Extending Earthquakes Reach Through Cascading David Marsan and - PowerPoint PPT Presentation

地震発生論セミナー Extending Earthquakes’ Reach Through Cascading David Marsan and Olivier Lengliné Kawai lab M1; Lina Yamaya 1

地震発生論セミナー Research question If we can separate aftershocks that were directly triggered by the mainshock, the physical mechanism that causes direct triggering (static or dynamic stress changes, fluid flow, afterslip, etc.) can be studied. mainshock aftershock aftershock aftershock aftershock aftershock aftershock aftershock aftershock aftershock aftershock 2

地震発生論セミナー Data • Earthquakes in southern California from 1 January 1984 to 31 December 2002. • Number of earthquakes is 6190. • m ≥ 3 (magnitude cutoff 𝑛 𝑑 = 3) 3

地震発生論セミナー Method 𝜇 𝑦, 𝑢 = 𝜇 0 + 𝜇 𝑗 (𝑦, 𝑢) 𝑢 𝑗 <𝑢 𝜇 𝑦, 𝑢 : observed (dressed) seismicity rate density 𝜇 0 : background seismicity rate density 𝜇 𝑗 𝑦, 𝑢 : bare contribution of earthquake 𝑗 (representing the aftershocks directly caused by earthquake 𝑗 ) They assume only (i) The triggering process is linear. (ii) A mean-field response to the occurrence can be estimated that depends only on its magnitude. 4

地震発生論セミナー 1. 𝑥 𝑗,𝑘 = 𝛽 𝑘 𝜇 𝑦 𝑗 − 𝑦 𝑘 , 𝑢 − 𝑢 𝑗 , 𝑛 𝑗 (𝑢 𝑗 < 𝑢 𝑘 ) i : mainshock j : any shocks 0 (𝑓𝑚𝑡𝑓) 0: background 𝑥 0,𝑘 = 𝛽 𝑘 𝜇 0 𝜇 0 : Background seismicity rate density The normalization coefficients 𝛽 𝑘 such that 𝜇 𝑗 : Bare seismic rate density 𝑘−1 𝑥 𝑗,𝑘 + 𝑥 0,𝑘 = 1 𝑗=1 These two steps are iterated 1 2. 𝑂 𝑛 ×𝜀𝑢×𝑇( ∆𝑦 ,𝜀𝑠) 𝑗,𝑘∈𝐵 𝑥 𝑗,𝑘 𝜇 ∆𝑦 , ∆𝑢, 𝑛 = until convergence where A is the set of pairs such that is reached. 𝑦 𝑗 − 𝑦 𝑘 = ∆𝑦 ± 𝜀𝑠, 𝑛 𝑗 = 𝑛 ± 𝜀𝑛, 𝑢 𝑗 − 𝑢 𝑘 = 𝑢 ± 𝜀𝑢 𝑂 1 𝜇 0 = 𝑈 × 𝑇 𝑥 0 , 𝑘 𝑘=1 5

地震発生論セミナー Result Omori – Utsu decay 𝜇 𝑢 𝑢, 𝑛 = 𝜓𝑢 −𝑞 Fig. 1 - A Fig. 1 - C The rates decayed more slowly when considering the full cascade including indirectly triggered aftershocks. 6

地震発生論セミナー Omori – Utsu decay 𝜇 𝑢 𝑢, 𝑛 = 𝜓𝑢 −𝑞 Dressed p values were 0.2~0.4 smaller than the bare p values. Fig. 2 - A 7

地震発生論セミナー Omori – Utsu decay 𝜇 𝑢 𝑢, 𝑛 = 𝜓𝑢 −𝑞 Productivity parameter : 𝜓~10 𝑏𝑛 𝑏 = 0.60 ± 0.07 (bare) 𝑏 = 0.66 ± 0.04 (dressed) Nearly the same Fig. 2 - B 8

地震発生論セミナー 𝑠 𝑀 −3 (based on Utsu and Seki) 𝜇 𝑡 𝑦, 𝑧, 𝑛 ~ 1 + Fig. 1 - B Fig. 1 - D The dressed kernels (continuous lines) are compared to the bare ones (color dashed lines). The densities ls have been vertically shifted for clarity. 9

地震発生論セミナー 𝑠 𝑀 −3 𝜇 𝑡 𝑦, 𝑧, 𝑛 ~ 1 + Due to the limited resolution on the relative hypocenter positions (~400m) 6.6km 0.25km Fig. 2 - D Fig. 3 - A 𝑀~10 0.43𝑛 (close to the 10 0.5𝑛 dependence expected for the rupture length of small to intermediatesize earthquakes) 10

地震発生論セミナー Durations of aftershocks (i) Calculating, for all the mainshocks, the delays after which the last direct and last indirect aftershocks occurred (ii) Averaging these delays conditioned on the magnitude of the mainshock Fig. 2 - C • Bare : independent of the mainshock magnitude, short (on the order of 10 to 15 days for m ≥ 3 aftershocks ). • Dressed : duration ~10 0.35𝑛 • Short-lasting triggering mechanisms, acting at the time scale of a few days, could be the key process, along with the cascading effect, in controlling earthquake dynamics. 11

地震発生論セミナー Mean epicentral distance vs time following the mainshock 𝑠~𝜀𝑢 𝐼 𝑠/𝑀~𝜀𝑢 𝐼 Fig. 2 - E Fig. 2 - F 𝐼 = −0.01 ± 0.03 (bare) 𝐼 = 0.08 ± 0.02 (bare) 𝐼 = −0.19 ± 0.04 (dressed) 𝐼 = −0.21 ± 0.06 (dressed) 12

地震発生論セミナー Gutenberg-Richter laws Fig. 3 - B 𝑐 = 1.05 ± 0.01 (all earthquakes) 𝑐 = 1.06 ± 0.03 (background earthquakes) Nearly the same The dynamic rupture extent is not a priori controlled by the triggering mechanism (either previous earthquakes or aseismic processes such as tectonic loading) at work. 13

地震発生論セミナー Background rate ・ 0.17 / day 19.5% of the total rate for 𝑛 𝑑 = 3 ( 𝑛 𝑑 = 3 consistent with other studies (18%~24%, non parametric method)) 32% : 𝑛 𝑑 = 4 68% : 𝑛 𝑑 = 5 A larger cutoff causes the removal of small triggering earthquakes. The 19.5% proportion at 𝑛 𝑑 = 3 is therefore an overestimation of the actual background contribution. 14

地震発生論セミナー Latitude Latitude Latitude Latitude Fig. 4 2000 • identifying an underlying m ≥ 3 earthquakes Poisson process 1500 • Removing the aftershock Background 1000 clusters following large main 500 shocks (1992 landers and 0 1999 Hector Mine) 15

地震発生論セミナー • The statistical dependence between earthquakes increases when decreasing the value of mc, so that the remaining set of declustered mainshocks heavily depends on 𝑛 𝑑 . • Because of this cascading, the aftershock sequence initiated by a mainshock is substantially extended, mostly in time. • What appears at first as an aftershock cluster related to a well-identified mainshock is mostly caused by intermediate aftershocks. • When decreasing 𝑛 𝑑 , the direct triggering effect due to large mainshocks could potentially be even further reduced relative to direct triggering by small shocks. 16