The combined analysis of remagnetization circles and direct observations in palaeomagnetism

Details The combined analysis of remagnetization circles and direct observations in palaeomagnetism The combined analysis of remagnetization circles and direct observations in palaeomagnetism

Jan 1988

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988e%26psl..87..161m&link_type=abstract

Earth and Planetary Science Letters, Volume 87, Issue 1-2, p. 161-172.

Statistics

249

Scientific paper

When demagnetizing rocks in palaeomagnetism, an unterminated great circle path is sometimes obtained instead of a direct observation or endpoint determined from the linear segment near the origin of a Zijderveld plot. Such a situation cannot successfully be analysed using packages such as LINEFIND or Linearity Spectrum Analysis (LSA). It is possible to make optimum use of the great circle information by specifying constraints in the form of an arc of the great circle along which the estimate of the actual direction must lie. This specification overcomes the bias problems inherent in most analyses of converging great circles. Given M endpoints or direct observations and N great circles the maximum likelihood analysis based on all available information is easily performed. An iterative procedure is used to determine the positions of N variable-direction unit vectors so that the length, R, of the vector resultant of all (M + N) unit vectors is a maximum. Standard Fisher statistics then apply, with a slight modification for the numbers of degrees of freedom. If κ is the precision parameter then an approximately unbiased estimate for (1/κ) is given by (1/k) where: k=2M+N-2/2(M+N-R).
If α is the angle between the estimated direction and the true direction then a cone of confidence (1 - p) about the mean direction has a semi-angle αp given by: cos αp=1-N'-1/κR[(1/p)1/(N'-1)-1] with N' = M + N/2.

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