Exploring aftershock properties with depth

Transcription

1 Exploring aftershock properties with depth Peter Shebalin 1,2, Clément Narteau 2, Matthias Holschneider 3 1 International Institute of Earthquake Prediction Theory and Mathematical Geophysics, Moscow, Russia shebalin@mitp.ru 2 Institut de Physique du Globe de Paris, France narteau@ipgp.fr 3 Institutes of Applied and Industrial Mathematics, Universität Potsdam, Germany matthias.holschneider@googl .com

2 Strong dependence of c-value on depth (to avoid focal mechanism effect we consider vertical strike-slip faults in California) 1/(t+c) 1/(t+c) p min 1.0 c (day) p sec

3 Main shock depths / aftershock depths: no big difference 20 Mainsocks depth, km 20 Aftershocks depth, km

4 Les zones 20-km large le long les failles verticales strike-slip en Californie l

5 c-value-depth in different segments (a) (b) (c) (d) Northern San Andreas Calaveras Bartlett Spring Hayward l (e) (f) (g) (h) Maacama San Andreas Creeping Section Southern San Andreas Elsinore (i) (j) (k) (l) San Jacinto Imperial Landers Laguna Salada

6 How to avoid the possible effect of non-complete catalog? We use the same rules as in [Narteau et al., 2009] 1) We consider the interval from 10 seconds to 24 hours 2) Limited main shock range: from 2.8 to 4.0 3) Limited aftershock magnitude range: from 1.8 to 2.8 l 4) Simple rule to select aftershocks: hypocentral distance <4km from mainshock (results do not depend much on this choice) 5) Secondary aftershock sequences (after large aftershocks) are disregarded 6) Séquences containing events with magnitude larger than mainshockqui are disregarded. Deselection according 5 and 6 <3% of events We construct stacks of events according the mainshock depths (2 km sliding window). Minimum number of events in a stack - 50

7 Bayesian analysis: difference is statistically significant h=5-7 km l h=10-12 km

8 The delay of the power-law decay (c-value) depends on stress. Our basic hypothesis band Limited Power Law (LPL) model. (Narteau et al., JGR, 2002) c t b 1/λ b Aftershock The distribution temporal of stresses distribution in and is near a the main superposition shock fault is highly of a large heterogeneous. number of exponents. We assume uniform distribution limited by some value σ b. The distribution of stresses in and near the main shock We suppose fault is the highly aftershock heterogeneous. rate at stress Short σ is equal: exponents occur λ=λ high o exp(σ/σ stress 0 sub-areas, -1) (1) long exponents in low stress sub-areas. Each asperity produces only one earthquake, accordingly the number of aftershocks at stress σ is δn(t, σ)/δt=-λ(σ) Ν(t,σ) (2) Faster So at each than specific power-law stress decay the at decay the end is exponential of the sequence is caused by a deficit of long exponents. Integrating exponential One of possible N(t,σ) interpretations obtained from is eq. (1) over all σ, we have the total rate of aftershocks: Λ(t)=A(γ(p,λ In this talk we consider b t) - γ(p,λ aftershock a t))/t sequences p (3) Where γ(p,x) incomplete Gamma function; over short times. It is natural to use differential stress σ=σ 1 -σ 3

9 LPL vs Omori-Utsu LPL! Λ! =!!!!!!!!!!"!=!!!,!!!!!!,!!!,!!!!!!!! =!!!!!!!!!!,!! =!(!! ),!!! =!(!! )!!!!!!,! =!!!!!!!!"!"!Incomplete!Gamma!function!! Omori-Utsu Λ! =! (! +!)!! p = 1!!!!!!!!! = 0!!!!!c! 1/!!! c(p=1) estimated in (t s,t e ) è <log t> - (log t e log t s )/2

10 Geometric mean instead of the c-value c(p=1) è <log t> - (log t e log t s )/2 <log10(t)> 0.5log10(tstop/tstart) <log10(t)> 0.5log10(tstop/tstart) <log10(t)>=0.371log10(c) c(p=1), days

11 c(p=1) è <log t> - (log t e log t s )/2 (a) (b) (c) (d) Northern San Andreas Calaveras Bartlett Spring Hayward Northern San Andreas Calaveras Bartlett Spring Hayward

12 c(p=1) è <log t> - (log t e log t s )/2 (e) (f) (g) (h) Maacama San Andreas Creeping Section Southern San Andreas Elsinore Maacama San Andreas Creeping Section Southern San Andreas Elsinore

13 c(p=1) è <log t> - (log t e log t s )/2 (i) (j) (k) (l) San Jacinto Imperial Landers Laguna Salada San Jacinto Imperial Landers Laguna Salada

14 Effect of magnitudes? (c-value may depend both on main shock and aftershock magnitudes) Stacks according to the main shock magnitude Stacks according to the aftershock magnitude Average magnitudes main shocks aftershocks No effect!!! Magnitudes slightly decrease at 5-15 km C-value should not decrease, but it does

15 Interpretation (depths 5 to 15 km) τ > τ r =µσ n + τ 0 (1) For strike-slip faults σ 2 is vertical; we assume [Sibson, 1974] σ 2 =(σ 1 +σ 3 )/2, τ 0 =0, and find minimal value of R=σ 1 /σ 3, required to initiate sliding: then the sliding initiation criterion is: R =[(1+µ 2 ) 1/2 -µ] -2 (2) (σ 1 -σ 3 ) > 2(R -1)/(R +1) ρgh (1-γ) (3) ρgh (1-γ) = ρgh P overburden pressure

16 Interpretation (depths 5 to 15 km) (3) gives an upper limit σ b of the distribution of σ=σ 1 -σ 3 in the aftershock zone (LPL model): σ b =2(R -1)/(R +1) ρgh (1-γ), R =[(1+µ 2 ) 1/2 -µ] -2 From c(p=1) 1/λ b and λ b =λ 0 exp(σ b /σ 0-1), assuming µ and γ not depending of h, and considering gradient of log(c), we obtain: -d log(c)/d h = const 1 + const 2 (R -1)/(R +1) h The gradient of log(c), up to a constant, gives an estimate of µ. One landmark is sufficient to know the constant.

17 Estimating µ from gradient of log(c)

18 Problem of interpretation: positive gradient of log(c) for depths 0 5 km Zone of stable friction (0-5 km) velocity strengthening??? [Scholz, 1998] Number of earthquakes τ = [µ 0 +a log(v/v 0 )+b log(v 0 θ/l)] σ at steady state: τ = [µ 0 +(a-b) log(v/v 0 )] σ From: C.Scholz. Earthquakes and friction laws. Nature. 391, 38-42, 1998.

19 Problem of interpretation: positive gradient of log(c) for depths 0 5 km Role of fluids? Geysers Salton Sea (a) (b) (c) 1 Geysers Salton Sea Geothermal Field 1 Mammoth lakes Mammoth Lakes 1e Mainsocks depth, km 1e Drop of the normal stress (injections of fluides and vapor).

20 Conclusions The delay of the power-law decay of aftershock sequences is not zero This delay is connected to stress field: generally smaller delay (smaller c-value of Omori-Utsu law) corresponds to larger share stresses l Calibration of the c-value stress relation needs more detailed modeling C-value estimates may be replaced by geometric average of elapse times, normalized by time window