The Nelder-and-Mead simplex method is used to obtain optimal sets of Archie parameters (m, n, a) from resistivity measurements on core samples. This derivative-free optimization method, despite being a local search technique, avoids trapping by minor optima. We have found that the method is very effective, highly efficaceous, and easily implemented on a PC. The agreement between the results obtained from this method and those from the nonlinear least-squares approach is remarkable.
Recently, an improved data-analysis method was used in determining Archie parameters -- m, n, and a. The method is based on the minimization of the differences between measured and calculated water saturations based on nonlinear least-squares. In this paper we cast this minimization problem as a problem in constrained optimization; we adopted the simplex method of Nelder and Mead for optimization.
A brief description of the method precedes the description of data used and the results obtained by this method, which are compared with those from nonlinear least-squares method.
In a companion paper, which follows, we introduce another novel approach of fuzzy regression, which is more appropriate than the classical regression when either the model is fuzzy or the data are sparse.