Astronomy and Astrophysics – Astronomy
Scientific paper
Nov 1999
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999geoji.139..547l&link_type=abstract
Geophysical Journal International, Volume 139, Issue 2, pp. 547-555.
Astronomy and Astrophysics
Astronomy
1
Magnetic Anomalies, Numerical Techniques, Spherical Harmonics
Scientific paper
Just as the FFT has revolutionized data processing and numerical solution of differential equations in Cartesian geometry, so also would a fast spherical harmonic transform revolutionize many geophysical problems in spherical geometry. Algorithms have recently been published with a theoretical asymptotic operation count of O(d(log 2d)2), where d==> ∞is the number of harmonics. We have developed and extended one such algorithm that uses recurrence relations for associated Legendre functions for both increasing and decreasing degree. The algorithm limits the ranges of spherical harmonic degree spanned by the recurrence relations automatically to produce a given accuracy. Tests on synthetic series and a Magsat lithospheric anomaly model show the new algorithm to be faster than conventional Gauss-Legendre quadrature for maximum degree L=127, and three times faster for L=511. However, numerical instabilities prevent the theoretical asymptotic speed from being reached, and further gains at higher degree are unlikely.
Gubbins David
Lesur Vincent
No associations
LandOfFree
Evaluation of fast spherical transforms for geophysical applications does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Evaluation of fast spherical transforms for geophysical applications, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Evaluation of fast spherical transforms for geophysical applications will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-1286582