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 — the gold standard for this combination.
• 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.)