rates | R Documentation |
Functions to estimate the declustering probabilities, background seismicity rate and clustering (triggering) coefficient for a fitted ETAS model.
probs(fit) rates(fit, lat.range = NULL, long.range = NULL, dimyx=NULL, plot.it=TRUE)
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. |
The function probs
returns estimates of the declustering probabilities
p[j] = 1 - mu(x[j], y[j])/lambda(t[j], x[j], y[j]|H_t[j])
where 1-p[j] is the probability that event j is a background event.
The function rates
returns kernel estimate of the background
seismicity rate mu(x,y) and the clustering (triggering)
coefficient
omega(x,y)=1-mu(x,y)/Lambda(x,y)
where Lambda(x,y) 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).
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 t=t_{start} + T
Abdollah Jalilian jalilian@razi.ac.ir
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.
etas
# 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)
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