Geostatistical Conditional Simulation Research Articles

Quantification of contaminant mass discharge and uncertainties: Method and challenges in application at contaminated sites

Contaminant mass discharge (CMD) estimation involves combining multilevel concentration and flow measurements to quantify the contaminant mass passing through a control plane downgradient of a point source. However, geological heterogeneities and limited data introduce uncertainties that complicate CMD estimation and risk assessment. Although CMD is increasingly used in groundwater management, methods for quantifying and handling these uncertainties are still needed. This study develops and tests a CMD estimation method based on Bayesian geostatistics to quantify CMD uncertainties using data from a control plane perpendicular to the contaminant plume.By combining geostatistical conditional simulations of the spatial concentration distribution with the flow, an ensemble of CMD realizations is generated, from which a cumulative distribution function is derived. A key element of this approach is the use of a macrodispersive transport model to simulate the spatial concentration trend. This ensures that the estimated concentration reflects the expected physical behavior of the contaminant plume while also allowing the integration of site-specific conceptual information.The method is applicable to plumes with dissolved contaminants, such as chlorinated solvents, petroleum hydrocarbons, Per- and polyfluoroalkyl substances (PFAS) and pesticides. Site-specific conceptual understanding is used to inform the prior probability density functions of the structural model parameters and to define acceptable simulated concentration limits. We applied the method at three sites contaminated with chlorinated ethenes, demonstrating its robustness across varying information levels and data availability.Our results shows that strong site-specific conceptual knowledge and high sampling density constrain the CMD uncertainty (CV = 21 %) and results in estimated model parameters and a spatial concentration distribution that agrees well with the conceptual model. For a site with less data and limited conceptual knowledge, CMD and concentration distribution estimates are still feasible, though with higher uncertainty (CV = 41 %). Extending the method to account for multiple source zones and complex plume migration improved parameter identification and reduced the 95 % CMD confidence interval by 11 % ([4950–8750] to [5090–8480] g yr−1), while also providing a spatial concentration distribution in better agreement with the plume conceptualization.This study highlights the importance of integrating site-specific conceptual knowledge in CMD estimation, particularly for less-sampled sites. The method can furthermore assist in identifying remediation targets, evaluating remedial effectiveness, and optimizing sampling strategies.

Assessing Contaminant Mass Discharge Uncertainty With Application of Hydraulic Conductivities Derived From Geoelectrical Cross‐Borehole Induced Polarization and Other Methods

AbstractA new methodology was developed to support contaminant mass discharge (CMD)‐based risk assessment of groundwater contamination downgradient of point source zones. Geoelectrical cross‐borehole induced polarization (IP) data were collected at a site undergoing in situ remediation of chlorinated solvents for determining 2D hydraulic conductivity (K) distributions with an inversion model resolution of 0.15 m (vertically) x 0.50 m (horizontally) in three control planes from 10 to 20 m depth. Additionally, 18 slug tests and 31 grain size distribution analyses (GSA) from the control planes, were used for K‐estimation. The geometric means and variance of the IP, slug test, and GSA derived K‐estimates were consistent with previously studied sandy aquifers. Furthermore, the vertical variation in K between two geological settings, a sandy till and a meltwater sand formation, was clearly identified by the IP K‐estimates. The vertical variation was backed up by hydraulic profiling tool (HPT) measurements. Random realizations of CMD were simulated based on the cross‐borehole IP derived K‐values. For comparison, the CMD was also estimated with a geostatistical conditional simulation approach, using the data from slug tests and GSAs. The high IP resolution captured the small scale variations in K across the transects and led to CMD predictions with a narrow uncertainty interval, whereas slug test and GSA either under‐ or overestimated the magnitude of the areas with the highest CMD. Applying the geophysical cross‐borehole method for estimating K‐distributions in addition to traditional methods would improve CMD‐based risk assessment and evaluation of remediation performance at contaminated sites.

A probabilistic approach to the estimation of radioactive contaminant inventories at a nuclear waste disposal site

Routine site inspections are often conducted to gather data on radiation contamination on the surface and below ground near nuclear waste disposal areas. These observations are used to calculate total radiation inventory and its spatial delineation. The statistical kriging approach is often used to spatially interpolate contamination data, and it generates predictions at unsampled sites that are then utilized to calculate the contaminated site's radiation inventory. The kriging output, however, creates a point estimate of the inventory that omits the potential uncertainties from other sources. This paper presents a method for assessing the uncertainty of radiation inventories based on the geostatistical conditional simulation method – a simulation methodology that takes into account the observations made at the sampled sites. The radiation inventories' histograms are generated by conducting many conditional simulations of the projection map using a fitted kriging model. A practical implementation of the suggested approach is shown by evaluating total beta inventories and their spatial delineation using groundwater monitoring data at a nuclear waste disposal site.

Effect of spatial variability of soil properties and geostatistical conditional simulation on reliability characteristics and critical slip surfaces of soil slopes

Evaluation of the stability and determination of the Critical Slip Surface (CSS) of soil slopes are salient topics in geotechnical engineering. On the other hand, the stability and CSS are not only affected by soil heterogeneity but also by the boreholes’ location and method of predicting soil parameters in the domain of analysis. The unconditional simulation in which known data and its location are not incorporated may lead to results far from reality. Moreover, in some conditional simulations, the borehole data are directly mapped into the analysis section without taking the location of the known data into account, which can either overestimate or underestimate the stability of the slope. In the current study, the Finite Element Method (FEM) is coupled with the geostatistical method to evaluate the reliability characteristics and CSS distribution with consideration of the known data, location of boreholes, uncertainty of surcharge load, and soil heterogeneity. The results of a real case demonstrate that in comparison to the unconditional simulation, utilizing the conditional simulation improves the distribution of Factor of Safety (FS) by up to 14% while decreasing the related standard deviation by 4% to 40%. Moreover, conditional simulation offers a significant reduction in uncertainty of the slip surface and unsafe distance from the edge of the slope. Besides, it is concluded that soil heterogeneity has a major impact on CSS distribution and induces the local CSS, which cannot occur on a homogeneous slope.

Geostatistical semi-supervised learning for spatial prediction

Geoscientists are increasingly tasked with spatially predicting a target variable in the presence of auxiliary information using supervised machine learning algorithms. Typically, the target variable is observed at a few sampling locations due to the relatively time-consuming and costly process of obtaining measurements. In contrast, auxiliary variables are often exhaustively observed within the region under study through the increasing development of remote sensing platforms and sensor networks. Supervised machine learning methods do not fully leverage this large amount of auxiliary spatial data. Indeed, in these methods, the training dataset includes only labeled data locations (where both target and auxiliary variables were measured). At the same time, unlabeled data locations (where auxiliary variables were measured but not the target variable) are not considered during the model training phase. Consequently, only a limited amount of auxiliary spatial data is utilized during the model training stage. As an alternative to supervised learning, semi-supervised learning, which learns from labeled as well as unlabeled data, can be used to address this problem. However, conventional semi-supervised learning techniques do not account for the specificities of spatial data. This paper introduces a spatial semi-supervised learning framework where geostatistics and machine learning are combined to harness a large amount of unlabeled spatial data in combination with typically a smaller set of labeled spatial data. The main idea consists of leveraging the target variable’s spatial autocorrelation to generate pseudo labels at unlabeled data points that are geographically close to labeled data points. This is achieved through geostatistical conditional simulation, where an ensemble of pseudo labels is generated to account for the uncertainty in the pseudo labeling process. The observed labels are augmented by this ensemble of pseudo labels to create an ensemble of pseudo training datasets. A supervised machine learning model is then trained on each pseudo training dataset, followed by an aggregation of trained models. The proposed geostatistical semi-supervised learning method is applied to synthetic and real-world spatial datasets. Its predictive performance is compared with some classical supervised and semi-supervised machine learning methods. It appears that it can effectively leverage a large amount of unlabeled spatial data to improve the target variable’s spatial prediction.

Three-dimensional geotechnical-layer mapping in Seoul using borehole database and deep neural network-based model

Despite the increase in demand for three-dimensional (3D) subsurface geology maps, the attainment of reliable geotechnical characterization of specific regions and development of corresponding optimization models remains a challenging task. This can be attributed to the large volume of geotechnical survey data and uncertainties associated with the use of relevant stochastic and geostatistical approaches. This paper presents the design of an optimum deep neural network (DNN)-based learning model for reliable classification of geotechnical layers of the 3D underground space in Seoul, South Korea. A large-scale borehole database was created to this end using geotechnical-layer depths and 3D spatial coordinates of a borehole dataset for Seoul. It is based on stepwise outlier detection and has been preprocessed via correction and normalization of missing values. The best-fitting model was obtained by optimizing the hyperparameters of a DNN-based classifier, and its performance was evaluated in terms of precision and accuracy. Subsequently, a 3D grid network was established to facilitate local geotechnical-layer classification, and its performance was evaluated by applying the proposed DNN-based model for each unit lattice. The accuracy of the resulting 3D geotechnical-layer map was validated via a comparison against the corresponding thematically classified maps that depict the two-dimensional (2D) density of gravitational anomalies, 2D topsoil properties, and 3D geotechnical-layer classification based on geostatistical conditional simulations.

Reducing uncertainty in geologic CO2 sequestration risk assessment by assimilating monitoring data

Geologic CO2 sequestration sites usually have large uncertainty in geological properties, such as uncertainty in permeability and porosity fields. Geological uncertainty leads to significant uncertainty in predicted risk metrics such as CO2 plume extent, CO2/brine leakage rates through wellbores, and impacts to drinking water quality in groundwater aquifers due to CO2/brine leakage, all of which will impact the approach for post injection site care (PISC). Pre-injection risk assessment can be used to quantify the amount of uncertainty in different predicted risk metrics. However, it cannot account for the potential value of monitoring data (e.g., CO2 saturation and pressure measurements) acquired during the operation of CO2 storage. In this study, we demonstrate how uncertainty in predicted risks can be reduced by performing monitoring data assimilation. An ensemble of geological reservoir models, constrained by direct measurements (such as permeability estimates from exploratory wells), are generated by geostatistical conditional simulation. As the monitoring data from the storage site become available, they are assimilated into models using a recently developed data assimilation method, ES-MDA with geometric inflation factors (ES-MDA-GEO). The reservoir models, calibrated through multiple data assimilation iterations, are used to predict future risks and reduction in their uncertainties. The proposed approach for the quantification of uncertainty reduction in risk assessment is demonstrated with two examples: a generalized 3D synthetic case and a synthetic field case based on the Rock Springs Uplift site in southwestern Wyoming.

Integrated Reservoir Characterisation for Petrophysical Flow Units Evaluation and Performance Prediction

Introduction: An improved understanding of complex clastic reservoirs has led to more detailed reservoir description using integrated approach. In this study, we implemented cluster analysis, geostatistical methods, reservoir quality indicator technique and reservoir simulation to characterize clastic system with complex pore architecture and heterogeneity. Methods: Model based clustering technique from Ward’s analytical algorithm was utilised to transform relationship between core and calculated well logs for paraflow units (PFUs) classification in terms of porosity, permeability and pore throat radius of the reservoir. The architecture of the reservoir at pore scale is described using flow zone indicator (FZI) values and the significant flow units characterized adopting the reservoir quality index (RQI) method. The reservoir porosity, permeability, oil saturation and pressure for delineated flow units were distributed stochastically in 2D numerical models utilising geostatistical conditional simulation. In addition, production behaviour of the field is predicted using history matching. Dynamic models were built for field water cut (FWCT), total field water production (FWPT) and field gas-oil-ratio (FGOR) and history matched, considering a number of simulation runs. Results: Results obtained showed a satisfactory match between the proposed models and history data, describing the production behaviour of the field. The average FWCT peaked at 78.9% with FWPT of 10 MMSTB. Consequently, high FGOR of 6.8 MSCF/STB was obtained. Conclusion: The integrated reservoir characterisation approach used in this study has provided the framework for defining productive zones and a better understanding of flow characteristics including spatial distribution of continuous and discrete reservoir properties for performance prediction of sandstone reservoir.

Scenario reduction using machine learning techniques applied to conditional geostatistical simulation

Abstract One of the basic factors in mine operational optimization is knowledge regarding mineral deposit features, which allows to predict its behavior. This could be achieved by conditional geostatistical simulation, which allows to evaluate deposit variability (uncertainty band) and its impacts on project economics. However, a large number of realizations could be computationally expensive when applied in a transfer function. The transfer function that was used in this study was the NPV net present value. Hence, there arises a necessity to reduce the number of realizations obtained by conditional geostatistical simulation in order to make the process more dynamic and yet maintain the uncertainty band. This study made use of machine-learning techniques, such as multidimensional scaling and hierarchical cluster analysis to reduce the number of realizations, based on the Euclidean distance between simulation grids. This approach was tested, generating 100 realizations by the sequential Gaussian simulation method in a database. Proving that similar uncertainty analysis results can be obtained from a smaller number of simulations previously selected by the methodology described in this study, when compared to all simulations.

Modelling Geomechanical Heterogeneity of Rock Masses Using Direct and Indirect Geostatistical Conditional Simulation Methods

An accurate characterization and modelling of rock mass geomechanical heterogeneity can lead to more efficient mine planning and design. Using deterministic approaches and random field methods for modelling rock mass heterogeneity is known to be limited in simulating the spatial variation and spatial pattern of the geomechanical properties. Although the applications of geostatistical techniques have demonstrated improvements in modelling the heterogeneity of geomechanical properties, geostatistical estimation methods such as Kriging result in estimates of geomechanical variables that are not fully representative of field observations. This paper reports on the development of 3D models for spatial variability of rock mass geomechanical properties using geostatistical conditional simulation method based on sequential Gaussian simulation. A methodology to simulate the heterogeneity of rock mass quality based on the rock mass rating is proposed and applied to a large open-pit mine in Canada. Using geomechanical core logging data collected from the mine site, a direct and an indirect approach were used to model the spatial variability of rock mass quality. The results of the two modelling approaches were validated against collected field data. The study aims to quantify the risks of pit slope failure and provides a measure of uncertainties in spatial variability of rock mass properties in different areas of the pit.

Boreholes plans optimization methodology combining geostatistical simulation and simulated annealing

Nowadays, the prospection plans have the difficult task of ensuring a more complete and rich characterization of the rock mass for the purpose of optimizing costs and increasing safety in geotechnical projects. Currently, boreholes location and depth are mainly defined based on experience and know-how of professionals, as such, it is user-dependent. Hence, there is a lack of methodologies to help the decision-makers in defining the optimal location of boreholes (with relevant information). Therefore, this paper presents a methodology based on the use of geostatistical conditional simulation allied to a stochastic global optimization algorithm (Simulated Annealing) to develop optimized boreholes plans comparing a uni-objective and a multi-criteria optimization approaches. In this work, the optimized location is considered the one that minimizes uncertainty translated by either the average local variance or the average width of 95% probability intervals of simulated values at unsampled locations. This methodology was applied using preliminary information obtained from previously executed boreholes using as variable the empirical rock mass classification system, Rock Mass Rating, in a Chilean deposit.

Towards acoustic monitoring of a mixed demersal fishery based on commercial data: The case of the Northern Demersal Scalefish Fishery (Western Australia)

Ongoing monitoring of complex, mixed species environments is a challenging task. In this study, the potential of acoustic and catch data collected aboard a commercial fishing vessel, in combination with geostatistical variance estimates, are explored as a means to derive information on the distribution and abundance of key species groups within selected fishing regions. The FV Carolina M, a trap fishing vessel which operates in waters off Broome, Western Australia, in the Northern Demersal Scalefish Fishery, was equipped with Simrad ES70 echosounders, operated at 38 and 120kHz. Optical recordings of catch were also obtained, in addition to the acoustic data, during routine fishing operations in 2014. Three regions, where both optical and acoustic datasets were available, were selected for analysis. Geostatistical conditional simulations were used to combine acoustic density information with species composition proportions and length distributions within the catch. For each of the input datasets 250 simulations were conducted, from which individual and combined sampling CVs were derived. Conversion of acoustic densities into abundance estimates was achieved through application of target strength to length relationships (TS-L). Where TS-L was unavailable in the literature for a particular species it was estimated through a Kirchhoff-ray mode model. TS-L equations were estimated for rankin cod (Epinephelus multinotatus)(TSRC=20 log10(L)−79.6), triggerfish (Balistidae) (TSTF=20 log10(L)−77.7) and spangled emperor (Lethrinus nebulosus) (TSSE=20 log10(L)−70.8) at 38kHz. Sampling error was found to be generally low for catch proportions (<12%) and acoustic densities (<10%). Total sampling error CV for species group abundances within each of the three regions was 9%–38%, which is similar to typical estimates reported for acoustic surveys.

Patch‐based iterative conditional geostatistical simulation using graph cuts

AbstractTraining image‐based geostatistical methods are increasingly popular in groundwater hydrology even if existing algorithms present limitations that often make real‐world applications difficult. These limitations include a computational cost that can be prohibitive for high‐resolution 3‐D applications, the presence of visual artifacts in the model realizations, and a low variability between model realizations due to the limited pool of patterns available in a finite‐size training image. In this paper, we address these issues by proposing an iterative patch‐based algorithm which adapts a graph cuts methodology that is widely used in computer graphics. Our adapted graph cuts method optimally cuts patches of pixel values borrowed from the training image and assembles them successively, each time accounting for the information of previously stitched patches. The initial simulation result might display artifacts, which are identified as regions of high cost. These artifacts are reduced by iteratively placing new patches in high‐cost regions. In contrast to most patch‐based algorithms, the proposed scheme can also efficiently address point conditioning. An advantage of the method is that the cut process results in the creation of new patterns that are not present in the training image, thereby increasing pattern variability. To quantify this effect, a new measure of variability is developed, the merging index, quantifies the pattern variability in the realizations with respect to the training image. A series of sensitivity analyses demonstrates the stability of the proposed graph cuts approach, which produces satisfying simulations for a wide range of parameters values. Applications to 2‐D and 3‐D cases are compared to state‐of‐the‐art multiple‐point methods. The results show that the proposed approach obtains significant speedups and increases variability between realizations. Connectivity functions applied to 2‐D models transport simulations in 3‐D models are used to demonstrate that pattern continuity is preserved.

Evaluating total uncertainty for biomass- and abundance-at-age estimates from eastern Bering Sea walleye pollock acoustic-trawl surveys

Abstract A comprehensive evaluation of the uncertainty of acoustic-trawl survey estimates is needed to appropriately include them in stock assessments. However, this evaluation is not straightforward because various data types (acoustic backscatter, length, weight, and age composition) are combined to produce estimates of abundance- and biomass-at-age. Uncertainties associated with each data type and those from functional relationships among variables need to be evaluated and combined. Uncertainty due to spatial sampling is evaluated using geostatistical conditional (co-) simulations. Multiple realizations of acoustic backscatter were produced using transformed Gaussian simulations with a Gibbs sampler to handle zeros. Multiple realizations of length frequency distributions were produced using transformed multivariate Gaussian co-simulations derived from quantiles of the empirical length distributions. Uncertainty due to errors in functional relationships was evaluated using bootstrap for the target strength-at-length and the weight-at-length relationships and for age–length keys. The contribution of each of these major sources of uncertainty was assessed for acoustic-trawl surveys of walleye pollock in the eastern Bering Sea in 2006–2010. This simulation framework allows a general computation for estimating abundance- and biomass-at-age variance–covariance matrices. Such estimates suggest that the covariance structure assumed in fitting stock assessment models differs substantially from what careful analysis of survey data actually indicate.

A space-time geostatistical approach for ensemble rainfall nowcasting

Nowcasting systems are essential to prevent extreme events and reduce their socio-economic impacts. The major challenge of these systems is to capture high-risk situations in advance, with good accuracy, location and time. Uncertainties associated with the precipitation events have an impact on the hydrological forecasts, especially when it concerns localized flash flood events. Radar monitoring can help to detect the space-time evolution of rain fields, but nowcasting techniques are needed to go beyond the observation and provide scenarios of rainfall for the next hours of the event. In this study, we investigate a space-time geostatistical framework to generate multiple scenarios of future rainfall. The rainfall ensemble is generated based on space-time properties of precipitation fields given by radar measurements and rainfall data from rain gauges. The aim of this study is to investigate the potential of a framework that applies a geostatistical conditional simulation method to generate an ensemble nowcasting of rainfall fields. The Var region (south eastern France) and 14 events are used to validate the approach. Results show that the proposed method can be a solution to combine information from radar fields and rain gauges to generate nowcasting rainfall fields adapted for flash flood alert.

Generating precipitation ensembles for flood alert and risk management

AbstractFloods are major natural disasters that, in several occasions, can be responsible for life losses and severe economic damages. Flood forecasting and alert systems are needed to anticipate the arrival of these events and mitigate their impacts. They are particularly important for risk management and response in the nowcasting of flash floods. In this case, precipitation fields are crucial and is important to consider uncertainties coming from the observed precipitation fields used as input data to the system. One approach to take into account these uncertainties is to generate an ensemble of possible scenarios of observed precipitation. The aim of this study is to investigate the potential of a framework that applies a geostatistical conditional simulation method to generate an ensemble of precipitation fields that can be used as input to a distributed rainfall–runoff model to produce probabilistic flood alert maps. The Var region (southeastern France) and 17 events are used to validate the approach. Results show that the proposed method can be useful to generate realistic precipitation scenarios and, ultimately, to provide information on the probability of discharges exceeding critical flood thresholds. It can be a solution to combine information from radar fields and rain gauges to generate precipitation ensembles and quantify uncertainties in input data for hydrological modelling.

Improving processing by adaption to conditional geostatistical simulation of block compositions

One of the key usages of geostatistics has long been the prediction of the spatial structure of orebodies. This is used for the evaluation of resources and/or reserves and for further planning of the mining and beneficiation process schedule. For most applications, and until quite recently, metal grade has been regarded as the central property of study and the main objective has been to distinguish between ore and waste. However, recently other properties have come into focus through better analytical methods, such as automated mineralogy (see e.g. Fandrich et al. 2007), and new geostatistical methods considering more complex information, such as kriging of compositions (Pawlowsky-Glahn and Olea, 2004). Two ores with the same chemical composition can have totally different mineralogies and microfabrics, which will result in different recoveries, energy requirements, or reagent consumptions, thus yielding very different mass streams. An ore is thus no longer understood as represented by a single value element, but through a complex microfabric (Hagni, 2008). This perspective allows quantitative insight into relevant properties of different ore and gangue minerals (Sutherland and Gottlieb, 1991), potentially containing poison elements or phases (e.g. Houot, 1983) that modify the efficiency of downstream processing steps or require additional treatment. Accordingly, processing choices have become more complex. Grade-based studies allow a mere ‘beneficiate-or-dump’ decision. With the advent of these analytical and methodological advances, it is possible to better adapt processing to the ore mined due to a more profound understanding of the processing required. For instance, good knowledge of microfabric properties can reduce energy consumption, if overgrinding is avoided, which also results in improved recovery by avoiding losses due to poor liberation (Wills and Napier-Munn, 2006). Similarly, accurate information on mineral composition may permit the specification of a cut-off in any separation technique (magnetic, electrostatic, or density-based), optimally weighting recovery and further processing costs. Or depending on the proportion of fines generated during milling, desliming might or might not be necessary. Finally, different concentrations of chemicals might be needed for an optimal flotation process as a function of the composition of the concentrate. These Improving processing by adaption to conditional geostatistical simulation of block compositions

Application of sequential Gaussian simulation to quantify the surface wave magnitude uncertainty within the faulted regions

Geostatistical simulations have been recently widely used in the geological and mining investigations. Variogram, the fundamental tools of geostatistics, can identify the spatial distribution of the regionalized variable within the area. One of the important issues of geostatistical simulation in seismotectonics is producing uncertainty maps, which could be applicable to predict earthquake parameters through the site locations especially for civil structures like bridges. It can help engineers to design the structure of interest better. Earthquake parameters as for example seismic fault and surface wave magnitude (Ms) have significant impact on the feasibility study of the civil structures. In this research, a method is presented to produce uncertainty maps for seismic fault and surface wave magnitude, Ms. For this aim, information related to surface wave magnitude and fault trace in Zagros region (SW of Iran) has been collected. Then, the relationships between them through the site location have been investigated and analyzed by conditional geostatistical simulation. In order to quantify the uncertainty of each parameter, the uncertainty formula after generating the E-type maps has been provided and discussed. Finally, in “Talgah Bridge” site, these uncertainty maps were produced to interpret the impact of the surface wave magnitude and fault trace in this specific civil structure.

Non-parametric simulations-based conditional stochastic predictions of geologic heterogeneities and leakage potentials for hypothetical CO2 sequestration sites

The present study focuses on understanding the leakage potentials of the stored supercritical CO2 plume through caprocks generated in geostatistically created heterogeneous media. For this purpose, two hypothetical cases with different geostatistical features were developed, and two conditional geostatistical simulation models (i.e., sequential indicator simulation or SISIM and generalized coupled Markov chain or GCMC) were applied for the stochastic characterizations of the heterogeneities. Then, predictive CO2 plume migration simulations based on stochastic realizations were performed and summarized. In the geostatistical simulations, the results from the GCMC model showed better performance than those of the SISIM model for the strongly non-stationary case, while SISIM models showed reasonable performance for the weakly non-stationary case in terms of low-permeability lenses characterization. In the subsequent predictive simulations of CO2 plume migration, the observations in the geostatistical simulations were confirmed and the GCMC-based predictions showed underestimations in CO2 leakage in the stationary case, while the SISIM-based predictions showed considerable overestimations in the non-stationary case. The overall results suggest that: (1) proper characterization of low-permeability layering is significantly important in the prediction of CO2 plume behavior, especially for the leakage potential of CO2 and (2) appropriate geostatistical techniques must be selectively employed considering the degree of stationarity of the targeting fields to minimize the uncertainties in the predictions.

Risk quantification in grade variability of gold deposits using sequential Gaussian simulation

Risk quantification in grade is critical for mine design and planning. Grade uncertainty is assessed using multiple grade realizations, from geostatistical conditional simulations, which are effective to evaluate local or global uncertainty by honouring spatial correlation structures. The sequential Gaussian conditional simulation was used to assess uncertainty of grade estimates and illustrate simulated models in Sivas gold deposit, Turkey. In situ variability and risk quantification of the gold grade were assessed by probabilistic approach based on the sequential Gaussian simulations to yield a series of conditional maps characterized by equally probable spatial distribution of the gold grade for the study area. The simulation results were validated by a number of tests such as descriptive statistics, histogram, variogram and contour map reproductions. The case study demonstrates the efficiency of the method in assessing risk associated with geological and engineering variable such as the gold grade variability and distribution. The simulated models can be incorporated into exploration, exploitation and scheduling of the gold deposit.