bmc.prior: BMC Prior

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

Description

Define the prior model of the Bayesian Magnitude of Completeness (BMC) method (Mignan et al., 2011) by fitting a function of the form m_c = c₁d^c₂+c₃ the observed completeness magnitude per cell and d the distance from the cell center to the k^th nearest seismic station.

Usage

bmc.prior(mc.obs, stations, kth = 4, support = "calibrated",
  dist.calc = "fast")

Arguments

mc.obs	a data frame of the observed mc map defined by the function mc.geogr
stations	the seismic network data frame of parameters: lon the seismic station longitude lat the seismic station latitude ... other station attributes
kth	the kth nearest seismic station used for distance calculation (if not provided, kth = 4)
support	the information supporting the prior model: "calibrated" or "data" (if not provided, support = "calibrated" - see Details)
dist.calc	the method to be used to evaluate distances (if not provided, dist.calc = "fast"; read Details of function d.geogr2km)

Details

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.

Value

A list of:

the BMC prior model parameter list:

• c1, c2, c3 the empirical parameters

• sigma the standard deviation

• kth the k^th 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 k^th nearest seismic station per cell (in km)

References

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

See Also

bmc; bmc.prior.default; d.geogr2km; mc.geogr

Examples

# 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")

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