Deterministic inversion of electromagnetic (EM) data yields a single best fitting resistivity model of the subsurface, which can be used to interpret the geological subsurface. Such a model fails to capture the uncertainty in both resistivity and geology. This limitation is critical, as multiple, geologically dissimilar subsurface configurations can yield equivalent EM responses, meaning a single model representation can be inaccurate or even misleading. Probabilistic inversion of the EM data provides a principled solution by characterizing the range of subsurface models consistent with data, and thereby explicitly quantifying uncertainty in both the geophysical and geological models.Here we invert by rejection sampling of pre-computed geophysical and geological 1D prior models. This allows for fast and efficient probabilistic inversion of large-scale EM surveys containing thousands of soundings. An added benefit of using pre-computed geological models is the possibility to encode geological expert knowledge into the models as direct information. In this context expert knowledge can be many things, for example the resistivity-lithology relationship, the chronological sequence of geological units, or the relative occurrence of various lithologies to name a few.In the presentation, we demonstrate how such a probabilistic inversion workflow can be set up and applied on towed transient EM data from geophysical surveys in varying geological settings. The required inputs are (i) a geophysical dataset consisting of EM soundings, and (ii) an expert-based assessment of the plausible geological subsurface architectures in the survey area. Optionally, geophysical and lithological well logging can be used to further constrain the inversion. We will highlight the tool/software (GeoPrior1D) we have developed to construct prior ensembles with encoded geological knowledge, especially suited for such a workflow. GeoPrior1D is an open-source tool for generating ensembles of one-dimensional geological and geophysical models that explicitly represent prior models for probabilistic inversion problems.Finally, we present key outcomes of the probabilistic modelling. This includes resistivity models with uncertainty, lithological models with uncertainty (entropy), class probabilities, and various themed maps. The produced models and maps, always accompanied by rigorously quantified uncertainties, enable better and more reliable decision-making across applications such as geohazard risk assessment, resource volume estimates, groundwater modelling, and much more.

GeoPrior1D is an open-source tool for generating ensembles of one-dimensional (1D) geological and geophysical models that explicitly represent prior models for probabilistic inversion. Instead of relying on analytical prior expressions, GeoPrior1D defines priors through a probabilistic generator that produces random 1D realizations consistent with user-specified geological rules. These rules capture conceptual understanding of subsurface architecture - such as geological successions, layer thickness distributions, lithology-resistivity relationships, and groundwater levels corresponding to different geological settings. The resulting ensemble forms a statistically defined prior model that can be directly used in probabilistic inversion or uncertainty analysis. GeoPrior1D includes a graphical interface for configuration and visualization. It outputs reproducible HDF5 files and is implemented in MATLAB and Python under the MIT license. Together, these elements provide a transparent and flexible framework for linking geological knowledge with quantitative geophysical modeling.

PET images often make small lesions difficult to identify because of noise and system blur. We address this by developing and evaluating MlPET , a fast localized machine-learning method that approximates a computationally expensive probabilistic sampling approach while reducing noise and increasing spatial resolution. Building on a probabilistic deconvolution framework with informed priors, MlPET replaces computationally demanding Markov chain Monte Carlo sampling with a localized neural network trained to directly estimate the posterior mean of voxel activity from small image neighborhoods. The method incorporates scanner-specific point spread functions (PSF), spatially correlated noise modeling, and flexible prior information. Performance was evaluated on NEMA phantom data acquired on three PET systems (GE Discovery MI, Siemens Biograph Vision 600, and Siemens Biograph Vision Quadra Edge) under varying reconstruction settings and acquisition times. On NEMA IEC phantom data, MlPET produced contrast-recovery coefficients consistently higher than PET and frequently close to 1.0 (including the 10 mm sphere in several settings), while simultaneously reducing background noise and improving spatial definition. The effective point-spread function (PSF) full width at half maximum (FWHM) was on average reduced from about 2 mm in PET to below 1 mm with MlPET , corresponding to roughly a 2.5× decrease in effective blur. Comparable image quality was obtained at 40–80 s acquisition time using MlPET versus 900 s with conventional PET. A clinical example in a breast cancer patient illustrates potential clinical applicability. MlPET provides a computationally efficient approach for quantitative probabilistic post-reconstruction PET image analysis. By combining informed priors with the speed of a neural network, it achieves both noise suppression and resolution enhancement. The method shows promise for improved small-lesion detectability and quantitative reliability in clinical PET imaging. Future clinical studies will evaluate its performance on patient data and quantify effects under realistic prior uncertainty.

Geological models are essential for mapping the accessibility and extent of subsurface resources. Traditionally, these models have been based on deterministic inversion of geophysical data, which provide estimates of geophysical (and not geological) parameters, but fail to capture the full uncertainty. Probabilistic inversion methods have been proposed to address this issue, allowing for, in principle, inference about geological model parameters with detailed uncertainty characterization from geophysical data. In practice, borehole data, often available in the form of lithological descriptions, offer an additional source of information that can further enhance the inference of model parameters. We discuss how to quantify and incorporate uncertainties in lithological borehole data into probabilistic inversion frameworks using a likelihood based on the multinomial distribution. We identify key obstacles in quantifying class probabilities for lithological categories, related to both independent information about all model parameters and information about groups of model parameters. We demonstrate the effect of different strategies for quantifying lithological borehole information. For example, the straightforward assumption of full independence may misrepresent our knowledge and lead to an intractable numerical problem. By explicitly quantifying borehole data, our approach enables integration of borehole data into a probabilistic framework that can be used, for example, in joint probabilistic inversion, with the scope of producing geological models with better description of uncertainties. Lastly, we introduce a flexible method to generate geological prior models and demonstrate how quantified borehole information can be inverted using look-up tables of lithological one-dimensional prior realizations.

Geophysical surveying with electrical and electromagnetic data is commonly used for e.g. groundwater assessment and resource exploration. These methods measure subsurface resistivity, whereas the primary end-user interest is in subsurface properties like lithology. Inferring lithological information from resistivity data is, thus, a fundamental challenge in geological modeling that requires a quantitative resistivity-lithology relationship. Often, local resistivity log data is lacking, and this relationship is therefore reliant on subjective manual interpretation, based on experience from similar geological settings. This study presents a novel probabilistic methodology for establishing a quantitative, site-specific resistivity-lithology relationship based on co-located towed transient electromagnetic (tTEM) data and lithological logs. The probabilistic approach inverts co-located tTEM soundings using uninformative priors to generate posterior samples of 1D resistivity models that are consistent with the observed data. These models are then combined with co-located lithological descriptions from boreholes to establish a probabilistic resistivity-lithology relation. The method incorporates a weighting function that accounts for uncertain layer boundaries and the resolution limitations of the tTEM method. The distributions are modeled using Kernel Density Estimation to establish the final probabilistic relationship. It is exemplified, how this relationship can be used to generate a joint prior of lithology and resistivity models across an entire survey area, enabling the generation of probabilistic lithology maps with quantified uncertainty. The methodology is first validated using two synthetic test cases and subsequently applied to field data from two survey areas in Denmark. The results demonstrate that well-defined relationships can be established when high-quality, co-located data are available.

We develop and evaluate MlPET, a fast localized machine learning approach for probabilistic PET image analysis addressing the noise-resolution trade-off in conventional reconstructions. MlPET replaces computationally demanding Markov chain Monte Carlo sampling with a localized neural network trained to estimate posterior mean voxel activity from small image neighborhoods. The method incorporates scanner-specific point spread functions, spatially correlated noise modeling, and flexible priors. Performance was evaluated on NEMA IEC phantom data from three PET systems (GE Discovery MI, Siemens Biograph Vision 600, and Quadra) under varying reconstruction settings and acquisition times. On phantom data, MlPET achieved contrast recovery coefficients consistently higher than standard PET and close to 1.0 (including 10 mm spheres), while reducing background noise and improving spatial definition. Effective pointspread function full width at half maximum decreased from approximately 2 mm in standard PET to below 1 mm with MlPET, a 2.5 fold reduction in blur. Comparable image quality was obtained at 40-80 s acquisition time with MlPET versus 900 s with conventional PET. MlPET provides an efficient approach for quantitative probabilistic post-reconstruction PET analysis. By combining informed priors with neural network speed, it achieves noise suppression and resolution enhancement without altering reconstruction algorithms. The method shows promise for improved small-lesion detectability and quantitative reliability in clinical PET imaging. Future studies will evaluate performance on patient data.

The 'Informative Mapping of Construction Aggregate Resources Through Statistical Data Analysis (INTEGRATE)' project explores an innovative approach to mapping raw materials, such as construction aggregates, by using electromagnetic (EM) measurements alongside geological prior information, statistical relationships between geological and geophysical parameters, and borehole data. By integrating information from diverse sources using state-of-the-art probabilistic data integration and inversion methods, the project aims to create a more efficient and accurate framework for locating aggregate resources. The key goal is to enable end users to make informed decisions in both the exploration and exploitation phases, based on maximum available information in the most accessible way. We describe the full INTEGRATE workflow, which consists of (a) quantifying prior spatial geological information, (b) quantifying geophysical information, (c) quantifying information from boreholes, and then (d) combining this information into one consistent statistical model representing the combined information, using efficient sampling models. We discuss what methodology is available today, and what is still needed to be developed in order to achieve the goal. An example of the current state of the framework is provided to demonstrate how end-users can make informed decisions with the specific goal of identifying construction aggregates.

Accurate, efficient, and accessible forward modeling of geophysical processes is essential for understanding them and for inversion of geophysical data. Various algorithms are available for predicting data with the time domain electromagnetic method (TDEM). These algorithms differ in their approach and implementation, making some more suitable than others for specific applications. In this study, we compare three different algorithms for calculating the solution to the 1D forward response problem in TDEM, provided by Geoscience Australia, AarhusInv and SimPEG. Our comparison focuses on four main aspects: efficiency, accuracy, generality and convenience. Efficiency is evaluated from the perspective of computational speed. Accuracy is evaluated in two steps. First, we analyze the relative modeling error of each algorithm’s forward calculation for conductive half-space models, compared to an analytic solution. Secondly, we evaluate the accuracy of the algorithms relative to each other in the context of more complex earth models where no analytic solutions exist. This evaluation assumes a realistic TDEM instrument. Generality is the ability to model a variety of real TDEM scenarios. Lastly, we assess the convenience of each algorithm by considering factors such as ease of use, extensibility, code accessibility, and licensing requirements. We find that no single tested forward algorithm is best for all cases. AarhusInv is accurate and fast while it also has the most options for modeling real TDEM systems, but it requires a license, and is the hardest forward algorithm to interface to. SimPEG is open source, fast, easy to install and results may easily be shared, but has accuracy limitations at early times when modeling real systems with gate integration and low-pass filters. Lastly, Geoscience Australia is open source, accurate, and fast, but can only model dipole sources.

Of the roughly 50.000 mines that were deployed in Danish waters during the First and Second World Wars, the Royal Danish Navy estimates that 4.000 to 6.000 units remain unexploded. Naval mines are to this day regularly found by fishermen or during surveys related to offshore construction work and reported to the Royal Danish Navy who then undertakes their controlled detonation. Seismic and hydroacoustic signals from naval mine explosions have been recorded by distributed acoustic sensing (DAS) on subsea fiber optic cabling where the hydroacoustic waves are readily identified. We have developed a simple technique that uses inversion of the travel time of hydroacoustic signals to determine the location of explosions. The technique has also been tested on hydroacoustic waves from a marine air gun seismic survey that crosses a fiber cable in shallow water monitored by DAS. We present the inversion results in addition to the data processing and analysis.

Local approaches have gained interest because they can provide fast approximate solutions for inverse problems. Following the idea of split-and-conquer, one aims to effectively condition variables to data using only small parts of the big model. We study and compare local approaches for conditioning in the context of seismic amplitude data and tomography, with two datasets relevant to improved oil and gas recovery in the North Sea and groundwater characterization in Denmark. In our comparison we study a local variant of an extended rejection sampler, termed localized extended rejection sampler (LERS), and a local ensemble transform Kalman filter (LETKF). Using various output statistics, we investigate the performance of the methods at marginal (e.g. mean and variance) level and joint properties (e.g. volume uncertainty and connectivity) of the subsurface variables of interest. Computed posterior statistics are compared with a reference Markov chain Monte Carlo solution. The results highlight benefits of the methods, such as fast reliable performance on the marginal properties, while joint properties in the more difficult cases show potential challenges of applying these local methodologies. Based on the results in our two cases, we discuss the applicability of the methods. We conclude that the localization methods are efficient and useful for estimating marginal properties and associated uncertainty, and can be an inexpensive tool for evaluating the need for further data processing. Local assimilation as outlined here is not suitable for generating posterior realizations of the spatial process variables.

Many 3D hydrostratigraphic models of the subsurface are interpreted as deterministic models, where an experienced modeler combines relevant geophysical and geological information with background geological knowledge. Depending on the quality of the information from the input data, the interpretation phase will typically be accompanied by an estimated qualitative interpretation uncertainty. Given the qualitative nature of uncertainty, it is difficult to propagate the uncertainty to groundwater models. In this study, a stochastic-simulation-based methodology to characterize interpretation uncertainty within a manual-interpretation-based layer model is applied in a groundwater modeling setting. Three scenarios with different levels of interpretation uncertainty are generated, and three locations representing different geological structures are analyzed in the models. The impact of interpretation uncertainty on predictions of capture zone area and median travel time is compared to the impact of parameter uncertainty in the groundwater model. The main result is that in areas with thick and large aquifers and low geological uncertainty, the impact of interpretation uncertainty is negligible compared to the hydrogeological parameterization, while it may introduce a significant contribution in areas with thinner and smaller aquifers with high geologic uncertainty. The influence of the interpretation uncertainties is thus dependent on the geological setting as well as the confidence of the interpreter. In areas with thick aquifers, this study confirms existing evidence that if the conceptual model is well defined, interpretation uncertainties within the conceptual model have limited impact on groundwater model predictions.

We introduce a novel age-depth modeling approach called CosmoChron that integrates both cosmogenic nuclide concentrations and other age constraints, such as radiocarbon and OSL ages, from different depths in a sedimentary sequence. Based on probabilistic inverse modeling, CosmoChron constrains the age-depth relationship of a sedimentary sequence along with associated uncertainties. Knowledge about the sample origins and the accumulation process is incorporated in the prior model. The 26 Al/ 10 Be ratio is computed at different depths in the forward model by accounting for different pre-burial scenarios, radioactive decay and post- burial production of 26 Al- 10 Be, which is directly tied to the age-depth relation itself. Synthetic test cases demonstrate the method's ability to construct accurate age- depth relationships given by the posterior distribution, even for complex scenarios that include slow and varying accumulation rates, complex pre-burial histories, hiatuses, and unconformities. Based on observed unconformities, users have the option to manually input hiatuses into the model at specific depths, which allows estimation of their durations. Application of CosmoChron to real 26 Al/ 10 Be data from the Laujunmiao section in China yields ages that are similar to those obtained with conventional burial dating methods for specific stratigraphic layers. However, the associated uncertainties are significantly reduced with CosmoChron (by-47 % on average) because it exploits the vertical coupling of data combined with knowledge of the relative age of the samples, which must become younger towards the top of the profile. Additionally, the age-depth model reflets the duration of three hiatuses inferred from unconformities observed in the field. When CosmoChron is applied to OSL-derived ages from Jingbian section A on the Chinese Loess Plateau, covering the last-140 ka, the method produces results that are almost identical to those obtained with the well-established Bacon age-depth modeling approach. CosmoChron consequently offers a new, versatile and reliable tool to construct age- depth models for Quaternary sediment sequences.

<p>“All models are wrong but some are useful” (most often credited to George Cox) is a commonly used aphorism, probably because it resonates with some truth to many. We argue though, that it would be more correct to say “All <em>deterministic</em> models are wrong but some are useful “. Here, a deterministic model refers to any single, and in some quantitative way ‘optimal’ model, typically the results of minimizing some objective function. A deterministic model may be useful to use as a base for making decisions, but, it may also lead to disastrous results. The real disturbing issue with deterministic models is that we do not know whether it is useful for a specific application, because of a lack of uncertainties.</p> <p>On the other hand, a probabilistic model, that is described by a probability density, or perhaps by many realizations of a probability density, can represent in principle arbitrarily complex uncertainty. In the simplest case where the probabilistic model is represented by a maximum entropy uncorrelated uniform distribution, one can say that “The simplest probabilistic model is true but not very useful.“.  It is true in the sense that the real Earth model is represented by the probabilistic model, i.e. it is a possible realization from the probabilistic model, but not very useful, as little to no information about the Earth can be inferred.</p> <p>In an ideal case, a probabilistic model can be set up from a variety of different sources, such that it is both informative (low entropy), and consistent with an actual subsurface model in which case we can say “An informative probabilistic model can be true and also very useful.“. Any uncertainty in the probabilistic model can then be propagated to any other related uncertainty assessment using simple Monte Carlo methods. In such a case clearly, uncertainty is useful.</p> <p>In practice though, when a probabilistic Earth model has been constructed from different sources (such as structural geology, well logs, and geophysical data) then one will often find that the uncertainty of each source of information will be underestimated, such that the combined model will describe too little uncertainty. This can lead to potentially worse decision-making than when using a deterministic model (that one knows is not correct), as one may take a decision related to a low probability of a risky scenario that may simply be related to the underestimation and/or bias of the uncertainty.</p> <p>We will show examples of constructing both deterministic and probabilistic Earth models, based on a variety of geo-based information. We hope to convince the audience, that a probabilistic model can be designed such that it is consistent with the actual subsurface, and at the same time provides an optimal base for decision-makers and risk analysis.</p> <p>In the end, we argue that: Uncertainty is not only useful but essential, to any decision-making, but also that it is of utmost importance that the underlying information is quantified in an unbiased way. If not, a probabilistic model may simply provide a complex base in which to take wrong decisions.</p>

Heterogeneous glacial deposits dominate large parts of the Northern Hemisphere. In these landscapes, high-resolution characterization of the geology is crucial for understanding contaminant transport. Geological information is mostly obtained from multiple boreholes drilled during a site investigation, but such point-based data alone do not always provide the required resolution to map small-scale heterogeneity between boreholes. Crosshole ground penetrating radar (GPR) is suggested as a tool for adding credible geological information between boreholes at contaminated site investigations in industrial sites where infrastructure, such as electrical installations, can pose a challenge to other geophysical methods. GPR data are sensitive to the dielectric permittivity and the bulk electrical conductivity, which can be related to the distribution of water content and sand/clay occurrences. Here we present a detailed crosshole GPR dataset collected at an industrial contaminated site in a clay till setting. The data are processed using a novel inversion approach where information on changes in the velocity and attenuation of the radar signal are obtained independently. The GPR results are compared to borehole logs, grain size analyses, and relative permeability data from the site. The GPR data analysis provided valuable information on the understanding of the lateral geological variability. A silt layer with a thickness of a few decimeters, likely important for flow characterization, was confirmed and resolved by GPR data. Our findings suggest that crosshole GPR has the potential for contributing with high-resolution geological information by filling the data gap between boreholes, thereby becoming a relevant tool in contaminated site investigations.

Probabilistic methods for geophysical inverse problems allow the use of arbitrarily complex prior information in principle. Geostatistical techniques, such as multiple-point statistics (MPS), for describing spatial correlation models and higher-order statistics have been proposed to achieve this inversion task, in which stochastic algorithms such as Markov chain Monte Carlo (McMC) are incorporated. However, stochastic sampling and optimization often require a large number of iterations, and thus geostatistical sampling of the prior model can become computationally demanding. To overcome this challenge, a deep learning model, namely conditional generative adversarial networks (CGANs), is proposed, which allows one to perform a random walk to sample the complex prior distribution. CGANs simulate conditional realizations conditioned to the available hard conditioning data, that is, direct measurements, while preserving the geometrical structure of the model parameters of interest and replicating the sequential Gibbs sampling algorithm. Despite the need for a training step, for a large number of simulations, CGANs are more efficient than traditional geostatistical simulation algorithms such as single normal equation simulation (SNESIM). The proposed methodology is used as part of the extended Metropolis algorithm to predict the distributions of categorical facies in two examples, a dune environment in the Gobi Desert and a channel system in an idealized subsurface reservoir, from indirect observational data such as acoustic impedance. The inversion results are compared to the extended Metropolis algorithm using standard MPS sampling.

In probabilistic inversion of geophysical data, one must describe the expected noise in the system, and any prior information. In a geoscience context, prior information can provide a quantitative description of the expected spatial variability and correlations of the geology. But in practical inversion cases, driven by difficulty in quantifying geological information and computational complexity, an analytical mathematical smooth prior model is often chosen to describe the spatial variability. This is one of the primary reasons that realistic geological structures are difficult to resolve in geophysical models. Thus, there is currently a need for investigating and proposing practical ways of capturing complex (and often qualitative) geological information in statistical prior models that can be used in probabilistic inversion, which satisfies both the geologist, geophysicist, engineer and the geostatistician. In this research we show how a 1D statistical prior model can be designed that emulates the spatial distribution found in 188 boreholes with Miocene and Quaternary deposits from a study area (approx. 177,5 km2) near Horsens, Denmark. The prior model is built in two major steps 1) a multidimensional distribution describing the sub-division of major geological elements (here represented by lithologies from defined geological periods) and 2) a truncated pluri-Gaussian distribution describing the internal structure of lithologies within each element. The presented prior model can both be used to generate independent realizations, which can be used as part of the extended rejection sampler, as well as allowing the possibility of doing a "random walk" in the model space, as required by the extended Metropolis algorithm. We demonstrate, as an example, how the developed prior model can be used in a probabilistic inversion of airborne transient electromagnetic (AEM) data and discuss the implications the use of such informed prior models can have.

Decision-making related to groundwater management often relies on results from a deterministic groundwater model representing one ‘optimal’ solution. However, such a single deterministic model lacks representation of subsurface uncertainties. The simplicity of such a model is appealing, as typically only one is needed, but comes with the risk of overlooking critical scenarios and possible adverse environmental effects. Instead, we argue, that groundwater management should be based on a probabilistic model that incorporates the uncertainty of the subsurface structures to the extent that it is known. If such a probabilistic model exists, it is, in principle, simple to propagate the uncertainties of the model parameter using multiple numerical simulations, to allow a quantitative and probabilistic base for decision-makers. However, in practice, such an approach can become computationally intractable. Thus, there is a need for quantifying and propagating the uncertainty numerical simulations and presenting outcomes without losing the speed of the deterministic approach.This presentation provides a probabilistic approach to the specific groundwater modelling task of determining well recharge areas that accounts for the geological uncertainty associated with the model using a deep neural network. The results of such a task are often part of an investigation for new abstraction well locations and should, therefore, present all possible outcomes to give informative decision support. We advocate for the use of a probabilistic approach over a deterministic one by comparing results and presenting examples, where probabilistic solutions are essential for proper decision support. To overcome the significant increase in computation time, we argue that this problem can be solved using a probabilistic neural network trained on examples of model outputs. We present a way of training such a network and show how it performs in terms of speed and accuracy. Ultimately, this presentation aims to contribute with a method for incorporating model uncertainty in groundwater modelling without compromising the speed of the deterministic models.

Results from numerical simulations play a vital role in the decision process of everyday groundwater management. However, these simulations can be time-consuming for large-scale investigations, and it can be necessary to apply approximate methods instead.This study investigates the abilities of a neural network to replicate simulated drawdown from groundwater abstraction in a numerical groundwater model of the Egebjerg catchment, Denmark. We follow a generalised methodology that uses the information within the deterministic numerical model to create a training set for the neural network to learn from and extend the method to work in a 3D Danish groundwater model case. We compare the abilities of the trained neural network with the results of conventional computations in terms of speed and accuracy and argue that this approach has the potential to improve decision support for decision-makers within groundwater management.

Accounting for an accurate noise model is essential when dealing with real data, which are noisy due to the effect of environmental noise, failures and limitations in data acquisition and processing. Quantifying the noise model is a challenge for practitioners in formulating an inverse problem, and usually, a simple Gaussian noise model is assumed as a white noise model. Here we propose a pragmatic approach to use an estimated seismic wavelet to capture the correlated noise model (coloured noise) for the processed reflection seismic data. We assess the proposed method through a direct inversion of post-stack seismic data associated with a carbonate reservoir of an oil field in southwest Iran to porosity, using a probabilistic sampling-based inversion algorithm. In the probabilistic formulation of the inverse problem, we assume eight different noise models with varying bandwidth and magnitude and investigate the corresponding posterior statistics. The results indicate that if the correlated nature of the noise samples is ignored in the noise covariance matrix, some unrealistic features are generated in porosity realizations. In addition, if the noise magnitude is underestimated, the inversion algorithm overfits the data and generates a biased model with low uncertainty. Furthermore, by considering an imperfect bandwidth for the noise model, the error is propagated to the posterior realizations. Assuming the correlated noise in a probabilistic inversion resolves these issues significantly. Therefore, for inverting real seismic data where the estimation of the magnitude and correlations of the noise is not straightforward, the wavelet, which is estimated from the real seismic data, provides a good proxy for describing the correlation of the noise samples or equivalently the bandwidth of the noise model. In addition, it might be better to overestimate the noise magnitude than to underestimate it. This is true especially for an uncorrelated noise model and to a lesser degree also for the correlated noise model.

SUMMARY A test site containing 24 targets of various disarmed unexploded ordnance (UXO) and non-UXO items were placed on a beach on the island of Rømø (Denmark) in a 600 m × 100 m area. Scalar magnetic anomalies were measured at 3–5 m altitude using an uncrewed aerial vehicle (UAV), towing a bird with a three-sensor triangular configuration to achieve a dense coverage with flight lines of 2 m spacing. The triple-sensor data set is utilized in a probabilistic inversion setup to infer the magnetic moments of the 24 targets. The purpose of the study, is to try and distinguish between different types of ferromagnetic objects (UXO, non-UXO) using magnetic anomaly data. The inversion methodology uses different forward models (prolate spheroids, rectangular prisms) to infer target shape, size and orientation in an attempt to discriminate between UXO and non-UXO items. Stochastic inversions are carried out using different prior assumptions of remanent magnetization strength (10, 50 and 80 per cent) of the induced dipole moment. Among the three levels of remanent magnetization strength in the prior, only some cases of discrimination seem evident for the lowest strength of remanence. One item is correctly classified as a true-negative (i.e. non-UXO) when assuming low remanent magnetization strength (10 per cent of the induced moment). However, at low remanent strength, one false-negative classification emerges, making any discrimination unreliable when assuming such low remanent magnetization. In addition to the discrimination study, different covariance models are utilized to optimize the inversion by addressing correlated errors and noise in the triple-sensor data set. Three covariance models are tested to try and account for spatially correlated noise and potential errors among the three sensors of each overflight. In many cases, the covariance models presented show a potential increase in sampling efficiency and consistency between data and the noise model, suggesting a more robust approach to a noise model in magnetic anomaly inversions. If the noise model is poor, however, it may bias the results by addressing the anomaly signal as noise. The inversions with correlated noise models are compared with inversions using a simple uncorrelated noise model. For several cases of data anomalies, differences between the inversion estimates when using correlated and uncorrelated noise models were evident, indicating that some bias may appear when assuming uncorrelated noise. Due to the general high presence of correlated signals in magnetic survey data, correlated noise models can significantly improve the overall uncertainty estimate of the estimated dipole moment. The study demonstrates, in terms of the 24 targets considered, that discrimination between UXO and non-UXO using magnetics is difficult. However, when using scalar magnetic data of high quality and resolution, the estimated dipole moments are often well resolved and uniquely defined in magnitude and position. This could provide valuable posterior information for future inversion studies by building a library of inferred magnetic moments from targets that have been found and inspected.