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Polynomial surfaces are a very useful tool in order to represent the geomagnetic field over small area of the Earth's surface. Nevertheless, the method has not always been applied with enough precision, nor its limitations are considered in detail. This work analyses the conditions of applicability of this method to data from the aeromagnetic survey of the Spanish mainland accomplished in 1986, and the fulfilment of the necessary conditions to enhance a merely descriptive model to produce another of inferential character. The best statistical adjustment with only descriptive character, valid for the whole Spanish mainland, is a third degree model. The study proves that the conditions of validity for inferential models are met using polynomials of second and third degree in restrictive areas, but not over the whole Iberian Peninsula. In this case, the model of second degree is proposed as the best option because of its simplicity and the extension of its region of validity. To a great extent, the restrictions to enhance the descriptive models are due to the own nature, specially to their geographical dependence, and can also affect the analysis of other kinds of geophysical data.

Application of the polynomial adjustment to the aeromagnetic survey of the Spanish Mainland; Requirements and shortcomings