mc.geogr: Completeness Magnitude Mapping

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

Description

Map the completeness magnitude m_c for a seismicity data frame seism, following one of three possible geographical mappings (see Details).

Usage

mc.geogr(seism, method, mapping, mbin = 0.1, box = NULL, dbin = NULL,
  nmin = NULL, R = 30, stations = NULL, kth = 4, params = NULL,
  dist.calc = "fast", n.bootstrap = 0)

Arguments

seism	an earthquake catalog data frame of parameters: lon the earthquake longitude lat the earthquake latitude m the earthquake magnitude ... other earthquake parameters
method	the method to be used to evaluate mc: "mode", "mbass", or "gft" (see Details of function mc.val)
mapping	the mapping to be used: "grid", "circle.cst", or "circle.opt" (see Details)
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)
nmin	the minimum number of earthquakes required to evaluate mc (if not provided, nmin = 4 for method = "mode", otherwise nmin = 50; see explanation in Mignan et al., 2011)
R	the cylinder radius in kilometers for "mapping = circle.cst" (if not provided, R = 30)
stations	the seismic network data frame for "mapping = circle.opt", 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 in "mapping = circle.opt" (if not provided, kth = 4)
params	the BMC prior parameter list to be used for "mapping = circle.opt" (if not provided, uses the default parameters from function bmc.prior.default): 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
dist.calc	the method to be used to evaluate distances (if not provided, dist.calc = "fast"; read Details of function d.geogr2km)
n.bootstrap	the number of bootstraps (if not provided, n.bootstrap = 0)

Details

"mapping = grid" computes m_c for earthquakes located in each cell of bin size dbin.

"mapping = circle.cst" computes m_c for earthquakes located in cylinders centered on each cell and with radius R (see the smoothing impact of increasing radius in Mignan et al., 2011).

"mapping = circle.opt" computes m_c for earthquakes located in cylinders centered on each cell and with variable radius estimated from the seismic network spatial density (Mignan et al., 2011). This method aims at minimizing m_c spatial heterogeneities by using a smaller radius in the dense parts of the network where m_c changes faster.

The completeness magnitude m_c is evaluated for n.bootstrap bootstraps, with mc.obs the mean value and sigma.obs the standard error. For n.bootstrap = 0, sigma.obs = NA.

The function calls geosphere::distHaversine to calculate distances between geographical points.

Value

The data frame of 4 parameters:

• lon the longitude of the cell center

• lat the latitude of the cell center

• mc.obs the completeness magnitude m_c observed in the cell

• sigma.obs the m_c 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.prior; bmc.prior.default; d.geogr2km; mc.val

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)

# map mc in a grid
mc.grid <- mc.geogr(seism, "mode", "grid", dbin = 0.1)
image(matrix(mc.grid$mc.obs, nrow=length(unique(mc.grid$lon)), ncol=length(unique(mc.grid$lat))))

# map mc with cylinder smoothing (this may take a few minutes!)
mc.cst <- mc.geogr(seism, "mbass", "circle.cst", dbin = 0.1, R = 20)
image(matrix(mc.cst$mc.obs, nrow=length(unique(mc.cst$lon)), ncol=length(unique(mc.cst$lat))))

# 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 mc with optimal sample size (this takes a few minutes!)
# (minimizes mc heterogeneities while maximizing sample size)
mc.opt <- mc.geogr(seism, "mode", "circle.opt", dbin = 0.1, stations = stations)
image(matrix(mc.opt$mc.obs, nrow=length(unique(mc.opt$lon)), ncol=length(unique(mc.opt$lat))))

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