Numerical methods for scientists and engineers (2nd ed.)
Numerical methods for scientists and engineers (2nd ed.)
Numerical Recipes in C++: the art of scientific computing
Numerical Recipes in C++: the art of scientific computing
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Gravimetric geoid computation is often based on modified Stokes's integration, where Stokes's integral is evaluated with some stochastic or deterministic kernel modification. Accurate numerical evaluation of Stokes's integral requires the modified kernel to be integrated across the area of each discretised grid cell (mean kernel). Evaluating the modified kernel at the center of the cell (point kernel) is an approximation, which may result in larger numerical integration errors near the computation point, where the modified kernel exhibits a strongly nonlinear behavior. The present study deals with the computation of whole-of-the-cell mean values of modified kernels, exemplified here with the Featherstone-Evans-Olliver (1998) kernel modification [Featherstone, W.E., Evans, J.D., Olliver, J.G., 1998. A Meissl-modified Vanicek and Kleusberg kernel to reduce the truncation error in gravimetric geoid computations. Journal of Geodesy 72(3), 154-160]. We investigate two approaches (analytical and numerical integration), which are capable of providing accurate mean kernels. The analytical integration approach is based on kernel weighting factors which are used for the conversion of point to mean kernels. For the efficient numerical integration, Gauss-Legendre quadrature is applied. The comparison of mean kernels from both approaches shows a satisfactory mutual agreement at the level of 10^-^4 and better, which is considered to be sufficient for practical geoid computation requirements. Closed-loop tests based on the EGM2008 geopotential model demonstrate that using mean instead of point kernels reduces numerical integration errors by ~65%. The use of mean kernels is recommended in remove-compute-restore geoid determination with the Featherstone-Evans-Olliver (1998) kernel or any other kernel modification under the condition that the kernel changes rapidly across the cells in the neighborhood of the computation point.