Aseismic slip in earthquake nucleation and self-similarity: evidence from Parkfield, California

1. Aseismic slip in earthquake nucleation and self-similarity: evidence from Parkfield, California Mortiz Heimpel, Peter Malin (1998)

2. D S Main findings • Detecting limit (point D) can be different from point S, which represents earthquake magnitude deviating from self-similar rupture. • By examine the effect of background noise on earthquake event detection, the detecting limit at Parkfield is found to be M = 0.3 (point D). • Based on statistical mechanics, they claim point S corresponds to the critical earthquake nucleation size, which is M = 0.9 (point S) in Parkfield.

3. Detecting limit D: stations dots: events 10 km Parkfield Downhole Digital Seismic Network (DDSN) array.

4. Detecting limit • Assumptions: • Earthquake are randomly distributed in time. • The seismic noise level due to wind and humanity activity is greater during the day than at night. Near the detecting limit, the events during the day have a large probability to be missed than at night. Rydelek and Sacks (1989)

5. Detecting limit – Schuster’s test Day-to-night noise modulation method (Schuster’s test): Step 1: Put events into different sub-catalogues according to their magnitude. Step 2: In each catalogue, each earthquake is represented by a unit vector, with direction given by the time in local 24 hour clock of an event. Step 3: A catalogue of events produces a ‘walk’ in phase space. If PR> 5%, the catalogue is complete (above detecting limit). If PR < 5%, the catalogue is incomplete (below detecting limit).

6. Detecting limit • At Parkfield, the detecting limit is found to be M = 0.3 • For those incomplete catalogue, the ‘walk’ deviates toward to the night direction, consistent with assumption 2.

7. D S Physical interpretation of point S Gutenburg-Ritcher Relation : For self-similar rupture, the magnitude-frequency relation satisfies: log N ~ a – b M, b ≈ 1 b = 1

8. K  One interpretation - critical nucleation length Lc (1 of 2) Sliding is stable if: For spring-slider model governed by the rate and state friction law: Sliding is unstable (stick-slip) if: In continuum elastic model, the effective spring stiffness K: length of slip region It implies that for unstable sliding (or seismic event): Lc is the critical nucleation length

9. log N Mv M Critical nucleation length Lc (2 of 2). If slip region L< Lc, Slip is slow and quasi-static, almost without sesimic radiation (no earthquake). If slip region L> Lc, Slip transits to dynamic rupture with significant seismic radiation (earthquake). Theoretically, we expect that earthquake has a minimum sizeLc.. There is no event with rupture region smaller than Lc. But inreality, m, Lc and s are not homogenous, therefore Lc varies in a wide range, and we cannot observe a sudden cut-off in magnitude-frequency map.

10. Interpretation of point S in this paper (1 of 2). Asperity failure model (Heimpel 1996): Fault surface is defined as consisting of a large number of asperties. Rupture area grows by sequentially breaking asperities at rupture boundary. Probability of asperity failure: sis the shear stress at this asperity. From facture mechanics, at rupture boundary: K is stress intensity factor. And q is stress drop, assuming constant Heimpel (1996) It relates p(s) with rupture area A, and thus earthquake moment Mo.

11. D earthquake nucleation area nucleation magnitude S b = 1 Interpretation of point S in this paper (2 of 2). After mathematical manipulations (details in Heimpel (1996)), the probability of a rupture with area > A: The model is best fit to the data with nucleation magnitude: Mv = 0.9 Comment: its derivation is not very convincing! e.g. WA(A = Av) = 0.5

12. Remarks on Mv “Nucleation area” in Parkfield: Earthquake moment Earthquake nucleation length: If using rate and state friction: Assume h= 1,m= 30 GPa,s= 100 MPa and (b - a) = 0.005, the characteristic slip distance Dc:

13. D ?