b.guten: Estimates the parameter of the Gutenberg-Richter law.

In etasFLP: Mixed FLP and ML Estimation of ETAS Space-Time Point Processes for Earthquake Description

Estimates the parameter of the Gutenberg-Richter law.

Description

Estimates the parameter of the Gutenberg-Richter law for the magnitude distribution of earthquakes, given a threshold magnitude; it uses moment estimator on transformed data.

Usage

b.guten(magn, m0=min(magn))

Arguments

magn	a vector of magnitudes coming from an earthquake catalog.
m0	A threshold value. Only values of magn not less than m0 will be used.

Details

Maximum likelihodd estimation for the Gutenberg-Richter Law:

\log_{10} N(>m) = a - b \ M

where N(>m) is the number of events exceeding a magnitude m and a,b are two parameters: a is related to the total seismicity rate of the region while b, to be estimated, should be usually near 1.

Catalog is assumed to be complete (in a certain space-time region) at least for a magnitude m0, that is, every earthquake of magnitude at least m0 in that space-time region, is certainly present in the catalog.

Value

b	estimate of the parameter b of the Gutenberg-Richter Law.
se	estimate of the standard error of the estimate b.

Note

the plot produced by magn.plot can be used to have an idea, for a given catalog, of the magnitude threshold value.

Author(s)

Marcello Chiodi

References

Gutenberg, B. and Richter, C. F. (1944). Frequency of earthquakes in California. Bulletin of the Seismological Society of America, 34, 185-188.

See Also

magn.plot

Examples

data(italycatalog)
b.guten(italycatalog$magn1)

etasFLP documentation built on Sept. 14, 2023, 5:06 p.m.