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Heterogeneity + sparse sampling = uncertainty

Heterogeneity + sparse sampling = uncertainty

An important aspect of geology is the characterization of geological sites that are now frozen in time and space. The geological processes that led to the present day preserved distribution of rock properties were acting at all scales and were transient, nonlinear, and chaotic; this leads to variability and heterogeneity at all scales. Our direct sampling of a geological site tends to be quite sparse because of drilling costs. Geophysical data are more extensive, but they include some noise in the measurements and measure properties at a larger scale than we must know them. It is axiomatic that heterogeneity and sparse sampling lead to uncertainty. Yet, there is but one inaccessible truth at the geological site.

This geological site with five wells has shale drapes that could have a large impact on production. The size, shape, and location of the shale drapes could never be predicted from the available well data; we are faced with significant uncertainty.


Decision makers want to quantify and manage uncertainty to make the best possible development decisions. They want decisions that are robust with respect to over- or under-predicting resources. They want to assess the value of new information. They want to compare the uncertainty between geological sites. The geologist must provide high-resolution 3D numerical models of the site that have realistic patterns of heterogeneity and, when taken together, provide a defensible assessment of uncertainty. Geostatistics provides tools for constructing such models given widely spaced measurements and various data types. Geostatistical tools have proven themselves in the last 25 years.

The application of geostatistical tools does not commonly fall within the conventional training of geologists. Most learn the tools from software vendors, short courses, and mentoring. There are few reference texts to help geologists with the complex interdependent modelling decisions that must be made; Pyrcz and Deutsch (2014) covers some important points. Here are three:
The physics of deposition, diagenesis, and structural deformation are not encoded in geostatistical algorithms. Geostatistical tools, including variogram-based methods, object-based methods, and multiple point statistics, permit the generation of numerical models that mimic our conceptual model within the limits of the inferred statistics. A well-reasoned conceptual model is essential. Often geostatistical models include a significant deterministic component informed directly by expert geological mapping. The results of geostatistical modelling may provide unexpected insights into the geological site through the integration of disparate data and concepts, but mostly the results are high-resolution numerical models for resource calculation and flow simulation.
Geostatistical sophistication cannot overcome bad input data and a flawed conceptual model. In fact the resulting heterogeneity models may mask data issues. We must accept the provided measurements and move on with numerical modelling, otherwise we will not have the decision support information that management requires. At the same time, we cannot simply take the data at face value and accept a preliminary and perhaps flawed conceptual model, otherwise the numerical models are not useful. Uncertainty and bias in the data and conceptual model, and alternative geological scenarios, must be considered.
Uncertainty sources must be sought out. Uncertainty must be assigned to the data. Many input statistical parameters are inferred from the data; uncertainty must be assigned to these. Modelling decisions and parameters must be specified for each algorithm, and uncertainty must be assigned to these too. Measurement and parameter uncertainty transfers through to the uncertainty in the resources or reserves. The sensitive data, parameters, or modelling choices are rarely known ahead of time; they are observed after we have sought them out.

There is uncertainty everywhere: the precise location of the data, its processing and interpretation, our understanding of geological processes, parameters to the geostatistical algorithms, and so on. But after seeking out the critical aspects of uncertainty, our current best assessment must support time-sensitive and business-critical decisions. You have to stop somewhere.

Pyrcz, M J and C V Deutsch (2014). Geostatistical Reservoir Modeling, 2nd edition. Oxford University Press. 433 p.

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