Time-domain Electromagnetic Data Research Articles

A multidimensional AI-trained correction to the 1D approximate model for Airborne TDEM sensing

The computational resources required to solve the full 3D inversion of time-domain electromagnetic data are immense. To overcome the time-consuming 3D simulations, we construct a surrogate model, more precisely, a data-driven statistical model to replace the 3D simulations. It is trained on 3D data and predicts the approximate output much faster. We construct a surrogate model that predicts the discrepancy between a 1D subsurface model and a deviation of the 1D assumption. The latter response is fastly computable with a semi-analytical 1D forward model. We exemplify the approach on a two-layered case. The results are encouraging even with few training samples. Given the computational cost related to the 3D simulations, there are limitations in the number of training samples that can be generated. In addition, certain applications require a wide range of parameters to be sampled, such as the electrical conductivity parameters in a saltwater intrusion case. The challenge of this work is achieving the best possible accuracy with only a few thousand samples. We propose to view the performance in terms of learning gain, representing the gain from the surrogate model whilst still acknowledging a residual discrepancy. Our works open new avenues for effectively simulating 3D TDEM data.

Adaptive laterally constrained inversion of time-domain electromagnetic data using hierarchical Bayes

Laterally constrained inversion (LCI) of time-domain electromagnetic (TEM) data is effective in recovering quasi-layered models, particularly in sedimentary environments. By incorporating lateral constraints, LCI enhances the stability of the inverse problem and improves the resolution of stratified interfaces. However, a limitation of the LCI is the recovery of laterally smooth transitions, even in regions unsupported by the available data sets. Therefore, we have developed an adaptive LCI scheme within a Bayesian framework. Our approach introduces user-defined constraints through a multivariate Gaussian prior, wherein the variances serve as hyperparameters in a hierarchical Bayes algorithm. By simultaneously sampling the model parameters and hyperparameters, our scheme allows for varying constraints throughout the model space, selectively preserving lateral constraints that align with the available data sets. We demonstrate the effectiveness of our adaptive LCI scheme through a synthetic example. The inversion results showcase the self-adaptive nature of the strength of the constraints, yielding models with smooth lateral transitions while accurately retaining sharp lateral interfaces. An application to field TEM data collected in Laizhou, China, supports the findings from the synthetic example. The adaptive LCI scheme successfully images quasi-layered environments and formations with well-defined lateral interfaces. Moreover, the Bayesian inversion provides a measure of certainty, allowing for a comprehensive illustration of the confidence in the inversion results.

Assessing and Improving the Robustness of Bayesian Evidential Learning in One Dimension for Inverting Time-Domain Electromagnetic Data: Introducing a New Threshold Procedure

Understanding the subsurface is of prime importance for many geological and hydrogeological applications. Geophysical methods offer an economical alternative for investigating the subsurface compared to costly borehole investigations. However, geophysical results are commonly obtained through deterministic inversion of data whose solution is non-unique. Alternatively, stochastic inversions investigate the full uncertainty range of the obtained models, yet are computationally more expensive. In this research, we investigate the robustness of the recently introduced Bayesian evidential learning in one dimension (BEL1D) for the stochastic inversion of time-domain electromagnetic data (TDEM). First, we analyse the impact of the accuracy of the numerical forward solver on the posterior distribution, and derive a compromise between accuracy and computational time. We also introduce a threshold-rejection method based on the data misfit after the first iteration, circumventing the need for further BEL1D iterations. Moreover, we analyse the impact of the prior-model space on the results. We apply the new BEL1D with a threshold approach on field data collected in the Luy River catchment (Vietnam) to delineate saltwater intrusions. Our results show that the proper selection of time and space discretization is essential for limiting the computational cost while maintaining the accuracy of the posterior estimation. The selection of the prior distribution has a direct impact on fitting the observed data and is crucial for a realistic uncertainty quantification. The application of BEL1D for stochastic TDEM inversion is an efficient approach, as it allows us to estimate the uncertainty at a limited cost.

Time-Domain Electromagnetic Noise Suppression Using Multivariate Variational Mode Decomposition

Noise suppression is essential in time-domain electromagnetic (TDEM) data processing and interpretation. TDEM data are typically in broadband signal, which makes it difficult to separate the signal in the whole frequency band. The conventional methods tend to process data trace by trace, ignoring the lateral continuity between channels. This paper proposes a workflow based on multivariate variational mode decomposition (MVMD) and multivariate detrended fluctuation analysis (MDFA) to deal with the noise in 2-D TDEM data. The proposed method initially employs MVMD to decompose TDEM signals into a series of intrinsic mode functions (IMFs). Subsequently, MDFA is used to calculate the scaling exponent of each IMF, facilitating the selection of signal-dominant IMFs. Finally, the signal IMFs are summed up to reconstruct the TDEM signal. Both simulation and field results demonstrate that, by considering the lateral continuity of data across channels, the proposed method is more effective at noise removal than other single-channel data processing techniques.

A new technique inversion Time-Domain electromagnetic data

Time-Domain Electromagnetic (TDEM) data modeling, especially for central-loop configurations, is often achieved through 1D inversion models. This study aims to enhance the accuracy and efficiency of TDEM data inversion by employing the Born Approximation method to address calculation and convergence speed issues. We also utilize the modified Symbiotic Organism Search (mSOS), a global optimization algorithm capable of handling multi-minimum problems in non-linear objective functions, to optimize the inversion process. Our research includes the assessment of the accuracy and performance of this approach through inversion modeling on both synthetic and field data. The accuracy of the synthetic data was evaluated based on the algorithm's capability to retrieve the values of the synthetic data, as indicated by the small relative error between the synthetic model parameters and the calculated model. In the case of field data modeling, the accuracy relied on the consistency achieved when modeling the data with different numbers of layers. Additionally, we considered the time required to perform the inversion as an evaluation metric for inversion performance. For the synthetic data case, the algorithm produced relatively accurate models with misfit values of approximately 0 % and low relative error values. In the field data case, the inversion models demonstrated consistency and reduced misfit values when the data was modeled with different numbers of layers, specifically 8.72 % for the 2-layer model, 3.92 % for the 3-layer model, and 2.61 % for the 4- and 5-layer models. Both datasets required less than 19 min for 10,000 iterations. These findings highlight the innovative nature of the mSOS algorithm and its potential for practical applications in TDEM inversion studies.

Three-Dimensional Inversion of Induced Polarization Effects in Airborne Time Domain Electromagnetic Data Using the GEMTIP Model

This paper discusses the physical and mathematical principles of the airborne induced polarization (IP) method. The possibility of extracting information about the IP properties of rocks from airborne survey data has become a subject of active research recently. We introduce a method for the joint inversion of the airborne EM data into the electrical conductivity and IP parameters based on the generalized effective-medium theory of induced polarization (GEMTIP). We also present the results of the inversion of the airborne EM data collected over the Echum Project Area, in Northwestern Ontario, Canada, into 3D conductivity and chargeability models. Obtaining IP physical property models from an airborne geophysical survey may result in a paradigm change in mineral exploration by pulling more information and value from airborne EM surveys.

Geometric 2.5D inversion of marine time domain electromagnetic data with application to hydrocarbon deposits prospecting

To solve the problem of detection and delineation of marine hydrocarbon deposits located at different depths in an inhomogeneous medium, we propose an approach to 2.5D inversion of electromagnetic (EM) data measured in the time domain (TD) using a differentially normalized method of electrical prospecting. The approach is based on geometric inversion, in which block structures are used to parameterize the geological medium. The sizes of blocks in the initial model are set depending on the depth. Bathymetry is taken into account as a 3D surface. As a result of inversion, the coordinates of block boundaries and conductivity inside blocks and layers are determined. The minimized functional is represented as a sum of weighted residuals between computed and practical data and regularizing terms. Adaptive regularization is used to satisfy parameter constraints. To solve a 3D forward problem and calculate derivatives with respect to parameters, the finite element method (FEM) is used. We propose to use a priori data on the depth of the target layers and use various options of block structures with an analysis of possible uncertainties in detecting target bodies and determining their boundaries. We present the results of a 2.5D inversion of field data obtained in one of the areas in the North Sea. Target bodies discovered as a result of inversion are confirmed by well data. Coincidences were obtained both for productive wells and for dry ones. Using synthetic data for various geoelectric models and options of block structures, we justify the proposed approach to the inversion of marine TD EM data and make recommendations for its use.

Three-dimensional inversion of airborne time-domain electromagnetic data for ground sources

While most airborne time-domain electromagnetic (ATEM) surveys are carried out using moving-source systems, semi-airborne systems that use a ground-based source, such as GREATEM, have gained popularity in recent years because they allow for more in-depth exploration than moving-source systems. We presented a three-dimensional inversion method for interpreting transient data collected in semi-airborne surveys. Our method is based on a Gauss–Newton minimization approach. The forward problem is solved in the frequency domain using a secondary-field finite-difference technique, and the resulting solution and sensitivity are Fourier-transformed to the time domain using a digital filter. The sensitivities are evaluated by the adjoint-equation method, except for those of a surface region immediately below the source, which are derived by forward modeling the response of a perturbed model based on finite differences. We tested our inversion method on synthetic and real data. The synthetic tests show that the resolution capability of the semi-airborne surveys is dependent on the location of the ground source, which suggests that it is desirable to employ multiple source locations and perform joint inversion of all data sets to ensure the reliability of semi-airborne surveys. Finally, the real data example demonstrates that the recovered conductive zone is consistent with the known distribution of the mineralized zone.

1.5D Time Domain Electromagnetic Inversion Using Global Optimization Methods and Parallel Processing

An innovative comparative study among three different global optimization methods (GOMs) to invert time domain electromagnetic data (TDEM), was applied in the 1.5D subsurface resistivity imaging. These stochastic methods allow the incorporation of different kinds of constraints in the objective function, due to the easiness of implementation in their algorithms and their computational efficiency. Nevertheless, global optimization methods, like any other based on swarm intelligence cost much computational time, including problems with a high number of unknown parameters and when the forward modeling involves time-consuming calculations such as Gaver-Stehfest inverse transforms, Hankel transforms, and others. To overcome this difficulty, we developed a parallel pure MPI version of each GOM, allowing the distribution of the computation among several cores of a cluster. The performances of the classic version of particle swarm optimization (PSO), grey wolf optimizer (GWO), and whale optimization algorithm (WOA) using MPI parallelism for solving 1.5D TDEM inverse problems are compared here in a set of synthetic and real data. The principal outcomes show: (1) These GOMs reproduce quite well the distribution of subsurface resistivity either synthetic models or real data, (2) WOA and PSO exhibit better computational performances, converging first than GWO, (3) WOA provided better performance in the final value achieved of the cost function than PSO and GWO, and (4) pure MPI parallelism provided a 17x and 50x speedup in the computation time for both synthetic and real data, respectively. In a better way to classify this comparison, we analyzed the solutions using total variation (TV) and Global smoothness (GS) constraints, to identify smooth and sharp structures. Additionally, we have diminished the computational time execution with the parallel solution (MPI version of each stochastic traditional method) against the sequential processing.

Bayesian Inversion of Time Domain Electromagnetic (TDEM) Synthetic Data using Langevin Monte Carlo (LMC)

The inversion of time domain electromagnetic (TDEM) data is an ill-posed problem. This makes the standard inversion procedure, which is to linearize the related objective function. Then take a deterministic approach to determine a solution that can minimize the said objective function, which has the potential to be trapped in a local minimum. In this study, we solved the problem of TDEM data inversion using the Bayesian framework by generating a sample from the posterior distribution. The posterior distribution contains information related to the uncertainty of the TDEM data and the results of the forward modeling formulation, and prior information about the subsurface parameter model. In conducting the sampling process, we use the Langevin Monte Carlo (LMC) algorithm, one of many gradient-based Markov chain Monte Carlo (MCMC) sampling algorithms. Bayesian inversion was performed on synthetic data generated through the forward modeling of several test models. We used a model with varying thickness and resistivity values for inversion. We also added a prior probability distribution related to the smoothness constraint between resistivity values in adjacent layers allowing sharp and smooth transitions.

A Comparative Analysis of Three Computational-Intelligence Metaheuristic Methods for the Optimization of TDEM Data

We focus on the performances of three nature-inspired metaheuristic methods for the optimization of time-domain electromagnetic (TDEM) data: the Genetic Algorithm (GA), the Particle Swarm Optimization (PSO) and the Grey Wolf Optimizer (GWO) algorithms. While GA and PSO have been used in a plethora of geophysical applications, GWO has received little attention in the literature so far, despite promising outcomes. This study directly and quantitatively compares GA, PSO and GWO applied to TDEM data. To date, these three algorithms have only been compared in pairs. The methods were first applied to a synthetic example of noise-corrupted data and then to two field surveys carried out in Italy. Real data from the first survey refer to a TDEM sounding acquired for groundwater prospection over a known stratigraphy. The data set from the second survey deals with the characterization of a geothermal reservoir. The resulting resistivity models are quantitatively compared to provide a thorough overview of the performances of the algorithms. The comparative analysis reveals that PSO and GWO perform better than GA. GA yields the highest data misfit and an ineffective minimization of the objective function. PSO and GWO provide similar outcomes in terms of both resistivity distribution and data misfits, thus providing compelling evidence that both the emerging GWO and the established PSO are highly valid tools for stochastic inverse modeling in geophysics.

Flower Pollination and Elitism Algorithms for Inversion of TDEM Data

Hybridization of algorithms can enhance the overall search capabilities to get the optimal solution. The aim of this study was to invert Time Domain Electromagnetic (TDEM) data using the Flower Pollination Algorithm (FPA) as a new inversion scheme technique. FPA was originally inspired by the fertilization process of flowers, in which pollen transfer grains from male flowers to female flowers. The modeling of TDEM data was done by combining the FPA and elitism (eFPA) techniques. The applicability was tested on forward modeling data and observed data in MATLAB 2017a. In testing the algorithm, we used a model from homogeneous half space to a multi-layer model using different parameters (resistivity and thickness). In addition, in the inversion process, we used field data with various starting model approaches. Based on the results of the TDEM data modeling, FPA and eFPA can both be applied as algorithmic techniques for inversion modeling of TDEM data. The eFPA technique gave better results than FPA.

3D Constrained Gravity Inversion and TEM, Seismic Reflection and Drill-Hole Analysis for New Target Generation in the Neves–Corvo VMS Mine Region, Iberian Pyrite Belt

Located in the Iberian pyrite belt, the Neves–Corvo mine is a world-class massive sulfide deposit and the largest operating mine in Portugal with underground mining down to 1000 m depth focused on massive and stockwork Cu, Zn, Pb rich ores. Gravimetric data have had a leading role in the discovery of the seven known deposits, together with time-domain electromagnetic (TEM) ground data. In this work, we present the results of a 3D constrained gravity inversion carried out with legacy ground gravity data. The 3D gravity inversions were carried out using an updated density database containing approximately 142,000 measurements. A recently constructed 3D geological model based on reprocessed 2D seismic reflection, 3D seismic, TEM and updated geology from detailed surface mapping and drill-hole data, was used to constrain the inversions. The results show multiple high-density anomalies that may indicate the presence of mineralization at depth. These anomalies were therefore cross-checked with holes previously drilled. Approximately 97% of more than 1000 available surface drill-holes located on or at a distance of less than 200 m from the high-density anomalies intersected mineralization. However, gravity anomalies have been drilled in the past and particularly dense black shales or rhyolitic/gabbroic rocks have been intersected. To increase the success of future drilling, gravimetric anomalies have been correlated spatially with high-conductivity TEM zones and strong-amplitude seismic reflections, because igneous rocks usually present weak-to-moderate conductivity and a massive column of black shales presents a seismic signature quite different from that of mineralization. We concluded that some of these locations represent high-quality targets to consider following up with drilling and further exploration.

Integrating neural networks in least-squares inversion of airborne time-domain electromagnetic data

Airborne time-domain electromagnetic surveys produce extremely large data sets with thousands of line kilometers of data and millions of possible models to explain the data. Inversion of such data sets to obtain the resistivity structures of the subsurface is computationally intensive and involves calculation of a significant number of forward and derivative responses for solving the least-squares inverse problem. The flight altitude of the airborne system needs to be included in the modeling, which adds further complexity. We propose to integrate neural networks in a damped iterative least-squares inversion framework to expedite the inversion process. We train two separate neural networks to predict the forward responses and partial derivatives independently for a broad range of resistivity structures and flight altitudes. Data inversion is not only used for producing the final subsurface models but also used during data processing, or to produce intermediate results during a survey. With these purposes in mind, we provide three inversion schemes with a tunable balance between computational time and modeling accuracy: (1) numerical forward responses used initially in combination with neural network derivatives, and the derivatives switched to a numerical solution in final iterations, (2) numerical forward responses in combination with neural network derivatives used throughout the inversion, and (3) only neural network forward responses and derivatives used in inversion. Experiments on field data find that we improve inversion speed without any loss in modeling accuracy with our first approach, whereas the second scheme gives a significant speedup at the cost of minor and often acceptable deviations in the inversion results from the conventional nonlinear inversion. The last approach is the fastest and captures the overall resistivity structures quite well. Therefore, depending on the modeling accuracy, inversion speedup factors of up to 50 are realized by using the proposed schemes.

Geometric 3-D inversion of airborne time-domain electromagnetic data with applications to kimberlite pipes prospecting in a complex medium

We consider an approach to solving 3-D inverse problems of airborne time-domain electromagnetic (TD-EM) survey in complex geoelectrical conditions, when the responses of target objects in the measured signal are relatively small and mixed with responses of rugged topography, 3-D inhomogeneities in overburden layers, and other interfering 3-D objects. For parameterization of the geoelectrical model of the geological medium, global and local structures are used. A block structure is a grid with large cells whose boundaries can move during the inversion process. Block structures are characterized by two types of parameters: geometric and physical. Geometric parameters include the coordinates of the boundaries of blocks in block structures, which are used for recovering local bodies or 3-D inhomogeneities within the layers, and physical parameters are the conductivities inside the blocks. In addition, the geometric parameters include displacements of control points, which are used for describing curved surfaces. The functional employed for inversion includes regularizing terms that allow controlling the self-crossing of geometric boundaries and extension of physical parameters beyond the boundaries of the allowed values range. Regularization coefficients are calculated adaptively at each iteration of the nonlinear 3-D inversion. In order to separate the responses of 3-D inhomogeneities located under the overburdens from those of 3-D inhomogeneities inside the overburdens, we propose to carry out 3-D inversion in two stages. At the first stage, over a shortened time range, we recover the conductivity distribution using global block structures and the shape of the boundaries of the overburden layers using control points. At the second stage, the entire time range is used. In those places where the significant residuals remained at late times, local block structures are employed to recover local objects (including target ones) under the overburden layers. This enables us to define quite accurately the position in plan, top border depth, and type of 3-D inhomogeneities, which are located under the overburdens, at the second stage of geometric inversion. To calculate 3-D time-domain electromagnetic fields, we use the vector finite element method implemented on optimized non-conforming hexahedral meshes with the possibility of adjoining the faces of several finite elements to the face of one finite element. The workability of the proposed approaches is demonstrated on synthetic airborne TD-EM data as well as on experimental airborne data, which are obtained as a result of methodical work over the kimberlite pipe deposit. The proposed geoelectrical model parameterization and the approach to 3-D inversion allow the discovery of relatively small 3-D target objects, when many non-target objects, including 3-D inhomogeneities in the overburdens, give several times greater responses in the measured signals.

A novel trans-dimensional Bayesian inversion strategy for airborne time-domain electromagnetic data

The trans-dimensional Bayesian inversion method based on statistical theory regards the inversion parameters as random variable, it not only provides a reasonable inverse model based on the probability, but also offers the probability distribution and the uncertainty information of the inverse model parameters. However, for the conventional trans-dimensional Bayesian inversion, the model sampling efficiency and inversion convergence rate are influenced by several factors, and it requires sampling over a big model space, those limit the application of the trans-dimensional Bayesian inversion for airborne time-domain electromagnetic data. In this paper, we present a novel trans-dimensional Bayesian inversion strategy for airborne time-domain electromagnetic data, which uses a combining sampling update method to implement the model sampling. This method uses the block-wise updating method to run only one Markov chain with the initial state constructed by conductivity-depth imaging during the burn-in period, and adopts the component-wise updating method with an adaptive sampling step size to perform multiple Markov chains in parallel after the burn-in period ends. The effectiveness of the novel Bayesian inversion strategy was validated by both synthetic data and survey data. The experimental results showed that this inversion strategy can not only obtain better inversion results, but also shorten the burn-in period and reduce the total sampling times of the Markov chain.

Bayesian subsampling of time-domain electromagnetic data using kernel density product

The Bayesian method is a powerful tool to estimate the resistivity distribution and associated uncertainty from time-domain electromagnetic (TDEM) data. Because the forward simulation of the TDEM method is computationally expensive and a large number of samples are needed to globally explore the model space, the full Bayesian inversion of the TDEM data is limited to layered models. To make the high-dimensional Bayesian inversion tractable, we have adopted a divide-and-conquer strategy to speed up the Bayesian inversion of TDEM data. First, the full data sets and model spaces are divided into disjoint batches based on the coverage of the sources so that the independent and highly efficient Bayesian subsampling can be conducted. Then, the samples from each subsampling procedure are combined to get the full posterior. To obtain an asymptotically unbiased approximation to the full posterior, a kernel density product method is used to reintegrate samples from each subposterior. The model parameters and their uncertainty are estimated from the full posterior. Our method is tested on synthetic examples and applied to a field data set acquired with a large fixed-loop configuration. The 2D section from the Bayesian inversion revealed several mineralized zones, one of which matches well with the information from a nearby drillhole. The field example indicates the ability of the Bayesian inversion to infer reliable resistivity and uncertainty.

Geophysical characterisation of geologic features with mining implications from ERT, TDEM and seismic reflection (Mining District of Linares-La Carolina, Spain)

In this study, the effectiveness of different geophysical techniques is analysed in relation to the imaging of geological structures with mining interest. To achieve this goal, the old district of Linares-La Carolina (Southeast Spain) is chosen due to the presence of dense swarm of mineralised dykes, primarily consisting of galena (PbS). In particular, the western boundary of the mining district is studied. At this westernmost area the veins lose their continuity due to regional fractures which resulted in the abandoning of the extracting labours.Direct information from both the surface geology and several boreholes are used as ground-truth calibration and verification for the geophysical tools used in this study.The seismic response is characterised by high-amplitude reflectors, generally at the base of the sedimentary cover. The seismic profiles suggest lateral changes in the thickness and the existence of fractures affecting the sedimentary cover and/or the top of the acoustic basement. However, this technique has proved ineffective when studying the Palaeozoic substrate, precisely at those areas where the veins are hosted.Electrical resistivity tomography (ERT) studies suggest fractures and lateral changes in the facies, in both the sedimentary cover and the Palaeozoic basement. The basement shows phyllites in the granite intrusion, which are crucial for the elastic properties of the hosting rock and therefore indicate areas prone to further mineralisation. Time-domain electromagnetic (TDEM) data, which is an excellent complement to the two previous techniques, have also been collected. Data have been taken with different configurations and varying measurement parameters at each sounding station. This approach has made it possible to compare the effectiveness benefits and drawbacks of the different methods.

Nonlinear Inversion Using Very Fast Simulated Annealing for Horizontal Electric Dipole Time-Domain Electromagnetic Data

A nonlinear stochastic inversion scheme, called very fast simulated annealing (VFSA), was applied to the time-domain electromagnetic data generated from a horizontal electric dipole. The forward formulation of the vertical magnetic field was expressed in the Laplace domain by applying the Hankel integral transform. Time-domain transformation was performed by applying the inverse Laplace transform using the Gaver–Stehfest algorithm. In this study, for noise-free synthetic data, the VFSA scheme yielded the smallest misfit and an inverted resistivity model that resembled the test model. The addition of 5% random noise to the synthetic data produced the same level of misfit and a model that still mimicked the test model. However, the addition of 10% noise to the synthetic data resulted in a misfit value that was three times that of the first two values and a resistivity model with a large discrepancy with the test model, particularly at large depths. These results indicate the efficacy of the VFSA inversion scheme for inferring the subsurface resistivity structure from the electromagnetic data. This inversion scheme was applied to field data measured in a volcanic environment. The general pattern of the resistivity structure inferred by the VFSA inversion is consistent with the structure obtained previously by using a deterministic inversion scheme.

1D Stochastic Inversion of Airborne Time-Domain Electromagnetic Data with Realistic Prior and Accounting for the Forward Modeling Error

Airborne electromagnetic surveys may consist of hundreds of thousands of soundings. In most cases, this makes 3D inversions unfeasible even when the subsurface is characterized by a high level of heterogeneity. Instead, approaches based on 1D forwards are routinely used because of their computational efficiency. However, it is relatively easy to fit 3D responses with 1D forward modelling and retrieve apparently well-resolved conductivity models. However, those detailed features may simply be caused by fitting the modelling error connected to the approximate forward. In addition, it is, in practice, difficult to identify this kind of artifacts as the modeling error is correlated. The present study demonstrates how to assess the modelling error introduced by the 1D approximation and how to include this additional piece of information into a probabilistic inversion. Not surprisingly, it turns out that this simple modification provides not only much better reconstructions of the targets but, maybe, more importantly, guarantees a correct estimation of the corresponding reliability.