chi.mle: chi-value

In amignan/rseismNet: Earthquake Frequency-Magnitude Distribution & Network Statistics

Description

Estimate the χ-value (i.e. slope) of the incomplete part of the elemental frequency-magnitude distribution with χ = κ - β, κ representing the earthquake detection parameter (Mignan, 2012).

Usage

chi.mle(m, mc, mbin = 0.1)

Arguments

m	a numeric vector of earthquake magnitudes
mc	the completeness magnitude value
mbin	the magnitude binning value (if not provided, mbin = 0.1)

Details

χ is estimated similarly to β, by using the maximum likelihood estimation method (Aki, 1965).

Value

The numeric value of χ.

References

Aki, K. (1965), Maximum likelihood estimate of b in the formula log N = a - bM and its confidence limits, Bull. Earthquake Res. Inst. Univ. Tokyo, 43, 237-239

Mignan, A. (2012), Functional shape of the earthquake frequency-magnitude distribution and completeness magnitude, J. Geophys. Res., 117, B08302, doi: 10.1029/2012JB009347

See Also

beta.mle; efmd.sim; mc.val

Examples

theta <- list(kappa = 2 * log(10), beta = log(10), mc = 2)
m.angular <- efmd.sim(1e4, theta)
mdistr <- fmd(m.angular)
plot(mdistr$mi, mdistr$Ni, log = "y")
points(mdistr$mi, mdistr$ni)
chi <- chi.mle(m.angular, theta$mc)
chi + theta$beta   # = kappa
beta <- beta.mle(m.sim, theta$mc)
abline(v = theta$mc, lty = "dotted", col = "red")
abline(a = log10(mdistr$ni[which(mdistr$mi >= theta$mc)[1]]) +
   beta / log(10) * theta$mc, b = -beta / log(10), col = "red")
abline(a = log10(mdistr$ni[which(mdistr$mi <= theta$mc)[length(which(mdistr$mi <= theta$mc))]]) -
   chi / log(10) * theta$mc, b = chi / log(10), col = "red")

amignan/rseismNet documentation built on July 8, 2019, 6:53 p.m.