bmc: BMC Wrapper

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

Description

Run all the steps of the Bayesian Magnitude of Completeness (BMC) method (Mignan et al., 2011) and produce a spatial data frame of the completeness magnitude (observed, predicted, and posterior) and associated uncertainties (observed, predicted, and posterior).

Usage

bmc(seism, stations, support = "fast", mbin = 0.1, box = NULL,
  dbin = NULL, kth = 4, dist.calc = "fast")

Arguments

seism	an earthquake catalog data frame of parameters: lon the earthquake longitude lat the earthquake latitude m the earthquake magnitude ... other earthquake parameters
stations	the seismic network data frame of parameters: lon the seismic station longitude lat the seismic station latitude ... other station attributes
support	the information supporting the BMC method: only "fast" available so far)
mbin	the magnitude binning value (if not provided, mbin = 0.1)
box	a vector of the minimum longitude, maximum longitude, minimum latitude and maximum latitude, in this order (if not provided, box is calculated from the geographical limits of seism)
dbin	the spatial binning value (if not provided, dbin is calculated such that the map is made of 10 longitudinal cells based on box)
kth	the kth nearest seismic station used for distance calculation (if not provided, kth = 4)
dist.calc	the method to be used to evaluate distances (if not provided, dist.calc = "fast"; read Details of function d.geogr2km)

Details

It is a wrap-up of other functions. See Examples of the function bmc.bayes for a possible break-down of the different steps of the BMC method.

The support = "fast" approach is the only one provided for the BMC wrapper so far. It consists in estimating the optimal observed completeness magnitude m_c by directly using the default BMC prior model. The model is then calibrated to the optimal observed m_c. Finally, the Bayesian method is applied. This fast approach was successfully tested in a number of regions (e.g., Kraft et al., 2013; Mignan et al., 2013; Mignan and Chouliaras, 2014; Tormann et al., 2014; Panzera et al., 2017).

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

Kraft, T., Mignan, A., Giardini, D. (2013), Optimization of a large-scale microseismic monitoring network in northern Switzerland, Geophys. J. Int., 195, 474-490, doi: 10.1093/gji/ggt225

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

Panzera, F., Mignan, A., Vogfjord, K.S. (2017), Spatiotemporal evolution of the completeness magnitude of the Icelandic earthquake catalogue from 1991 to 2013, J. Seismol., 21, 615-630, doi: 10.1007/s10950-016-9623-3

Tormann, T., Wiemer, S., Mignan, A. (2014), Systematic survey of high-resolution b value imaging along Californian faults: inference on asperities, J. Geophys. Res. Solid Earth, 119, 2029-2054, doi: 10.1002/2013JB010867

See Also

bmc.bayes; 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))

# Apply the BMC method (this may take a few minutes)
res <- bmc(seism, stations, dbin = 0.1)

#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.