ELLIPSOIDAL STOKES BOUNDARY-VALUE PROBLEM WITH ELLIPSOIDAL CORRECTIONS IN THE BOUNDARY CONDITION VAHIDE. ARDESTANI 1 AND ZDENEK. MARTINEC 2 Summary: We would like to solve the Stokes boundary-value problem taking into consideration the ellipsoidal corrections in the boundary condition in ellipsoidal coordinates The original problem, i.e., the ellipsoidal Stokes boundary-value problem has been solved by Martinec and Grafarend (1997) We use the same pliilosophy expressed by Martinec (1998) to solve the spherical Stokes boundary-value problem with ellipsoidal corrections in the boundary condition We wish to show the magnitude of the integration kernel describing the effect of the ellipsoidal corrections in the boundary condition in a cap around the computational point. Key words: Ellipsoidal Stokes boundary-value problem, ellipsoidal corrections, numerical results 1. INTRODUCTION There are several options of linearizing the boundary-value problem of determining the gravimetric geoid. One option is to use the ellipsoidal approximation in both gravity and geometry spaces. This approach seems to be the most precise since the linearization errors are equal to 0.2 mgal and 2 mm (Martinec, 1998) in gravity and geometry spaces respectively This approximation does not remove the ellipsoidal correction terms in the boundary condition for anomalous gravity, The analytical forms of these corrections are derived in Heck (1991). The first step in solving this type of boundary-value problem was made by Martinec and Grafarend (1997) who did not consider the ellipsoidal correction terms in the boundary condition for anomalous gravity. 2. ELLIPSOIDAL APPROXIMATION OF THE GEOID To begin with, let us introduce ellipsoidal coordinates {u,j,A) through the transformation relations into Cartesian coordinates {x,y,z} (Heiskanen and Moritz, 1967, sect. 1-19), 1 Address: Insititute of Geophysics, Tehran University, Tehran, Iran (e-mail: ebrahimz@chamran.ut.ac.ir) 2 Address: Department of Geophysics, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic Studia geoph. et geod. 45 (2001), 109-126 © 2001 StudiaGeo s.r.o., Prague 109