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etarpp {SAPP}

Residual Point Process of The ETAS Model
Package: 
SAPP
Version: 
1.0.3

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,

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}.

Values

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

Y.Ogata (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(x$time, x$magnitude, 2.5, 6.2,
         c(0, 0.63348E+02, 0.38209E-01, 0.26423E+01, 0.10169E+01),, 0.01, 7, 18.68)
 
## output a res-format dataset
  etarpp2(main2003JUL26, 2.5, 6.2,
         c(0, 0.63348E+02, 0.38209E-01, 0.26423E+01, 0.10169E+01),, 0.01, 7, 18.68)

Documentation reproduced from package SAPP, version 1.0.3. License: GPL (>= 2)