On the accurate numerical evaluation of geodetic convolution integrals
MetadataShow full item record
In the numerical evaluation of geodetic convolution integrals, whether by quadrature or discrete/fast Fourier transform (D/FFT) techniques, the integration kernel is sometimes computed at the centre of the discretised grid cells. For singular kernels - a common case in physical geodesy - this approximation produces significant errors near the computation point, where the kernel changes rapidly across the cell. Rigorously, mean kernels across each whole cell are required. We present one numerical and one analytical method capable of providing estimates of mean kernels for convolution integrals. The numerical method is based on Gauss-Legendre quadrature (GLQ) as efficient integration technique. The analytical approach is based on kernel weighting factors, computed in planar approximation close to the computation point, and used to convert non-planar kernels from point to mean representation. A numerical study exemplifies the benefits of using mean kernels in Stokes?s integral. The method is validated using closed-loop tests based on the EGM2008 global gravity model, revealing that using mean kernels instead of point kernels reduces numerical integration errors by a factor of ~5 (at a grid-resolution of 10 arc minutes). Analytical mean kernel solutions are then derived for 14 other commonly used geodetic convolution integrals: Hotine, Etvs, Green-Molodensky, tidal displacement, ocean tide loading, deflection-geoid, Vening-Meinesz, inverse Vening-Meinesz, inverse Stokes, inverse Hotine, terrain correction, primary indirect effect, Molodensky's G1 term and the Poisson integral. We recommend that mean kernels be used to accurately evaluate geodetic convolution integrals, and the two methods presented here are effective and easy to implement.
The original publication is available at : http://www.springerlink.com
Showing items related by title, author, creator and subject.
Hirt, Christian (2011)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 ...
Pratapa, Suminar (2003)Crystallite (or grain) size and strain within a polycrystalline material may have a profound influence on its physical properties, eg. the fracture toughness, wear and thermal shock resistance. A diffraction pattern for ...
Amos, Matthew (2007)One goal of modern geodesy is the global unification of vertical datums so that height data from them can be properly integrated. This thesis studies the unification of the 13 disparate levelling- and tide-gauge-based ...