Improved convergence rates for the truncation error in gravimetric geoid determination

When Stokes's integral is used over a spherical cap to compute a gravimetri c estimate of the geoid, a truncation error results due to the neglect of g ravity data over the remainder of the Earth. Associated with the truncation error is an error kernel defined over these two complementary regions. An important observation is that the rate of decay of the coefficients of the series expansion for the truncation error in terms of Legendre polynomials is determined by the smoothness properties of the error kernel. Previously published deterministic modifications of Stokes's integration kernel involv e either a discontinuity in the error kernel or its first derivative at the spherical cap radius. These kernels are generalised and extended by constr ucting error kernels whose derivatives at the spherical cap radius are cont inuous up to an arbitrary order. This construction is achieved by smoothly continuing the error kernel function into the spherical cap using a suitabl e degree polynomial. Accordingly, an improved rate of convergence of the sp ectral series representation of the truncation error is obtained.