Open AccessStatistical analysis of palaeomagnetic inclination data
Author(s) -
Enkin Randolph J.,
Watson Geoffrey S.
Publication year - 1996
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.1996.tb05305.x
Subject(s) - declination , confidence interval , statistics , estimator , geology , geodesy , interval (graph theory) , mathematics , block (permutation group theory) , variance (accounting) , rotation (mathematics) , algorithm , geometry , physics , accounting , combinatorics , astronomy , business
SUMMARY 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, , is a biased estimator, the bias is negligible with shallow data. Using co‐inclination and precision K *= 1/variance, we find that the arithmetic mean and associated 95 per cent confidence interval are acceptable estimates when . When inclination is steep and or precision low, numerical methods must be applied. We develop the likelihood function for θ and K and offer an efficient method to find its maximum, (), and to calculate the confidence interval. When , 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.