Modeling seismic swarms triggered by aseismic transients Andrea L. Llenos, Jeffrey J. McGuire, Yoshihiko Ogata (June 26 th , Uemura Kansuke)
ETAS model Cumulative function: cumulative number of events predicted by ETAS Transformed time: π π = Ξ π’ π t i : occurrence time of i th event
Usual EQ and swarm From 2005 Obsidian Buttes catalog Cumulative Number of Events Extrapolate to swarm activity Calculate ETAS parameters from Usual EQ Transformed Time Ξ( t i ) Transformed Time Ξ( t i )
Usual EQ and swarm From 2005 Kilauea catalog
Usual EQ and swarm 2002&2007 Boso swarms
ETAS model and swarms β’ ETAS lacks a quantitative relationship between seismicity rate and stress/stressing rate. β’ Swarms = EQs which do not obey Omoriβs law Swarms = anomaly of aseismic stressing rate. β’ Rate-state model of Dieterich(1994) can treat Stress perturbations due to β¦ change in stressing rate. β’ magma intrusions β’ dike intrusions β’ movements of volatiles(e.g., CO2) DIETERICH + ETAS β’ aqueous fluid flow = [ETAS with stressing rate ] model? β’ slow slips
Obsidian Buttes γ» Strike slip γ» Slow slip Kilauea γ» South flank of Kilauea Volcano γ» Slow earthquake Boso γ» Recurring slow slip
Swarms driven by slow slip β’ Slow slip = geodetic data Swarms = seismic data β’ Energy release β’ Slow slip: Mw β 6.5 β Swarm : Mw β 4 (repeating slow EQ at offshore of central Honshu; Ozawa et al., 2007) β’ Slow slip: Mw β 5.7 β Swarm : Mw β 5.5 (strike-slip fault in the Salton Trough; Lohman and McGuire, 2007) Swarms: seismicity that cover unusually large area for their cumulative seismic moment. (Vidale and Shearer, 2006)
Combining the ETAS and rate-state model β’ ETAS lacks a quantitative relationship between seismicity rate and stress/stressing-rate. β’ Swarms = EQs which do not obey Omoriβs law Swarms = anomaly of aseismic stressing rate. β’ Rate-state model of Dieterich(1994) can handle temporal change in stressing rate. DIETERICH + ETAS = [ETAS with stressing rate ] model?
αΆ αΆ αΆ Rate-state model by Dieterich(1994) Reference seismicity rate Seismicity rate State variable Reference stressing rate Stressing rate π π΅π π’ , 1 π + π·π β If S, AΟ : constant β πΏ = π΅π characteristic relaxation time: π’ π = π
Rate-state model by Dieterich(1994) Ι€ Stress With EQ without EQ Stress rate Seismicity rate long β short relaxation time t a
Rate-state model by Dieterich(1994) For sudden change of stress ΞS π under constant stressing rate αΆ
αΆ αΆ For stress perturbation of same magnitude: ΞS= 0.1MPa, (and assuming that background stressing-rate is stationary) π π π = Aπ = 0.01 MPa, αΆ Ξ€ π π = 0.1 MPa yr , Ξπ = 0.1 πππ
αΆ αΆ π (number of aftershock) = π π (bg seis. along the aftershock seq.) π (stressingβrate) = (bg stressingβrate ) π π Higher stressing rate brings β More aftershocks β Higher K-value!!
Combining the ETAS and rate-state models Ξ± : is related to spatial extent of a stress step / independent of stressing rate. p : is essentially 1 from eq.5(below). (Though,there said to be influence of other factors, such as heterogeneity in temperature/heat flow or structure on fault, which is independent of stressing rate)
Combining the ETAS and rate-state models c : can be analytically derived from RSF-model. However, c can not be clearly obtained from observation, so it is not worthwhile discussing stressing rate dependence of c. K : relationship is unclear, but rate-state model predicts K increases with stressing rate. ΞΌ : relationship is unclear, though rate-state model predicts that bg seismicity rate depends on stressing rate.
Rate- state model predicts that β¦ Ξ± is independent of stressing rate. p is essentially 1 c is not worth discussing , as it cannot be well determined by observation. K increases with stressing rate, though relationship is unclear. ΞΌ depends on stressing rate, though relationship is unclear.
Adopting ETAS to swarm Poor quality of fit may be because ΞΌ was treated as constant, and it suggest stressing rate is time-variable.
Parameters of Obsidian Buttes Before & during swarm Event K ΞΌ Ξ± p c Boso 0.13 0.022 0.56 1.11 0.096 (2002) 0.07 2.09 0.9 1.0 0.0005 Kilauea 0.28 0.16 1.24 1.21 0.002 (2005) 0.96 0.89 0.61 0.92 0.003 Obsidia 0.61 0.031 0.88 1.1 0.001 n Buttes 1.4 225 1.05 1.0 0.001 Boso 0.20 0.013 0.55 0.88 0.0004 (2007) 0.61 2.4 1.37 1.0 0.0008 K does not increase so muchβ¦ Γ 10-1000 Γο½ 2 No change ΓοΌ - οΌ No change
Is K stressing-rate dependent? Helmstetter and Sornette, 2003 n=Kb/(b- Ξ± ) From geodetic data, stressing- rate was estimated to be γ¬γ¬γ¬ αΆ π ~ 1000 Γ αΆ π ππ during 2005 Obsidian swarms. πΏ ~ 1000 Γ πΏ π£π‘π£ππ ? ? ?
Rate-state prediction and actual aftershocks Rate-state prediction π = 1000 Γ αΆ For αΆ π ππ Usual EQ Actual M5.1 event during swarm
αΆ αΆ αΆ Contribution of AΟβ¦? Compare aftershock productivity N of ΞS = 1MPa Under two case: N1: bg stressing rate ( αΆ π ππ = 0.2MPa/yr) γ π has changed to 10 1 ~10 4 Γ αΆ π ππ N2: 3 days after αΆ π΅π 2005 Obsidian Buttes M5.1 π’ π, ππ = π ππ occurred 3 days after AΟ = 10 -3 MPa β t a = 1.8day stressing rate change. AΟ = 1 MPa β t a = 1800days β1 π΅π π π’ π (π΅π, αΆ π) = 1800days Γ 1MPa Γ π ππ
αΆ αΆ αΆ αΆ αΆ αΆ β1 π΅π π Contribution of AΟβ¦? π’ π π΅π, αΆ π = 1800days Γ 1MPa Γ β 3days π ππ Laboratory Experiment Depth of 4km π = 10 4 αΆ π ππ π = 10 3 αΆ π ππ Aftershock productivity Aftershock productivity π = 10 2 αΆ π ππ Increace of Increace of π = 10 1 αΆ π ππ AΟ [Mpa] AΟ [Mpa] From seismic observation
In short, During swarm, Substantial Increase of seismicity ( ΞΌ ) β’ Small increase in aftershock (K) β’ was observed, but those two cannot happen at once in rate-state model
CORRECTION OF ETAS MODEL
Combining the ETAS and rate-state model β’ ETAS does not explicitly include information of stress. β’ Swarms = anomaly of tectonic stressing rate. β’ Rate-state model of Dieterich(1994) can treat change in stressing rate. DIETERICH + ETAS = [ETAS + stressing rate ] model
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