# 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` an 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, param = c(0,0.96021e+02, 0.58563e-01, 0.96611e+00), zts = 0.0, tstart = 0.01, zte = 18.68, threshold = 2.5) # output a res-format dataset respoi2(main2003JUL26, param = c(0,0.96021e+02, 0.58563e-01, 0.96611e+00), zts = 0.0, tstart = 0.01, zte = 18.68, threshold = 2.5) ```

SAPP documentation built on July 2, 2020, 2:59 a.m.