Description Usage Arguments Details Value Function Attributes Problems and Inconsistencies References See Also Examples

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.

1 |

`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 threshold, i.e. |

`evalpts` |
a |

`params` |
vector of parameters for the proposed SRM model in the order |

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

`tplus` |
logical, |

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{10^[0.75(M_i-M_0)]}
*

and the summation is taken over those *i* such that *ti < t*, where *ti* denotes the event times.

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

`"increasing"`

.

Runs much slower than `linksrm_gif`

. Should set up matrices `St1`

and `St2`

as in `linksrm_gif`

.

Cited references are listed on the PtProcess manual page.

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

.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | ```
# 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)
``` |

PtProcess documentation built on Nov. 17, 2017, 7:12 a.m.

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