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

Description Usage Arguments Details Value References Examples

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

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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`	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.

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 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)

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, 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)