A discrete contraction conjecture for estimating gravity fields on irregular closed surfaces

Abstract

We construct an estimator for gravitational potential on an irregular closed surface as a finite spherical polynomial, based on a finite number of sample observations. This estimator is a natural discrete adaptation of an approximation for gravitational potential suggested by Sanso and Sideris. We consider the following discrete analogue of their conjecture: that the error in our estimator is a contraction operator, implying that the estimation process can be iterated to approximate gravitational potential to arbitrarily levels of accuracy. We then offer evidence for the conjecture through a series of numerical simulations and conclude with a simulation using a model of the Earth’s topography and real-world data.