Choosing between two-point and multipoint methods

Parts 3-9 have built up a portfolio of geostatistical methods: kriging (OK, SK, UK, KED), continuous simulation (SGS, LU), indicator methods (IK, SISIM, TGSIM, plurigaussian, object-based), multipoint methods (SNESIM, FILTERSIM, DS, MS-CCSIM), and generative ML (GANs, diffusion). Method choice is the central decision in any geostatistical workflow. This section provides a structured framework, a decision tree, and explicit guidance for combining methods.

The three-axis decision framework

Method selection is governed by three orthogonal axes:

• Variable type: continuous Gaussian (or Gaussian after normal-score transform); continuous non-Gaussian; binary facies; multi-category facies.
• Spatial structure: two-point (smooth or layered, pair-correlation-driven) vs multipoint (channels, dendrites, clinoforms, complex connectivity).
• Data context: dense vs sparse hard data; one TI vs none vs many training fields; few vs many realisations needed.

The combination of values on these axes points to a specific method or small set of candidates.

The "simplest-valid-method" heuristic

Production geostatistics has a strong bias toward the simplest method that passes validation:

• Start with the simplest method consistent with the variable type (kriging for Gaussian, SISIM for binary, TGSIM for ordered facies).
• Run diagnostic validation against MULTIPLE structural metrics (variogram, pattern statistics, transitions, connectivity, visual analog comparison).
• If the simpler method passes, ship it. Simplicity, interpretability, computational cheapness, and ease of communication all favour the simpler tool.
• If it fails (e.g., realisations look wrong despite variogram match, or downstream flow metrics are biased), escalate to MPS or generative ML.

Caveat: do not escalate just because the simpler method is "trendy" or "obvious"; only escalate when validation evidence demands it.

The complete decision tree (verbal)

• Continuous + Gaussian + two-point: SGS (§7.3). Add proportion trend / KED for sparse data.
• Continuous + non-Gaussian + two-point: multi-cutoff IK + SISIM (§8.2-§8.3).
• Binary facies + simple geometry: SISIM (§8.3).
• Multi-cat + ordered facies + simple geometry: TGSIM (§8.4).
• Multi-cat + unordered facies + complex 2D adjacency: plurigaussian (§8.4) or multi-facies SISIM.
• Multipoint structure + one quality TI + categorical: SNESIM (§9.2).
• Multipoint structure + one quality TI + continuous: FILTERSIM (§9.3) or Direct Sampling.
• Multipoint structure + no TI + can construct + sparse data: object-based (§8.4).
• Multipoint structure + many training fields + many realisations needed: diffusion model (§9.4).
• Multipoint structure + many training fields + interpretability critical: use one of the training fields as a TI for SNESIM/FILTERSIM instead.

Combining methods in production workflows

Real workflows rarely use a single method. Common combinations:

• Object-based-as-TI + SNESIM: when no analog is available, run a fast object-based simulation to create a TI, then use SNESIM for dense-data conditioning. Bridges the conditioning weakness of object-based with the multipoint power of SNESIM.
• MPS-as-training-data + diffusion: run SNESIM to create a corpus of 1,000 realisations, train a diffusion model on the corpus, use the diffusion model for fast downstream uncertainty propagation. Bridges SNESIM's sampling cost with diffusion's speed.
• SGS + indicator post-processing: simulate continuous porosity with SGS, threshold to get facies, post-process for exceedance maps.
• Co-located variables: kriging-with-secondary (§5) for trends + SISIM for residual facies modelling.

Communicating method-choice uncertainty

Most geostatistical reports communicate WITHIN-method uncertainty (P10/P50/P90 across realisations) but skip METHOD-CHOICE uncertainty. Modern best practice:

• Specify the method-choice decision tree explicitly in the report (variables, structure, data context).
• Run the next-simpler method as a sanity check, even if you proceeded with a more complex one.
• For high-stakes decisions, run TWO methods and compare deliverables, e.g., SISIM and SNESIM both with the same hard data, then compare ensemble means and uncertainty maps.
• State the method's ASSUMPTIONS prominently: stationarity, two-point vs multipoint, training-image quality.

Try it

• Start with all defaults: continuous Gaussian variable + two-point + moderate data + one TI + few realisations + ordered facies. The recommendation is SGS with a proportion trend, because the data are not dense enough to inform regions far from the wells by the variogram alone. Switch the data density to "Dense" and the recommendation drops the trend to plain SGS, the gold standard for a Gaussian two-point field with dense data.
• Switch the variable type to "Binary facies". The recommendation now becomes SISIM. The structure axis is still two-point, so we stay in the variogram-driven world.
• Switch the structure to "Multipoint (channels, dendrites, ...)". The recommendation becomes SNESIM (if categorical) or FILTERSIM (if continuous). The two-point methods are ruled out by the structural complexity.
• Switch the TI availability to "Many training fields". The recommendation becomes diffusion or GAN, they exploit the training-data abundance. Notice the note suggesting to use one of the fields as a TI for SNESIM if interpretability is critical.
• Switch TI availability to "No TI; no analog data". The recommendation becomes object-based simulation. This is the fallback for multipoint structure with no training data.
• Switch the variable to "Multiple categorical facies" with ordered adjacency. Recommendation: TGSIM. Switch to unordered: recommendation changes to plurigaussian.
• Observe the validation reminder at the bottom: regardless of method choice, validate with multiple diagnostics. Method choice is not a substitute for validation.

A consulting firm has tendered a project to characterise a fluvial reservoir using "modern AI / ML methods". You suspect the right answer is multi-facies SISIM with a vertical proportion trend, NOT a deep generative model. How would you defend the simpler choice to a client who wants "AI"?

What you now know

Geostatistical method choice is governed by variable type, spatial structure, and data context. Start with the simplest valid method; escalate to MPS or generative ML only when validation demands. Combine methods when no single tool covers all aspects of the problem. Communicate method-choice uncertainty alongside within-method uncertainty. This closes Part 9: the next part walks through six reservoir-characterisation capstones that apply this entire framework end-to-end.

Mark section complete →

References

• Pyrcz, M.J., Deutsch, C.V. (2014). Geostatistical Reservoir Modeling, 2nd ed. Oxford. (Method-selection chapter; one of the best practitioner's references.)
• Caers, J. (2011). Modeling Uncertainty in the Earth Sciences. Wiley. (Method-choice as a modelling decision.)
• Mariethoz, G., Caers, J. (2014). Multiple-point Geostatistics. Wiley-Blackwell. (When to use MPS vs two-point methods.)
• Pyrcz, M.J., Sech, R., Covault, J. et al. (2015). "Stratigraphic rule-based reservoir modeling." Bulletin of Canadian Petroleum Geology. (Hybrid object-based + MPS workflow.)
• Lopez, S., Cojan, I., Rivoirard, J., Galli, A. (2009). "Process-based stochastic modelling: meandering channelized reservoirs." Analogue and Numerical Modelling of Sedimentary Systems. (Object-based + dense-data hybrid.)