Accelerating Precursory Activity in Statistical Fractal Automata

1. Accelerating Precursory Activityin Statistical Fractal Automata Dion Weatherley and Peter Mora QUAKES, Univ. of Qld., Australia.

2. Outline • Model Description • Results from a parameter space study • Event size scaling • Evolution of mean stress • Stress field evolution • Accelerating precursory activity • Summary of results • Effect of varying the fractal dimension • Conclusions and questions

3. Model Description • Uniform rectangular grid of cells • Each cell has two properties • Constant, scalar Strength • Variable, scale Stress • Uniform loading of all cells • Cell failure when a cell’s stress exceeds its strength • Nearest Neighbour stress redistribution • Periodic boundary conditions

4. Event size scaling

5. Mean Stress Evolution • models with a char. event distribution (A) • relatively low time-averaged mean stress • large, saw-tooth fluctuations • models with a roll-over distribution (D) • high time-averaged mean stress • small, irregular fluctuations • models with high dissipation (C) • near-constant mean stress • models with GR-scaling (D) • correspond with drop in time-averaged mean stress • mark a transition from large to small fluctuations

6. Snapshots of Stress Evolution

7. Accelerating Precursory Activity • Select the 100 largest events in each simulation for analysis. • Define Tf as the time of the large event. • Vary To and m within a range. • Compute A,B via least squares fit. • Compare power-law with a linear fit. • Select best power-law fit for each event. • Count number of good power-law fits for each simulation = fit probability.

8. Summary of Results • Accelerating Precursory Activity in models with: • overabundance of larger events • relatively low time-averaged mean stress • large, saw-tooth fluctuations in mean stress • relatively smooth stress field over broad regions • Constant rate of activity in models with: • an under-abundance of large events • high, near-constant mean stress • stress field dominated by small-scale heterogeneity • Evidence for a distinct transition between two modes of activity • GR-scaling only for simulations along a line through parameter space • change in character of mean stress fluctuations across this line • change in stress field heterogeneity across this line • probability of accelerating precursory activity drops to near-zero at this line

9. Effect of varying the Fractal Dimension of cell Strengths D=1.875 D=2.625 D=2.250

10. Conclusions and some Questions • Accelerating Precursory Activity occurs in models in which: • there is an overabundance of larger events • these large events perturb the system from a state of high stress • stress redistribution smoothes the stress field within failed region • long-range clustering of cell strengths (smaller fractal dimension) • Stress field heterogeneity apparently a factor determining the mode of activity • relatively smooth stress field corresponds with accelerating activity • a stress field dominated by small-scale heterogeneity corresponds with a constant rate of activity • Some questions to motivate discussions • Is the transition line a SPINODAL i.e. a line of Critical Points? • How might one formulate a mathematical description for these models? • Are these models any more or less appropriate as earthquake analogues than pseudo-spinodal or SOC models?