Comparison of Newton’s Integral in the Space and Frequency Domains

Newton’s integral can be evaluated either in the space domain by a direct integration approach or in the frequency domain by a spherical harmonic approach. In the first approach Newton’s integral is evaluated by a discretised numerical integration using the gravitational potential (or its derivatives) caused by regularly shaped bodies such as prisms or tesseroids (i.e., spherical or elliptical volume elements, respectively). The second approach expresses Newton’s integral by spherical harmonic expansions of height or density functions, which can be interpreted as the gravitational effect of different mass layers. This paper studies the theoretical and practical differences between both approaches. The gravitational effect of the global topographic masses, described here by equivalent rock heights, is evaluated using both approaches and the results compared. Numerical results for the gravitational potential are given for evaluation points located directly on the Earth’s surface and at different heights (e.g., flight levels) above it.