Modelling the Earth's Geomagnetic Field to High Degree and Order

1365-246X

Blackwell Publishing Journal Backfiles 1879-2005

Geosciences

We present a method for modelling the Earth's magnetic field to very high degree and order in terms of spherical harmonics. the method exploits the orthogonality of the spherical functions, using, in part, the method of Gauss-Legendre quadrature. This method is compared to a simpler quadrature method (Newton-Cotes). We show that the Gauss-Legendre technique is more accurate in most cases than Newton-Cotes quadrature, and in all cases, even where the two give about the same results, that the Gauss-Legendre method is more efficient in that it requires less data and hence less computation. the two quadrature methods are applied to sets of radial field data computed from an n= 29 model which simulate Magsat observations. the results are that direct integration of a complete global coverage of observations using Newton-Cotes produces errors in the spatial spectrum comparable to that of the geomagnetic field at n= 9, whereas Gauss-Legendre gives exact recovery. When 7° of polar region data are removed to simulate the Magsat orbit, both methods fail, although Gauss-Legendre gives somewhat less noisy results. However, when the analysis is performed on residuals to a field truncated at n= 15, both methods give comparable levels of noise. Simple interpolation of data over the pole is seen to reduce the errors significantly beyond n= 50. Addition of synthetic noise is seen to provide a means of evaluating the accuracy of coefficients derived from actual data. A theoretical relation is derived relating this noise and the altitude of observation to the resulting errors in the spatial spectrum.

Electronic Resource