Reformulation of Stokes's theory for higher than second‐degree reference field and modification of integration kernels

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Abstract
An argument is put forward in favor of using a model gravity field of a degree and order higher than 2 as a reference in gravity field studies. Stokes's approach to the evaluation of the geoid from gravity anomalies is then generalized to be applicable to a higher than second‐order reference spheroid. The effects of truncating Stokes's integration and of modifying the integration kernels are investigated in the context of the generalized approach. Several different modification schemes, starting with a Molodenskij‐like modification and ending with the least squares modification, are studied. Particular attention is devoted to looking at both global and local biases and mean square errors of the individual schemes.