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SIETAS model: Swarm-informed triggering, earthquake diffusion, and multiscaling applied to the current Campi Flegrei unrest

Cataldo Godano

Anna Tramelli and Vincenzo Convertito

Giuseppe Petrillo*

  • Istituto Nazionale di Geofisica e Vulcanologia (INGV), Osservatorio Vesuviano, Via Diocleziano 328, 80125 Napoli, Italy

  • *Contact author: giuseppe51289@gmail.com
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Phys. Rev. Research 8, 043055 – Published 15 October, 2026

DOI: https://doi.org/10.1103/wv9d-2wjc

Abstract

Earthquake diffusion is commonly interpreted either as the migration of fluids or as the propagation of triggering cascades within branching processes. In the latter framework, anomalous diffusion emerges naturally from the long-memory kernels of epidemic-type aftershock sequence (ETAS) models. Here, we introduce a swarm-informed ETAS (SIETAS) model designed to describe volcanic seismic swarms. The model combines a temporally truncated power-law triggering kernel with a spatially localized logistic kernel, thereby introducing intrinsic temporal and spatial scales into the triggering process. Using an AI earthquake catalog from the ongoing Campi Flegrei unrest, we show that SIETAS provides a substantially better description of seismicity than the standard ETAS formulation. We further demonstrate that earthquake diffusion exhibits clear multiscaling behavior characterized by three effective scaling regimes. Analytical arguments based on branching-process theory and continuous-time random walks indicate that the SIETAS kernels generate a crossover from transient anomalous diffusion to an effectively normal-diffusive regime, followed by saturation due to finite subcriticality. We discuss how the observed multiscaling behavior may emerge from the interplay between short-time triggering, finite temporal memory, finite spatial localization, and secondary components of the triggering kernel. These results establish a connection between swarm-informed earthquake triggering and multiscale diffusion phenomena in volcanic environments.

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Phys. Rev. Research 8, 043055– Published 15 October, 2026
  • Received 19 June 2026
  • Accepted 27 August 2026
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