Categorical facies modeling

Categorical facies modelling is the spatial assignment of discrete labels — shale/sand/conglomerate, channel/levee/floodplain, ore/waste/overburden — to every cell of a 2D or 3D grid, conditioned on hard data (wells, outcrops). Three families of methods dominate: multi-facies SISIM (extending §8.3), TRUNCATED GAUSSIAN SIMULATION (a transform-based alternative), and OBJECT-BASED modelling (placement of geological objects). Each has a sweet spot.

Multi-facies SISIM, generalised

For $K$ facies, define indicator fields $I_k(x) = \mathbb{1}[\text{facies}(x) = k]$, $k = 1, \dots, K$. At each unsampled cell $x_v$:

• Run simple indicator kriging on each facies indicator using the current conditioning set: $\hat{P}_k(x_v)$ for $k = 1, \dots, K$.
• Apply ORDER-RELATION CORRECTION: clip each $\hat{P}_k$ to $[0,1]$; renormalise so $\sum_k \hat{P}_k = 1$. The result is a valid PMF on the K facies.
• Draw a category from the cumulative-sum: pick $u \sim \text{Uniform}(0,1)$, select the $k$ such that $\sum_{j<k} \hat{P}$j \le u < \sum{j \le k} \hat{P}_j.
• Update the conditioning set with the drawn facies (one new indicator value per cell, propagating through ALL K indicator-kriging systems on downstream cells).

For each cell SISIM solves $K$ kriging systems — $K$ times the cost of single-indicator SISIM. Production runs limit the search neighbourhood (16–32 conditioning points within ~1.5 ranges) and use random multiple-grid paths.

Proportion trends: how geology enters cell-based modelling

Geological knowledge often imposes a non-stationary prior: shale-dominated near the top of a sequence, sand in the middle, conglomerate at the base; or proximal facies near a sediment source and distal facies further away. Encode this with a depth/lateral-dependent prior $\mathbf{p}(x) = (p_1(x), \dots, p_K(x))$. Then simple indicator kriging is applied to residuals:

so the local mean is the trend value, and kriging only models residuals from it. Trend specification is itself a modelling decision — from data (well-log proportions plotted vs depth and smoothed) or from geological interpretation (sequence-stratigraphic framework).

Truncated Gaussian Simulation (TGSIM)

An alternative cell-based method: simulate a SINGLE underlying multiGaussian field $Y(x)$ (e.g. via SGS, §7.3), then threshold it at $K-1$ cutoffs $t_1 < t_2 < \dots < t_{K-1}$ to produce facies:

Pros: ONE Gaussian field, ONE variogram model, automatic order-relation consistency, easy proportion control (set $t_k$ from desired global proportions via the standard-normal quantile). Cons: the cutoff scheme imposes an ARTIFICIAL ORDERING on the facies (facies $k$ is always "between" $k-1$ and $k+1$ in Y-space). Adjacent facies in the truncation order MUST be spatially adjacent — impossible for, say, sand bracketed by shale on both sides without going through an intermediate "transition" facies.

PLURIGAUSSIAN extends TGSIM to two correlated Gaussian fields with a 2D facies-region map, breaking the strict ordering constraint at the cost of more modelling decisions.

Object-based methods

For complex geological shapes (channels, levees, lobes, deltas) that two-point statistics cannot capture, OBJECT-BASED methods drop pixel-by-pixel simulation entirely. Geological objects with parameterised shapes (sinuous channel + levee, ellipsoidal sand body) are placed in the grid via Poisson processes with intensities controlled by facies proportions. Examples: fluvsim (channelised reservoirs), ellipsim, FLUMY.

Pros: geologically realistic shapes; explicit object hierarchies (channel-belt → channel → levee). Cons: HARD TO CONDITION to dense well data — placing objects to honour every well's facies often requires iterative retraction-replacement schemes that scale poorly. For dense data, cell-based methods (SISIM, TGSIM, or MPS in §9) are usually preferred.

Choosing a method

Try it

• Defaults: trend strength = 0.50, range = 5.0, 8 realisations. The TOP canvas shows 8 SISIM realisations as vertical columns (depth top-to-bottom). Three facies are colour-coded: gray = shale, gold = sand, dark-brown = conglomerate. Dotted lines mark the 6 hard-data wells. Note all realisations honour the wells.
• Increase trend strength to 1.00. Strong vertical gradient: shale dominates the top, sand the middle, conglomerate the bottom — even in cells far from hard data. The BOTTOM canvas shows P_sim(facies) at each depth as horizontal bars per facies; the dashed white line is the per-cell prior P_k(z). With strong trend, P_sim hugs the trend prior away from hard data.
• Set trend strength to 0.00 (stationary). The trend prior becomes a flat line at the global proportions (1/6 shale, 3/6 sand, 2/6 conglomerate from the 6 hard data). Now realisations are dominated by local conditioning + spatial continuity, not by a geological trend.
• Vary the range from 1.5 to 10.0. Short range → realisations look noisy with rapid facies switching; long range → thick, continuous facies bodies. Long range also makes hard-data influence reach further (smoother probability-bar shapes).
• Click Resample. All realisations change while hard data and probability bars remain consistent — the per-cell probabilities are model-determined, only the draws are stochastic.
• Compare globally: with N = 8 realisations the global facies proportions in the readout will be noisier than with N = 16 (or 32 if implemented), but should converge to the trend-weighted prior as N → ∞.

A reservoir team has 12 wells in a clastic sequence with vertical proportion curves showing shale 0.6 / sand 0.3 / conglomerate 0.1 at the top grading to 0.1 / 0.4 / 0.5 at the base, and they need 100 realisations for flow simulation. Which method — multi-facies SISIM with vertical trend, TGSIM, or object-based — would you propose and why? What would change your answer if there were only 4 wells?

What you now know

Categorical facies modelling has three main approaches. Multi-facies SISIM (cell-based, two-point) is the workhorse for moderate-density data and simple connectivity, easily extended with proportion trends. TGSIM (and plurigaussian) trade flexibility for algorithmic simplicity and automatic consistency, at the cost of artificial facies orderings. Object-based methods give realistic geological shapes but struggle with dense conditioning. Method choice is dictated by data density, geological complexity, and downstream use — flow simulation, mining selectivity, contaminant transport.

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References

• Matheron, G., Beucher, H., de Fouquet, C., Galli, A., Guerillot, D., Ravenne, C. (1987). "Conditional simulation of the geometry of fluvio-deltaic reservoirs." SPE 16753. (Original truncated-Gaussian framework.)
• Goovaerts, P. (1997). Geostatistics for Natural Resources Evaluation. Oxford. (SISIM with proportion trends.)
• Deutsch, C.V., Journel, A.G. (1998). GSLIB, 2nd ed. Oxford. (sisim, tgsim, fluvsim.)
• Armstrong, M. et al. (2011). Plurigaussian Simulations in Geosciences, 2nd ed. Springer.
• Pyrcz, M.J., Deutsch, C.V. (2014). Geostatistical Reservoir Modeling, 2nd ed. Oxford. (Practitioner's comparison of facies-modelling methods.)