Shaping filters and the upward continuation problem

Abstract

An attempt is made to bridge the gap between closed-form harmonic upward continuation (HUC) of analytic covariance functions of the disturbing potential of the anomalous local gravity field and the numerical shaping filter construction when the local gravity vector is modelled in the framework of Kalman filtering. Some fundamental concepts of the local gravity field, interpreted as a stochastic process that is stationary in the plane and harmonic in the upper half space, are reviewed. The shaping-filter modelling technique for the local gravity vector is introduced. To determine the relation between the disturbing potential covariance function and the gravity vector covariance matrix, the role of the so-called admissible pair is established. It is shown that rescaling an admissible pair leads to an analogue rescaling of the shaping filter matrices derived hereof; no cumbersome numerical recalculations are necessary. The class of covariance functions whose corresponding shaping filters possess a closed-form HUC are identified as models whose HUC can be interpreted as a rescaling.