beta.mle: Gutenberg-Richter beta-value

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

Description

Estimate the β-value (i.e. slope) of the Gutenberg-Richter model (Gutenberg and Richter, 1944) by using the maximum likelihood estimation method (Aki, 1965).

Usage

beta.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

Note that β = b log(10).

Value

The numeric value of β.

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

Gutenberg, B., Richter, C.F. (1944), Frequency of earthquakes in California, Bull. Seismol. Soc. Am., 34, 184-188

See Also

mc.val

Examples

beta <- log(10); mc <- 2; mbin <- 0.1
m <- round(mc - mbin / 2 + rexp(1e3, beta), digits = log10(1/mbin))
beta.mle(m, mc, mbin)

theta <- list(kappa = 3 * log(10), beta = 1.2*log(10), mc = 1.5)
m.angular <- efmd.sim(1e3, theta)
beta.mle(m.angular, theta$mc, mbin)

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