Occurrence of Finite-Time Singularities in Epidemic Models of Rupture, Earthquakes, and Starquakes

2001/12/31 by D. Sornette, Didier Sornette, Agnès Helmstetter +1 · 5 citations
Earth and Planetary Sciences · Economics, Econometrics and Finance · Physics and Astronomy · #Complex Systems and Time Series Analysis #Earthquake Detection and Analysis #cond-mat.stat-mech #earthquake and tectonic studies

paper · pdf · doi:10.1103/physrevlett.89.158501

published as Physical Review Letters 89 (15) 158501 (20 Sept 2002) · Revtex document of 4 pages including 1 eps figure

openalex publication_date 2002/09/20 · arxiv created 2003/08/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a new kind of critical stochastic finite-time singularity, relying on the interplay between long-memory and extreme fluctuations. We illustrate it on the well-established epidemic-type aftershock model for aftershocks, based solely on the most solidly documented stylized facts of seismicity (clustering in space and in time and power law Gutenberg-Richter distribution of earthquake energies). This theory accounts for the main observations (power law acceleration and discrete scale invariant structure) of critical rupture of heterogeneous materials, of the largest sequence of starquakes ever attributed to a neutron star, as well as of earthquake sequences.

Citations

• Statistical Models for Earthquake Occurrences and Residual Analysis for Point Processes

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