Regularity analysis of oil exploration borehole logs: A case study from Algeria

Due to their local regularity properties, well logs are successfully modeled using multifractional Brownian motions. These local fractal processes provide a consistent framework to explore regularity of the logs, measured by the Hölder exponent (H), at all depths in the logged interval. This paper presents the results of a regularity analysis carried out on datasets recorded in three Algerian oil boreholes located in different geological settings. This analysis allows to draw valuable information related to the well formations. The regularity profiles, or the Hölder exponent functions, mainly those obtained from the “porosity-dependent” logs (sonic, density and neutron), exhibit a strong correlation with the lithology. Each lithological change is marked by a jump in H value. In addition, for a given well, the computed regularity profiles show a very significant correlation between them. That is, the regularity is a robust property which can be successfully used to characterize lithological heterogeneities of layers. On the other hand, this study does not reveal any relation between the recorded physical property and its estimated regularity degree for each log, and low correlation coefficients are generally observed between these parameters.