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Improved Earthquake Forecasting Model Based on Long-term Memory in Earthquake
Yongwen Zhang, Dong Zhou, Jingfang Fan, Warner Marzocchi, Yosef Ashkenazy, Shlomo Havlin
TL;DR
Existing ETAS forecasting models do not reproduce important long-term memory characteristics found in earthquake catalogs. This paper generalizes ETAS with short- and long-term triggering mechanisms, reproducing observed memory in Italian and South California catalogs and significantly improving earthquake forecasting.
Problem
Existing earthquake forecasting models lack some central earthquake features, including observed long-term memory and crossover behavior in real catalogs.
Source: pp. 3–4Method
The paper modifies and generalizes ETAS by introducing short- and long-term triggering mechanisms through two productivity parameters.
Source: p. 4Results
The revised ETAS model accurately reproduces short- and long-term/distance memory in Italian and South California catalogs and significantly improves earthquake forecasting.
Source: pp. 2, 4Takeaways & Limitations
The revised ETAS formulation accounts for observed short- and long-term memory in the studied earthquake catalogs.
Source: pp. 2, 4Earthquakes may be almost unpredictable because their nature can be erratic.
Source: p. 3
Abstract
from arXiv · showhide
A prominent feature of earthquakes is their empirical laws including memory (clustering) in time and space. Several earthquake forecasting models, like the EpidemicType Aftershock Sequence (ETAS) model, were developed based on earthquake empirical laws. Yet, a recent study showed that the ETAS model fails in reproducing significant long-term memory characteristics found in real earthquake catalogs. Here we modify and generalize the ETAS model to include short- and long-term triggering mechanisms, to account for the short- and long-time memory (exponents) recently discovered in the data. Our generalized ETAS model reproduces accurately the short- and long-term/distance memory observed in the Italian and South California earthquake catalogs. The revised ETAS model is also found to significantly improve earthquake forecasting.
Data
The study uses Italian and South California earthquake catalogs with stated time spans and magnitude-completeness thresholds.
- The Italian catalog spans 1981–2017 and is complete for earthquakes above M0 = 3.0.Source: Data · p. 14
- Catalog completeness means that all events above the specified magnitude threshold are included.Source: Data · p. 14
- The South California catalog spans 1981–2018 and is complete for earthquakes above M0 = 2.031.Source: Data · p. 14
The revised ETAS Model
The revised ETAS model represents earthquake occurrence as a space-time stochastic process with background activity and triggering from prior events. It adds magnitude-dependent short- and long-term productivity while retaining temporal and spatial clustering mechanisms.
The revised ETAS Model
- The conditional rate λ combines background intensity with triggering contributions from prior earthquake events.The background term is µ(x, y), while historical events contribute through magnitude-, time-, and distance-dependent factors.Source: The revised ETAS Model · p. 14
- Two productivity parameters, α1 and α2 with α1 ≥ α2, encode the revised model’s crossover in triggering behavior.When α1 = α2, Eq. 2 reduces to the original ETAS model.Source: The revised ETAS Model · p. 15
- The revised model gives an earlier historical event a larger triggering rate when fewer than the crossover number of events separate it from the target event.Source: The revised ETAS Model · p. 15
- Temporal aftershock clustering uses the Omori law, whose parameters are c and p.Source: The revised ETAS Model · p. 15
- Spatial clustering uses a kernel whose scale ζ increases with the triggering earthquake’s magnitude through ζ = D exp[γm(Mi − M0)].The parameters q, D, and γm are estimated, and triggering distance therefore depends on the magnitude of the triggering event.Source: The revised ETAS Model · p. 15
- For Italy, ETAS2 uses A = 3.26, α1 = 2.0, α2 = 1.4, and h = 2 × 10^5, corresponding to a crossover number of 200 at M0 = 3.0.The original ETAS1 uses α1 = α2 = 1.5; other revised-model parameters are retained from the original specification.Source: The revised ETAS Model · p. 15