Performance of three types of Stokes's kernel in the combined solution forthe geoid

When regional gravity data are used to compute a gravimetric geoid in conju nction with a geopotential model, it is sometimes implied that the terrestr ial gravity data correct any erroneous wavelengths present in the geopotent ial model. This assertion is investigated. The propagation of errors from t he low-frequency terrestrial gravity field into the geoid is derived for th e spherical Stokes integral, the spheroidal Stokes integral and the Moloden sky-modified spheroidal Stokes integral. It is shown that error-free terres trial gravity data, if used in a spherical cap of limited extent, cannot co mpletely correct the geopotential model. Using a standard norm, it is shown that the spheroidal and Molodensky-modified integration kernels offer a pr eferable approach. This is because they can filter out a large amount of th e low-frequency errors expected to exist in terrestrial gravity anomalies a nd thus rely more on the low-frequency geopotential model, which currently offers the best source of this information.