SAPP (version 1.0.9-1)

etasim: Simulation of Earthquake Dataset Based on the ETAS Model

Description

Produce simulated dataset for given sets of parameters in the point process model used in ETAS.

Usage

etasim1(bvalue, nd, threshold = 0.0, reference = 0.0, param)
etasim2(etas, tstart, threshold = 0.0, reference = 0.0, param)

Value

etasim1 and etasim2 generate a etas-format dataset given values of 'no.', 'magnitude' and 'time'.

Arguments

bvalue

\(b\)-value of G-R law if etasim1.

nd

the number of the simulated events if etasim1.

etas

a etas-format dataset on 9 variables (no., longitude, latitude, magnitude, time, depth, year, month and days).

tstart

the end of precursory period if etasim2.

threshold

threshold magnitude.

reference

reference magnitude.

param

five parameters \(\mu\), \(K\), \(c\), \(\alpha\) and \(p\).

Details

There are two versions; either simulating magnitude by Gutenberg-Richter's Law etasim1 or using magnitudes from \(etas\) dataset etasim2. For etasim1, \(b\)-value of G-R law and number of events to be simulated are provided. stasim2 simulates the same number of events that are not less than threshold magnitude in the dataset \(etas\), and simulation starts after a precursory period depending on the same history of events in \(etas\) in the period.

References

Ogata, Y. (2006) Computer Science Monographs, No.33, Statistical Analysis of Seismicity - updated version (SASeies2006). The Institute of Statistical Mathematics.

Examples

## by Gutenberg-Richter's Law 
etasim1(bvalue = 1.0, nd = 999, threshold = 3.5, reference = 3.5,
        param = c(0.2e-02, 0.4e-02, 0.3e-02, 0.24e+01, 0.13e+01))

## from a etas-format dataset
data(main2003JUL26)  # The aftershock data of 26th July 2003 earthquake of M6.2
etasim2(main2003JUL26, tstart = 0.01, threshold = 2.5, reference = 6.2,
        param = c(0, 0.63348e+02, 0.38209e-01, 0.26423e+01, 0.10169e+01))