Book Description

The effect of topography on gravity gradient data is considered and the effect of topography on the solution of the geodetic boundary value problem by using analytical downward continuation is also investigated. The validity of solving Molodensky's problem by using the analytical downward continuation is inspected. Even though it has been shown that the analytical downward continuation solution is equivalent to Molodensky's solution which is considered theoretically perfect, a very small topographic effect exists. This effect is trivial and can be neglected in the numerical computations. It is also shown that a spherical harmonic expansion cannot exactly represent the disturbing potential outside the Brillouin sphere and nearby the earth at the same time. If the points are nearby the earth (between the Brillouin sphere and the earth's surface), there is a topographic effect to the geopotential represented by a spherical harmonic expansion whose coefficients are determined by using the gravity anomalies analytically downward continued onto the ellipsoid. This effect is the same as the solving of the Molodensky's problem by using the analytical downward continuation. The convergence problem of the analytical downward continuation is also investigated under planar approximation. It is shown that the downward continuation is convergent almost everywhere, except at the infinite point of the circular frequency omega = infinity. This is important for geopotential modeling. Gradiometers. (edc).