SAPP (version 1.0.4)

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)

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 $p$.

Value

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

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

Y.Ogata (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(1.0, 999, 3.5, 3.5, 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, 0.01, 2.5, 6.2,
          c(0, 0.63348e+02, 0.38209e-01, 0.26423e+01, 0.10169e+01))