RFOC (version 3.4-10)

alpha95: 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)

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

Arguments

az

vector of azimuths, degrees

iang

vector of dips, degrees

Author

Jonathan M. Lees<[e-mail]>

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: $$ K = \frac {N-1} { N-R} $$ $$ S = \frac{81^{\circ} }{\sqrt{K}} $$

$$ \kappa = \frac{log( \frac{\epsilon_1}{\epsilon_2} )}{log(\frac{\epsilon_2}{\epsilon_3} )} $$ $$ \alpha_{95} = cos^{-1} \left[ 1 - \frac {N-R}{R} \left( 20^{\frac{1}{N-1}} - 1 \right) \right] $$ where \(\epsilon\)'s are the relevant eigenvalues of matrix MAT and angles are in degrees.

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')