Statistics – Computation
Scientific paper
Aug 1982
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982georl...9..812p&link_type=abstract
Geophysical Research Letters, vol. 9, Aug. 1982, p. 812-815.
Statistics
Computation
35
Geomagnetism, Spherical Harmonics, Spline Functions, Least Squares Method, Mathematical Models
Scientific paper
The geophysical method of harmonic splines produces magnetic field models at th5 core surface which are maximally smooth to the extent that they minimize certain special norms, and do not exhibit the highly oscillatory fields generated by models derived from a least-square analysis with a truncated sphe5ical harmonic series. Such modeling, however, calls for the solution of a square system of equations whose dimension is equal to a number of data too large to be practical. An alternative method for the production of nearly optically smooth models is proposed in which a subset of the spline functions corresponding to observation locations, or 'knots', is selected to yield a smooth distribution of knots throughout the earth's surface. One then proceeds to find the smoothest model subject to an appropriate fit to all the data, having reduced the computational problem to one comparable to a least-squares analysis.
Parker Robert L.
Shure Loren
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