[G02-1] Theory and methods

[G02-1-06] Direct topographical effect on the airborne gravity disturbance for Helmert's second method of condensation

^○Jianliang Huang, Marc Veronneau, John W. Crowley (Natural Resources Canada, Ottawa, Canada)

Helmert's second method of condensation removes the topographical mass and compensates using a thin mass layer on the geoid, transforming the Earth's gravitational potential to a harmonic field in the space between the geoid and topographical surface. Consequently, the Helmert(ized) gravity anomaly can be continued from the Earth's surface downward to the geoid to meet the requirement of Stokes's integral for the determination of the geoid in the harmonic Earth's gravity field. Finally the geoid can be determined by restoring the topography from the Helmert mass layer. In this process, the Helmert gravity anomaly is determined from the Molodensky-type free-air anomaly by evaluating and correcting for the direct and second indirect topographical effects (DTE and SITE) on the Earth's surface. The Molodensky-type anomaly is defined by the difference between the gravity value at a point on the Earth's surface and the normal gravity at the corresponding point on the telluroid. This approach is suitable when the gravity observation and orthometric/normal height are available on the Earth's surface. The airborne gravity observations provide the gravity disturbance, as ellipsoidal height is generally measured at flight level. To apply Helmert's second method of condensation to the gravity disturbance, only the direct topographical effect is required at flight level. In this paper, we first formulate the direct topographical effect on the gravity disturbance at flight level in terms of both Newton's integral and spherical harmonic series, then numerically determine the requirements on spatial and spectral resolutions of digital elevation model (DEM) for the evaluation of DTE at various flight levels.