The hierarchical decomposition method and its application in recognizing Marcellus Shale lithofacies through combining with neural network

• Investigate class hierarchical structure.
• Develop the hierarchical decomposition method and the whole workflow for multi-class classification.
• Enhance Marcellus Shale lithofacies recognition more reliable and higher cross-validation accuracy.

The three dimensional (3-D) distribution of shale lithofacies has been approved to be helpful for recognizing shale gas productive areas at basin and regional scales. To build the 3-D model, the successful prediction of shale lithofacies by conventional logs is critical. Thus, a hierarchical decomposition (HD) method for multi-class classification was proposed and developed through decomposing the original multi-class problem into several simpler sub-problems on the basis of the class hierarchy. This method can effectively combine the mathematical methods and professional knowledge, and also overcome several drawbacks existing in the common decomposition methods, such as one-against-all, one-against-one and error-correcting output code. Due to the feature that the misclassification in upper-level sub-problems will be handed down into the lower-level sub-problems, the error control and recovery algorithms were generated in this HD method, including setting higher threshold in upper levels, deciding classes through voting method based on the K-fold cross validation, and re-classifying the meta-class when its child class cannot be decided. By using the HD, the cross validation correct ratio of core data sample and pulsed neutron spectroscopy data sample was improved from 85.7% to 89.0% and from 77.8% to 79.5%, respectively, which strongly supports the HD as a promising method for solving multi-class classification problems. In this paper, the comprehensive methodology of the HD for multi-class classification was explained, and the enhanced recognition of Marcellus Shale lithofacies in the Appalachian Basin was also demonstrated.