Ambiguity analysis of well‐log data

Abstract

Ambiguity in a geophysical interpretation problem is the possibility of accepting more than one solution caused either by solution nonuniqueness or instability. Nonuniqueness is related to the existence of more than one solution regardless of the precision of observations. On the other hand, instability is related to the acceptance of different solutions producing data fittings within the expected observational errors. We studied the ambiguity in the inversion of well‐logging data using a method based on the analysis of a finite number of acceptable solutions, which are ordered, in the solution space, according to their contributions to the overall ambiguity. The analysis of the parameter variations along these ordered solutions provides an objective way to characterize the most ambiguous parameters. Because this analysis is based on the geometry of an ambiguity region, empirically estimated by a finite number of alternative solutions, it is possible to analyze the ambiguity due not only to errors in the observations, but also to discrepancies between the interpretation model and the true geology. Moreover, the analysis can be applied even in the case of a nonlinear interpretation model. The analysis was performed with recorded data, and compared with the analysis using singular value decomposition, leading to comparable results. Following the determination of the most ambiguous parameters, a reparameterization is possible by grouping these parameters into a single parameter leading to a simpler interpretation model and, therefore, to a drastic reduction in the ambiguity.