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

 respoi R Documentation

## The Residual Point Process of the ETAS Model

### 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` 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

``````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 June 7, 2023, 5:45 p.m.