Maximum Likelihood Instead of Least Squares in Fracture Analysis by Means of a Simple Excel Sheet with VBA Macro

Abstract

This technical note illustrates a linear regression algorithm based on the Maximum Likelihood Estimation (MLE), with a related Excel spreadsheet and VBA program, adapted to the case of fracture aperture data sets in which sampling of the smallest values is problematic. The method has been tested by means of Monte Carlo simulations and exhibits significantly better convergence against Least Squares criterion (LSM). As the method is conceptually simple and, following the indications illustrated here, the relative spreadsheet can be easily designed, it may be routinely used, instead of the Least Squares, in fracture analysis. Furthermore, the proposed method, with the appropriate modifications, might be potentially extended to other cases in geology and geophysics, in which significant biases at the lower limits of the sampling scale occur.