Statistical analysis of palaeomagnetic inclination data

Abstract

Palaeomagnetic studies on bore core or on tectonically disturbed localities often lose declination information, but the inclination still offers important palaeogeographic information. While the arithmetic mean of inclinations, Ī, is a biased estimator, the bias is negligible with shallow data. Using co-inclination θ̄ = 90° - |Ī| and precision κ* = 1/variance, we find that the arithmetic mean and associated 95 per cent confidence interval are acceptable estimates when θ̄√κ*>400°. When inclination is steep and /or precision low, numerical methods must be applied. We develop the likelihood function for θ and κ and offer an efficient method to find its maximum, (θ̂, κ̂), and to calculate the confidence interval. When θ̂√κ̂<200°, the confidence interval is asymmetric about the mean. When sites are collected from several rigid blocks, the relative declinations within each block can be useful. Using 'block-rotation Fisher analysis', better inclination estimates with tighter confidence intervals can be made, even on very steep data. We describe how to apply these methods to an inclination-only fold test. The techniques are illustrated on real data and are tested extensively using numerical simulations.