alpha95 {RFOC}R Documentation

95 percent confidence for Spherical Distribution

Description

Calculates conical projection angle for 95% confidence bounds for mean of spherically distributed data.

Usage

alpha95(az, iang)

Arguments

az vector of azimuths, degrees
iang vector of dips, degrees

Details

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} }{sqrt{K}}

kappa = frac{log( frac{ε_1}{ε_2} )}{log(frac{ε_2}{ε_3} )}

α_{95} = cos^{-1} <=ft[ 1 - frac {N-R}{R} ( 20^{frac{1}{N-1}} - 1 ) right]

where ε's are the relevant eigenvalues of matrix MAT and angles are in degrees.

Value

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

Author(s)

Jonathan M. Lees<jonathan.lees@unc.edu>

References

Davis, John C., 2002, Statistics and data analysis in geology, Wiley, New York, 637p.

See Also

addsmallcirc

Examples


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')




[Package RFOC version 1.0-5 Index]