Open AccessThe least‐squares line and plane and the analysis of palaeomagnetic data
Author(s) -
Kirschvink J. L.
Publication year - 1980
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1980.tb02601.x
Subject(s) - principal component analysis , line (geometry) , geology , subtraction , mathematics , geometry , geodesy , mathematical analysis , statistics , arithmetic
Summary The classic, multivariate technique of principal component analysis can be used to find and estimate the directions of lines and planes of best least‐squares fit along the demagnetization path of a palaeomagnetic specimen, thereby replacing vector subtraction, remagnetization circles and difference vector paths with one procedure. Eigenvalues from the analysis are the variance of the data along each principal axis, and provide a relative measure of collinearity or coplanarity which may be used to define a general palaeomagnetic precision index. Demagnetization planes found with principal component analysis may be used in place of difference vector paths for locating Hoffman—Day directions, avoiding unnecessary vector subtraction and intensity truncation steps. Two methods are discussed for jointly estimating an average remanence direction from demagnetization lines and planes.