Self-affine and ARX-models zonation of well logging data

Zonation of time series into models which their parameters are piecewise constant are important and well-studied problems. Geophysical well logging data often show a complex pattern due to their multifractal nature. In a multifractal system, any pieces of it are established by a distinct exponent that can characterize them. This feature has the capability to cluster them. Self-affine zonation by Auto Regressive model with exogenous inputs (ARX) is a new approach which places well logging segments in the clusters which are more self-affine against the other clusters. This approach was performed and compared with a conventional ARX zonation in the well logging data of three different oilfields in southern parts of Iran. The results showed a good accuracy for detecting homogeneous lithological segments and led to a precise interpretation process to update the reservoir architecture.