alpha95: 95 percent confidence for Spherical Distribution

Description Usage Arguments Details Value Author(s) References See Also Examples

Description

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

Usage

1
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} }{√{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.

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

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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')

RFOC documentation built on May 2, 2019, 1:38 p.m.