A Common Origin for Aftershocks, Foreshocks, and Multiplets
Karen R. Felzer1, Rachel E. Abercrombie2, G`ran Ekstr`m1
1Harvard University, 2Boston University Definitions of clustered seismicity
Aftershock Sequence
Large initial smaller subsequent earthquake earthquakes
Doublets or Multiplets
Earthquake(s) are similar in size. Max ∆M = 0.4, max ∆t = 2 days. (Lay and Kanamori, 1980; Wesnousky et al., 1986; Xu and Schwartz, 1993.)
Foreshock Sequence
small initial larger subsequent earthquake earthquake Do these distinctions indicate different physics? Objectives
Earthquake Statistics
Test predictions of the single mode triggering model
Test challenges to the single mode triggering model Single Mode Triggering Model
One earthquake triggers slip at the hypocenter of n future earthquakes, where n is proportional to the initial earthquake's area%10M
The triggered earthquakes grow to random magnitudes from the Gutenberg-Richter a-bM distribution (N=10 )
The triggered earthquakes may be smaller, the same size, or larger than the trigger Single Mode Triggering Predictions
Number of earthquakes -bM2 bM P(M2) % 10 triggered by M1%10 1
b(M -M ) P(M1 triggering M2) % 10 1 2
1. Regional aftershock and doublet rates should vary linearly with each other
2. Regional aftershock and foreshock rates should vary linearly with each other
b(M -M ) 3. N(M2 aftershocks) % 10 1 2
4. Larger foreshock more triggered earthquakes larger mainshock more probable Testing the predictions: counting clustered earthquakes
x aftershock one doublet epicenter two doublets
x = 2.5 x fault length t = 2 Days
event type min M1 min M2 M1 - M2 (∆M) Catalog doublet 6.4 6.0 -0.4#∆M#0.4 CMT & NEIC 1975-2002 aftershock 6.6 5.6 0.4#∆M#1.0
foreshock 5.6 5.7 ∆M< 0.0 Single Mode Triggering Prediction #1 Regional aftershock and doublet rates vary linearly with each other ✔
Aftershock rate vs. Doublet rate 0.14 Data points are 0.12 from:
The Kuriles 0.1 The Solomon Islands New Hebrides 0.08 The Phillipines predicted The Aleutians New Zealand 0.06 relationship Sumatra West Coast, N. America 0.04 Japan Doublets/mainshock Southern America r = 0.60 Mid-ocean Ridges 0.02 χ2 Tibet = 24.8 Italy 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Aftershocks/mainshock
t = 2 days x = 2.5 x fault length Single mode triggering prediction #2 Aftershock and foreshock rates vary with each other ✔
Aftershock Rate vs. Foreshock Rate 0.05 Data points
0.04 The Kuriles The Solomon Islands New Hebrides The Phillipines 0.03 predicted The Aleutians relationship New Zealand Sumatra West Coast, N. America 0.02 Japan Southern America Mid-ocean Ridges Foreshocks/mainshock 0.01 r = 0.46 Tibet χ2 = 18.4 Italy
0 0 0.1 0.2 0.3 0.4 Aftershock/mainshock
t = 2 days x = 2.5 x fault length Single mode triggering prediction #3 % b(Μ1 − Μ2) N(M2 aftershocks) 10 ✔ Aftershock magnitude distribution 100 "aftershocks" "foreshocks" 10-1
10-2 aftershock < aftershock > mainshock mainshock
10-3
Aftershocks/mainshock predicted 10-4 relationship
10-5 1.5 1 0.5 0 -0.5 -1 -1.5 -2 -2.5 -3 Mainshock ML - Aftershock ML (Μ1 − Μ2) California earthquakes, 1975-2001, M$2.2 (101,680 eqs) t = 2 days x = 2 x fault length Single mode triggering prediction #4
Larger individual foreshocks are more likely to trigger a large mainshock ✔
Foreshock ML vs. mainshocks/foreshock 10 0
predicted relationship -1 10 lsq best fit line
10 -2
10 -3 4.5 mainshocks/foreshock
$ -4 L 10 M "foreshocks" "aftershocks"
10 -5 2 2.5 3 3.5 4 4.5 5 5.5 6 foreshock ML
t = 2 days x = 2 x fault length Model Challenge #1 The Solomon Islands have too many doublets
Aftershock rate vs. Doublet rate Data points are 0.14 from:
The Kuriles 0.12 The Solomon Islands Solomon New Hebrides 0.1 Islands The Phillipines The Aleutians New Zealand 0.08 Sumatra predicted West Coast, N. America relationship Japan 0.06 Southern America Mid-ocean Ridges 0.04 Tibet Doublets/mainshock Italy r = 0.60 0.02 χ2 = 24.8 2 Earthquake Density 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Aftershocks/mainshock
region epicenters/50 km Test: Does the doublet rate in the Solomon Islands disprove Single Mode Triggering?
10,000 Monte Carlo Trials Input Output Number of mainshocks single mode Number of Aftershock rate triggering doublets Earthquake magnitude model randomly distribution produced
no. observed in % time expected from doublet magnitude Solomons random fluctuation M$6 6 38%
M$7 4 18%
Observed doublet rates in the Solomons are consistent with single mode triggering Model Challenge #2
Triggering cannot work small large
Implications of Challenge #2
Foreshocks occur because of stressing by the nucleation phase of the mainshock
Predictions of Challenge #2
Nucleation phase size should scale with mainshock magnitude
Mainshock magnitude should influence foreshock occurrence Test: Does mainshock size influence foreshocks?
Fraction of California mainshocks Mainshock ML vs. number of # # with largest foreshock 2.2#ML#4.5 foreshocks 2.2 ML 4.5 1 70 0.9 60 0.8 r = 0.0715 0.7 50 0.6 40 0.5 0.4 30 0.3 20 0.2 Number of foreshocks 10 fraction of mainshocks fraction 0.1 0 0 4.5 5 5.5 6 6.5 7 7.5 4.5 5 5.5 6 6.5 7 7.5 mainshock ML mainshock ML There is no statistical correlation found between mainshock size and foreshock magnitude or number Conclusions
Aftershock, doublet, and foreshock rates vary linearly with each other
The magnitudes of triggered earthquakes may be reproduced by chosing random values from the Gutenberg-Richter distribution
Foreshock size influences mainshock occurrence
Mainshock size does not influence foreshocks
Aftershocks, foreshocks, and doublets all result from a single physical triggering process