bmc.bayes: BMC Bayesian Map

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

Description

Compute the map of the posterior completeness magnitude and posterior standard error based on the maps of the observed and predicted completeness magnitudes.

Usage

bmc.bayes(mc.obs, mc.pred, sigma.pred)

Arguments

mc.obs	a data frame of 4 parameters defined by the function mc.geogr: lon the longitude of the cell center lat the latitude of the cell center mc.obs the completeness magnitude mc in the cell sigma.obs the mc standard error in the cell
mc.pred	a vector of mc predicted values per cell
sigma.pred	a vector of the BMC prior model standard deviation, repeated for all cells

Details

This is the final step of the Bayesian Magnitude of Completeness (BMC) method (Mignan et al., 2011).

Value

The data frame of 8 parameters:

• lon the longitude of the cell center

• lat the latitude of the cell center

• mc.obs the observed m_c in the cell

• sigma.obs the observed standard error in the cell

• mc.pred the predicted m_c in the cell

• sigma.pred the prior model standard deviation in the cell

• mc.post the posterior m_c in the cell

• sigma.post the posterior standard error in the cell

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

See Also

bmc; bmc.prior; bmc.prior.default; 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)

# reduce catalogue size for faster computation
seism <- subset(seism, yr >= 2008)

# 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 & predicted mc (quick & dirty)
mc.obs <- mc.geogr(seism, "mode", "grid", dbin = 0.1, n.bootstrap = 100)
prior <-  bmc.prior(mc.obs, stations)
mc.pred <- (prior[[1]]$c1 * prior[[2]]$d.kth ^ prior[[1]]$c2 + prior[[1]]$c3)
sigma.pred <- rep(prior[[1]]$sigma, nrow(mc.obs))
res <- bmc.bayes(mc.obs, mc.pred, sigma.pred)

#display the 6 BMC maps (mc.obs, mc.pred, mc.post, sigma.obs, sigma.pred, sigma.post)
image(matrix(res$mc.obs, nrow=length(unique(res$lon)), ncol=length(unique(res$lat))))
image(matrix(res$mc.pred, nrow=length(unique(res$lon)), ncol=length(unique(res$lat))))
image(matrix(res$mc.post, nrow=length(unique(res$lon)), ncol=length(unique(res$lat))))
image(matrix(res$sigma.obs, nrow=length(unique(res$lon)), ncol=length(unique(res$lat))))
image(matrix(res$sigma.pred, nrow=length(unique(res$lon)), ncol=length(unique(res$lat))))
image(matrix(res$sigma.post, nrow=length(unique(res$lon)), ncol=length(unique(res$lat))))

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