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. As we discuss in this paper, it is particularly useful in describing complex stochastic nonlinear systems characterized by fat-tail statistics rather than Gaussian normal statistics. In this paper we discuss ideas and applications arising from the use of NT to understand earthquake dynamics. The usual end-user applications of fault-based studies are often applied to risk of a particular geographic location, so it seems best to start the analysis with that geographic region. Rather than focus on an individual earthquake faults, we have found it more productive to 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. From this different philosophical point of view, we first discuss methods to use NT, counts of small earthquakes, to evaluate the current state of a regional collection of faults. We then use these concepts to first discuss the nucleation physics of large earthquakes. We introduce the idea of nowcasting, a term originating from economics and finance. The goal of nowcasting is to determine the current state of the fault system, or put another way, the current state of progress through the earthquake cycle. This is in contrast to forecasting, which is the calculation of probabilities of future large earthquakes. Finally, 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.

Seismic nowcasting uses counts of small earthquakes as proxy data to estimate the current dynamical state of an earthquake fault system . The result is an earthquake potential score that characterizes the current state of progress of a defined geographic region through its nominal earthquake “cycle.” The count of small earthquakes since the last large earthquake is the natural time that has elapsed since the last large earthquake (Varotsos et al., 2006, https://doi.org/10.1103/PhysRevE.74.021123 ). In addition to natural time, earthquake sequences can also be analyzed using Shannon information entropy (“information”), an idea that was pioneered by Shannon (1948, https://doi.org/10.1002/j.1538‐7305.1948.tb01338.x ). As a first step to add seismic information entropy into the nowcasting method, we incorporate magnitude information into the natural time counts by using event self‐information. We find in this first application of seismic information entropy that the earthquake potential score values are similar to the values using only natural time. However, other characteristics of earthquake sequences, including the interevent time intervals, or the departure of higher magnitude events from the magnitude‐frequency scaling line, may contain additional information.

No abstract