Inverse of integrated Omori's law

Inverse of integrated Omori's law

Usage

Inv_Int_ETAS_time_trig_function(theta, omega, th)

Arguments

theta

ETAS parameters list(mu=mu, K=K, alpha=alpha, c=c, p=p)

omega

Value of the integral to be inverted, vector

th

Time from which the integral is calculated scalar

Value

Value of the start of the temporal domain used to calculate the integral

Details

Considering the integral of Omori's law $$\omega = \int_{t_h}^{T_2}\left(\frac{t - t_h}{c} + 1\right)^{-p} dt$$ The function applied to the value \(\omega\) returns the value of \(t_h\).