respoi {SAPP}

The residual point process of the ETAS model
Package:
SAPP
Version:
1.0.3

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 1.0.3. License: GPL (>= 2)