Modeling swarms as a random walk within a branching process
Nicholas J. van der ElstSubmitted August 30, 2026, SCEC Contribution #15446, 2026 SCEC Annual Meeting Poster #TBD
Assessing the earthquake hazard during seismic swarms presents a unique challenge in operational forecasting. Whereas aftershock sequences follow a typical temporal decay pattern (Omori’s law) that allows for an estimate of the duration of the sequence, swarms follow no such law. In some cases, a region may have a sufficient history of swarm activity to inform an empirical duration model. However, these models appear memoryless - the swarm appears to have a constant daily probability of either ending or continuing.
Swarms can be modelled as a branching or epidemic process, even when the driving is external. In a cascade model, a swarm is the special case where each earthquake ‘triggers’ exactly one additional earthquake. Cascade models like the Epidemic Type Aftershock Sequence can be tuned to give swarm-like behavior, but this requires breakdown of self-similarity (b = alpha = 1). Usually swarm seismicity is modeled as an increase in background rate, a decrease in the magnitude scaling alpha and an increase in b-value. This is sometimes paired with a smaller Mmax in the magnitude distribution. This gives a cascade with relatively many smaller earthquakes that are linked to each other, rather than to a central large event.
Here I propose an alternative cascade model where the swarm-like behavior is controlled by a single parameter: the maximum magnitude difference dMmax between a parent and offspring. Even for self-similar conditions (b = alpha = 1), this model gives a range of behavior from mainshock-aftershock to swarm-like, depending on dMmax. Swarms, with high overall b-value and large branching depth, emerge when productivity is high but dMmax is low, (around 1.5 units of magnitude or less), and the sequence must grow larger through multiple generations of triggering. The swarm takes on characteristics of a biased random walk in maximum magnitude, where the branching depth and size of the largest aftershock are related to the magnitude drift per generation. For a swarm to end, it must ‘walk’ itself to smaller magnitudes and out of the observable magnitude range.
Key Words
swarm, magnitude, magnitude difference
Citation
van der Elst, N. J. (2026, 08). Modeling swarms as a random walk within a branching process. Poster Presentation at 2026 SCEC Annual Meeting.
Related Projects & Working Groups
Earthquake Forecasting and Predictability (EFP)
