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

## Description

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

## Usage

 ```1 2 3``` ```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,

F(t) = B(t-t_0) + K{ c^{(1-p)}-(t-t_i+c)^{(1-p)} }/(p-1)

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.

## Value

 `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

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

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10``` ```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) ```

SAPP documentation built on May 30, 2017, 2:32 a.m.