dc.contributor.author Hirt, Christian dc.contributor.author Featherstone, Will dc.contributor.author Claessens, Sten dc.date.accessioned 2017-01-30T11:28:29Z dc.date.available 2017-01-30T11:28:29Z dc.date.created 2011-05-01T20:01:27Z dc.date.issued 2011 dc.identifier.citation Hirt, Christian and Featherstone, Will and Claessens, Sten. 2011. On the accurate numerical evaluation of geodetic convolution integrals. Journal of Geodesy. 85 (8): pp. 519-538. dc.identifier.uri http://hdl.handle.net/20.500.11937/12053 dc.identifier.doi 10.1007/s00190-011-0451-5 dc.description.abstract 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. dc.publisher Springer - Verlag dc.subject Gauss-Legendre quadrature dc.subject numerical integration dc.subject point kernel dc.subject mean kernel dc.subject kernel weighting factor dc.subject Convolution integrals dc.title On the accurate numerical evaluation of geodetic convolution integrals dc.type Journal Article dcterms.source.volume 85 dcterms.source.startPage 519 dcterms.source.endPage 538 dcterms.source.issn 09497714 dcterms.source.title Journal of Geodesy curtin.note The original publication is available at : http://www.springerlink.com curtin.department Department of Spatial Sciences curtin.accessStatus Open access
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