rates {ETAS} | R Documentation |
Declustering Probabilities, Background Seismicity Rate and Clustering Coefficient
Description
Functions to estimate the declustering probabilities, background seismicity rate and clustering (triggering) coefficient for a fitted ETAS model.
Usage
probs(fit)
rates(fit, lat.range = NULL, long.range = NULL,
dimyx=NULL, plot.it=TRUE)
Arguments
fit |
A fitted ETAS model. An object of class |
lat.range |
Latitude range of the rectangular grid. A numeric vector of length 2. |
long.range |
Longitude range of the rectangular grid. A numeric vector of length 2. |
dimyx |
Dimensions of the rectangular discretization grid for the geographical study region. A numeric vector of length 2. |
plot.it |
Logical flag indicating whether to plot the rates or return them as pixel images. |
Details
The function probs
returns estimates of the declustering probabilities
where is the probability that event
is a background event.
The function rates
returns kernel estimate of the background
seismicity rate and the clustering (triggering)
coefficient
where is the total spatial intensity
function.
The argument dimyx
determines the rectangular discretization
grid dimensions. If it is given, then it must be a numeric vector
of length 2 where the first component dimyx[1]
is the
number of subdivisions in the y-direction (latitude) and the
second component dimyx[2]
is the number of subdivisions
in the x-direction (longitude).
Value
If plot.it=TRUE
, the function produces plots of the
background seismicity and total spatial rate, clustering coefficient
and conditional intensity function at the end of study period.
If plot.it=FALSE
, it returns a list with components
bkgd the estimated background siesmicity rate
total the estimated total spatial rate
clust the estimated clustering coefficient
lamb the estimated conditional intensity function at time
Author(s)
Abdollah Jalilian jalilian@razi.ac.ir
References
Zhuang J, Ogata Y, Vere-Jones D (2002). Stochastic Declustering of Space-Time Earthquake Occurrences. Journal of the American Statistical Association, 97(458), 369–380. doi:10.1198/016214502760046925.
Zhuang J, Ogata Y, Vere-Jones D (2006). Diagnostic Analysis of Space-Time Branching Processes for Earthquakes. In Case Studies in Spatial Point Process Modeling, pp. 275–292. Springer Nature. doi:10.1007/0-387-31144-0_15.
Zhuang J (2011). Next-day Earthquake Forecasts for the Japan Region Generated by the ETAS Model. Earth, Planets and Space, 63(3), 207–216. doi:10.5047/eps.2010.12.010.
See Also
Examples
# preparing the catalog
iran.cat <- catalog(iran.quakes, time.begin="1973/01/01",
study.start="1996/01/01", study.end="2016/01/01",
lat.range=c(25, 42), long.range=c(42, 63), mag.threshold=4.5)
print(iran.cat)
## Not run:
plot(iran.cat)
## End(Not run)
# initial parameters values
param01 <- c(0.46, 0.23, 0.022, 2.8, 1.12, 0.012, 2.4, 0.35)
# fitting the model and
## Not run:
iran.fit <- etas(iran.cat, param0=param01)
## End(Not run)
# estimating the declustering probabilities
## Not run:
pr <- probs(iran.fit)
plot(iran.cat$longlat.coord[,1:2], cex=2 * (1 - pr$prob))
## End(Not run)
# estimating the background seismicity rate and clustering coefficient
## Not run:
rates(iran.fit, dimyx=c(100, 125))
iran.rates <- rates(iran.fit, dimyx=c(200, 250), plot.it=FALSE)
summary(iran.rates$background)
## End(Not run)