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

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.

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mainshock aftershock aftershock aftershock aftershock aftershock aftershock aftershock aftershock aftershock aftershock

• Earthquakes in southern California from 1 January 1984 to 31

December 2002.

• Number of earthquakes is 6190.
• m ≥ 3 (magnitude cutoff 𝑛𝑑 = 3)

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Data

𝜇 𝑦, 𝑢 = 𝜇0 +

𝑢𝑗<𝑢

𝜇𝑗(𝑦, 𝑢) 𝜇 𝑦, 𝑢 : observed (dressed) seismicity rate density 𝜇0 : background seismicity rate density 𝜇𝑗 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.

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Method

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𝑥𝑗,𝑘 = 𝛽𝑘𝜇 𝑦𝑗 − 𝑦𝑘 , 𝑢 − 𝑢𝑗, 𝑛𝑗 (𝑢𝑗 < 𝑢𝑘) (𝑓𝑚𝑡𝑓) 𝑥0,𝑘 = 𝛽𝑘𝜇0 The normalization coefficients 𝛽𝑘 such that

𝑗=1 𝑘−1

𝑥𝑗,𝑘 + 𝑥0,𝑘 = 1 𝜇 ∆𝑦 , ∆𝑢, 𝑛 =

1 𝑂𝑛×𝜀𝑢×𝑇( ∆𝑦 ,𝜀𝑠) 𝑗,𝑘∈𝐵 𝑥𝑗,𝑘

where A is the set of pairs such that 𝑦𝑗 − 𝑦𝑘 = ∆𝑦 ± 𝜀𝑠, 𝑛𝑗 = 𝑛 ± 𝜀𝑛, 𝑢𝑗 − 𝑢𝑘 = 𝑢 ± 𝜀𝑢 𝜇0 = 1 𝑈 × 𝑇

𝑘=1 𝑂

𝑥0, 𝑘

1. 2.

These two steps are iterated until convergence is reached.

i : mainshock j : any shocks 0: background 𝜇0: Background seismicity rate density 𝜇𝑗 : Bare seismic rate density

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The rates decayed more slowly when considering the full cascade including indirectly triggered aftershocks.

Result

• Fig. 1 - A
• Fig. 1 - C

Omori –Utsu decay 𝜇𝑢 𝑢, 𝑛 = 𝜓𝑢−𝑞

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Dressed p values were 0.2~0.4 smaller than the bare p values.

• Fig. 2 - A

Omori –Utsu decay 𝜇𝑢 𝑢, 𝑛 = 𝜓𝑢−𝑞

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𝑏 = 0.60 ± 0.07 (bare) 𝑏 = 0.66 ± 0.04 (dressed)

• Fig. 2 - B

Omori –Utsu decay 𝜇𝑢 𝑢, 𝑛 = 𝜓𝑢−𝑞 Productivity parameter : 𝜓~10𝑏𝑛

Nearly the same

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The dressed kernels (continuous lines) are compared to the bare ones (color dashed lines). The densities ls have been vertically shifted for clarity.

• Fig. 1 - B
• Fig. 1 - D

𝜇𝑡 𝑦, 𝑧, 𝑛 ~ 1 + 𝑠 𝑀 −3 (based on Utsu and Seki)

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6.6km 0.25km 𝑀~100.43𝑛 (close to the 100.5𝑛 dependence expected for the rupture length of small to intermediatesize earthquakes)

Due to the limited resolution on the relative hypocenter positions (~400m)

• Fig. 2 - D
• Fig. 3 - A

𝜇𝑡 𝑦, 𝑧, 𝑛 ~ 1 + 𝑠 𝑀 −3

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(i) Calculating, for all the mainshocks, the delays after which the last direct and last indirect aftershocks occurred (ii) Averaging these delays conditioned

• n the magnitude of the mainshock
• Bare : independent of the mainshock magnitude,

short (on the order of 10 to 15 days for m ≥ 3 aftershocks).

• Dressed : duration ~100.35𝑛
• 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.

• Fig. 2 - C

Durations of aftershocks

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𝐼 = −0.01 ± 0.03 (bare) 𝐼 = −0.19 ± 0.04 (dressed)

• Fig. 2 - E
• Fig. 2 - F

𝐼 = 0.08 ± 0.02 (bare) 𝐼 = −0.21 ± 0.06 (dressed)

𝑠~𝜀𝑢𝐼 𝑠/𝑀~𝜀𝑢𝐼

Mean epicentral distance vs time following the mainshock

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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.

𝑐 = 1.05 ± 0.01 (all earthquakes) 𝑐 = 1.06 ± 0.03 (background earthquakes)

• Fig. 3 - B

Gutenberg-Richter laws

Nearly the same

・0.17 / day 19.5% of the total rate for 𝑛𝑑 = 3 (𝑛𝑑 = 3 consistent with other studies (18%~24%, non parametric method)) 32% : 𝑛𝑑 = 4 68% : 𝑛𝑑 = 5 A larger cutoff causes the removal of small triggering earthquakes. The 19.5% proportion at 𝑛𝑑 = 3 is therefore an

• verestimation of the actual background contribution.

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Background rate

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Latitude Latitude Latitude Latitude Background m ≥ 3 earthquakes

2000 1500 1000 500

• identifying an underlying

Poisson process

• Removing the aftershock

clusters following large main shocks (1992 landers and 1999 Hector Mine)

• Fig. 4

• The statistical dependence between earthquakes increases

when decreasing the value of mc, so that the remaining set

• f declustered mainshocks heavily depends on 𝑛𝑑.
• 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 𝑛𝑑, the direct triggering effect due to large

mainshocks could potentially be even further reduced relative to direct triggering by small shocks.

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