Magnitude-dependent chaos in earthquakes

Large earthquakes are among the most devasting natural events and the most serious sources of risk in several regions worldwide. Earthquakes are not random phenomena; however, they usually show highly chaotic behaviors, making a reliable mid-term forecast challenging. Then, a deeper understanding of their underlying mechanisms is needed. Here, we develop a mathematical framework to incorporate multiscale physics, capable of describing both deterministic and chaotic systems, to model earthquake dynamics. Our results suggest that its sensitivity from initial and boundary conditions is inversely proportional to earthquake magnitude, seismic events being the outcome of a long-lasting process of crustal destabilization operated by tectonic stress over different spatial scales. This implies that large events may exhibit reduced chaotic behavior compared to smaller earthquakes. To validate this hypothesis, we conducted numerical simulations with heterogeneous fault conditions (as in Venegas-Aravena et al., 2023; 2024). The results indicate that large earthquakes, usually occurring in regions with higher residual energy, are less susceptible to change their final magnitude due to small variations in fault conditions. Moreover, poorly chaotic behaviors appear to be linked to lower b-values, i.e., the exponent of the frequency-magnitude distribution of earthquakes. This suggests that the higher variability in earthquake magnitudes associated with larger b-values may be indicative of structural complexity or strongly heterogeneous stress conditions. We compare the statistical properties of our numerical simulations with real earthquake data. The statistical similarities observed between the simulated and natural earthquakes support the hypothesis that large seismic events may be less chaotic than smaller ones. References Venegas-Aravena P.; 2023: Geological earthquake simulations generated by kinematic heterogeneous energy-based method: Self-arrested ruptures and asperity criterion. Open Geosci. 15(1):1-20. https://doi.org/10.1515/geo-2022-0522. Venegas-Aravena P., Crempien J.G.F., and Archuleta RJ.; 2024: Fractal Spatial Distributions of Initial Shear Stress and Frictional Properties on Faults and Their Impact on Dynamic Earthquake Rupture. Bull. Seismol. Soc. Am. 114(3): 1444–1465. https://doi.org/10.1785/0120230123.