Kernel Fisher discriminant analysis (KFD) can map well log data into a nonlinear feature space to make a linear non-separable problem of fracture identification become a linear separable one. Commonly, KFD employs one kernel. However, the prediction capacity of KFD based on one kernel is limited to some extent, especially for a complex classification problem, such as fracture identification in tight sandstone reservoirs. To alleviate this problem, we employed a multiple kernel Fisher discriminant analysis (MKFD) method to recognize fracture zones. MKFD utilizes multi-scaled Gaussian kernel functions instead of a single kernel to realize the optimal nonlinear mapping. To assess the effectiveness of MKFD in fracture identification for complex reservoirs, we chose a dataset from tight sandstone reservoirs in China to implement comparison experiments. In the experiments, we used the MKFD with ten Gaussian kernels to map the original well logs into nonlinear feature spaces so that we could obtain appropriate features for fracture identification. The comparison results demonstrated that the accuracy of fracture identification by MKFD improved about 13.4% over KFD and MKFD also outperformed KFD in the blind well test, although the improvement of generalization ability of MKFD was not very obvious. Overall, MKFD can provide an accurate means for the identification of fracture zones in tight reservoirs. In this work, we also summarized the problems for fracture identification by MKFD.
Kernel Fisher Discriminant Analysis Based on a Regularized Method for Multiclassification and Application in Lithological Identification
