Geostatistics

Mining technology



Studio 3 Geostatistics Introduction
Studio 3 offers a selection of geostatistical functions including inverse distance, nearest neighbor and a selection of kriging estimation methods and variogram model fitting. The computations include covariance and other parameters. The interactive variogram fitting process allows the user to display the experimental variograms, and to choose from a wide range of models and parameters; multiple nested structures and anisotropy are included. The models may be further refined statistically using cross validation techniques.















Grade Estimation:

* Variograms and/or cross variograms for up to 24 different variables in a single run
* automatic calculation of indicator values based on cut-offs
* restrict by the specified key field eg rock type, or BHID to give downhole variograms
* exclude pairs with the same keyfield value
* optimized sample search for fast calculation
* normal, relative and lognormal variograms
* variograms for all directions calculated in a single run
* optional rotated coordinate system ensures flexibility in definition of directions
* options include angles of regularisation, cylindrical radius, lag tolerance, etc
* output to a database file, and/or the print file together with summary statistics

Studio 3 Geostatistics Features
Estimation Features:

* multiple grades can be estimated in a single run
* optimization of sample searching for fast processing speed
* the same grade can be estimated by different methods
* different search volumes and estimation parameters can be used for the different grades
* rectangular or ellipsoidal search volume with anisotropy
* a dynamic search volume allowing the volume to be increased if there are insufficient samples
* restriction of the number of samples by octant
* restriction of the number of samples by key field
* estimation by zone, with separate parameters for each zone
* wide selection of variogram model types for both normal and lognormal kriging
* automatic transformation of data if the input model is a rotated model
* calculation of recovered values for different cutoffs
* unfolding option available for all estimation types
* parent cell estimation
* selective update of partial model

Estimation Methods:

* Nearest Neighbor
* Inverse Power of Distance
* Ordinary Kriging
* Simple Kriging
* Lognormal Kriging
* Indicator Kriging
* Sichel's t Estimator

Studio 3 Geostatistics - Variogram Calculation
Variogram calculation includes the following features:

* Variograms and/or cross variograms for up to 24 different variables calculated in a single run.
* Automatic calculation of indicator variograms based on cut-offs.
* Key field option allows variogram calculation to be restricted by the specified key field eg rock type, or borehole identifier to give downhole variograms.
* Optimization of sample search for fast calculation.
* Variogram calculation includes normal, relative and lognormal variograms.
* Directional variograms for up to 100 different azimuth/dip combinations calculated in a single run.
* Optional rotated coordinate system ensures flexibility in definition of directions.
* Smaller lag interval for smaller distances.
* Options include angles of regularisation, cylindrical radius, lag tolerance, etc.
* Output to a database file, and/or the print file together with summary statistics.


Studio 3 Geostatistics - Block Models
Grade estimation for block models includes the following features:

* Grade interpolation into a block model includes the following functionality:
* A choice of interpolation methods including Nearest Neighbour, Inverse Power of Distance, Ordinary Kriging, Simple Kriging, Lognormal Kriging and Multiple Indicator Kriging.
* A consistent set of search volume and estimation parameters for all methods.
* Optimization of sample searching to improve processing speed.
* Multiple grades can be estimated in a single run.
* The same grade can be estimated by different methods.
* Different search volumes and estimation parameters can be used for the different grades.
* Rectangular or ellipsoidal search volume with anisotropy.
* A dynamic search volume allowing the volume to be increased if there are insufficient samples.
* Restriction of the number of samples by octant.
* Restriction of the number of samples by key field.
* Estimation by zone, with separate parameters for each zone.
* Wide selection of variogram model types for both normal and lognormal kriging.
* Automatic transformation of data if the input model is a rotated model.
* Unfolding option available for all estimation types.
* Parent cell estimation.
* Selective update of partial model.

Studio 3 Geostatistics - Cross Validation
Cross Validation - XVALID

The cross-validation process XVALID is designed to assist in the selection of parameters for grade estimation, using the cross-validation method. The input data file is the sample data which will later be used for estimating grades into a block model. For kriging it allows different model variograms to be tested and compared. For inverse power of distance it allows different powers to be compared. The input to XVALID is consistent with the input required for the grade estimation process ESTIMA. In fact the three input parameter files are identical for the two processes. The cross-validation method works by removing each point in turn from the data file and estimating its value from the remaining data. In this way a table of actual and estimated values is created. A detailed statistical analysis is then carried out comparing the actuals and estimates. One or more of the estimation parameters can then be changed and the process rerun to see whether the new parameters improve the results of the statistical analysis. The method is therefore iterative, requiring several runs to establish the best set of parameters.

Cross Validation Optimization

Cross-validation is an iterative process – you make your first estimate, look at the stats, change one of the parameters, and try again to see if you improve the stats. XVOPT does all this for you. You need to define an initial or base set of parameters as before, but you also specify a minimum and maximum for each parameter. Then you define a step size for discrete increments between the maximum and minimum. XVOPT then just loops round for all possible combination of parameters and calculates the statistics. So what you also need to do is to define a sort of objective function. You specify weights for each statistic defining their relative importance, and penalty for the distance of the actual statistic from it’s target value. defining their relative importance, and a penalty for the distance of the actual statistic from its target value. The process then calculates the penalty for each run, weights them and finds the one with the lowest penalty points.

Studio 3 Geostatistics - Interactive Variogram Fitting
The interactive variogram fitting process includes the following features:

* Interactive model fitting, with mouse control
* Multi-structure models
* Choice of models: spherical, power (e.g. linear, exponential, gaussian or De Wijsian
* Model parameters saved on file for direct input to kriging process
* Display of model parameters on graphics screen
* Auto scaling of display limits and grid interval as variograms are added or removed
* Mouse selection of variograms to be shown or hidden
* Automatic selection of perpendicular variograms
* Legend control, including XYZ annotation of model axes
* Legend includes cut-off grade for indicator variograms
* User control of colour, line type and symbol for each variogram
* Mouse selection of model axes
* Optional display of number of sample pairs
* Optional display of sample variance
* Variogram point removed if insufficient pairs
* Toggle between full grid and tick marks
* Restructured menus for ease of use
* Online help

Studio 3 Geostatistics - Interactive Variogram Fitting (contd.)
The following image displays the VARFIT process in action:















Studio 3 Geostatistics - Other Options (1)
SMUMOD The SMUMOD process uses the 'Lognormal Shortcut' method to estimate the recovered tonnage and recovered grade above a single user defined cut-off for a specified size of Selective Mining Unit (smu). The input file must be a standard model file containing a kriged grade estimate and a kriged variance. The output model file contains all the fields from the input file plus two additional fields: •the proportion of the block above the cut-off; •the grade of the proportion above cut-off. A Selective Mining Unit (SMU) is the smallest block size that can be mined selectively. The Dimension of an SMU are defined by parameter.

SMUHIS
The SMUHIS process creates a histogram file by evaluating a kriged model using the 'Lognormal Shortcut' method and estimating the tonnage distribution over the range of cutoffs specified for the histogram intervals for a specified size of Selective Mining Unit (smu). The data in this file can then be used to create grade/tonnage plots.

FFUNC
FUNC estimates the geostatistical F function. That is the variance of a point in a block based on a variogram model which is selected from the input variogram model file. The block whose F value is to be calculated is simulated by a 3 dimensional matrix of discretisation points. The F value is calculated as the average value of the variogram between each possible pair of discretisation

Studio 3 Geostatistics - Other Options (2)
Multiple Indicator Kriging (MIK)
The only transform used in Multiple Indicator Kriging (MIK) is the transform from a grade to a 0 or 1. The Affine Correction Method is used to take the output file from ESTIMA and correct the grades for SMU size. Details of the Affine Correction Method are given in Applied Geostatistics by Isaaks and Srivastarva pages 471-472.

Declustering Sample Data - DECLUST
Options:
Random Sample
Psuedo Random Sample
Sample Nearest Grid Center
Mean of Samples in Grid

Grade Estimation for Irregular Panels - PANELEST
The PANELEST command estimates the grade and variance of 2D or 3D panels. Panels are defined either as a set of strings, or as a set of 2D or 3D discretisation points. The interpolation methods available are nearest neighbour, inverse power of distance or kriging. In particular the process allows you to estimate a grade and a kriged variance for...
any perimeter, without the need to create a block model.
a subset of cells from a block model.
an enclosed wireframe represented by a 3D array of points.