Long-range Automaton Models of Earthquakes: Power-law Accelerations, Correlation Evolution, and Mode-switching

Abstract

-We introduce a conceptual model for the in-plane physics of an earthquake fault. The model employs cellular automaton techniques to simulate tectonic loading, earthquake rupture, and strain redistribution. The impact of a hypothetical crustal elastodynamic Green's function is approximated by a long-range strain redistribution law with a r Àp dependance. We investigate the influence of the effective elastodynamic interaction range upon the dynamical behaviour of the model by conducting experiments with different values of the exponent (p). The results indicate that this model has two distinct, stable modes of behaviour. The first mode produces a characteristic earthquake distribution with moderate to large events preceeded by an interval of time in which the rate of energy release accelerates. A correlation function analysis reveals that accelerating sequences are associated with a systematic, global evolution of strain energy correlations within the system. The second stable mode produces Gutenberg-Richter statistics, with near-linear energy release and no significant global correlation evolution. A model with effectively short-range interactions preferentially displays Gutenberg-Richter behaviour. However, models with long-range interactions appear to switch between the characteristic and GR modes. As the range of elastodynamic interactions is increased, characteristic behaviour begins to dominate GR behaviour. These models demonstrate that evolution of strain energy correlations may occur within systems with a fixed elastodynamic interaction range. Supposing that similar mode-switching dynamical behaviour occurs within earthquake faults then intermediate-term forecasting of large earthquakes may be feasible for some earthquakes but not for others, in alignment with certain empirical seismological observations. Further numerical investigation of dynamical models of this type may lead to advances in earthquake forecasting research and theoretical seismology.

Stress Correlation Function Evolution in Lattice Solid Elasto-dynamic Models of Shear and Fracture Zones and Earthquake Prediction

“…Recent observations of growing correlation lengths in seismicity data prior to large earthquakes provide additional support for the critical point hypothesis for earthquakes (ZOELLER et al, 2001). Studies of different classes of CA models indicate that the stress field may evolve like that of critical point system or selforganized critical systems, depending on the rules used in the CA model to approximate the rupture and stress redistribution processes (SAMMIS and SMITH, 1999;WEATHERLEY et al, 2000WEATHERLEY et al, , 2002. Here we study the evolution in the stress correlation function in a physically based numerical model which accurately simulates the elasto-dynamics of a stress transfer and rupture in simplified 2-D systems (MORA and PLACE, 1994;PLACE and MORA, 1999).…”

Segmentation of fault networks determined from spatial clustering of earthquakes

“…It is also necessary to clearly understand the mechanical interactions within a given fault network, in order to possibly achieve earthquake prediction or forecasting with a reasonable accuracy, both in the space and time dimensions. On more fundamental grounds, understanding the relationships between faults (or more generally earthquake generating cluster centers) at different scales can help to develop a metatheory based on the renormalization group approach [ Wilson , 1975; Allégre et al , 1982] to advance on the understanding and modeling of seismicity and rupture processes as a critical phenomenon [ Sornette , 2006; Bowman et al , 1998; Weatherley et al , 2002], as the size of an upcoming event may be correlated with the range of scales over which earthquake clustering properties change collectively (thus yielding a measure of the correlation length).…”

Search for direct empirical spatial correlation signatures of the critical triggering earthquake model

“…More recently, using a cellular automaton model, Weatherly et al (2002) showed that the overall behaviour of seismicity depends strongly on the exponent of the elastic Green's function (that we took equal to 3, that is, corresponding to a rather short interaction range). In particular, they showed that for this value of 3 for the exponent they did not observe any critical behaviour before a large event.…”