Conditional probability of what? Example of the Nankai interface in Japan

When the timing of the most recent event on a fault is known and when quasi-periodicity is inferred, it is customary to require time-dependent conditional probabilities for that fault. A lot of applications rely on these numbers, including emergency planning, prioritizing retrofits, (re-)insurance pricing, and reserve setting. For very simple fault network geometries and faulting behaviors, the question "conditional probability of what?" is easily answered. It is the probability of the characteristic full-segment event on that fault. However, for either more complex fault networks or more complex faulting behaviors, it is not as easy. We propose a method for building a recurrence model for megathrust events on the Nankai interface in Japan. Historically, this interface has ruptured every 150 yrs on average either in individual large earthquakes spanning the whole region from Tokai in the northeast to the western edge of the Nankai segment or even into the Hyuganada region (1707-type events) or in clusters of two adjacent earthquakes (Nankai-Tonankai, e.g., 1944-1946). The method analyzes the family of events that can reset stresses on the fault and makes use of the earthquake history, convergence rate, and inferred megathrust slip per event. The first step calculates the probability for large events to happen on the Nankai interface. The second step assigns relative weights to the possible scenarios. The last step proposes an intracluster distribution for interevent times when the "event" is a cluster of two large adjacent earthquakes. It is developed to be a more self-consistent analysis than one that would look at the recurrence of large earthquakes on each segment independently. Similar approaches might be useful in other settings where the most constrained conditional probability might be that for any of a series of possible stress resetting events across a number of faults, fault strands, or fault segments.