Support Vector Machines for Classification and Mapping of Reservoir Data

Abstract

Support Vector Machines (SVM) is a new machine learning approach based on Statistical Learning Theory (Vapnik-Chervonenkis or VC-theory). VC-theory has a solid mathematical background for the dependencies estimation and predictive learning from finite data sets. SVM is based on the Structural Risk Minimisation principle, aiming to minimise both the empirical risk and the complexity of the model, providing high generalisation abilities. SVM provides non-linear classification SVC (Support Vector Classification) and regression SVR (Support Vector Regression) by mapping the input space into high-dimensional feature space using kernel functions, where the optimal solutions are constructed. The paper presents the review and contemporary developments of the advanced methodology based on Support Vector Machines (SVM) for the analysis and modelling of spatially distributed information. The methodology developed combines the power of SVM with well known geostatistical approaches and tools including exploratory data analysis and exploratory variography. Real case studies (classification and regression) are based on reservoir data with 294 vertically averaged porosity data and 2D seismic velocity and amplitude. A porosity classification and regression maps are generated using SVC/SVR and the results are compared with geostatistical models.