Residual Point Process of the ETAS Model
Description
Compute the residual data using the ETAS model with MLEs.
Usage
etarpp(time, mag, threshold = 0.0, reference = 0.0, parami, zts = 0.0, tstart,
zte, ztend = NULL, plot = TRUE)
etarpp2(etas, threshold = 0.0, reference = 0.0, parami, zts = 0.0, tstart, zte,
ztend = NULL, plot = TRUE)
etarpp(time, mag, threshold = 0.0, reference = 0.0, parami, zts = 0.0, tstart,
zte, ztend = NULL, plot = TRUE)
etarpp2(etas, threshold = 0.0, reference = 0.0, parami, zts = 0.0, tstart, zte,
ztend = NULL, 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).
|
threshold |
threshold magnitude.
|
reference |
reference magnitude.
|
parami |
initial estimates of five parameters μ , K ,
c , α and p .
|
zts |
the start of the precursory period.
|
tstart |
the start of the target period.
|
zte |
the end of the target period.
|
ztend |
the end of the prediction period. If NULL (default)
the last time of available data is set.
|
plot |
logical. If TRUE (default) the graphs of cumulative number
and magnitude against the ordinary time and transformed time are plotted.
|
Details
The cumulative number of earthquakes at time t
since t0
is given
by the integration of λ(t)
( see etasap
)
with respect to the time t
,
Λ(t)=μ(t−t0)+KΣiexp[α(Mi−Mz)]{c(1−p)−(t−ti+c)(1−p)}/(p−1),
where the summation of i
is taken for all data event. The output of
etarpp2
is given in a res-format dataset which includes the column of
{Λ(ti),i=1,2,...,N}
.
Value
trans.time |
transformed time Λ(ti),i=1,2,...,N .
|
no.tstart |
data number of the start of the target period.
|
resData |
a res-format dataset on 7 variables
(no., longitude, latitude, magnitude, time, depth and transformed 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
etarpp(time = x$time, mag = x$magnitude, threshold = 2.5, reference = 6.2,
parami = c(0, 0.63348e+02, 0.38209e-01, 0.26423e+01, 0.10169e+01),
tstart = 0.01, zte = 7, ztend = 18.68)
## output a res-format dataset
etarpp2(main2003JUL26, threshold = 2.5, reference = 6.2,
parami = c(0, 0.63348e+02, 0.38209e-01, 0.26423e+01, 0.10169e+01),
tstart = 0.01, zte = 7, ztend = 18.68)
data(main2003JUL26)
x <- main2003JUL26
etarpp(time = x$time, mag = x$magnitude, threshold = 2.5, reference = 6.2,
parami = c(0, 0.63348e+02, 0.38209e-01, 0.26423e+01, 0.10169e+01),
tstart = 0.01, zte = 7, ztend = 18.68)
etarpp2(main2003JUL26, threshold = 2.5, reference = 6.2,
parami = c(0, 0.63348e+02, 0.38209e-01, 0.26423e+01, 0.10169e+01),
tstart = 0.01, zte = 7, ztend = 18.68)