Volcano and Earthquake Hazards in the Crater Lake Region, Oregon
Probability of a Future Volcanic Eruption
Estimating the probability of a volcanic eruption occurring within a hazard zone requires not only knowledge of eruptive frequency in the past but also assumptions about the regularity of eruptions in time and their distribution within the area in question. Lacking age information for every vent, we treat the opening of new regional volcanic vents as a random process. We assume that regional volcanism has no memory of previous events such that the process has a Poisson distribution.
This may not be true of large, central-vent volcanoes such as Mount Rainier or ancestral Mount Mazama, which have erupted many times from the same conduit system. The probability of an eruption occurring somewhere in the stated region at a new vent during a specified number of years, an exponential function, reduces to simply the average recurrence rate times the length of the period of interest for time periods that are short (tens of years) relative to the average recurrence interval (thousands of years).
On the basis of the total number of eruptive episodes in the past ~100,000 years, exclusive of Mount Mazama, the average recurrence interval is about 10,000 years. The annual probability of an eruption occurring near Crater Lake, then, is around one chance in 10,000, or 10-4, and the 30-year probability is about one chance in 330, or 3×10-3. These estimates are, at best, very approximate because volcanic eruptions are triggered by the interplay of complex processes and there is no guarantee that events occurring in the future will adhere to the simplistic model used to estimate probabilities.