bfmd.sim: Simulation of the Bulk FMD

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

Description

Simulate the bulk earthquake frequency magnitude distribution (bFMD) by applying the Thinning Method (Lewis and Shedler, 1979) to the curved FMD model of Ringdal (1975); Ogata and Katsura (1993; 2006).

Usage

bfmd.sim(N, theta, mbin = 0.1, mmin = 0, mmax = 9)

Arguments

N	the approximate number of earthquakes to simulate
theta	a list of 3 parameters: beta the Gutenberg-Richter parameter value mu the mean value of the cumulative normal distribution sigma the standard deviation of the cumulative normal distribution
mbin	the magnitude binning value (if not provided, mbin = 0.1)
mmin	the minimum magnitude value (if not provided, mmin = 0)
mmax	the maximum magnitude value (if not provided, mmax = 9)

Details

The bulk FMD model is the product of the Gutenberg-Richter model and a detection function defined as the cumulative Normal distribution. Its FMD has a curved shape in the log-lin space and corresponds to the case where the completeness magnitude m_c is variable (the FMD curvature representing the m_c distribution; read more in Mignan, 2012; Mignan and Chen, 2016).

Value

A numeric vector of approximatively N earthquake magnitudes.

References

Lewis, P.A.W., Shedler, G.S. (1979), Simulation of nonhomogeneous poisson processes by thinning, Naval Res. Logistics, 26, 403-413 doi: 10.1002/nav.3800260304

Mignan, A. (2012), Functional shape of the earthquake frequency-magnitude distribution and completeness magnitude, J. Geophys. Res., 117, B08302, doi: 10.1029/2012JB009347

Mignan, A., Chen, C.-C. (2016), The Spatial Scale of Detected Seismicity, Pure Appl. Geophys., 173, 117-124, doi: 10.1007/s00024-015-1133-7

Ogata, Y., Katsura, K. (1993), Analysis of temporal and spatial heterogeneity of magnitude frequency distribution inferred from earthquake catalogues, Geophys. J. Int., 113, 727-738

Ogata, Y., Katsura, K. (2006), Immediate and updated forecasting of aftershock hazard, Geophys. Res. Lett., 33, L10305, doi: 10.1029/2006GL025888

Ringdal, F. (1975), On the estimation of seismic detection thresholds, Bull. Seismol. Soc. Am., 65, 1631-1642

See Also

beta.mle; bfmd.pdf

Examples

theta <- list(beta = log(10), mu = 2, sigma = 0.3)
m.sim <- bfmd.sim(1e3, theta)
mdistr <- fmd(m.sim)
plot(mdistr$mi, mdistr$Ni, log = "y")
points(mdistr$mi, mdistr$ni)

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