Description Usage Arguments Details Value References See Also Examples
Estimate the completeness magnitude mc from the earthquake frequency magnitude distribution (FMD) using different published methods.
1 | mc.val(m, method, mbin = 0.1)
|
m |
a numeric vector of earthquake magnitudes |
method |
the method to be used: |
mbin |
the magnitude binning value (if not provided, |
method = "mode"
calculates the mode of the vector of magnitudes
m
. Applies to angular FMDs (Mignan, 2012), otherwise systematically
underestimates mc.
method = "mbass"
("median-based analysis of the segment slope")
determines the main breakpoints of the earthquake FMD. mc
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.
mc 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 mc
estimation methods, see Mignan and Woessner (2012). For further comparisons of
"mbass"
and "gft"
, see Mignan and Chouliaras (2014).
The numeric value of mc.
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
beta.mle
; bfmd.sim
; efmd.sim
; fmd
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 | # 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"))
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