1998A&A...338..111L

This paper is the first of a series aimed at developing and applying a new modelling technique for magnetic fields of chemically peculiar (CP) stars. Newly introduced observational techniques provided us evidence that the ``oblique rotator model'' with a simple dipolar field is not sufficient to describe the magnetic morphology of CP stars, and that the problem of inverting data must be approached within a more sophisticated framework. In this paper we consider the configuration produced by the superposition of a dipole and a quadrupole, and we study in detail the behaviour of some observational quantities related to the magnetic field, i.e. the ``mean longitudinal field'', the ``crossover'' and the ``mean square field'', which are obtained from Stokes I and V observations. We illustrate the diagnostic content of the combined analysis of these three kinds of measurement, and we discuss some intrinsic limitations of the method. We present an algorithm for inverting the data, which has been tested against numerical simulations. We examine the possibility of recovering the stellar magnetic configuration from real measurements, by taking into account the problems related to the observational errors.