EVALUATION OF TOPOGRAPHICAL EFFECTS IN PRECISE GEOID COMPUTATION FROMDENSELY SAMPLED HEIGHTS

In this paper we investigate the behaviour of Newton's kernel in the i ntegration for topographical effects needed for solving the boundary v alue problem of geodesy. We follow the standard procedure and develop the kernel into a Taylor series in height and look at the convergence of this series when the integral is evaluated numerically on a geograp hical grid, as is always the case in practice. We show that the Taylor series converges very rapidly for the integration over the ''distant zone'', i.e., the zone well removed from the point of interest. We als o show that the series diverges in the vicinity of the point of intere st when the grid becomes too dense. Generally, when the grid step is s maller than either the height of the point of interest, or the differe nce between its height and those of the neighbouring points. Thus we c laim that the Taylor series version of Newton's kernel cannot be used for evaluating topographical effects on too dense a topographical mesh .