Conditional simulation: measuring the uncertainty an estimate hides
Conditional simulation produces many equally likely models of a deposit that all honour your samples, so you can measure how much the grade could vary instead of reporting a single smooth estimate.
An estimate gives one answer per block and, being a weighted average, it is smoother than reality. Simulation adds back the variability the estimate removes, while still passing through the samples. Running many realisations gives, for each block, a mean, a standard deviation and percentiles such as P10, P50 and P90. These measure local uncertainty and can drive classification and risk assessment.
Why an estimate is not enough
Kriging, RBFs and SVR produce the best single guess at each location. Because they average, high grades are pulled down and low grades up, and the map is smoother than the real deposit. That is the right behaviour for a best estimate of a block grade, but it understates variability, and it cannot show how uncertain the tonnes and grade above a cut-off really are.
What simulation does
Conditional simulation generates realisations that have the same statistics and spatial continuity as your samples and reproduce the sample values at their locations. Each realisation is a plausible deposit. Differences between realisations show where the grade is poorly constrained. Between samples, realisations spread out. Close to samples, they converge.
Turning bands in GEOREKA
GEOREKA uses the turning bands method. It builds a three-dimensional random field from many one-dimensional simulations along random directions, then conditions it to the samples. Two practical points follow:
- Local conditioning. Each target block is conditioned on a limited number of nearest samples (64 by default) instead of solving one huge system for all samples. The cost does not explode as the number of samples grows.
- GPU evaluation. The evaluation at the targets runs on the GPU where one is available.
Each run records the mean, standard deviation and the P10, P50 and P90 for every cell, and optionally every realisation.
Normal scores, trends and declustering
- Normal-score transform. Gaussian simulation assumes normally distributed values, which grades rarely are, so the grades are transformed to normal scores, simulated, and transformed back. The back-transform keeps the results within the range of the data.
- Local mean model. Where a trend exists, you can simulate the residual from a base trend. In GEOREKA this is done in Gaussian space, so the trend is removed and re-added in the transformed units and the result remains within the data range and never goes negative.
- Declustering. Preferential drilling biases the histogram that the transform is built from. Declustering weights are available in the simulation workflow so that the target distribution represents the whole domain.
Using the results
- Classification. The coefficient of variation or interval width of each block can set Measured, Indicated and Inferred classes, see resource classification methods.
- Risk. Tonnes and grade above cut-off can be reported for each realisation instead of as a single number.
- Drilling decisions. Areas with a wide spread are where another hole would reduce uncertainty most.
Pitfalls
- Simulation reproduces the model you give it. If the domain, variogram or range is wrong, the uncertainty it reports is wrong too, and it is wrong with confidence.
- Use enough realisations for the statistic you need. Percentiles in the tails need more than a mean.
- Within a domain, the method assumes stationarity, so domain boundaries still matter.
Estimation gives the best single answer. Simulation tells you how much to trust it. Validate the model of continuity first, then simulate.
Keep reading
Learn how the model of continuity is checked in validating a resource estimate.
Apply it
Simulate on your own model
Conditional simulation with turning bands is part of Premium. Resource estimation in GEOREKA →
Common questions
Conditional simulation FAQ
What is conditional simulation?
A method that generates many equally likely models of the grade that honour the sample data and reproduce its statistics and spatial continuity, so that uncertainty can be measured.
What is the difference between kriging and conditional simulation?
Kriging gives one smooth best estimate. Simulation gives many realisations with realistic variability. Their average approaches the kriged estimate, and their spread measures uncertainty.
Why is a normal-score transform used?
Gaussian simulation assumes normally distributed values. The transform converts grades to a normal distribution, and the back-transform returns results in grade units within the data range.
How many realisations do I need?
Enough for the statistic you need. A mean stabilises quickly, while tail percentiles need more realisations. Check by adding more and seeing if the result changes.