PtProcess (version 3.1-1)

srm_gif: Conditional Intensity for Stress Release Model

Description

This function calculates the value of the conditional intensity of a Stress Release Model (SRM). Spatial coordinates of the events are not taken into account.

Usage

srm_gif(data, evalpts, params, tplus=FALSE)
srm_gif(data, evalpts=NULL, params, TT)

Arguments

data

a data frame containing the event history, where each row represents one event. There must be columns named time, usually the number of days from some origin; and magnitude which is the event magnitude less the magnitude

evalpts

a vector, matrix or data.frame. If a vector, the elements will be assumed to represent the required evaluat

params

vector of parameters for the proposed SRM model in the order $\code{c}(a, b, c)$.

TT

vector of length 2, being the time interval over which the integral of the conditional intensity function is to be evaluated.

tplus

logical, $\lambda_g(t|{\cal H}_t)$ is evaluated as $\lambda_g(t^+|{\cal H}_t)$ if TRUE, else $\lambda_g(t^-|{\cal H}_t)$.

Value

• 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.

synopsis

srm_gif(data, evalpts, params, TT=NA, tplus=FALSE)

Problems and Inconsistencies

Runs much slower than linksrm_gif. Should set up matrices St1 and St2 as in linksrm_gif.

Details

Vere-Jones (1978) proposed the stress release model, being a stochastic version of elastic rebound theory (Reid, 1910). The SRM assumes a deterministic increase in stress over time, and a stochastic release through earthquake events. The conditional intensity function is $$\lambda_g(t) = \exp{a + b[t - cS(t)]},$$ where $$S(t) = \sum_i 10^{0.75(M_i-M_0)}$$ and the summation is taken over those $i$ such that $t_i < t$, where $t_i$ denotes the event times.

See Also

General details about the structure of conditional intensity functions are given in the topic gif.

Examples

#  Treating North China as one region

data(NthChina)
p <- c(-2.46, 0.0113, 0.851)
times <- seq(0, 517, 0.5)

par.default <- par(mfrow=c(2,1), mar=c(4.1, 4.1, 0.5, 1))
plot(times+1480, srm_gif(NthChina, times, params=p), type="l",
     ylab=expression(lambda[g](t)),
     xlab="", xlim=c(1480, 2000))
plot(NthChina$time+1480, NthChina$magnitude+6, type="h",
     xlim=c(1480, 2000), ylim=c(5.8, 8.6),
     xlab="Year", ylab="Magnitude")

par(par.default)