bfmd.pdf: PDF of the Bulk FMD

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

Description

Compute the probability density function (PDF) of the bulk frenquency-magnitude distribution (FMD), as defined by Ogata and Katsura (2006) (see also Ringdal, 1975; Ogata and Katsura, 1993).

Usage

bfmd.pdf(m, theta)

Arguments

m	a numeric vector of earthquake magnitudes
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

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 densities.

References

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.sim

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