Regularity Analysis Applied to Well Log Data

Summary

Well logs are largely used for oil exploration and production in order to obtain geological information of rocks. Several parameters of the rocks can be scanned and interpreted in term of lithology and of the quantity and kind of fluids within the pores. Generally the drilled rocks are mostly sedimentary and the modelling is mainly petrophysical. Here we analyze four logs from the KTB Main Borehole, drilled for the German Continental Deep Drilling Program. The hole cuts across crystalline rocks like amphibolites, amphibolite-metagabbros, gneiss, variegated units and granites.

A multifractal model is assumed for the logs and they are analyzed by a new methodology called Regularity Analysis (RA), which maps the measured logs to profiles of Holder exponents or regularity. The regularity generalizes the degree of differentiability of a function from integer to real numbers and it is useful to describe algebraic singularities related not only to the classical model of jump discontinuity, but to any other kind of ‘edge’ variations. We aim at a) characterizing the lithological changes of the drilled rocks; and b) identifying the zones of macro and micro fractures. The RA was applied to several geophysical well logs (density, magnetic susceptibility, self potential and electrical resistivity) and allowed consistent information about the KTB well formations. All the regularity profiles independently obtained for the logs provide a clear correlation with lithology and from each log we derived a similar segmentation in terms of lithological units.

A slightly different definition of regularity, called an average-local regularity, yields a good correlation between each known major fault and local maxima of the regularity curves. The regularity profiles were also compared with the KTB “Fracture Index” (FI), showing a meaningful relation among maxima of regularity and maxima of fracture index.