Numerical solution of geodetic boundary value problems using a global reference field

One of the most serious practical limitations of boundary element methods f or gravity field determination is that they cannot make efficient use of ex isting satellite geopotential models. Three basic approaches to solving the problem are developed: (1) alternative representation formulas; (2) modifi ed kernel functions of classical representation formulas; and (3) modified trial and test spaces. The three methods are tested and compared for the al timetry-gravimetry II boundary value problem. It is shown that there is in fact a significant improvement when compared to the pure boundary element s olution. Most promising is the method of multiscale trial and test spaces w hich, in addition, yields sparse system matrices.