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Abstract: Modeling Stratigraphy Using Common Sense

Ulf Nordlund, Magnus Silfversparre

Many of the variables in dynamic stratigraphic models, e.g., regional tectonism, eustasy, isostasy, and compaction, are relatively easy to model numerically using simple mathematical functions. The spatial and temporal distribution of different sediment types is much more difficult to model since this requires the formalization of complex nonlinear relationships among interdependent variables. A simple mathematical equation describing even a single depositional system will rarely, if ever, be found. The complexity is obvious when trying to quantify in detail the different aspects of deposition and erosion.

This is in sharp contrast to the relative ease with which we, through speech or in writing, are able to describe qualitatively the where, what and how much of deposition and erosion. Given the conditions (in the form of quantitative and/or qualitative information about climate, surface morphology, sea-level change, subsidence rates, etc.) a geologist can, depending on experience, give a rather detailed account of the expected distribution of different types of sediment. The question is: how can this type of imprecise and vague information be captured and put to work in a simulation model?

Fuzzy logic is a branch of mathematical logic which includes a methodology for the quantitative treatment of imprecise, ambiguous and vague data. It provides a means to build dynamic stratigraphic models based on qualitative information. Deposition and erosion in such models are controlled by a fuzzy system based on fuzzy sets and fuzzy rules. In the context of basin modeling, fuzzy sets may be conceptual entities such as much, little, far from shore, rather deep, sandy clay, and warm climate. Examples of rules are "low energy then mud" or "if shallow and exposed to waves then sand." The fuzzy sets and rules may be based on experience, expert opinions, empirically derived data, or common sense.

The approach of using fuzzy sets and rules has some extremely appealing characteristics. First, it allows us to incorporate qualitative data in a manner that is easily conceptualized. It also makes it very easy to test conceptual models or individual assumptions, even if these are only available in linguistic form. Furthermore, as we are not tied to any rigid built-in equations, the strategy for controlling deposition and erosion can be partly or completely modified at any time, even in the midst of a simulation. It should also be noted that in spite of the apparent simplicity, fuzzy systems are very powerful at modeling nonlinear relationships involving several variables.

Fuzzim is a software tool written by the authors that allows construction of simulation models using a user-defined fuzzy system for control of deposition and erosion. The models generated operate in 3D and erode, transport and deposit different types of sediment. The result is a three-dimensional account of lithologies, porosities, relative ages, and thicknesses. We show how Fuzzim works, and briefly discuss the methods used. Using a few examples, we also demonstrate some of the advantages in using a fuzzy approach. Specifically, we show that it is also possible to handle relatively complex depositional settings, e.g. involving salt tectonics and mixed clastic-carbonate environments, using a fuzzy controller.

AAPG Search and Discovery Article #90956©1995 AAPG International Convention and Exposition Meeting, Nice, France