# alpha95: 95 percent confidence for Spherical Distribution In RFOC: Graphics for Spherical Distributions and Earthquake Focal Mechanisms

## 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.

addsmallcirc

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 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.