What Is Natural Time?
An event-counting framework introduced by Varotsos et al. that reveals seismic patterns invisible to clock-based analysis.
The Core Idea
Natural time replaces the conventional clock-time axis with a count of seismic events. In natural time, the nth earthquake in a catalogue has a timestamp of χn = n/N, where N is the total number of events in the window. The energy released by each event is the "weight" assigned to that moment.
This seemingly simple substitution reveals something powerful: it filters out the irregular inter-event times that make seismicity hard to model and replaces them with a uniform, comparable scale of stress and strain accumulation.
Why It Works Better Than Clock Time for Seismicity
Seismic systems do not progress at a steady rate. After a major earthquake, aftershock sequences create thousands of events in hours; in quiet periods, weeks pass with almost no activity. Clock-based models that treat these periods equivalently miss the underlying physics: what matters is how many events have occurred since the last significant earthquake, not how many days have passed.
- Event-based progression: the count of small earthquakes measures stress and strain accumulation in a region - the metric that actually drives seismic cycles.
- No decluttering required: natural time is uniformly valid whether aftershocks dominate, background seismicity dominates, or both contribute.
- Entropy dynamics: natural time statistics reveal when a seismic system is approaching a critical state - a key input to the EPS calculation.
- Aftershock robustness: because aftershocks are part of the energy release sequence, they contribute meaningfully rather than being treated as noise.
Natural Time and the Seismic Cycle
In the Bikos (2024) framework, an "earthquake cycle" is defined as the sequence of seismic events - at all magnitudes - between successive large events (M≥6.0) in a defined geographic region. Natural time counts through this cycle; when the count approaches the end of the distribution of past cycle lengths, the Earthquake Potential Score rises.
This is fundamentally different from recurrence models on individual faults: it works at the regional scale, across the entire network of active faults in California.
Primary Source
Natural time analysis was introduced by Varotsos, Sarlis, and Skordas. For the specific application to earthquake nowcasting see: Bikos, A.N. (2024). Seismic Nowcasting: A Systemic Artificial Neural Network Predictive Model. Geoinformatics & Geostatistics: An Overview, 12:4. Full text available: Bikos (2024) PDF.