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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]

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]

Deep learning (DL) techniques have recently attracted considerable attention in the field of seismic data denoising. However, most DL-based seismic denoising models require a considerable number of paired noisy–clean samples for training, which limits their application in practice. In this paper, a novel self-supervised DL scheme for noise attenuation in reflection seismic data is proposed based on the Neighbor2Neighbor strategy. The proposed method adopts a U-shaped convolutional network as the main network and incorporates regularization loss during training to improve the stability of network training, thereby constructing an end-to-end self-learning process for seismic data denoising. Specifically, a neighborhood subsampling workflow is built on single noisy seismic data to generate paired noisy images for training. Next, an unsupervised evaluation metric, grounded solely in noisy data, is adopted to quantitatively evaluate the performance of the denoising algorithm without labeled data. The application to synthetic datasets suggests that the proposed method achieves better denoising results than traditional (e.g., f−x deconvolution and wavelet analysis) and self-supervised methods, and rivals a widely used supervised DL model, the denoising convolution neural network. In real application to seismic data denoising without noise-free labels, the proposed method more effectively suppresses migration artifacts and random noise while better preserving the signal integrity compared to other methods. These improvements demonstrate that the proposed method is an independent, novel, and powerful data-driven DL scheme suitable for real seismic data denoising. [ABSTRACT FROM AUTHOR]

Geographic information system-based mineral prospectivity mapping (MPM) aims to generate targets by combining multiple proxy layers containing geology, geochemistry, and geophysics information based on an available understanding of geological processes and translating it into critical targeting criteria. However, factors such as an imperfect geological understanding with numerous heuristic natures and intrinsic biases, the inaccuracy and sparsity of datasets, and multiple selections of predictive methods adversely affect the results of MPM and jeopardize the reliability of decision-making in exploration. Thus, a series of knowledge-driven and data-driven MPM approaches to counterbalance these disadvantages have been proposed. Uncertainty is defined as a metric of the various scales of the likelihood and consequences, which is helpful to quantitatively represent the above risks. In this paper, the uncertainty in the final three-dimensional prospectivity map is analyzed and interpreted in terms of quantification, visualization, and comparison of different predictive approaches, and a novel technology is proposed based on a (1 + ε) approximate global optimum strategy derived from the truth discovery society. It outputs the globally optimal truth (p*) as the overall mathematical expectation and a set of weights w i as the representation of reliability. Here, a previous study of the Haoyaoerhudong gold deposit, which is one of the largest black-rock-series-type gold mines in China, was reevaluated. The method demonstrated the following advantages: (i) sorted the reliability of potential models built by multiple predictive variables and different mathematical methods, (ii) provided a "best-guess-decision" prospectivity result by combining the best reliability model from w i and the signal-to-noise ratio (SNR) of the risk–return model, and (iii) provided a statistically final uncertainty model by combining p* and risk information. [ABSTRACT FROM AUTHOR]

The classification of seabed sediments is an essential aspect of marine spatial planning and management. Multibeam echo sounders (MBESs) have been widely used for efficient and reliable sediment classification. However, feature optimization is a complex and difficult task that requires considerable effort and domain expertise. In addition, selecting the optimal number of features and avoiding redundancy can pose challenges and ultimately lead to suboptimal classification performance. To address these limitations, this paper proposes a new approach to classifying seabed sediments by combining the parametric uniform manifold approximation and projection (PUMAP) feature optimization method with a convolutional neural network (CNN). MBES data are used to generate the main textures and bathymetric features, which are then transmitted via the CNN network. PUMAP is used to construct a representative graph from the extracted features and optimize the graph in a low-dimensional space using the weight of an autoencoder. The proposed approach was tested with MBES data from an Irish Sea survey. The results show that the proposed approach outperforms conventional sediment classification methods, with total accuracy of 97.20%, an F1 score of 97.31%, and a kappa of 0.9638. [ABSTRACT FROM AUTHOR]

This paper presents a method for tetrahedral mesh generation for subsurface reservoir structural modeling based on sequentially cutting an input tetrahedral grid with geological surfaces represented by implicit functions. Most of the existing literature on meshing to implicit surfaces mainly focuses on independent closed surfaces, making it hardly applicable to subsurface structural modeling where, in addition to occasional closed surfaces (e.g., detached salt diapirs), the subsurface model is typically made of a mixture of multiple intersecting finite surfaces (e.g., faults) and infinite surfaces (e.g., horizons). This peculiar setting sometimes makes it challenging to build a sealed structural surface model (i.e., a boundary representation model), which is the starting point of traditional, but also challenging, constrained Delaunay solid mesh generation. The method presented herein bypasses the creation of a sealed surface model and generates a solid mesh directly from point sets and/or a set of topologically disconnected surfaces; the sealed surface model is obtained as a byproduct, if needed. [ABSTRACT FROM AUTHOR]

The research presented in this paper aims at providing a statistical model that is capable of estimating soil water content based on weather data. The model was tested using a long-time series of field experimental data from continuous monitoring at a test site in Oltrepò Pavese (northern Italy). An innovative statistical function was developed in order to predict the evolution of soil–water content from precipitation and air temperature. The data were analysed in a framework of robust statistics by using a combination of robust parametric and non-parametric models. Specifically, a statistical model, which includes the typical seasonal trend of field data, has been set up. The proposed model showed that relevant features present in the field of experimental data can be obtained and correctly described for predictive purposes. [ABSTRACT FROM AUTHOR]

With the emergence of the coronavirus disease 2019 (COVID-19) pandemic in Portugal, a geostatistical tool was developed to model the spatial distribution of COVID-19 risk to support decision-making and policymakers. Based on a block direct sequential simulation algorithm, the model provides detailed disease risk estimates and associated spatial uncertainty. However, uncertainty is difficult to visualize with the estimated risk, and is usually overlooked as a tool to support decision-making. Ignoring uncertainty can be misleading in evaluating risk, since the amount of uncertainty varies throughout the spatial domain. The EpiGeostats R package was developed to solve this problem, since it integrates the geostatistical model and visualization tools to deliver a single map summarizing disease risk and spatial uncertainty. This paper briefly describes the methodology and package functions implemented for interfacing with the tools in question. The use of EpiGeostats is illustrated by applying it to real data from COVID-19 incidence rates on mainland Portugal. EpiGeostats is a powerful tool for supporting decision-making in the context of epidemics, since it combines a well-established geostatistical model for disease risk mapping with simple and intuitive ways of visualizing results, which prevent fine-scale inference in regions with high-risk uncertainty. The package may be used for similar problems such as mortality risk, or applied to other fields such as ecology or environmental epidemiology. [ABSTRACT FROM AUTHOR]

Acknowledged as a significant health hazard, increasing attention has been given to indoor and geogenic radon for some 20 years. One part of the efforts is surveying in order to assess the geographical extent of the hazard. Results acquired in surveys serve to support decisions in radon abatement policy, aimed to reduce exposure and consisting in prevention, mitigation and remediation measures. One particular element is delineation of so-called radon priority areas, or areas in which the hazard is such that abatement measures should be implemented with priority. These areas are estimated from radon measurements supported by different modelling methods. Methods which are based on estimating local probabilities that radon concentration exceeds a reference level often rely on measures of local variability, expressed for example by the geometric standard deviation or the coefficient of variation, because these describe the shape of the distribution whose tail areas are the sought-after probabilities. Evidently, delineation of radon priority areas thus depends, apart from mean concentration, on dispersion within the area whose priority status shall be assessed. A second use of spatial variability measures of radon is survey planning, because the sample size necessary to estimate a mean with given precision depends on the dispersion of the quantity to be assessed. It is estimated through pilot surveys or derived from general knowledge. The large radon databases accumulated for years allow more detailed insight into spatial properties of dispersion, some of which are discussed in this paper, in the first place the relation between local dispersion and mean and sampling density. Not least, they also grant insight—so far mostly speculative—about the process, understood as a stochastic process, which generates the spatial dynamic. Main conclusions are that a proportional effect in logarithmic scale exists and has an effect on estimation of local exceedance probability and that one should keep in mind that results, for example the local status as a radon priority area, depend on the estimation method. [ABSTRACT FROM AUTHOR]

Measuring geotechnical and natural hazard engineering features, along with pattern recognition algorithms, allows us to categorize the stability of slopes into two main classes of interest: stable or at risk of collapse. The problem of slope stability can be further generalized to that of assessing landslide susceptibility. Many different methods have been applied to these problems, ranging from simple to complex, and often with a scarcity of available data. Simple classification methods are preferred for the sake of both parsimony and interpretability, as well as to avoid drawbacks such as overtraining. In this paper, an experimental comparison was carried out for three simple but powerful existing variants of the well-known nearest neighbor rule for classifying slope/landslide data. One of the variants enhances the representational capacity of the data using so-called feature line segments, while all three consider the concept of a territorial hypersphere per prototype feature point. Additionally, this experimental comparison is entirely reproducible, as Python implementations are provided for all the methods and the main simulation, and the experiments are performed using three publicly available datasets: two related to slope stability and one for landslide susceptibility. Results show that the three variants are very competitive and easily applicable. [ABSTRACT FROM AUTHOR]

Carranza and Laborte ([6]) were the first to demonstrate the application and value of the random forest algorithm in data-driven predictive mapping of mineral prospectivity in a data-poor area. Graph B Professor Emmanuel John M. Carranza b has been selected by the International Association for Mathematical Geosciences (IAMG) Awards Committee (Chair, Xiaogang (Marshall) Ma) as the 34th winner of the William Christian Krumbein Medal of the IAMG. Carranza and Sadeghi ([7]) and Carranza et al. ([8]) demonstrated how to link data-driven predictive mapping of mineral prospectivity and quantitative estimation of undiscovered deposits, with examples in data-rich and data-poor areas. [Extracted from the article]

Understanding the structure and mineralogical composition of a region is an essential step in mining, both during exploration (before mining) and in the mining process. During exploration, sparse but high-quality data are gathered to assess the overall orebody. During the mining process, boundary positions and material properties are refined as the mine progresses. This refinement is facilitated through drilling, material logging, and chemical assaying. Material type logging suffers from a high degree of variability due to factors such as the diversity in mineralization and geology, the subjective nature of human measurement even by experts, and human error in manually recording results. While laboratory-based chemical assaying is much more precise, it is time-consuming and costly and does not always capture or correlate boundary positions between all material types. This leads to significant challenges and financial implications for the industry, as the accuracy of production blasthole logging and assaying processes is essential for resource evaluation, planning, and execution of mine plans. To overcome these challenges, this work reports on a pilot study to automate the process of material logging and chemical assaying. A machine learning approach has been trained on features extracted from measurement-while-drilling (MWD) data, logged from autonomous drilling systems (ADS). MWD data facilitate the construction of profiles of physical drilling parameters as a function of hole depth. A hypothesis is formed to link these drilling parameters to the underlying mineral composition. The results of the pilot study discussed in this paper demonstrate the feasibility of this process, with correlation coefficients of up to 0.92 for chemical assays and 93% accuracy for material detection, depending on the material or assay type and their generalization across the different spatial regions. The results achieved are significant, showing opportunities to guide further drilling processes, provide chemistry data with downhole resolution, and continuously update mine plans as the mine progresses. [ABSTRACT FROM AUTHOR]

Geomechanical modeling of the fracturing process accounts for the physical factors that inform the propagation and termination of the fractures. However, the resultant models may not honor the fracture statistics derived from auxiliary sources such as outcrop images. Stochastic algorithms, on the other hand, generate natural fracture maps based purely on statistical inferences from outcrop images excluding the effects of any physical processes guiding the propagation and termination of fractures. This paper, therefore, focuses on presenting a methodology for combining information from geomechanical and stochastic approaches necessary to obtain a fracture modeling approach that is geologically realistic as well as consistent with the geomechanical conditions for fracture propagation. As a prerequisite for this integration approach, a multi-point statistics-based stochastic simulation algorithm is implemented that yields the probability of fracture propagation along various paths. The application and effectiveness of this probability integration paradigm are demonstrated on a synthetic fracture set. [ABSTRACT FROM AUTHOR]