confirmed from the available data of the original landfill design (solid black line in Figures 3 and 4).

The close agreement between the well-observed leachate levels (white-filled zones) and the anomalies on the inverted models validates the physical interpretation and confirms the reliability of the global inversion framework.

Petrophysical parameters and uncertainty analysis

Figures 3g and 3h present the models of volumetric water content (θ) and cation exchange capacity (CEC), respectively. The water content model (Figure 3g) reveals high-saturation areas between 80 and 180 m along the profile and at a depth between 15 and

35 m, where θ exceeds 30-40%. These areas correlate well with the leachate levels recorded in wells P2, while the low leachate levels in P1 (almost dry) are in good agreement with the respective lower water content. The CEC model (Figure 3h) shows high values (above 100 meq/100g) between 100 and 130 m along the profile, likely to correlate with organic-rich waste and high microbial activity, while intermediate values (20-100 meq/100g) are retrieved in the remaining waste mass. In contrast, the upper and lower layers exhibit uniformly low CEC values (<20 meq/100g), consistent with the presence of covering and bottom layers, respectively.

Additionally, the inversion reliability is shown for both models in Figure 4 in terms of standard deviation (Figures 4a-4b) and correlation (Figure 4c) values, as well as by the misfit progress with iterations (Figure 4d).

High uncertainties are noted at the lateral and bottom zones of the resistivity profile, as expected due to the combined effect of the low sensitivity and high mean resistivity values. In contrast, the middle portion of the model shows low standard deviations, particularly around the P2 piezometer. The correlation matrix (Figure 4c) shows mostly weak off-diagonal correlations, with few localised clusters of positive correlation and a clear correlation observed in the filter-applied regions. These correlations are a product of the median filter used for stabilisation purposes and indicate minor trade-offs between neighbouring cells. Finally, we clearly see in Figure 4d that all runs converge toward a similar minimum misfit value, demonstrating the repeatability and robustness of the global inversion algorithm. This behaviour also confirms that the global minimum is reliably identified despite the non-linear and non-unique nature of the problem.

Practical implications and conclusions

From a practical perspective, the results of this study offer two main benefits for landfill operators and environmental authorities, such as:

• An improved localisation of leachate hotspots (including the associated uncertainty);

• Informing quantitively drainage design, pumping strategy and/ or new installation of monitoring wells;

• Supporting the geotechnical risk assessment, particularly in landfills located on slopes, where leachate saturation may impact slope stability.

These advantages align with broader goals in sustainable landfill management, including compliance with environmental regulations, minimisation of long-term risks, and optimisation of post-closure monitoring.

From a more geophysical point of view, this study demonstrates the application and effectiveness of a global inversion approach — based on the Very Fast Simulated Annealing (VFSA) algorithm — applied to ERT and IP datasets in the context of leachate detection within a MSW landfill. Compared to conventional local methods, the VFSA-based strategy allows for enhanced model exploration and quantitative uncertainty assessment (Sen and Stoffa, 2013). In fact, variations in waste composition, compaction, permeability, and degradation processes lead to small and localised zones of accumulation that may not be captured by traditional smoothness-constrained inversions. Therefore, a global inversion approach is well-suited to account for such complexity, offering a means to delineate these zones with associated confidence estimates.

Although the low resistivity values can be directly interpreted as a proxy for leachate accumulations, the integral chargeability is expected to decrease proportionally to the increase of saturation, due to the increase of fluid and surface conductivity, thus yielding lower IP responses (Flores-Orozco et al., 2020). Conversely, high chargeability anomalies are mainly due to biogeochemically active zones (high organic matter), which is responsible for high rates of microbial activity, resulting in high polarisation that surpasses the high salinity and conductivity (De Donno et al., 2025). Therefore, we overcome this residual ambiguity in interpreting the geophysical models by using well-established petrophysical relationships, which are given in this case in terms of integral chargeability (Revil et al., 2020), though alternative formulations are available also for spectral (i.e. Cole-Cole) parameters (e.g. Weller at al., 2013). The two distinct anomalies corresponding with high water content (Figure 3g) and high CEC values (Figure 3h), confirm that high saturation and significant biologically active conditions pertain to two separated areas in the waste mass. The agreement between the inverted models and the leachate levels logged in piezometers provides strong validation for this method, particularly in complex landfill environments where physical heterogeneity and chemical gradients are pronounced. However, the current approach relies only on empirical petrophysical relationships to derive water content and CEC, while calibration of petrophysical parameters (i.e. cementation exponent, waste density) with laboratory data could improve their reliability.

Finally, the convergence behaviour observed across all ten runs confirms the reproducibility and robustness of the global inversion strategy. Furthermore, the model covariance and correlation analyses offer valuable insights into parameter trade-offs and spatial resolution, which are rarely available in local inversion schemes. Despite these strengths, computational demand remains significant, particularly using high-resolution meshes and/or multi-parameter datasets. Although parallelisation of the multiple runs helped us to drastically reduce the computation effort, future developments could benefit from GPU acceleration or adaptive mesh refinement to optimise performance.

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