Assessing the impact of conceptual mineral systems uncertainty on prospectivity predictions

The past two decades have seen a rapid adoption of artificial intelligence methods applied to mineral exploration. More recently, the easier acquisition of some types of data has inspired a broad literature that has examined many machine learning and modelling techniques that combine exploration criteria, or ‘features’, to generate predictions for mineral prospectivity. Central to the design of prospectivity models is a ‘mineral system’, a conceptual model describing the key geological elements that control the timing and location of economic mineralisation. The mineral systems model defines what constitutes a training set, which features represent geological evidence of mineralisation, how features are engineered and what modelling methods are used. Mineral systems are knowledge-driven conceptual models, thus all parameter choices are subject to human biases and opinion so alternative models are possible. However, the effect of alternative mineral systems models on prospectivity is rarely compared despite the potential to heavily influence final predictions. In this study, we focus on the effect of conceptual uncertainty on Fe ore prospectivity models in the Hamersley region, Western Australia. Four important considerations are tested. (1) Five different supergene and hypogene conceptual mineral systems models guide the inputs for five forest-based classification prospectivity models model. (2) To represent conceptual uncertainty, the predictions are then combined for prospectivity model comparison. (3) Representation of three-dimensional objects as two-dimensional features are tested to address commonly ignored thickness of geological units. (4) The training dataset is composed of known economic mineralisation sites (deposits) as ‘positive’ examples, and exploration drilling data providing ‘negative’ sampling locations. Each of the spatial predictions are assessed using independent performance metrics common to AI-based classification methods and subjected to geological plausibility testing. We find that different conceptual mineral systems produce significantly different spatial predictions, thus conceptual uncertainty must be recognised. A benefit to recognising and modelling different conceptual models is that robust and geologically plausible predictions can be made that may guide mineral discovery.     

Coping with uncertainties through an automated workflow for 3D reservoir modelling of carbonate reservoirs

Reliable 3D modelling of underground hydrocarbon reservoirs is a challenging task due to the complexity of the underground geological formations and to the availability of different types of data that are typically affected by uncertainties.In the case of geologically complex depositional environments,such as fractured hydrocarbon reservoirs,the uncertainties involved in the modelling process demand accurate analysis and quantification in order to provide a reliable confidence range of volumetric estimations.In the present work,we used a 3D model of a fractured carbonate reservoir and populated it with different lithological and petrophysical properties.The available dataset also included a discrete fracture network(DFN)property that was used to model the fracture distribution.Uncertainties affecting lithological facies,their geometry and absolute positions(related to the fault system),fracture distribution and petrophysical properties were accounted for.We included all different types of uncertainties in an automated approach using tools available in today's modelling software packages and combining all the uncertain input parameters in a series of statistically representative geological realizations.In particular,we defined a specific workflow for the definition of the absolute permeability according to an equivalent,single porosity approach,taking into account the contribution of both the matrix and the fracture system.The results of the analyses were transferred into a 3D numerical fluid-dynamic simulator to evaluate the propagation of the uncertainties associated to the input data down to the final results,and to assess the dynamic response of the reservoir following a selected development plan.The"integrated approach"presented in this paper can be useful for all technicians involved in the construction and validation of 3D numerical models of hydrocarbon-bearing reservoirs and can potentially become part of the educational training for young geo-scientists and engineers,since an integrated and well-constructed workflow is the backbone of any reservoir study.     

Multivariate Modelling of Geometallurgical Variables by Projection Pursuit

The integration of geological and geometallurgical data can significantly improve decision-making and optimize mining production due to a better understanding of the resources and their metallurgical performances. The primary-response rock property framework is an approach to the modelling of geometallurgy in which quantitative and qualitative primary properties are used as proxies of metallurgical responses. Within this framework, primary variables are used to fit regression models to predict metallurgical responses. Whilst primary rock property data are relatively abundant, metallurgical response property data are not, which makes it difficult to establish predictive response relationships. Relationships between primary input variables and geometallurgical responses are, in general, complex, and the response variables are often non-additive which further complicates the prediction process. Consequently, in many cases, the traditional multivariate linear regression models (MLR) of primary-response relationships perform poorly and a better alternative is required for prediction. Projection pursuit is a powerful exploratory statistical modelling technique in which data from a number of variables are projected onto a set of directions that optimize the fit of the model. The purpose of the projection is to reveal underlying relationships. Projection pursuit regression (PPR) fits standard regression models to the projected data vectors. In this paper, PPR is applied to the modelling of geometallurgical response variables. A case study with six geometallurgical variables is used to demonstrate the modelling approach. The results from the proposed PPR models show a significant improvement over those from MLR models. In addition, the models were bootstrapped to generate distributions of feasible scenarios for the response variables. Our results show that PPR is a robust technique for modelling geometallurgical response variables and for assessing the uncertainty associated with these variables.     

FASTREACT – An efficient numerical framework for the solution of reactive transport problems

In the framework of safety assessment studies for geological disposal, large scale reactive transport models are powerful inter-disciplinary tools aiming at supporting regulatory decision making as well as providing input to repository engineering activities. Important aspects of these kinds of models are their often very large temporal and spatial modelling scales and the need to integrate different non-linear processes (e.g., mineral dissolution and precipitation, adsorption and desorption, microbial reactions and redox transformations). It turns out that these types of models may be computationally highly demanding. In this work, we present a Lagrangian-based framework, denoted as FASTREACT, that aims at solving multi-component-reactive transport problems with a computationally efficient approach allowing complex modelling problems to be solved in large spatial and temporal scales. The tool has been applied to simulate radionuclide migration in a synthetic heterogeneous transmissivity field and the results have been successfully compared with those obtained using a standard Eulerian approach. Finally, the same geochemical model has been coupled to an ensemble of realistic three-dimensional transport pathways to simulate the migration of a set of radionuclides from a hypothetical repository for spent nuclear fuel to the surface. The results of this modelling exercise, which includes key processes such as the exchange of mass between the conductive fractures and the matrix, show that FASTREACT can efficiently solve large-scale reactive transport models.     

基于Monte Carlo模拟的三维剖面地质界线不确定性分析

三维剖面地质界线是构建三维地质结构模型的重要基础数据,其不确定性会影响三维模型的几何形态和属性分布。以单一分布为假设前提的统计学不确定性分析方法掩盖了其他概率分布特征对模型的影响。突破单一误差分布条件的假设前提,本文使用Monte Carlo方法模拟了不同概率分布情况下地质剖面数据中地质界线的抽样采集,以及地质界线空间分布的不确定性;依托地质界线空间位置与地质属性的耦合关系,提出了用地质属性概率分布实现地质界线空间不确定性的定量可视化,并结合实际地质剖面探讨了多种概率分布条件下地质界线的空间不确定性。实例研究表明,基于Monte Carlo模拟的不确定性分析方法可以突破单一误差分布假设条件,结合地质属性概率可充分揭示出建模数据的内在不确定性与模型外在要素形态之间的耦合关系。     

Sensitivity and uncertainty analyses for performance assessment modeling

Sensitivity and uncertainty analyses methods for computer models are being applied in performance assessment modeling in the geologic high-level radioactive-waste repository program. The models used in performance assessment tend to be complex physical/chemical models with large numbers of input variables. There are two basic approaches to sensitivity and uncertainty analyses: deterministic and statistical. The deterministic approach to sensitivity analysis involves numerical calculation or employs the adjoint form of a partial differential equation to compute partial derivatives; the uncertainty analysis is based on Taylor series expansions of the input variables propagated through the model to compute means and variances of the output variable. The statistical approach to sensitivity analysis involves a response surface approximation to the model with the sensitivity coefficients calculated from the response surface parameters; the uncertainty analysis is based on simulation. The methods each have strengths and weaknesses.     

Integration of data constraints and potential field modelling — an example from southern lower saxony,Germany

Most of interpretational tasks in geophysics require an interdisciplinary knowledge and integration of information from comprehensive data bases. Towards this end a combination of different geophysical surveys employing seismics, gravity and magnetics, provides new insights into the structures and tectonic evolution of natural deposits together with geological and petrological studies. No doubt, any interdisciplinary approach is essential for numerical modelling of these structures and the processes acting on it. The interpretation of garvity and magnetics by 3D modelling requires data from other independent sources, due to the ambiguity of these methods.In close cooperation with geologists and computer scientists we are developing an object oriented model of the southern rim of the Northwest German Basin which consists of information from industry wells, stratigraphy and geophysical parameters (e.g. density and susceptibility). GOCAD is used for geometrical modelling purposes, IGMAS handels the interactive modifications of geophysical model parameters and geometry. Both modelling programs are supported by an object oriented data base system which will guarantee the consistency of data and models.Combined interpretations of the southern basin are presented and show, how the information from different geo-disciplines is visualized in order to ease the modelling process.     

The topology of geology 2: Topological uncertainty

Uncertainty is ubiquitous in geology, and efforts to characterise and communicate it are becoming increasingly important. Recent studies have quantified differences between perturbed geological models to gain insight into uncertainty. We build on this approach by quantifying differences in topology, a property that describes geological relationships in a model, introducing the concept of topological uncertainty. Data defining implicit geological models were perturbed to simulate data uncertainties, and the amount of topological variation in the resulting model suite measured to provide probabilistic assessments of specific topological hypotheses, sources of topological uncertainty and the classification of possible model realisations based on their topology. Overall, topology was found to be highly sensitive to small variations in model construction parameters in realistic models, with almost all of the several thousand realisations defining distinct topologies. In particular, uncertainty related to faults and unconformities was found to have profound topological implications. Finally, possible uses of topology as a geodiversity metric and validation filter are discussed, and methods of incorporating topological uncertainty into physical models are suggested.     

Application of uncertainty analysis to groundwater pollution modeling

Prediction and evaluation of pollution of the subsurface environment and planning remedial actions at existing sites may be useful for siting and designing new land-based waste treatment or disposal facilities. Most models used to make such predictions assume that the system behaves deterministically. A variety of factors, however, introduce uncertainty into the model predictions. The factors include model and pollution transport parameters and geometric uncertainty. The Monte Carlo technique is applied to evaluate the uncertainty, as illustrated by applying three analytical groundwater pollution transport models. The uncertainty analysis provides estimates of statistical reliability in model outputs of pollution concentration and arrival time. Examples are provided that demonstrate: (a) confidence limits around predicted values of concentration and arrival time can be obtained, (b) the selection of probability distributions for input parameters affects the output variables, and (c) the probability distribution of the output variables can be different from that of the input variables, even when all input parameters have the same probability distribution     

Using Sequential Indicator Simulation as a Tool in Reservoir Description: Issues and Uncertainties

Flow simulation studies require an accurate model of the reservoir in terms of its sedimentological architecture. Pixel-based reservoir modeling techniques are often used to model this architecture. There are, however, two problem areas with such techniques. First, several statistical parameters have to be provided whose influence on the resulting model is not readily inferable. Second, conditioning the models to relevant geological data that carry great uncertainty on their own adds to the difficulty of obtaining reliable models and assessing model reliability. The Sequential Indicator Simulation (SIS) method has been used to examine the impact of such uncertainties on the final reservoir model. The effects of varying variogram types, frequencies of lithology occurrence, and the gridblock model orientation with respect to the sedimentological trends are illustrated using different reservoir modeling studies. Results indicate, for example, that the choice of variogram type can have a significant impact on the facies model. Also, reproduction of sedimentological trends and large geometries requires careful parameter selection. By choosing the appropriate modeling strategy, sedimentological principles can be translated into the numerical model. Solutions for dealing with such issues and the geological uncertainties are presented. In conclusion, each reservoir modeling study should begin by developing a thorough quantitative sedimentological understanding of the reservoir under study, followed by detailed sensitivity analyses of relevant statistical and geological parameters.     

Flood inundation mapping sensitivity to riverine spatial resolution and modelling approach

An innovative approach in the investigation of complex landscapes for hydraulic modelling applications is the use of terrestrial laser scanner (TLS) that can lead to a high-resolution digital elevation model (DEM). Another notable factor in flood modelling is the selection of the hydrodynamic model (1D, 2D and 1D/2D), especially in complex riverine topographies, that can influence the accuracy of flood inundation area and mapping. This paper uses different types of hydraulic–hydrodynamic modelling approaches and several types of river and riparian area spatial resolution for the implementation of a sensitivity analysis for floodplain mapping and flood inundation modelling process at ungauged watersheds. Four data sets have been used for the construction of the river and riparian areas: processed and unprocessed TLS data, topographic land survey data and typical digitized contours from 1:5000-scale topographic maps. Modelling approaches combinations consist of: one-dimensional hydraulic models (HEC-RAS, MIKE 11), two-dimensional hydraulic models (MIKE 21, MIKE 21 FM) and combinations of coupled hydraulic models (MIKE 11/MIKE 21) within the MIKE FLOOD platform. Historical flood records and estimated flooded area derived from an observed extreme flash-flood event have been used in the validation process using 2 × 2 contingency tables. Flood inundation maps have been generated for each modelling approach and landscape configuration at the lower part of Xerias River reach at Volos, Greece, and compared for assessing the sensitivity of input data and model structure uncertainty. Results provided from contingency table analysis indicate the sensitivity of floodplain modelling on the DEM spatial resolution and the hydraulic modelling approach.     

Real-time Uncertain Geological Boundaries Updating for Improved Block Model Quality Control Based on Blast Hole Data: A Case Study for Golgohar Iron Ore Mine in Southeastern Iran

One main problem in the modeling of mineral deposits is to design a block model that divides the deposit into homogeneous subdomains. The spatial uncertainty in the geological boundaries becomes a critical factor prior to the modeling of the ore properties. For this reason, reducing the uncertainty of geological models leads to an improved mineral resource evaluation. This research work addresses the problem of updating the geological models by using actual online-sensor measurement data. A novel algorithm is provided, which integrates the discrete wavelet transform to the Ensemble Kalman Filter for assimilating online-sensor production data into geological models. The geological realizations in each time step are transformed to frequency coefficients and, after each assimilation step, the updated realizations are back-transformed to the original categorical distribution. Furthermore, a reconciliation process is performed to compare the online-sensor data derived from the production blocks and the updated realizations in each time step. The algorithm is illustrated through an application to the Golgohar iron deposit located in SW of Sirjan, Iran, and proves to reproduce the statistical parameters and connectivity values of the primary geological realizations.

     

Estimation of Hydraulic Conductivity and Its Uncertainty from Grain-Size Data Using GLUE and Artificial Neural Networks

Various approaches exist to relate saturated hydraulic conductivity (K _s) to grain-size data. Most methods use a single grain-size parameter and hence omit the information encompassed by the entire grain-size distribution. This study compares two data-driven modelling methods??multiple linear regression and artificial neural networks??that use the entire grain-size distribution data as input for K _s prediction. Besides the predictive capacity of the methods, the uncertainty associated with the model predictions is also evaluated, since such information is important for stochastic groundwater flow and contaminant transport modelling. Artificial neural networks (ANNs) are combined with a generalised likelihood uncertainty estimation (GLUE) approach to predict K _s from grain-size data. The resulting GLUE-ANN hydraulic conductivity predictions and associated uncertainty estimates are compared with those obtained from the multiple linear regression models by a leave-one-out cross-validation. The GLUE-ANN ensemble prediction proved to be slightly better than multiple linear regression. The prediction uncertainty, however, was reduced by half an order of magnitude on average, and decreased at most by an order of magnitude. This demonstrates that the proposed method outperforms classical data-driven modelling techniques. Moreover, a comparison with methods from the literature demonstrates the importance of site-specific calibration. The data set used for this purpose originates mainly from unconsolidated sandy sediments of the Neogene aquifer, northern Belgium. The proposed predictive models are developed for 173 grain-size K _s-pairs. Finally, an application with the optimised models is presented for a borehole lacking K _s data.     

Statistical modelling of thermal annealing of fission tracks in apatite

We develop an improved methodology for modelling the relationship between mean track length, temperature, and time in fission track annealing experiments. We consider “fanning Arrhenius” models, in which contours of constant mean length on an Arrhenius plot are straight lines meeting at a common point. Features of our approach are explicit use of subject matter knowledge, treating mean length as the response variable, modelling of the mean-variance relationship with two components of variance, improved modelling of the control sample, and using information from experiments in which no tracks are seen.

This approach overcomes several weaknesses in previous models and provides a robust six parameter model that is widely applicable. Estimation is via direct maximum likelihood which can be implemented using a standard numerical optimisation package. Because the model is highly nonlinear, some reparameterisations are needed to achieve stable estimation and calculation of precisions. Experience suggests that precisions are more convincingly estimated from profile log-likelihood functions than from the information matrix.

We apply our method to the B-5 and Sr fluorapatite data of Crowley et al. (1991) and obtain well-fitting models in both cases. For the B-5 fluorapatite, our model exhibits less fanning than that of Crowley et al. (1991), although fitted mean values above 12 μm are fairly similar. However, predictions can be different, particularly for heavy annealing at geological time scales, where our model is less retentive. In addition, the refined error structure of our model results in tighter prediction errors, and has components of error that are easier to verify or modify. For the Sr fluorapatite, our fitted model for mean lengths does not differ greatly from that of Crowley et al. (1991), but our error structure is quite different.     

Development and parameterisation of a complex hydrogeological model based on high-resolution direct-push data

Ongoing developments in geological and hydrogeological investigation techniques, especially direct-push methods, have led to an increase in the quality, density and spatial resolution of data available from such investigations. This has created new challenges in the development of numerical models in terms of accurately and efficiently translating detailed and complex conceptual models into effective numerical models. Suitable geometrical and numerical modelling tools are essential in order to meet these challenges. This paper describes the development of a three-dimensional hydrogeological flow model for a contaminated site near Berlin, Germany, based on high-resolution geological data obtained principally using direct-push methods. The available data were first interpreted to construct a detailed GIS-based geological model, which formed the basis of the conceptual site model. The conceptual model was then translated into a geometrical model, which was used to create a finite element numerical model. An innovative geometry object-based approach enabled the complex structural details of the conceptual model to be accurately reproduced in the numerical model domain. The resulting three-dimensional steady-state unconfined flow model was successfully calibrated using external automated calibration software, whereby parameter values for groundwater recharge and hydraulic conductivity were determined.     

Geological modeling and simulation of CO2 injection in the Johansen formation

The Johansen formation is a candidate site for large-scale CO₂ storage offshore of the south-western coast of Norway. An overview of the geology for the Johansen formation and neighboring geological formations is given, together with a discussion of issues for geological and geophysical modelling and integrated fluid flow modelling. We further describe corresponding simulation models. Major issues to consider are capacity estimation and processes that could potentially cause CO₂ to leak out of the Johansen formation and into the formations above. Currently, these issues can only be investigated through numerical simulation. We consider the effect of different boundary conditions, sensitivity with respect to vertical grid refinement and permeability/transmisibility data, and the effect of residual gas saturations, since these strongly affect the CO₂-plume distribution. The geological study of the Johansen formation is performed based on available seismic and well data. Fluid simulations are performed using a commercial simulator capable of modelling CO₂ flow and transport by simple manipulation of input files and data. We provide details for the data and the model, with a particular focus on geology and geometry for the Johansen formation. The data set is made available for download online.     

Spatial estimation of geotechnical parameters for numerical tunneling simulations and TBM performance models

In this paper, we further elaborate on a methodology dedicated to the modeling of geotechnical data to be used as input in numerical simulation and TBM performance codes. The expression “geotechnical data” refers collectively to the spatial variability and uncertainty exhibited by the boundaries and the mechanical or other parameters of each geological formation filling a prescribed 3D domain. Apart from commercial design and visualization software such as AutoCAD Land Desktop^® software and 3D solid modelling and meshing pre-processors, the new tools that are employed in this methodology include relational databases of soil and rock test data, Kriging estimation and simulation methods, and a fast algorithm for forward or backward analysis of TBM logged data. The latter refers to the continuous upgrade of the soil or rock mass geotechnical model during underground construction based on feedback from excavation machines for a continuous reduction of the uncertainty of predictions in unsampled areas. The approach presented here is non-intrusive since it may be used in conjunction with a commercial or any other available numerical tunneling simulation code. The application of these tools is demonstrated in Mas-Blau section of L9 tunnel in Barcelona.     

Entropy-Based Weighting in One-Dimensional Multiple Errors Analysis of Geological Contacts to Model Geological Structure

In each step of geological modeling, errors have an impact on measurements and workflow processes and, so, have consequences that challenge accurate three-dimensional geological modeling. In the context of classical error theory, for now, only spatial positional error is considered, acknowledging that temporal, attribute, and ontological errors—and many others—are part of the complete error budget. Existing methods usually assumed that a single error distribution (Gaussian) exists across all kinds of spatial data. Yet, across, and even within, different kinds of raw data (such as borehole logs, user-defined geological sections, and geological maps), different types of positional error distributions may exist. Most statistical methods make a priori assumptions about error distributions that impact their explanatory power. Consequently, analyzing errors in multi-source and conflated data for geological modeling remains a grand challenge in geological modeling. In this study, a novel approach is presented regarding the analysis of one-dimensional multiple errors in the raw data used for model geological structures. The analysis is based on the relationship between spatial error distributions and different geological attributes. By assuming that the contact points of a geological subsurface are decided by the geological attributes related to both sides of the subsurface, this assumption means that the spatial error of geological contacts can be transferred into specific probabilities of all the related geological attributes at each three-dimensional point, which is termed the “geological attribute probability”. Both a normal distribution and a continuous uniform distribution were transferred into geological attribute probabilities, allowing different kinds of spatial error distributions to be summed directly after the transformation. On cross-points with multiple raw data with errors that follow different kinds of distributions, an entropy-based weight was given to each type of data to calculate the final probabilities. The weighting value at each point in space is decided by the related geological attribute probabilities. In a test application that accounted for the best estimates of geological contacts, the experimental results showed the following: (1) for line segments, the band shape of geological attribute probabilities matched that of existing error models; and (2) the geological attribute probabilities directly show the error distribution and are an effective way of describing multiple error distributions among the input data.

     

Different ways of landslide geometry interpretation in a process of statistical landslide susceptibility and hazard assessment: Horná Súča (western Slovakia) case study

The article draws a comparison between different ways of landslide geometry interpretation in the scope of the statistical landslide hazard and risk assessment processing. The landslides are included as a major input variable, which are compared with all of the input parametric factors. Based on the above comparison the input data are classified and the final map of landslide susceptibility is constructed. Methodology of multivariate conditional analysis has been used for the construction of final maps. Unique condition units was developed by combination of geological map (lithological units) and slope angle map. Lithological units were derived from geological map and subsequently reclassified into 22 classes. Slope angle map was calculated from digital elevation model (contour map at a scale 1:10,000) and reclassified into nine classes. As a case study, a wide area of Horná Súča (western Slovakia) strongly affected by landsliding (predominantly made of Flysch) has been chosen. Spatial data in the form of parametric maps, as well as final statistical data set were processed in GIS GRASS environment. Four different approaches are used for landslides interpretation: (1) area of landslide body including accumulation zone, (2) area of depletion zone, (3) lines of elongated main scarps, (4) lines of main scarp upper edge. For each approach, a zoning map of landslide susceptibility was compiled and these were compared with each other. Depending on the interpretation approach, the final susceptibility zones are markedly different (in tens of percent).