The inverse problem of paleointensity determination

Analysis of paleointensity experimental data is often carried out using a special simple case of error-in-variable (EIV) formalism. Though mathematically sound, this approach is quite limited in the ways it offers to assess uncertainty and quality of the paleointensity estimates. The problem of paleointensity determination from experimental data is one of parameter estimation and it is more natural to treat it within the framework of inverse problem theory. In this paper, I present a new formulation of paleointensity estimation as an inverse problem whereby the entire paleofield vector is recovered from its measured components so that both its intensity and direction are obtained simultaneously. This formalism has several advantages including the flexibility to incorporate reliability criteria and consistency conditions objectively into the computational process as constraints and prior information. It also provides a wide range of appraisal tools to access error bounds and quality of the estimation results. Numerical experiments were carried out to validate the procedure using single- and multiple-specimen data and imposing different constraints including prior information on inclination, declination and expected paleointensity. The results indicate that inclination is the strongest constraint exerting the greatest control over the final paleointensity estimate. Small changes in inclination lead to relatively large changes in paleofield intensity estimates. Declination is a relatively weaker constraint and paleointensity is the weakest or least effective condition. Moreover, the results indicate that means and variances of paleointensity estimates computed by this procedure can differ by as much as 20% from those computed by the conventional method.