Long-range dependence in earthquake-moment release and implications for earthquake occurrence probability

Area of Science:

• Geophysics
• Complex Systems
• Statistical Seismology

Background:

• Mandelbrot's 1980s observation linked earthquakes to fractal self-similar sets.
• Investigating dynamical mechanisms for self-similarities in earthquake processes.
• Self-similar processes offer a convenient framework, invariant under space-time scaling.

Purpose of the Study:

• To demonstrate that long-range dependence is an inherent and universal feature of the seismic process.
• To analyze the space- and time-invariance of this feature.
• To develop a new probability model for earthquake occurrence incorporating long-range dependence.

Main Methods:

• Analysis of cumulative seismic moment series from Italy and worldwide.
• Application of Hurst's rescaled range (R/S) analysis.
• Development of a probability model allowing for dependent seismic events.

Main Results:

• Seismicity identified as a memory process with a Hurst exponent (H) of approximately 0.87.
• The Hurst exponent (H) is largely invariant across space and time, barring catalog incompleteness.
• Demonstration of universal long-range dependence in the seismic process.

Conclusions:

• Long-range dependence is a fundamental, universal characteristic of seismicity.
• Findings have significant implications for improving earthquake forecasting models.
• The developed probability model, unlike the Poisson model, accounts for dependent events and is transferable to other self-similar processes.