# etarpp: Residual Point Process of the ETAS Model In SAPP: Statistical Analysis of Point Processes

 etarpp R Documentation

## Residual Point Process of the ETAS Model

### Description

Compute the residual data using the ETAS model with MLEs.

### Usage

etarpp(time, mag, threshold = 0.0, reference = 0.0, parami, zts = 0.0, tstart,
zte, ztend = NULL, plot = TRUE)

etarpp2(etas, threshold = 0.0, reference = 0.0, parami, zts = 0.0, tstart, zte,
ztend = NULL, plot = TRUE)


### Arguments

 time the time measured from the main shock(t = 0). mag magnitude. etas a etas-format dataset on 9 variables (no., longitude, latitude, magnitude, time, depth, year, month and days). threshold threshold magnitude. reference reference magnitude. parami initial estimates of five parameters \mu, K, c, \alpha and p. zts the start of the precursory period. tstart the start of the target period. zte the end of the target period. ztend the end of the prediction period. If NULL (default) the last time of available data is set. plot logical. If TRUE (default) the graphs of cumulative number and magnitude against the ordinary time and transformed time are plotted.

### Details

The cumulative number of earthquakes at time t since t_0 is given by the integration of \lambda(t) ( see etasap ) with respect to the time t,

\Lambda(t) = \mu(t-t_0) + K \Sigma_i \exp[\alpha(M_i-M_z)]\{c^{(1-p)}-(t-t_i+c)^{(1-p)}\}/(p-1),

where the summation of i is taken for all data event. The output of etarpp2 is given in a res-format dataset which includes the column of \{\Lambda(t_i), i = 1, 2, ..., N\}.

### Value

 trans.time transformed time \Lambda(t_i), i = 1, 2, ..., N. no.tstart data number of the start of the target period. resData a res-format dataset on 7 variables (no., longitude, latitude, magnitude, time, depth and transformed time).

### References

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

### Examples

data(main2003JUL26)  # The aftershock data of 26th July 2003 earthquake of M6.2

## output transformed times and cumulative numbers
x <- main2003JUL26
etarpp(time = x$time, mag = x$magnitude, threshold = 2.5, reference = 6.2,
parami = c(0, 0.63348e+02, 0.38209e-01, 0.26423e+01, 0.10169e+01),
tstart = 0.01, zte = 7, ztend = 18.68)

## output a res-format dataset
etarpp2(main2003JUL26, threshold = 2.5,  reference = 6.2,
parami = c(0, 0.63348e+02, 0.38209e-01, 0.26423e+01, 0.10169e+01),
tstart = 0.01, zte = 7, ztend = 18.68)


SAPP documentation built on June 7, 2023, 5:45 p.m.