ALBERT

Notes: The determination of high-degree geopotential models currently requires accurate terrestrial gravity information on a global basis. For the regions where such information is unavailable or poor, it is important to develop procedures for the estimation of gravity anomalies, based on existing data sources. This paper examines the possibility of combining low-degree satellite-derived geopotential models with the harmonic coefficients of the topographic-isostatic potential implied by the Airy/Heiskanen isostatic hypothesis.The compilation of a new global topographic database that provides additional information pertaining to terrain type classification, ice coverage etc., is discussed first. Then the rigorous formulation for the determination of harmonic coefficients of the topographic-isostatic potential is extended to account for the various terrain types. This formulation, and a series expansion approach are implemented to determine topographic-isostatic coefficient sets complete to degree and order 360. These coefficients are then combined with satellite-derived models (GEM-T1/T2) to estimate 1°× 1° mean gravity anomalies. Comparisons of the estimated anomalies with observed values, as well as with anomalies derived from satellite altimetry, indicated the following. (a) Optimum results are obtained when the satellite models are used to degree 36 and the topographic-isostatic coefficients from 37 onwards. For example, when GEM-T2 to degree 36 is combined with the topographic-isostatic coefficients from 37 to 180, the root mean square (rms) anomaly difference with 6237 1°× 1° terrestrial values having a standard deviation less than 10 mgals, was ±18 mgals, which should be compared to the rms value of the terrestrial anomalies which was about ±27 mgals. The use of GEM-T2 alone up to degree 36 yields an rms discrepancy with the same terrestrial values of the order of ±22 mgal. (b) The effect of ice is significant and improves the quality of the estimated anomalies in polar regions where very limited gravity material exists. (c) The overall accuracy of the estimated anomalies is about equal to the overall accuracy of existing geophysically predicted anomalies. However, the use of the satellite model for the low degrees in the current procedure, may resolve problems associated with regional biases detected in the geophysical anomalies.

Notes: 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.