alpha95: 95 percent confidence for Spherical Distribution

In RFOC: Graphics for Spherical Distributions and Earthquake Focal Mechanisms

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{\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.

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<[e-mail]>

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')

RFOC documentation built on Sept. 8, 2023, 6:12 p.m.