Multi-scale statistical analysis of scan line data from reservoir analogues

The study of statistical distributions of structural features such as joint length, opening displacement (aperture) and spacing at different scales of observation is on the focus of research in the field of reservoir development and management, since they noticeably affect porosity and permeability of reservoir rocks. Recent studies (ORTEGA et alii, 20006) effectively confirmed that opening-mode fracture size distribution is well described by a power law. A review of the different types of artifacts in determining such distributions has been provided by ORTEGA et alii (2006), concerning systematic errors occurring at both extremities of the scale of observation. However, a nonsystematic, often more dangerous error is that associated with the uncertainty of the obtained sampling estimates, depending on the kind of aleatoric variables involved and statistical samples size (GUERRIERO et alii, 2009). In this paper we suggest specific, rigorous criteria for the analysis of joint spatial distributions, as well as for the analysis of probability distributions of sampling estimate errors affecting both exponent and coefficient of the power law. This is carried out taking into account methodological issues, mainly within the framework of multi-scale scan line data analysis.