95 percent confidence for Spherical Distribution
Calculates conical projection angle for 95% confidence bounds for mean of spherically distributed data.
alpha95(az, iang)
az |
vector of azimuths, degrees |
iang |
vector of dips, degrees |
Program calculates the cartesian coordinates of all poles, sums and returns the resultant vector, its azimuth and length (R). For N points, statistics include:
K = \frac {N-1} { N-R}
S = \frac{81^{\circ} }{√{K}}
κ = \frac{log( \frac{ε_1}{ε_2} )}{log(\frac{ε_2}{ε_3} )}
α_{95} = cos^{-1} ≤ft[ 1 - \frac {N-R}{R} ≤ft( 20^{\frac{1}{N-1}} - 1 \right) \right]
where ε's are the relevant eigenvalues of matrix MAT and angles are in degrees.
LIST:
Ir |
resultant inclination, degrees |
Dr |
resultant declination, degrees |
R |
resultant sum of vectors, normalized |
K |
K-dispersion value |
S |
spherical variance |
Alph95 |
95% confidence angle, degrees |
Kappa |
log ratio of eignevectors |
E |
Eigenvactors |
MAT |
matrix of cartesian vectors |
Jonathan M. Lees<jonathan.lees@unc.edu>
Davis, John C., 2002, Statistics and data analysis in geology, Wiley, New York, 637p.
addsmallcirc
paz = rnorm(100, mean=297, sd=10) pdip = rnorm(100, mean=52, sd=8) ALPH = alpha95(paz, pdip) ######### draw stereonet net() ############ add points focpoint(paz, pdip, col='red', pch=3, lab="", UP=FALSE) ############### add 95 percent confidence bounds addsmallcirc(ALPH$Dr, ALPH$Ir, ALPH$Alph95, BALL.radius = 1, N = 25, add = TRUE, lwd=1, col='blue') ############ second example: paz = rnorm(100, mean=297, sd=100) pdip = rnorm(100, mean=52, sd=20) ALPH = alpha95(paz, pdip) net() focpoint(paz, pdip, col='red', pch=3, lab="", UP=FALSE) addsmallcirc(ALPH$Dr, 90-ALPH$Ir, ALPH$Alph95, BALL.radius = 1, N = 25, add = TRUE, lwd=1, col='blue')
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