Estimating the predictability of the seismicity rate: The 1964 eruption of Shiveluch Volcano

This paper describes a method for estimating the predictability of the seismicity rate for volcanic edifices. The mathematical model is a nonlinear second-order differential equation, with our own algorithms for optimization and for estimating predictability. The method is illustrated by the 1964 eruption on Shiveluch Volcano. Calculations showed that the seismicity rate can be predicted with success for a time interval ranging between a few days and a few tens of days during the active phase and between a few tens of days and a few hundreds of days during the decay phase. The level of predictability is rather high, with the prediction distance exceeding the mean error by two to four orders of magnitude. The nonlinear character of both the active phase of the process and of its decay phase is close to the law of an equilateral hyperbola. The method, as developed in this paper, allows a realistic approach to the prediction of that part of the volcanic process which involves brittle deformation and/or rapid displacements of material along the newly arisen cracks.