respoi | R Documentation |

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

```
respoi(time, mag, param, zts, tstart, zte, threshold = 0.0, plot = TRUE)
respoi2(etas, param, zts, tstart, zte, threshold = 0.0, plot = TRUE)
```

`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 |

`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 |

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.

`trans.time` |
transformed time |

`cnum` |
cumulative number of events. |

`resData` |
a res-format dataset on 7 variables (no., longitude, latitude, magnitude, time, depth and trans.time) |

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

```
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)
```

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