Shortcomings in the determination of regional fields by polynomial fitting: A simple solution

The procedure of polynomial fitting by least-squares technique to obtain the regional field from potential field data is commonly used in processing geophysical data. However, it has been found that the unguarded use of this procedure with measured field data may lead to erroneous regional fields. This is due to the fact that the least-squares technique pre-supposes a random variation of the residual or anomaly field. This condition is rarely fulfilled in measured field data where there is the common occurrence of ‘deviatory field points’ in the residual field data. In this paper, a procedure to overcome the problem using robust statistics is described with the straight-forward Downhill Simplex method used to obtain the optimum coefficients for the polynomial. The method is illustrated with aeromagnetic field data from the Mamfe basin of Nigeria and Cameroon. The result shows that the trend of the regional field obtained from robust statistics is consistent with the trend in the aeromagnetic field obtained by using the method of cross-correlation trend analysis.