Nowcasting: A New Approach to the Statistics of Aftershocks

Since direct local determination of stress and strain in a given seismically-active area cannot be reliably achieved, the current seismic state of a region must be estimated by indirect means. Past attempts at hazard estimation were based on a variety of fault-focused methods that have proven to be problematic, an example being the Parkfield Prediction of the 1980s. Instead, we take a step backward and address the (simpler) problem of estimating the current state of a seismically-active area rather than its future hazard. We thus propose to borrow from economics the concept of nowcasting, which refers to the stochastic estimation of the current state of a system, in our case seismic hazard, using easily-obtainable data. The technique involves using the natural time, which is the numbers of small earthquakes between large earthquakes, along with the number of small earthquakes since the last large earthquake, to quantify the present hazard. We package the results in a single number, labeled EPS for earthquake potential score, interpreted to be the potential for occurrence of the next large earthquake having a magnitude larger than our reference magnitude. The advantage of our natural time approach is that it can be applied to non-stationary seismicity, such as aftershock sequences. To demonstrate the power of this formalism, we apply it to aftershock sequences of the Parkfield, Tohoku, and 2012 Indian Ocean mainshocks.