Fuzzy Logic Determination of Lithologies from Well Log Data: Application to the KTB Project Data set (Germany)

Fuzzy logic has been used for lithology prediction with remarkable success. Several techniques such as fuzzy clustering or linguistic reasoning have proven to be useful for lithofacies determination. In this paper, a fuzzy inference methodology has been implemented as a MATLAB routine and applied for the first time to well log data from the German Continental Deep Drilling Program (KTB). The training of the fuzzy inference system is based on the analysis of the multi-class Matthews correlation coefficient computed for the classification matrix. For this particular data set, we have found that the best suited membership function type is the piecewise linear interpolation of the normalized histograms; that the best combination operator for obtaining the final lithology degrees of membership is the fuzzy gamma operator; and that all the available properties are relevant in the classification process. Results show that this fuzzy logic-based method is suited for rapidly and reasonably suggesting a lithology column from well log data, neatly identifying the main units and in some cases refining the classification, which can lead to a better interpretation. We have tested the trained system with synthetic data generated from property value distributions of the training data set to find that the differences in data distributions between both wells are significant enough to misdirect the inference process. However, a cross-validation analysis has revealed that, even with differences between data distributions and missing lithologies in the training data set, this fuzzy logic inference system is able to output a coherent classification.