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Forty years and 157 papers later, research on contaminant source identification has grown exponentially in number but seems to be stalled concerning advancement towards the problem solution and its field application. This paper presents a historical evolution of the subject, highlighting its major advances. It also shows how the subject has grown in sophistication regarding the solution of the core problem (the source identification), forgetting that, from a practical point of view, such identification is worthless unless it is accompanied by a joint identification of the other uncertain parameters that characterize flow and transport in aquifers. [ABSTRACT FROM AUTHOR]

We briefly review the state-of-the-art machine learning (ML) algorithms for mineral exploration, which mainly include random forest (RF), convolutional neural network (CNN), and graph convolutional network (GCN). In recent years, RF, a representative shallow machine learning algorithm, and CNN, a representative deep learning approach, have been proved to be powerful tools for ML-based mapping for mineral exploration. In the future, GCN deserves more attention for ML-based mapping for mineral exploration because of its ability to capture the spatial anisotropy of mineralization and its applicability within irregular study areas. Finally, we summarize the original contributions of the six papers comprising this special issue. [ABSTRACT FROM AUTHOR]

The effectiveness of the method is demonstrated in a controlled case study using a real mine drill-hole dataset. The second paper on the issue is "Compression-based facies modelling" by Manzocchi et al., which addresses the issue of reproducing the connectivity in facies modeling, while at the same time respecting the facies proportions. The last paper closing the special issue is "Multivariate cross-validation and measures of accuracy and precision" by Mueller et al., which extends the cross-validation approach and associated performance measures from a single target variable to a multivariate case using regionalized compositions. [Extracted from the article]

The linear calibration model is a powerful statistical tool that can be utilized to predict an unknown response variable, Y, through observations of a proxy or predictor variable, X. Since calibration involves estimation of regression model parameters on the basis of a limited amount of noisy data, an unbiased calibration slope estimation is of utmost importance. This can be achieved by means of state-of-the-art, data-driven statistical techniques. The present paper shows that weighted least-squares for both variables estimation (WLSXY) is able to deliver unbiased slope estimations under heteroscedasticity. In the case of homoscedasticity, besides WLSXY, ordinary least-squares (OLS) estimation with bias correction (OLSBC) also performs well. For achieving unbiasedness, it is further necessary to take the correct regression direction (i.e., of Y on X) into account. The present paper introduces a pairwise moving block bootstrap resampling approach for obtaining accurate estimation confidence intervals (CIs) under real-world climate conditions (i.e., non-Gaussian distributional shapes and autocorrelations in the noise components). A Monte Carlo simulation experiment confirms the feasibility and validity of this approach. The parameter estimates and bootstrap replications serve to predict the response with CIs. The methodological approach to unbiased calibration is illustrated for a paired time series dataset of sea-surface temperature and coral oxygen isotopic composition. Fortran software with implementation of OLSBC and WLSXY accompanies this paper. [ABSTRACT FROM AUTHOR]

Intelligent identification of the different lithology of outcrops has been a major research challenge in the field of geology. The manual identification of outcrop lithology is labor-intensive and lacks systematicity and consistency. Intelligent lithology identification based on deep convolutional neural networks can significantly reduce such workload and also serves as the foundation for intelligent outcrop research. In this paper, we propose a workflow based on the DeepLabV3+ semantic segmentation neural network algorithm. The algorithm can intelligently identify the lithology of outcrop photos obtained by unmanned aerial vehicle (UAV) oblique photography. Based on this workflow, we can complete the tasks of dataset creation, model training, intelligent identification of outcrop lithology, and model accuracy evaluation. The dataset used in this paper is composed of high-resolution photos of the Fugu Tiansheng Bridge Shihezi Formation profile collected by UAV, which are annotated with three major categories and five subcategories of lithology. Then, we input the data into four types of neural networks, including a fully convolutional network (FCN), SegNet, U-Net, and DeepLabV3+, for training. The results indicate that the recognition accuracies of the four neural network algorithms, FCN, SegNet, U-Net, and DeepLabV3+, for outcrop lithology classification tasks based on UAV oblique photography images are 90.81%, 90.44%, 92.03%, and 93.88%, respectively. Among such algorithms, the DeepLabV3+ semantic segmentation neural network algorithm is reliable and accurate, and can provide a basis for intelligent lithology recognition. This is fundamental for promoting the automation, intelligence, and digitalization of geological outcrop research. [ABSTRACT FROM AUTHOR]

In this expository review paper, we show that co-kriging, a widely used geostatistical multivariate optimal linear estimator, has a diverse range of extensions that we have collected and illustrated to show the potential of this spatial interpolator. In the context of spatial stochastic processes, this paper covers scenarios including increasing the spatial resolution of a spatial variable (downscaling), solving inverse problems, estimating directional derivatives, and spatial interpolation taking boundary conditions into account. All these spatial interpolators are optimal linear estimators in the sense of being unbiased and minimising the variance of the estimation error. [ABSTRACT FROM AUTHOR]

This document is a special issue of the journal Mathematical Geosciences, focusing on the application of geostatistics in environmental contexts. The issue includes eight papers that were originally presented at the 14th International Conference on Geostatistics for Environmental Applications (geoENV2022) in Parma, Italy. The papers cover a wide range of topics, including soil water content estimation, radon dispersion, COVID-19 prediction, geophysical Bayesian inversion, seismic refraction data analysis, COVID-19 risk modeling, clustering approaches, and Bayesian kriging for radionuclide estimation. Each paper provides valuable insights into the latest research in geostatistics. [Extracted from the article]

The use of spreadsheets in numerical groundwater flow modeling, although not new, has yet to be fully exploited in educational settings. This teaching aid complements the one published earlier, broadening its scope from the numerical solution for a single-layer confined aquifer to include unconfined aquifers. It covers flow in horizontal layers and multilayered vertical cross-sections. The new spreadsheets can also handle hydraulic conductivity anisotropy, provided its principal directions align with the Cartesian axes. It can also manage irregular aquifer shapes, incorporate all three types of boundary conditions, and account for pumping and recharge in the modeling process. However, the flow regime remains at steady state. With the integration of these new features, the spreadsheet model becomes a versatile tool for simulating a great number of steady-state groundwater flow situations. This user-friendly platform enables students to swiftly experiment with diverse configurations, delve into the underlying mathematical expressions, and gain insight into the workings of more sophisticated numerical codes like MODFLOW. As a complement, and for verification purposes, Python Flopy scripts are provided for all examples in the GitHub repository where the spreadsheets can be accessed. [ABSTRACT FROM AUTHOR]

The discovery of gas in Groningen in 1959 has been a massive boon to the Dutch economy. From the 1990s onwards, though, gas production has led to induced seismicity. In this paper, we carry out a comprehensive exploratory analysis of the spatio-temporal earthquake catalogue. We develop a non-parametric adaptive kernel smoothing technique to estimate the spatio-temporal hazard map and to interpolate monthly well-based gas production statistics. Second- and higher-order inhomogeneous summary statistics are used to show that the state-of-the-art rate-and-state models for the prediction of seismic hazard fail to capture inter-event interaction in the earthquake catalogue. Based on these findings, we suggest a modified rate-and-state model that also takes into account changes in gas production volumes and uncertainty in the pore pressure field. [ABSTRACT FROM AUTHOR]

Brønnøy Kalk AS operates an open pit mine in Norway producing marble, mainly used by the paper industry. The final product is used as filler and pigment for paper production. Therefore, the quality of the product has utmost importance. In the mine, the primary quality indicator, called TAPPI, is quantified through a laborious sampling process and laboratory experiments. As a part of digital transformation, measurement while drilling (MWD) data have been collected in the mine. The purpose of this paper is to use the recorded MWD data for the prediction of marble quality to facilitate quality blending in the pit. For this purpose, two supervised classification modelling algorithms such as conventional logistic regression and random forest have been employed. The results show that the random forest classification model presents significantly higher statistical performance, and it can be used as a tool for fast and efficient marble quality assessment. [ABSTRACT FROM AUTHOR]

The role of data science has increased in the geosciences given the mounting recognition of the limitations associated with traditional physical model driven methods in describing complex phenomena and in explaining large amounts of conditioning Earth monitoring data, which have become readily available in the digital era. I Discover i Discovering patterns in geoscience data is a natural application for machine learning, which empowers experts with a relatively unbiased way to interpret the data and help account for the associated uncertainty more accurately. Overall, the collection of papers in this Special Issue demonstrates how data science methods can help tackle computational and uncertainty quantification problems in geosciences with great success. [Extracted from the article]

Kriging is the most widely used spatial interpolation method in geostatistics. For many environmental applications, kriging may have to satisfy the stationarity and isotropy hypothesis, and new techniques using machine learning suffer from a lack of labeled data. In this paper, we propose the use of deep image prior, which is a U-net-like deep neural network designed for image reconstruction, to perform spatial interpolation and conditional map generation without any prior learning. This approach allows us to overcome the assumptions for kriging as well as the lack of labeled data when proposing uncertainty and probability above a certain threshold. The proposed method is based on a convolutional neural network that generates a map from random values by minimizing the difference between the output map and the observed values. With this new method of spatial interpolation, we generate n maps to obtain a map of uncertainty and a map of probability of exceeding the threshold. Experiments demonstrate the relevance of the proposed methods for spatial interpolation on both the well-known digital elevation model data and the more challenging case of pollution mapping. The results obtained with the three datasets demonstrate competitive performance compared with state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Various rotation operations are required in paleomagnetism. These include transformations to the geographic coordinate system, tilt correction, and finding virtual geomagnetic poles. Different methods have been used for each rotation operation—graphical manipulation on stereonet, matrix calculation, and spherical trigonometry—and computer software has been developed based on these methods. Quaternions, which are commonly used in three-dimensional computer graphics, can handle rotations about arbitrary axes and provide a unified description of the various rotation operations in paleomagnetism. The conversion from a sample coordinate system to the geographic coordinate system depends on orientation methods that vary by sample type and laboratory. Traditionally, coordinate transformations have been computed using rotation matrices of Euler angles based on stereonet manipulation, but quaternions can flexibly accommodate samples oriented by different conventions. Tilt correction can be expressed as a single rotation around the strike direction of the formation. Virtual geomagnetic poles can be obtained by a single quaternion rotation instead of complicated spherical trigonometry. Python functions are provided for all of the rotation operations discussed in this paper, so the readers can incorporate these functions into their own programs to perform rotations using quaternions. [ABSTRACT FROM AUTHOR]

Extreme events such as natural and economic disasters leave lasting impacts on society and motivate the analysis of extremes from data. While classical statistical tools based on Gaussian distributions focus on average behaviour and can lead to persistent biases when estimating extremes, extreme value theory (EVT) provides the mathematical foundations to accurately characterise extremes. This motivates the development of extreme value models for extreme event forecasting. In this paper, a dynamic extreme value model is proposed for forecasting volcanic eruptions. This is inspired by one recently introduced for financial risk forecasting with high-frequency data. Using a case study of the Piton de la Fournaise volcano, it is shown that the modelling framework is widely applicable, flexible and holds strong promise for natural hazard forecasting. The value of using EVT-informed thresholds to identify and model extreme events is shown through forecast performance, and considerations to account for the range of observed events are discussed. [ABSTRACT FROM AUTHOR]

Recent years have seen a steady growth in the number of papers that apply machine learning methods to problems in the earth sciences. Although they have different origins, machine learning and geostatistics share concepts and methods. For example, the kriging formalism can be cast in the machine learning framework of Gaussian process regression. Machine learning, with its focus on algorithms and ability to seek, identify, and exploit hidden structures in big data sets, is providing new tools for exploration and prediction in the earth sciences. Geostatistics, on the other hand, offers interpretable models of spatial (and spatiotemporal) dependence. This special issue on Geostatistics and Machine Learning aims to investigate applications of machine learning methods as well as hybrid approaches combining machine learning and geostatistics which advance our understanding and predictive ability of spatial processes. [ABSTRACT FROM AUTHOR]

This paper describes a geostatistical approach to model and visualize the space–time distribution of groundwater contaminants. It is illustrated using data from one of the world's largest plume of trichloroethylene (TCE) contamination, extending over 23 km2, which has polluted drinking water wells in northern Michigan. A total of 613 TCE concentrations were recorded at 36 wells between May 2003 and October 2018. To account for the non-stationarity of the spatial covariance, the data were first projected in a new space using multidimensional scaling. During this spatial deformation the domain is stretched in regions of relatively lower spatial correlation (i.e., higher spatial dispersion), while being contracted in regions of higher spatial correlation. The range of temporal autocorrelation is 43 months, while the spatial range is 11 km. The sample semivariogram was fitted using three different types of non-separable space–time models, and their prediction performance was compared using cross-validation. The sum-metric and product-sum semivariogram models performed equally well, with a mean absolute error of prediction corresponding to 23% of the mean TCE concentration. The observations were then interpolated every 6 months to the nodes of a 150 m spacing grid covering the study area and results were visualized using a three-dimensional space–time cube. This display highlights how TCE concentrations increased over time in the northern part of the study area, as the plume is flowing to the so-called Chain of Lakes. [ABSTRACT FROM AUTHOR]

Gaussian process (GP) regression provides a probabilistic framework for modeling geochemistry in mineral resource estimation and environmental monitoring applications. An issue with this approach is that the kernel hyperparameters obtained by maximizing the log-marginal likelihood (LML) often produce GP posterior mean estimates that are overly smooth. This motivates the development of augmented kernels that are more capable of capturing the variability inherent in geological/geochemical processes than the existing stationary covariance functions like the Matérn kernels. This paper makes two contributions. First, it describes an extended class of stationary kernels that contain an extra smoothness hyperparameter (α ) which can be learned from the input data. Valid intervals for α that lead to positive semi-definiteness are determined. Second, it uses a statistical measure called the structural similarity index (SSIM) to quantify smoothness and the spatial fidelity of GP solutions with respect to the input samples. This provides a new way for validating and optimizing GP models. Statistical and spectral analyses provide insights into the behavior of α in the augmented kernels which retain useful properties such as sparsity. Results on the Northern Great Basin geochemical dataset demonstrate that, all things being equal, (1) adjusting α increases spatial fidelity in GP regression; (2) SSIM is a more reliable spatial quality measure than LML; and (3) the optimal α value obtained is correlated with the Wiener entropy of the random process, which indicates the spectral flatness of the chemical signal in the Fourier domain. For GP regression, function smoothness may be defined using Sobolev space. The results show that α regulates over-smoothing by moderating the rate of decay in the power spectrum of the equivalent kernel. [ABSTRACT FROM AUTHOR]