bmc.prior.default: Default BMC Prior

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

Description

List the parameters of the default prior model of the Bayesian Magnitude of Completeness (BMC) method, as defined in Mignan et al. (2011) for different k^th values (only kth = 3, 4 and 5 allowed, otherwise returns NULL).

Usage

bmc.prior.default(kth)

Arguments

kth	the kth nearest seismic station used for distance calculation (if not provided, kth = 4)

Details

The BMC default model is defined as the prior model evaluated for the Taiwan earthquake data (Mignan et al., 2011), as it represents the best constrained data set so far (read more on this in Mignan and Chouliaras, 2014). It often provides a better prior once calibrated to other data than a new fit to the data (see example given for the function bmc.prior). It is also used for rapid mapping of the optimal m_c map (see function mc.geogr).

Value

the BMC prior parameter list

• c1, c2, c3 the empirical parameters

• sigma the standard error

• kth the k^th nearest seismic station used for distance calculation

• support the information supporting the prior model (here support = "default")

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., 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; mc.geogr

Examples

# map the predicted mc for a set of simulated stations
box <- c(-5, 5, -5, 5); dbin <- 0.1  #degrees
sta.n <- 30
stations <- data.frame(lon = rnorm(sta.n), lat=rnorm(sta.n))
grid <- expand.grid(lon = seq(box[1], box[2], dbin), lat = seq(box[3], box[4], dbin))
grid.n <- nrow(grid)

kth <- 4
params <- bmc.prior.default(kth)
d <- sapply(1:grid.n, function(i) rseismNet::d.geogr2km(grid[i,], stations, method = "fast"))
d.kth <- sapply(1:grid.n, function(i) sort(d[,i])[kth])
mc.pred <- (params$c1 * d.kth ^ params$c2 + params$c3)
image(unique(grid$lon), unique(grid$lat),
  matrix(mc.pred, nrow=length(unique(grid$lon)), ncol=length(unique(grid$lat))))
points(stations, pch = 2)

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