STATISTICAL-ANALYSIS OF PALEOMAGNETIC INCLINATION DATA

Palaeomagnetic studies on bore core or on tectonically disturbed local ities often lose declination information, but the inclination still of fers important palaeogeographic information. While the arithmetic mean of inclinations, (I) over bar, is a biased estimator, the bias is neg ligible with shallow data. Using co-inclination theta = 90 degrees - \ (I) over bar\ and precision kappa = 1/variance, we find that the arit hmetic mean and associated 95 per cent confidence interval are accepta ble estimates when theta root kappa > 400 degrees. When inclination i s steep and/or precision low, numerical methods must be applied. We de velop the likelihood function for theta and kappa and offer an efficie nt method to find its maximum, (theta, kappa), and to calculate the co nfidence 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-o nly fold test. The techniques are illustrated on real data and are tes ted extensively using numerical simulations.