Natural Time, Nowcasting and the Physics of Earthquakes: Estimation of Seismic Risk to Global Megacities

Natural Time ("NT") refers to the concept of using small earthquake counts, for example of M > 3 events, to mark the intervals between large earthquakes, for example M > 6 events. The term was first used by Varotsos et al. (2005) and later by Holliday et al. (2006) in their studies of earthquakes. In this paper, we discuss ideas and applications arising from the use of NT to understand earthquake dynamics, in particular by use of the idea of nowcasting. Nowcasting differs from forecasting, in that the goal of nowcasting is to estimate the current state of the system, rather than the probability of a future event. Rather than focus on an individual earthquake faults, we focus on a defined local geographic region surrounding a particular location. This local region is considered to be embedded in a larger regional setting from which we accumulate the relevant statistics. We apply the nowcasting idea to the practical development of methods to estimate the current state of risk for dozens of the world's seismically exposed megacities, defined as cities having populations of over 1 million persons. We compute a ranking of these cities based on their current nowcast value, and discuss the advantages and limitations of this approach. We note explicitly that the nowcast method is not a model, in that there are no free parameters to be fit to data. Rather, the method is simply a presentation of statistical data, which the user can interpret. Among other results, we find, for example, that the current nowcast ranking of the Los Angeles region is comparable to its ranking just prior to the January 17, 1994 Northridge earthquake.