--> Abstract: Using Fuzzy Logic to Model Ambiguity in Geologic Processes, by A. C. Gary and M. Filewicz; #90928 (1999).

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GARY, ANTHONY C.1 and MARK FILEWICZ2
1Energy and Geoscience Institute, The University of Utah, Salt Lake City, Utah
2Unocal Corporation, Sugar Land, Texas.

Abstract: Using Fuzzy Logic to Model Ambiguity in Geologic Processes

In geology, a measured value (e.g., microfossil abundance, resistivity, impedance) is not usually diagnostic of a unique class (e.g., depositional environment, lithology). More commonly, a measured value is characteristic of a class rather than diagnostic, and has membership in other classes to varying degrees. Classical set theory or “crisp' set theory does not provide a direct method for handling membership in multiple classes. There is no satisfactory way “crisp” set theory can handle a graded transition between sets which is a common occurrence in biostratigraphy and sedimentology.

An alternative approach to “crisp” sets are “fuzzy” sets. Fuzzy set theory allows an observation to have multiple and partial memberships to different sets (Zadeh ,1965). The degree to which an observation belongs to a particular set is represented by a grade of membership value. The membership grades are derived from membership functions that represent the relationship of values of the domain variable (e.g., faunal or sedimentological parameter) to each set (e.g., depositional environment) to which they can belong. Simple fuzzy set operations (i.e., union, intersection, and complement) can then be applied to the membership grades to represent the degree of association among the parameters.

We used fuzzy logic to quantify transitions in the paleoenvironment of Neogene estuarine sediments from offshore China, based on the abundance of four faunal components: freshwater dinoflagellates, marine dinoflagellates,benthic foraminifera, and calcareous nannofossils. Simple membership functions were defined relating the abundance of each microfossil group to each of four pre-defined paleoenvironmental zones (i.e., freshwater, inner estuary, middle estuary, and outer estuary). The degree of association between samples and paleoenvironmental zones were determined by the union (i.e., maximum membership value) of the membership functions. To accommodate offshore transport, the freshwater dinoflagellate function was activated only in the absence of membership to middle or outer estuary paleoenvironments.

The resulting paleoenvironmental associations using fuzzy logic provide a considerably higher degree of detail than the more common binary representation of paleoenvironment associations. Transitions to different paleoenvironments were correlatable among wells and consistent with the interpretation of depositional environment from petrophysical and core data.

Zadeh, L. A., Fuzzy Sets; Information and Control, v. 8, pp. 338-353, 1965.

AAPG Search and Discovery Article #90928©1999 AAPG Annual Convention, San Antonio, Texas