Geostatistical Analysis

  • Geostatistical Analyses
    • Variography
      • Experimental Semi-variograms
      • Variographic Modelling
    • Computational Techniques
      • Data Selection
      • Block Selection
      • Computational Parameters
      • Analysis of Results

Geostatistical Analyses

VULCAN offers Geostatistical packages from three sources:

  • GSLIB (Stanford University)
  • Geostokos (Dr Isobelle Clark)
  • Mining an Resource Technology (M&RT, Perth, Western Australia)

While the data and block selection techniques are unique to VULCAN, the actual geostatistical algorithms are from the various sources.

Maptek has recently released its Track Surface module in VULCAN.

This module allows for the pre-conditioning of complex folded structures. The structure can be mathematically unfolded prior to estimation. This means that the geological distances are honoured in the estimation process. Once the estimation has been completed, the structure can be refolded to its current shape for further analysis.

Variography

The two steps discussed here involve the generation of an experimental semi-variograms and the subsequent modelling of the experiential variogram.

Experimental Semi-variograms

Generating a semi-variogram involves:

  • Data selection

  • Data selection for variogram calculation is of paramount importance. The variography programs supplied with the Variography Module support comprehensive data selection tools. These include the selection of data from various compositing groups and ASCII files, the intersection of data with triangulations and specific applications of character and numeric flags for selection ranges and excluding values. Conditional field restrictions can also be used.

  • Orientation functions

  • Many semi-variograms can be computed in a single run by specifying start and end orientations with a step size. The number of lags and lag distance can be set easily by the user. At run time, various types of semi-variograms can be calculated; the semi variogram, relative and pairwise semi-variograms, co-variogram, correlogram, log variogram, rodogram, madogram, and indicator variogram.

  • Variogram display

  • The setup of the variogram display is user definable and allows for the viewing of multiple semi-variograms at once. The default display includes the variance, while displaying the number of points is optional.

Variographic Modelling

Once an appropriate experiential variogram has been selected, it can be modelled interactively on screen. The nugget value, range and sill position can be "picked" off the screen, and each value connected typographically. Nested models can be edited in a similar fashion. Once all of the structures have been indicated the resultant model displays on screen. Vulcan supports the following mathematical models:

  • Spherical model
  • Exponential mode
  • Gaussian model
  • Linear model
  • De-Wijsian model

Once the semi-variogram has been modelled successfully the model can be saved to a file for later use in the estimation parameter file.

Checking the semi-variogram parameters is an important part of the evaluation process. The standard cross validation programs supplied with Vulcan allow for the quick analysis of standard errors, such as their distribution type and the correlation of estimated and actual values.

Computational Techniques

VULCAN offers four computational techniques:

  • Inverse Distance
  • Ordinary Kriging
  • Indicator Kriging
  • Stochastic Simulation

All interpolative techniques can be broken down into three basic components:

  1. Data selection
  2. Block selection (area of interest)
  3. Computational parameters - search radii, power functions etc.

All of these functions can easily be modified using the standard Vulcan panels.

Data Selection

Data can be selected from ASCII files or from Vulcan database structures. Various composite groups can be selected from the composite database.

The data can be restricted using numerical or character tags. These restrictions include data exclusions, data inclusion ranges and values to be ignored. Data may also be restricted by using complex conditional statements or by whether the composite lies in or outside a particular triangulation.

Facilities exist for providing data cut-off values, catering for the exclusion of outlier values. Declustering techniques include octant based searches and limiting the number of samples per borehole for a particular estimate. Outlier ranges can also be set separately, allowing the influence of outlier values to be limited. The minimum and maximum allowable number of samples may also be set.

Provision is made for saving the number of samples used in each individual estimate, as well as the average distance of the samples used from the block centre. The number of samples per drill hole can also be selected. Samples can be converted to logarithmic values in the calculation process.

Block Selection

Defining the blocks to be estimated in a particular estimation run is of vital importance. Vulcan caters for the selection of blocks by geological zone variables, numeric and character tags.

Selection of blocks by making use of inclusion and exclusion solids is commonly used in Vulcan. This solves the problem of mixing data populations and rock types. By selecting data and blocks by the same triangulation, population mixing is virtually impossible.

Computational Parameters

Vulcan 's panel structure makes the editing of computational parameters easy. Provision is made for flagging estimated blocks, storing the Kriging variance. The latest release also allows the actual data used for each estimate to be saved.

Directional factors such as search radii, ranges, and sills can be edited easily. The ellipsoidal shape can be viewed in scale, together with the raw or composite data and the blocks selected. This means that the errors associated with incorrect orientations are trapped early in the process. Anisotropic weightings can easily be edited, and the number of discretisations per block set. If using the inverse distance method, the power function can be adjusted to suit the particular deposit.

In addition to allowing the distribution of the computation across a network, provision is made for batching a series of variables. This means that a number of estimates can be calculated sequentially (for example, overnight) without user interaction.

Stochastic simulations cater for user defined random seed generation and distribution shape definition.

While the estimation is in progress, the number of blocks estimated as well as the percentage of total blocks is shown.

Analysis of Results

Once the estimation is complete, the results can be analysed and viewed in various ways in Vulcan. The blocks that have been estimated can be viewed in their 3 dimensional positions, while colour coded according to their estimated grades. The composites or drillholes can be viewed as well as triangulations, or any other pertinent information. The block model may be sliced and viewed in any orientation or contoured according to user defined contour schemes.

Vulcan supports easy to use plotting facilities. These allow the blocks to be plotted on any scale, together with the relevant information pertaining to each block or any other design information.