Inversão em geofísica de poço: um estudo sobre ambiguidade

Abstract

The ambiguity in the inversion of well-logging data is studied using the Q-mode factor analysis. This method is based on the analysis of a finite number of acceptable solutions, which are ordered, in the solution space, along the greatest direction of ambiguity. The analysis of the parameters variation along these ordered solutions provides an objective way to characterize the parameters playing a major role in the problem ambiguity. Because the Q-mode analysis is based on the geometry of an ambiguity region, empirically estimated by a finite number of alternate solutions, it is possible to analyse the ambiguity due not only to errors in the observations, but also to small discrepancies between the interpretation model and the true sources. Moreover, the analysis can be applied even in the cases of nonlinear interpretation models or nonlinear parameter dependence. The factor analysis was performed with synthetic data, and compared with the analysis using singular value decomposition, proving to be more efficient because of the less restrictive assumptions required in its application. As a result, it provides a more realistic way to characterize the ambiguity. Following the determination of the most influential parameters in the model ambiguity, a reparametrization is possible by grouping these parameters into a single parameter. Despite the inevitable loss of resolution this reparametrization leads to a drastic reduction in the model ambiguity.