Description Usage Arguments Details Value Function Attributes References See Also Examples
This function calculates the value of the ground intensity of a time-magnitude Epidemic Type Aftershock Sequence (ETAS) model. Spatial coordinates of the events are not taken into account.
1 |
data |
a data frame containing the event history, where each row represents one event. There must be columns named |
evalpts |
a |
params |
vector of parameter values in the following order: (mu, A, alpha, c, p). |
TT |
vector of length 2, being the time interval over which the integral of the ground intensity function is to be evaluated. |
tplus |
logical, lambda_g(t|Ht) is evaluated as lambda_g(t^+|Ht) if |
The ETAS model was proposed by Ogata (1988, 1998, 1999) for the modelling of earthquake mainshock-aftershock sequences. The form of the ground intensity function used here is given by
lambda_g(t|Ht) = mu + A sum{exp[alpha(Mi - M0)](1 + (t-ti)/c)^(-p)},
where ti denotes the event times and the summation is taken over those i such that ti < t.
Two usages are as follows.
1 2 |
The first usage returns a vector containing the values of lambda_g(t) evaluated at the specified points. In the second usage, it returns the value of the integral.
rate
is "decreasing"
.
Cited references are listed on the PtProcess manual page.
General details about the structure of ground intensity functions are given in the topic gif
.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 | # Tangshan: ground intensity and magnitude time plots
data(Tangshan)
p <- c(0.007, 2.3, 0.98, 0.008, 0.94)
bvalue <- 1
TT <- c(0, 4018)
x <- mpp(data=Tangshan,
gif=etas_gif,
marks=list(dexp_mark, NULL),
params=p,
gmap=expression(params),
mmap=expression(bvalue*log(10)),
TT=TT)
par.default <- par(mfrow=c(1,1), mar=c(5.1, 4.1, 4.1, 2.1))
par(mfrow=c(2,1), mar=c(4.1, 4.1, 0.5, 1))
plot(x, log=TRUE, xlab="")
plot(Tangshan$time, Tangshan$magnitude+4, type="h",
xlim=c(0, 4018),
xlab="Days Since 1 January 1974", ylab="Magnitude")
par(par.default)
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