Fitting global data with spherical harmonics

6 Fitting global data with spherical harmonics 

Given a finite number of measurements at a given latitude (90° — 6) and longitude f on the surface of the Earth, we look for a smooth function that could be fitted to the data and represent their variations to within any desired precision. Spherical harmonics are suitable because they make an orthogonal set of functions which can 

Let us assume that n measurements y( t h0,) (i = l,2.n) of one geochemical parameter are to be fitted with spherical harmonics to the degree m, i.e., with a function y, such as 

Latitude (90° — 6t) Longitude 206pb 204pb Latitude (90° — 9i) Longitude t i 2°6pb 204pb 

10 columns for S,dt). A is too large to be listed. The 15 coefficients lm and the 10 coefficients film can be obtained through the standard procedure and are listed in Table 5.10. 

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