Navigation in a model space with misfit-induced curvature

Kristopher A. Innanen

We investigate the consequences in inversion of adapting our geometrical picture of model space. We consider that model space is curved by the presence of the misfit or objective function. Within such a space, the simplest possible curves, equivalent to straight lines in flat space, are geodesics. Paths are normally followed by model estimates in the process of updating and in estimating uncertainty, and we examine the geodesics with this in mind - is it possible that visiting points in model space in the order determined by a geodesic is a valuable exercise? There are some hints that the answer may be yes. Geodesics computed with coordinates with lower (covariant) indices appear to orbit regions of model space surrounding the minimum of the objective function in a manner which may have application in uncertainty evaluation.