rates: Declustering Probabilities, Background Seismicity Rate and...

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ratesR Documentation

Declustering Probabilities, Background Seismicity Rate and Clustering Coefficient


Functions to estimate the declustering probabilities, background seismicity rate and clustering (triggering) coefficient for a fitted ETAS model.


  rates(fit, lat.range = NULL, long.range = NULL,
        dimyx=NULL, plot.it=TRUE)



A fitted ETAS model. An object of class "etas".


Latitude range of the rectangular grid. A numeric vector of length 2.


Longitude range of the rectangular grid. A numeric vector of length 2.


Dimensions of the rectangular discretization grid for the geographical study region. A numeric vector of length 2.


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


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.

See Also



  # 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)

  ## Not run: 
## 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)
## End(Not run)

ETAS documentation built on Nov. 28, 2022, 5:23 p.m.