Variogram Types and Data Transformations

• Variogram Types and Data Transformations
• • Normal Score Data Transformations
  • Log Data Transformations
  • Traditional Variograms
  • Pairwise Relative Variograms
  • Indicator Variograms
  • Cross Variograms
  • Madograms
  • General Relative Variograms
  • Covariance Variograms
  • Correlograms
  • Bi-Guassian Variograms

A variety of variograms and data transformations exist to evaluate grade continuity. Data transformations are applied to the data before a variogram is calculated, whereas variogram types change the formula used to calculate the variogram.

Note: The underlying data is not changed when applying a data transformation for a variogram and can still be used as normal for other calculations.

Supervisor supports the following data transformations and variogram types.

Note: If you are unsure of which variogram type or data transformation may suit your data, see Select an Appropriate Variogram Type or Data Transformation.

Normal Score Data Transformations

A normal score transformation converts any distribution of sample grades to a normal distribution. Variograms calculated with normal scores-transformed data are used to describe the grade continuity for single population normally distributed data. They are also useful for confirming ranges of grade continuity that have been established using other variogram types.

Log Data Transformations

Log transformations transform the data to a log scale prior to variogram calculation. These variograms are useful for single population positively skewed data sets to reduce the bias on variance due to extreme high grades.

Note: A modelled log variogram needs to be back-transformed before being used for kriging. The back transformation adjusts the nugget effect to reflect the true short scale variability of the data.

Traditional Variograms

Traditional variograms use raw data and have no data transformations or other variogram calculations applied. A traditional variogram describes the differences in grade values according to the separation distance between samples.

Pairwise Relative Variograms

Pairwise relative variograms are useful for establishing the range of continuity of grade when there are limited samples. Pairwise relative variograms do not provide a measure of variance. A pairwise variogram is calculated by scaling each pair in the variogram calculation by the average of the two grades of that pair. This reduces the influence of extreme differences in grades on the variogram calculation.

Pairwise variograms are best used on data with any type of distribution as a guide to interpret ranges of continuity when there are only a few samples in the data set.

Indicator Variograms

Indicator variograms are used when mixed populations are spatially integrated. An indicator variogram is used to investigate variations in grade continuity due to grade range.

Note: An indicator transform converts the sample data into sets of codes for each indicator. The indicators are based on the grades selected to represent the grade population.

Cross Variograms

Cross variograms describe the spatial correlation between two variables. Cross variograms are used to investigate, model and infer how a primary variable changes as a secondary variable changes. The cross variogram is required for co-kriging.

Madograms

Madograms use the absolute value of the differences between head and tail samples instead of the square of the differences.

General Relative Variograms

General Relative Variograms sum all data pairs at separation h, then divide by:

(half of (mean of head samples + mean of tail samples))².

Covariance Variograms

Covariance Variograms are calculated by subtracting (mean of head samples)*(mean of tail samples).

Correlograms

Correlograms are calculated by dividing each gamma value by:

(standard deviation of head samples)*(standard deviation of tail samples)

Bi-Guassian Variograms

Bi-Guassian Variograms allow you to perform a check for bivariate gaussianity.