Analysis of aperture values of stratabound fractures in bedded rock: Use of the maximum likelihood method in studying a truncated data set

Abstract

In this study, a truncated data set of aperture values of stratabound joints in carbonate rocks, already studied in a previous work and in which sampling of smallest fractures was problematic, has been reanalysed through regression analysis by means of Maximum Likelihood Estimation (MLE). This analysis criterion has been tested through Monte Carlo simulations, which demonstrated that MLE is able to correct the measurement bias due to truncation. The statistics corroborate as the median joint aperture value is mainly controlled by mechanical bed thickness, according to a linear regression law with non-zero intercept. The achieved results are of interest (i) from the viewpoint of statistical methodology as well as (ii) for the purpose of characterizing stratabound joint sets. With reference to point (i), the proposed method is significantly more reliable than the Least Squares Method (LSM). Therefore, it may be routinely employed in fracture analysis and potentially adapted also for other cases in which there is an analogue bias at lower limits of the sampling range. Regarding point (ii), these results provide a step ahead in characterizing and modeling of stratabound joint networks based on bed thickness data, which is relevant to identify pathways and storage systems in oil reservoir study, in hydrogeology and in all environmental problems involving ground fluids.