respoi {SAPP}

The residual point process of the ETAS model

Package:

SAPP

Version:

1.0.2

Description

Compute the residual of modified Omori Poisson process and display the cumulative curve and magnitude v.s. transformed time.

Usage

respoi(time,mag,param,zts,tstart,zte,threshold=0.0,plot=TRUE)

  respoi2(etas,param,zts,tstart,zte,threshold=0.0,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).
param: the four parameters B, K, c and p.
zts: the start of the precursory period.
tstart: the start of the target period.
zte: the end of the target period.
threshold: threshold magnitude.
plot: logical. If TRUE (default) cumulative curve and magnitude v.s. transformed time F(t_i) are plotted.

Details

The function respoi and respoi2 compute the following output for displaying the goodness-of-fit of Omori-Utsu model to the data. The cumulative number of earthquakes at time t since t_0 is given by the integration of f(t) with respect to the time t,

where the summation of i is taken for all data event.

respoi2 is equivalent to respoi except that input and output forms are different. When a etas-format dataset is given, respoi2 returns the dataset with the format as described below.

Values

trans.time: transformed time F(t_i), i=1,2,...,N.
cnum: cumulative number of events.
resData: a res-format dataset on 7 variables
(no., longitude, latitude, magnitude, time, depth and trans.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
  respoi(x$time, x$magnitude, c(0,0.96021E+02,0.58563E-01,0.96611E+00),
         0.0, 0.01, 18.68, 2.5)
 
# output a res-format dataset
  respoi2(main2003JUL26, c(0,0.96021E+02,0.58563E-01,0.96611E+00),
          0.0, 0.01, 18.68, 2.5)

Documentation reproduced from package SAPP, version 1.0.2. License: GPL (>= 2)