Description Usage Arguments Details Value References See Also Examples
Define the prior model of the Bayesian Magnitude of Completeness (BMC) method (Mignan et al., 2011) by fitting a function of the form mc = c1d^c2+c3 the observed completeness magnitude per cell and d the distance from the cell center to the kth nearest seismic station.
1 2 | bmc.prior(mc.obs, stations, kth = 4, support = "calibrated",
dist.calc = "fast")
|
mc.obs |
a data frame of the observed mc map defined by the
function |
stations |
the seismic network data frame of parameters:
|
kth |
the kth nearest seismic station used for distance
calculation (if not provided, |
support |
the information supporting the prior model: |
dist.calc |
the method to be used to evaluate distances (if not provided,
|
support = "calibrated"
uses the default BMC prior model defined by the function
bmc.prior.default
and calibrates it to the mc.obs
data by shifting the
residual average to 0, substracting it from c3 (see e.g., Mignan et al., 2013; Mignan
and Chouliaras, 2014).
support = "data"
directly fits the prior function to the mc.obs
data
by using the Nonlinear Least Squares function stats::nls
. If the estimation fails,
support = "calibrated"
is used instead.
A list of:
the BMC prior model parameter list:
c1
, c2
, c3
the empirical parameters
sigma
the standard deviation
kth
the kth nearest seismic station used for distance calculation
support
the information supporting the prior model
the input data frame:
mc
the completeness magnitude value per cell
d.kth
the distance to the kth nearest seismic station per
cell (in km)
Mignan, A., Werner, M.J., Wiemer, S., Chen, C.-C., Wu, Y.-M. (2011), Bayesian Estimation of the Spatially Varying Completeness Magnitude of Earthquake Catalogs, Bull. Seismol. Soc. Am., 101, 1371-1385, doi: 10.1785/0120100223
Mignan, A., Jiang, C., Zechar, J.D., Wiemer, S., Wu, Z., Huang, Z. (2013), Completeness of the Mainland China Earthquake Catalog and Implications for the Setup of the China Earthquake Forecast Texting Center, Bull. Seismol. Soc. Am., 103, 845-859, doi: 10.1785/0120120052
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
bmc
; bmc.prior.default
; d.geogr2km
; mc.geogr
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 32 33 34 35 36 | # download the Southern California relocated catalogue of Hauksson et al. (2012)
url <- "http://service.scedc.caltech.edu/ftp/catalogs/"
cat <- "hauksson/Socal_DD/hs_1981_2011_06_comb_K2_A.cat_so_SCSN_v01"
dat <- scan(paste(url, cat, sep = ""), what = "character", sep = "\n")
yr <- as.numeric(substr(dat, start=1, stop=4))
lat <- as.numeric(substr(dat, start=35, stop=42))
lon <- as.numeric(substr(dat, start=44, stop=53))
m <- as.numeric(substr(dat, start=63, stop=67))
seism <- data.frame(yr = yr, lon = lon,lat = lat, m = m)
# download the Southern California seismic network data
url <- "http://service.scedc.caltech.edu/station/weblist.php"
dat <- scan(url, what = "character", sep = "\n", skip = 7)
network <- substr(dat, start = 1, stop = 2)
sta.name <- substr(dat, start = 5, stop = 9)
sta.lat <- as.numeric(substr(dat, start = 52, stop = 59))
sta.lon <- as.numeric(substr(dat, start = 61, stop = 70))
sta.on <- as.numeric(substr(dat, start = 78, stop = 81))
sta.off <- as.numeric(substr(dat, start = 89, stop = 92))
stations <- data.frame(lon = sta.lon, lat = sta.lat, name = sta.name)
stations <- subset(stations, (network == "CI" & sta.off > min(seism$yr) & sta.on < max(seism$yr)))
stations <- subset(stations, (duplicated(name) == F))
# map the observed mc (this may take a few minutes)
mc.obs <- mc.geogr(seism, "mode", "grid", dbin = 0.1)
# test the two possible priors & plot
model.calibrated <- bmc.prior(mc.obs, stations, kth = 5)
model.fromdata <- bmc.prior(mc.obs, stations, kth = 5, support = "data")
data <- model.calibrated[[2]]
di <- seq(0, max(data$d.kth))
params.cal <- model.calibrated[[1]]
params.dat <- model.fromdata[[1]]
plot(data$d.kth, data$mc.obs)
lines(di, params.cal$c1*di^params.cal$c2+params.cal$c3, col="orange")
lines(di, params.dat$c1*di^params.dat$c2+params.dat$c3, col="red")
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