Data requirements for determining precise relative geoid heights from gravimetry

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Abstract
Global Positioning System (GPS)‐based receivers appear capable of obtaining Δh, the ellipsoidal height differences, to about 2–4 ppm of the distance separating the end points. The historical record of vertical crustal motion has been obtained from spirit leveling and therefore gives changes in elevation in terms of orthometric height. For GPS‐based height differences to be useful in extending the record of height change, the geoid‐ellipsoid separation ΔNneeds to be evaluated. But is it possible to find ΔNgravimetrically to the precision to which Δhcan be measured? This analysis shows that the inner zone contribution to ΔNcould be more precise than is Δhfrom GPS. This contribution to ΔNshould be better than ±5 cm over 100 km if the random errors in the 10 km by 10 km mean gravity anomalies do not exceed ±3 mGal and provided the gravity and elevation data used to obtain the gravity means are connected onto the national gravity and (at least) third‐order leveling networks, respectively. For lines of mean elevation greater than 2 km the error in ΔNwill exceed specifications unless the density of the subsurface material can be estimated to better than ±200 kg m−3. Results of other tests suggest that the remote zone contribution to ΔN(ψ > 2.0°) is adequately represented by high degree (nmax≅ 180) geopotential models. A small test with the suggested method, performed in the White Sands Test Area, appears to confirm the above data specifications and supports the conclusions of two other investigations that ΔNcan be evaluated from gravimetry to precisions which match that of Δhfrom GPS, at least over shorter lines.