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Geostatistics Essentials

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Range of Influence

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In geostatistics, the range of influence is the distance over which two points become uncorrelated. Knowing this range helps determine the spacing of drill holes in exploration and resource estimation.

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Mean Square Error

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Mean Square Error (MSE) measures the average of the squares of the errors, being the difference between the estimator and what is estimated. In mining, it’s critical for assessing the accuracy of resource estimation methods.

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Block Kriging

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Block Kriging is a variant of Kriging used to estimate the average value over a block of material rather than a point, which is essential for planning and evaluating mining blocks.

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Nugget Effect

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The nugget effect is the variance at very small distances, interpreted as measurement error or microscale variability. It's an important consideration when creating variograms for mineral resource estimations.

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Cut-off Grade

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The cut-off grade is the minimum metal grade at which a tonne of rock can be economically processed and is crucial in determining which parts of the deposit to mine.

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Universal Kriging

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Universal Kriging is a generalization of ordinary Kriging that incorporates a drift function, helping to model spatial trends within mineral deposits that cannot be captured by stationary models.

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Support Effect

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Support effect refers to the phenomenon that statistical properties of a dataset change when the size of the data support changes. In mining, understanding this is crucial for accurately estimating reserves at different scales of operation.

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Indicator Kriging

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Indicator Kriging is used for estimating the probability distribution of categorical variables, like ore and waste, which helps in classifying material in a mining operation.

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Cokriging

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Cokriging is a multivariate geostatistical technique where multiple correlated variables are simultaneously estimated. In mining, it is useful when considering multiple elements or properties of a deposit.

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Factorial Kriging

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Factorial Kriging is a multistage approach that separates spatial components at different scales, allowing for a better understanding of the various scales of geological phenomena affecting a mineral deposit.

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Isotropic Variogram

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An isotropic variogram assumes that the variable's correlation structure is the same in all directions, simplifying modeling in mining when direction does not significantly affect mineral distribution.

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Probability Kriging

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Probability Kriging is a technique that combines indicator and ordinary Kriging to estimate grade distributions taking into account both the quantity and quality (probability) of information.

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Estimation Variance

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Estimation Variance is a measure of the uncertainty associated with the predicted values of a resource, important for risk assessment in economic decisions in mining.

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Cross-Validation

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Cross-validation is a model validation technique for assessing how the results of a statistical analysis will generalize to an independent dataset, frequently used in resource estimation to ensure model reliability.

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Gaussian Process Regression

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This is a probabilistic model that assumes a Gaussian process governing the data generation, often used in geostatistics for predicting the spatial distribution of mineral deposits.

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Multivariate Normal Transform

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A Multivariate Normal Transform is used to convert non-normal variable distributions into a multivariate normal space, allowing for the application of methods like cokriging, which assume multivariate normality.

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Spatial Bootstrap

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Spatial Bootstrap involves resampling with replacement to assess the uncertainty of spatially correlated estimates, helping in understanding confidence levels in resource estimation.

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Variogram

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A variogram measures the spatial correlation of a variable by assessing how difference in the variable's value increases with distance. In mining, it's used to model and estimate mineral reserves by understanding spatial variability.

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Kriging

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Kriging is an advanced geostatistical procedure that generates an estimated surface from a scattered set of points with known values. It's widely used in mining for ore body estimation and grade control.

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Direct Block Estimation

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Direct Block Estimation involves estimating the value of large blocks as opposed to smaller samples, integrating information at a mine planning scale which directly affects the profitability of mining operations.

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Change of Support Model

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The Change of Support Model deals with the scale effect on distribution, used in converting block model estimates to different volume supports, significant in mine planning and valuation.

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Conditional Simulation

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Conditional Simulation is a technique that generates multiple equally probable realizations of a geologic scenario, giving a measure of the uncertainty in mineral deposit models.

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Geological Domaining

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Geological Domaining is the process of defining spatially distinct zones of consistent geology, which then guide the application of geostatistical methods in a mining context.

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Anisotropic Variogram

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An anisotropic variogram reflects directional differences in spatial variability, which is important in mining for modeling ore bodies with directional features like veins or layers.

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Pseudo Cross Variogram

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The Pseudo Cross Variogram is used for estimating the cross correlation between two variables at different locations in the absence of a true cross variogram, aiding in cokriging when cross-correlation data is limited.

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Disjunctive Kriging

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Disjunctive Kriging is a non-linear geostatistical method that can deal with distributions that are not multivariate normal, particularly useful for skewed distributions such as those for metal grades.

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Declustering

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Declustering is the process of weighting data to correct for sampling bias due to clustered sample locations, ensuring a fair representation of the mineral resource.

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Sequential Gaussian Simulation

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Sequential Gaussian Simulation (SGS) is used to generate multiple geologically realistic models of a mineral deposit, allowing for the analysis of uncertainty in grade and tonnage.

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Spatial Autocorrelation

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Spatial Autocorrelation is a measure of the degree to which a set of spatial data points is correlated with itself over distance, crucial for designing optimal sampling campaigns and understanding deposit continuity.

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