mc.val: Completeness Magnitude FMD-based Estimation

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

Description

Estimate the completeness magnitude m_c from the earthquake frequency magnitude distribution (FMD) using different published methods.

Usage

mc.val(m, method, mbin = 0.1)

Arguments

m	a numeric vector of earthquake magnitudes
method	the method to be used: "mode", "mbass", or "gft" (read Details)
mbin	the magnitude binning value (if not provided, mbin = 0.1)

Details

method = "mode" calculates the mode of the vector of magnitudes m. Applies to angular FMDs (Mignan, 2012), otherwise systematically underestimates m_c.

method = "mbass" ("median-based analysis of the segment slope") determines the main breakpoints of the earthquake FMD. m_c is defined as the change point that corresponds to the smallest probability of making an error when rejecting the null-hypothesis in a Wilcoxon-Mann-Whitney test (Amorese, 2007).

method = "gft" estimates the goodness-of-fit between the cumulative number of earthquakes observed and predicted by the Gutenberg-Richter model. m_c is defined as the lowest magnitude bin at which a fixed threshold R is first met. R is defined as a normalized absolute difference, fixed to 0.95. If the threshold is not reached, 0.90 is used. If again the threshold is not reached, the method = "mode" is used instead (Wiemer and Wyss, 2000).

Both "mode" and "mbass" methods are non-parametric while "gft" depends on the fitting of the Gutenberg-Richter model (see the function beta.mle). For a general review of FMD-based m_c estimation methods, see Mignan and Woessner (2012). For further comparisons of "mbass" and "gft", see Mignan and Chouliaras (2014).

Value

The numeric value of m_c.

References

Amorese, D. (2007), Applying a Change-Point Detecion Method on Frequency-Magnitude Distributions, Bull. Seismol. Soc. Am., 97, 1742-1749, doi: 10.1785/0120060181

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

Mignan, A., Woessner, J. (2012), Estimating the magnitude of completeness for earthquake catalogs, Community Online Resource for Statistical Seismicity Analysis, doi: 10.5078/corssa-00180805

Mignan, A., Chouliaras, G. (2014), Fifty Years of Seismic Network Performance in Greece (1964-2013): Spatiotemporal Evolution of the Completeness Magnitude, Seismol. Res. Lett., 85, 657-667 doi: 10.1785/0220130209

Wiemer, S., Wyss, M. (2000), Minimum Magnitude of Completeness in Earthquake Catalogs: Examples from Alaska, the Western United States, and Japan, Bull. Seismol. Soc. Am., 90, 859-869

See Also

beta.mle; bfmd.sim; efmd.sim; fmd

Examples

# Estimate mc for an angular FMD
theta <- list(kappa = 3 * log(10), beta = log(10), mc = 2)
m.angular <- efmd.sim(1e3, theta)
mc.val(m.angular, "mode")
mc.val(m.angular, "mbass")
mc.val(m.angular, "gft")

# Estimate mc for a curved FMD
theta <- list(beta = log(10), mu = 2, sigma = 0.5)
m.curved <- bfmd.sim(1e4, theta)
mc.mode <- mc.val(m.curved, "mode")
mc.mbass <- mc.val(m.curved, "mbass")
mc.gft <- mc.val(m.curved, "gft")
mdistr <- fmd(m.curved)
plot(mdistr$mi, mdistr$Ni, log = "y")
points(mdistr$mi, mdistr$ni)
abline(v=c(mc.mode, mc.mbass, mc.gft), lty=c("dotted","solid","dashed"))

# download the Southern California relocated catalogue of Hauksson et al. (2012)
url <- "http://service.scedc.caltech.edu/ftp/catalogs/"
dat <- "hauksson/Socal_DD/hs_1981_2016_comb_K4_A.cat_so_SCSN_v2q"
seism <- scan(paste(url, dat, sep = ""), what = "character", sep = "\n")
mbin <- 0.1
m <- round(as.numeric(substr(seism, start=63, stop=67)), digits = log10(1/mbin))
mc.mode <- mc.val(m, "mode")
mc.mbass <- mc.val(m, "mbass")
mc.gft <- mc.val(m, "gft")
mdistr <- fmd(m)
plot(mdistr$mi, mdistr$Ni, log = "y")
points(mdistr$mi, mdistr$ni)
abline(v=c(mc.mode, mc.mbass, mc.gft), lty=c("dotted","solid","dashed"))

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