Abstract
Seismic forecasting using a Brownian Passage Time distribution is presented in this chapter. Seismic forecasting is concerned with the probabilistic assessment of general seismic hazard, including the frequency and magnitude of earthquakes in a given area over a given period of time. Seismic forecasting generally look for trends that lead to an earthquake. The estimation of the time that a strong earthquake will occur requires the determination of the distribution that the earthquake recurrence time follows. Brownian Passage Time distribution describes reliably the physical processes related with earthquakes’ occurrence. The model assumes that the evolution of the stress loading between two earthquakes depends on the constant loading rate, and a random component, which follows the Brownian Relaxation Oscillator. Its hazard function is in good agreement with the temporal evolution of earthquake occurrence as the hazard rate is very low after an earthquake, and then increases as time passes, and takes a maximum value at the mean recurrence time and since then, it decreases asymptotically exhibiting a pure quasi-periodic temporal occurrence.