R: 95 percent confidence for Spherical Distribution

alpha95 {RFOC} | R Documentation

## 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} }{√{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

    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')

[Package RFOC version 3.4-3 Index]