The decay of the spectrum of the gravitational potential and the topography for the Earth

The spectrum of the Earth's gravitational potential and topography, as represented by spherical harmonic expansions to degree 180, have been computed. Modelling the decay in the form of Al−β, values of A and β for several degree (l) ranges were computed. For degree range 5–180, β was 2.54 for the potential and 2.16 for equivalent rock topography. The potential decay was somewhat slower than that (i.e. β = 3) implied by Kaula's rule. However, at high degree ranges, the β values were larger (3.20 for degrees 101–180) agreeing better with recent determinations from terrestrial gravity data and geoid undulations implied by satellite altimetric data. The values imply that the potential decays faster at higher l values. The values of β for topography were fairly uniform around 2 which agrees with a suggestion made by Vening-Meinesz in 1951. We also found that the β value for the Earth's potential agrees well with the value implied by the topography with Airy isostatic compensation with the depth of compensation equal to 30 km. However, the magnitude of the power implied by the topographic/isostatic potential was approximately one-third of the observed potential.