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.

  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')