HR: 0800h
AN: GP21A-0098    [Abstracts]
TI: The error of linear regression on demagnetizaion plots
AU: * Shibuya, H
EM: shibuya@sci.kumamoto-u.ac.jp
AF: Dep't Earth Sci., Kumamoto Univ., Kurokami, Kumamoto, 860-8555, Japan
AB: Multi-component analyses of progressive demagnetization plots are now common routine in paleomagnetic studies. The direction of each component is found using the linear regression. An algorism formulated by Kirschvink (1980) calculating the least square direction of each component is widely used, and known as the PCA (Primary Component Analysis) method. He gives a measure of the precision of fitting as MAD (Maximum Angular Dispersion), but does not formulate the error. The statistical model that Kirschvink (1980) assumes is a set of linearly aligned points with isotropic error of a 3- dimensional normal distributon. The line that the PCA gives is that of least sum of square errors. Generality is not lost using a coordinate of the X-axis aligned to the true direction. Assuming the dispersion of the error of each point is small, the mean square of the angle between fitted lines and X-axis ({σ_a}²) is derived as {σ_a}² = \frac{MAD_p²}{N}=\frac{MAD_s²}{N-2} where MAD_p and MAD_s denote the MAD of population and sample, respectively. The MAD that Kirschvink (1980) gives is MAD_s, which underestimates the dispersion when number of points are small, thus MAD_p(=MAD_s\frac{N}{N-2}) shall be used for a measure of the goodness of fitting. The 2-d normal distribution with this dispersion gives a confidence limit of significance level P as δ a _P = \sqrt{-\ln(1-P)}δ a (1.73 σ_a when P=95%) This relationship is reproduced well by a numerical simulation.
DE: 1533 Remagnetization
DE: 1540 Rock and mineral magnetism
DE: 1594 Instruments and techniques
SC: Geomagnetism and Paleomagnetism [GP]
MN: 2007 Fall Meeting