OPTIMAL TRANSFORMATIONS FOR MULTIPLE-REGRESSION - APPLICATION TO PERMEABILITY ESTIMATION FROM WELL LOGS

Conventional multiple regression for permeability estimation from well logs requires a functional relationship to be presumed. Because of th e inexact nature of the relationship between petrophysical variables, it is not always possible to identify the underlying functional form b etween dependent and independent variables in advance. When large vari ations in petrological properties are exhibited, parametric regression often fails or leads to unstable and erroneous results, especially fo r multivariate cases. In this paper, we describe a nonparametric appro ach for estimating optimal transformations of petrophysical data to ob tain the maximum correlation between observed variables. The approach does not require a priori assumptions of a functional form, and the op timal transformations are derived solely based on the data set. Unlike neural networks, such transformations can facilitate physically based function identification. An iterative procedure involving the alterna ting conditional expectation (ACE) forms the basis of our approach. Th e power of ACE is illustrated using synthetic as well as field example s. The results clearly demonstrate improved permeability estimation by ACE compared to conventional parametric-regression methods.