Lithology identification using kernel Fisher discriminant analysis with well logs

• KFD, an improved LDA with kernel trick, is introduced to identify lithology.
• It obtains nonlinear lithological features by raising and reducing dimensions.
• It enables geologists to get a deeper insight for the lithology identification model.
• Its principle of math and optimal parameter determination are presented in detail.
• The experiments show KFD is a practicable method for lithology identification.

Lithology identification is a key step in reservoir characterization. Linear discriminant analysis (LDA) is a widely used method for lithology identification. However, LDA suffers from the disadvantage that it can only extract linear features, whereas nonlinear features in the lithological feature space often play a role in lithology identification. In this paper, we introduce kernel Fisher discriminant analysis (KFD), an improved LDA with kernel trick, to overcome the shortcoming of LDA for lithology identification. It includes two processes: raising dimensions to get nonlinear information and reducing dimensions to get classification features. By these processes, it can obtain nonlinear classification features efficiently. To examine the effect of KFD for lithology identification, experiments are implemented on a field data set by KFD and auxiliary methods, namely LDA and traditional nonlinear discriminant analysis (quadratic discriminant analysis, QDA). By comparisons from different aspects, the results show that KFD outperforms LDA and QDA and it is a practicable method for lithology identification.