FAR-ZONE CONTRIBUTION IN ELLIPSOIDAL STOKES BOUNDARY-VALUE PROBLEM V.E. ARDESTANI 1 , Z. MARTINEC 2 1 Institute of Geophysics, Tehran University, Tehran, Iran (ebrahimz@chamran.ut.ac.ir) 2 Department of Geophysics, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic (zdenek@hervam.troja.mff.cuni.cz) Received: July 15, 2002; Accepted: September 4, 2003 ABSTRACT In the first attempt to solve the Stokes boundary-value problem in ellipsoidal coordinates numerically (Ardestani and Martinec, 2000), we focused on the near-zone contribution since the effect of the ellipsoidal Stokes function in the far-zone contribution is not considered. We present a method for solving the ellipsoidal Stokes integral in far-zone contribution. The numerical results of computing the magnitude of this term for an area in north of Canada are presented. K e y w o r d s : ellipsoidal Stokes integral, far-zone contribution, numerical results 1. INTRODUCTION As it is well known the shape of the geoid deviates from an ellipsoid of revolution much less than from a sphere, thus solving the Stokes boundary-value problem for gravity anomalies distributed on an ellipsoid of revolution reflects reality much better than a spherical Stokes integral. The Stokes boundary-value problem in ellipsoidal coordinates has theoreticallly defined and solved by Martinec and Grafarend (1997). The problem solved numerically by Ardestani and Martinec (2000) where the effect of the ellipsoidal correction which is defined in the term of the ellipsoidal Stokes function in the far-zone contribution is not considered. The remaining problem is how to solve the ellipsoidal Stokes integral including the ellipsoidal Stokes function for far-zone contribution. 2. ELLIPSOIDAL STOKES BOUNDARY-VALUE PROBLEM The ellipsoidal Stokes boundary-value problem is defined by Martinec and Grafarend (1997), , if , (1) 2 0 T ∇ = 0 u b > 2 T T f u u ∂ + = ∂ , if 0 u b = , (2) Stud. Geophys. Geod., 47 (2003), 719−723 719 © 2003 StudiaGeo s.r.o., Prague