Statistical analysis of palaeomagnetic inclination data

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, (I) over bar, is a biased estimator, the bias is negligible with shallow data. Using co-inclination theta = 90 degrees - \(I) over bar\ and precision kappa* = 1/variance, we find that the arithmetic mean and associated 95 per cent confidence interval are acceptable estimates when theta root kappa* > 400 degrees. When inclination is steep and/or precision low, numerical methods must be applied. We develop the likelihood function for theta and kappa and offer an efficient method to find its maximum, (theta, kappa), and to calculate the confidence interval. When theta root kappa < 200 degrees, 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.