# respoi {SAPP}

### 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)