Conditional Geostatistical Simulation
Also known as: Sequential Gaussian Simulation, SGS, Stochastic Simulation, Koşullu Simülasyon
Conditional Geostatistical Simulation — most commonly implemented as Sequential Gaussian Simulation (SGS) — generates multiple stochastic realizations of a spatial random field that are each consistent with observed sample data and with a fitted variogram model. Unlike kriging, which produces a single smoothed estimate, SGS reproduces the full spatial variability of the phenomenon. It is widely used by geoscientists, mining engineers, petroleum engineers, and environmental scientists who need to propagate spatial uncertainty through downstream models.
Key highlights
- Reproduces the full spatial variability described by the variogram, avoiding the smoothing artifact inherent in kriging.
- Provides multiple equiprobable realizations that enable rigorous Monte Carlo uncertainty propagation through any downstream model.
- Honors hard conditioning data exactly at sample locations by construction.
- Flexible enough to incorporate secondary variables (co-simulation) or inequality constraints through appropriate CCDF transformations.
Intuition
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How it works
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When to use it
Use conditional simulation when you need to quantify spatial uncertainty rather than obtain a single best estimate. It is appropriate when the variogram can be reliably fitted to the data and when a multi-Gaussian assumption for the transformed variable is defensible. Simulation is especially valuable for non-linear transfer functions — ore reserves, contaminant plume volumes, flow simulations — where the smooth kriging estimate would bias results. If a single optimal estimate suffices, kriging is simpler. If data are too sparse to fit a reliable variogram, simulation results may be unreliable.
Strengths & limitations
- Reproduces the full spatial variability described by the variogram, avoiding the smoothing artifact inherent in kriging.
- Provides multiple equiprobable realizations that enable rigorous Monte Carlo uncertainty propagation through any downstream model.
- Honors hard conditioning data exactly at sample locations by construction.
- Flexible enough to incorporate secondary variables (co-simulation) or inequality constraints through appropriate CCDF transformations.
- Computationally intensive: generating hundreds of realizations over fine grids can be demanding, though modern implementations (GSLIB, SGeMS, gstat) are optimized.
- Requires a reliable variogram model; poor variogram fitting leads to realizations with incorrect spatial continuity.
- The multi-Gaussian assumption may be violated for data with strong spatial connectivity of extreme values, such as channelized facies.
- Post-processing many realizations demands additional infrastructure for summarizing uncertainty (P10/P50/P90, probability maps).
Common pitfalls
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Applications
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Frequently asked
How many realizations do I need?
The required number depends on the stability of the statistic of interest. For simple spatial averages, 50–100 realizations often suffice. For tail quantiles, connectivity metrics, or flow simulations, 200–500 or more may be needed. A practical approach is to increase L until the empirical distribution of the target statistic stabilizes.
Does SGS always reproduce the variogram?
Each individual realization is a sample from the correct spatial distribution and will approximately reproduce the variogram on average across realizations, but any single realization will show statistical fluctuations around the model variogram. Averaging many realizations (the E-type) will reproduce the variogram mean but underestimate variance — it is not itself a valid realization.
What is the difference between conditional and unconditional simulation?
Unconditional simulation generates spatially correlated random fields consistent with a variogram model but ignores any observed data. Conditional simulation additionally constrains each realization to match the measured values at sample locations. For practical resource and risk assessment, conditional simulation is almost always the appropriate choice when data are available.
Sources
- 1.Goovaerts, P. (1997). Geostatistics for Natural Resources Evaluation. Oxford University Press.ISBN 978-0-19-511538-3
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Cite this page
ScholarGate. (2026, June 2). Conditional Geostatistical Simulation. ScholarGate. https://scholargate.app/spatial-analysis/conditional-simulation