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1
Interevent triggering induced by
wastewater injection in Oklahoma and
southern Kansas
Kamran Karimi
Joern Davidsen
Department of
Physics & Astronomy
10th
Annual Sponsors Meeting, Banff, Nov7-8, 2019
2
Injection-Induced Seismicity
Langenbruch & Zoback,
Sci. Adv (2016)
Monthly Rate of earthquakes
M > 3 in Oklahoma
3
Injection-Induced Seismicity
Question:
+ strong correlation but are there
any secondary processes?
https://maps.fractracker.org
Earthquake
Magnitude
Injection
Volume
0 50 100
4
Earthquake-earthquake Triggering
well-established in natural
seismicity but what about
induced seismicity?
Stresschange
Kilb et al. (2000)
Time
Distancefromthe
mainshock
5
Earthquake-earthquake Triggering
Stacked instantaneous
rates: aftershocks
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
FS AS
〈ρ〉
Hoadley
FS AS
Horn-River
0
0.25
0.5
0.75
1
FS AS FS AS FS AS
〈ρ〉
AS1 BS2
BS4
Maghsoudi et al. (2018)
Our focus:
spatial features of triggering cascades
Tectonic Vs. Induced
6
Declustering Method
Poisson Process With
Gutenberg-Richter Rate
earthquake : tj,~rj, mj
ose events with ti < tj
|~ri ~rj|df
tij 10 bmi
n⇤
ij = min{nij}
⌧⇤
ij
.
= t⇤
ij10 b
mi
2
r⇤
ij
.
= r⇤
ij10 b
mi
2
nij = ⇥ |~ri ~rj|df
⇥ tij<latexit sha1_base64="3bV7SThS3NOvZaNrlxWMXaq9Q/A=">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</latexit><latexit sha1_base64="3bV7SThS3NOvZaNrlxWMXaq9Q/A=">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</latexit><latexit sha1_base64="3bV7SThS3NOvZaNrlxWMXaq9Q/A=">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</latexit><latexit sha1_base64="3bV7SThS3NOvZaNrlxWMXaq9Q/A=">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</latexit>
.
= c ⇥ 10 b(mi mc)
<latexit sha1_base64="gTSylbbgrMa1lGYJDPqiWbyZ448=">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</latexit><latexit sha1_base64="gTSylbbgrMa1lGYJDPqiWbyZ448=">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</latexit><latexit sha1_base64="gTSylbbgrMa1lGYJDPqiWbyZ448=">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</latexit><latexit sha1_base64="gTSylbbgrMa1lGYJDPqiWbyZ448=">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</latexit>
Fractal Dimension
1.3 < df < 1.5<latexit sha1_base64="Vy2g97mHCUEprZMr7oGO68uTUIQ=">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</latexit><latexit sha1_base64="Vy2g97mHCUEprZMr7oGO68uTUIQ=">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</latexit><latexit sha1_base64="Vy2g97mHCUEprZMr7oGO68uTUIQ=">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</latexit><latexit sha1_base64="Vy2g97mHCUEprZMr7oGO68uTUIQ=">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</latexit>
Magnitude of
Completeness
mc = 2.8<latexit sha1_base64="G6xQrQ46Lt2ZPQBaExpvSh4QCBI=">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</latexit><latexit sha1_base64="G6xQrQ46Lt2ZPQBaExpvSh4QCBI=">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</latexit><latexit sha1_base64="G6xQrQ46Lt2ZPQBaExpvSh4QCBI=">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</latexit><latexit sha1_base64="G6xQrQ46Lt2ZPQBaExpvSh4QCBI=">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</latexit>
Zaliapin et al. (2008),
Zaliapin & Ben-Zion (2013),
Gu et al. (2013)
j
i0
i1
i2
ni0 j
<latexit
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Relocated Catalog:
Schoenball & Ellsworth (2017)
b-value
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7
Suitable Null Model Of
Uncorrelated Events
Declustering Method
Scaled Time
ScaledDistance Density Plots
Scaled Time
Actual Data Shuffled Data
8
Suitable Null Model Of
Uncorrelated Events
Declustering Method
Scaled Time
ScaledDistance
Background
Triggered
Density Plots
Background
Scaled Time
Actual Data Shuffled Data
9
Identified Clusters
Longitude
Latitude
-98.8°
-98.7°
36.4°
36.5°
2016-01-13
2016-02-02
2016-02-22
2016-03-13
3
4
5
6
Magnitude
-98°
-97°
-96° 0 1 2 3 4
10
0
10
1
10
2
10
3
10
4
2 3 4 510
7
10
8
10
9
m
m
Longitude
N⇥10bm
(c)
0 50
km
100
mc
1
0 10 20
10
Identified Clusters
Longitude
-98.8°
-98.7°
36.4°
36.5°
2016-01-13
2016-02-02
2016-02-22
2016-03-13
3
4
5
6
Longitude
Latitude
Magnitude
-98°
-97°
-96° 0 1 2 3 4
10
0
10
1
10
2
10
3
10
4
2 3 4 510
7
10
8
10
9
m
m
Longitude
N⇥10bm
(c)
0 50
km
100
mc
1
0 10 20
11
Identified Clusters
Longitude
-98.8°
-98.7°
36.4°
36.5°
2016-01-13
2016-02-02
2016-02-22
2016-03-13
3
4
5
6
Longitude
Latitude
Magnitude
-98°
-97°
-96° 0 1 2 3 4
10
0
10
1
10
2
10
3
10
4
2 3 4 510
7
10
8
10
9
m
m
Longitude
N⇥10bm
(c)
0 50
km
100
mc
1
0 10 20
12
Identified Clusters
Longitude
-98.8°
-98.7°
36.4°
36.5°
2016-01-13
2016-02-02
2016-02-22
2016-03-13
3
4
5
6
Longitude
Latitude
Magnitude
-98°
-97°
-96° 0 1 2 3 4
10
0
10
1
10
2
10
3
10
4
2 3 4 510
7
10
8
10
9
m
m
Longitude
N⇥10bm
(c)
0 50
km
100
mc
1
0 10 20
13
Identified Clusters
Longitude
-98.8°
-98.7°
36.4°
36.5°
2016-01-13
2016-02-02
2016-02-22
2016-03-13
3
4
5
6
Longitude
Latitude
Magnitude
-98°
-97°
-96° 0 1 2 3 4
10
0
10
1
10
2
10
3
10
4
2 3 4 510
7
10
8
10
9
m
m
Longitude
N⇥10bm
(c)
0 50
km
100
mc
1
0 10 20
14
Identified Clusters
Longitude
-98.8°
-98.7°
36.4°
36.5°
2016-01-13
2016-02-02
2016-02-22
2016-03-13
3
4
5
6
Longitude
Latitude
Magnitude
-98°
-97°
-96° 0 1 2 3 4
10
0
10
1
10
2
10
3
10
4
2 3 4 510
7
10
8
10
9
m
m
Longitude
N⇥10bm
(c)
0 50
km
100
mc
1
0 10 20
15
Identified Clusters
Longitude
-98.8°
-98.7°
36.4°
36.5°
2016-01-13
2016-02-02
2016-02-22
2016-03-13
3
4
5
6
Longitude
Latitude
Magnitude
-98°
-97°
-96° 0 1 2 3 4
10
0
10
1
10
2
10
3
10
4
2 3 4 510
7
10
8
10
9
m
m
Longitude
N⇥10bm
(c)
0 50
km
100
mc
1
0 10 20
16
Identified Clusters
Longitude
-98.8°
-98.7°
36.4°
36.5°
2016-01-13
2016-02-02
2016-02-22
2016-03-13
3
4
5
6
Longitude
Latitude
Magnitude
-98°
-97°
-96° 0 1 2 3 4
10
0
10
1
10
2
10
3
10
4
2 3 4 510
7
10
8
10
9
m
m
Longitude
N⇥10bm
(c)
0 50
km
100
mc
1
0 10 20
17
Identified Clusters
Longitude
-98.8°
-98.7°
36.4°
36.5°
2016-01-13
2016-02-02
2016-02-22
2016-03-13
3
4
5
6
Longitude
Latitude
Magnitude
-98°
-97°
-96° 0 1 2 3 4
10
0
10
1
10
2
10
3
10
4
2 3 4 510
7
10
8
10
9
m
m
Longitude
N⇥10bm
(c)
0 50
km
100
mc
1
0 10 20
18
Identified Clusters
Longitude
-98.8°
-98.7°
36.4°
36.5°
2016-01-13
2016-02-02
2016-02-22
2016-03-13
3
4
5
6
Longitude
Latitude
Magnitude
-98°
-97°
-96° 0 1 2 3 4
10
0
10
1
10
2
10
3
10
4
2 3 4 510
7
10
8
10
9
m
m
Longitude
N⇥10bm
(c)
0 50
km
100
mc
1
0 10 20
19
Spatial Properties
of Triggering
r<latexit
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<latexit
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<latexit
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<latexit
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Distance (km)
m<latexit sha1_base64="uIbhaxHObW9k+KtpSlNLCo0J2X4=">AAAB6HicbVDLSgNBEOz1GeMr6tHLYBA8hV0R9Bj04jEB84BkCbOT3mTMzOwyMyuEkC/w4kERr36SN//GSbIHTSxoKKq66e6KUsGN9f1vb219Y3Nru7BT3N3bPzgsHR03TZJphg2WiES3I2pQcIUNy63AdqqRykhgKxrdzfzWE2rDE/VgxymGkg4Ujzmj1kl12SuV/Yo/B1klQU7KkKPWK311+wnLJCrLBDWmE/ipDSdUW84ETovdzGBK2YgOsOOoohJNOJkfOiXnTumTONGulCVz9ffEhEpjxjJynZLaoVn2ZuJ/Xiez8U044SrNLCq2WBRngtiEzL4mfa6RWTF2hDLN3a2EDammzLpsii6EYPnlVdK8rAR+Jahflau3eRwFOIUzuIAArqEK91CDBjBAeIZXePMevRfv3ftYtK55+cwJ/IH3+QPVjYzx</latexit><latexit sha1_base64="uIbhaxHObW9k+KtpSlNLCo0J2X4=">AAAB6HicbVDLSgNBEOz1GeMr6tHLYBA8hV0R9Bj04jEB84BkCbOT3mTMzOwyMyuEkC/w4kERr36SN//GSbIHTSxoKKq66e6KUsGN9f1vb219Y3Nru7BT3N3bPzgsHR03TZJphg2WiES3I2pQcIUNy63AdqqRykhgKxrdzfzWE2rDE/VgxymGkg4Ujzmj1kl12SuV/Yo/B1klQU7KkKPWK311+wnLJCrLBDWmE/ipDSdUW84ETovdzGBK2YgOsOOoohJNOJkfOiXnTumTONGulCVz9ffEhEpjxjJynZLaoVn2ZuJ/Xiez8U044SrNLCq2WBRngtiEzL4mfa6RWTF2hDLN3a2EDammzLpsii6EYPnlVdK8rAR+Jahflau3eRwFOIUzuIAArqEK91CDBjBAeIZXePMevRfv3ftYtK55+cwJ/IH3+QPVjYzx</latexit><latexit sha1_base64="uIbhaxHObW9k+KtpSlNLCo0J2X4=">AAAB6HicbVDLSgNBEOz1GeMr6tHLYBA8hV0R9Bj04jEB84BkCbOT3mTMzOwyMyuEkC/w4kERr36SN//GSbIHTSxoKKq66e6KUsGN9f1vb219Y3Nru7BT3N3bPzgsHR03TZJphg2WiES3I2pQcIUNy63AdqqRykhgKxrdzfzWE2rDE/VgxymGkg4Ujzmj1kl12SuV/Yo/B1klQU7KkKPWK311+wnLJCrLBDWmE/ipDSdUW84ETovdzGBK2YgOsOOoohJNOJkfOiXnTumTONGulCVz9ffEhEpjxjJynZLaoVn2ZuJ/Xiez8U044SrNLCq2WBRngtiEzL4mfa6RWTF2hDLN3a2EDammzLpsii6EYPnlVdK8rAR+Jahflau3eRwFOIUzuIAArqEK91CDBjBAeIZXePMevRfv3ftYtK55+cwJ/IH3+QPVjYzx</latexit><latexit sha1_base64="uIbhaxHObW9k+KtpSlNLCo0J2X4=">AAAB6HicbVDLSgNBEOz1GeMr6tHLYBA8hV0R9Bj04jEB84BkCbOT3mTMzOwyMyuEkC/w4kERr36SN//GSbIHTSxoKKq66e6KUsGN9f1vb219Y3Nru7BT3N3bPzgsHR03TZJphg2WiES3I2pQcIUNy63AdqqRykhgKxrdzfzWE2rDE/VgxymGkg4Ujzmj1kl12SuV/Yo/B1klQU7KkKPWK311+wnLJCrLBDWmE/ipDSdUW84ETovdzGBK2YgOsOOoohJNOJkfOiXnTumTONGulCVz9ffEhEpjxjJynZLaoVn2ZuJ/Xiez8U044SrNLCq2WBRngtiEzL4mfa6RWTF2hDLN3a2EDammzLpsii6EYPnlVdK8rAR+Jahflau3eRwFOIUzuIAArqEK91CDBjBAeIZXePMevRfv3ftYtK55+cwJ/IH3+QPVjYzx</latexit>
ProbabilityDensity(km-1)
Triggered
Earthquakesuncertainties
20
Spatial Properties
of Triggering
↵ ' 0.4<latexit sha1_base64="WqBQsQOZhZGJhAo0wUUhhOBDIGI=">AAAB+XicbVBNS8NAEN3Ur1q/oh69LBbBU0mkoMeiF48V7Ac0oWy2k3bp7ibubgol9J948aCIV/+JN/+N2zYHbX0w8Hhvhpl5UcqZNp737ZQ2Nre2d8q7lb39g8Mj9/ikrZNMUWjRhCeqGxENnEloGWY4dFMFREQcOtH4bu53JqA0S+SjmaYQCjKULGaUGCv1XTcgPB2RQDMBT9ir1ftu1at5C+B14hekigo0++5XMEhoJkAayonWPd9LTZgTZRjlMKsEmYaU0DEZQs9SSQToMF9cPsMXVhngOFG2pMEL9fdEToTWUxHZTkHMSK96c/E/r5eZ+CbMmUwzA5IuF8UZxybB8xjwgCmghk8tIVQxeyumI6IINTasig3BX315nbSvar5X8x/q1cZtEUcZnaFzdIl8dI0a6B41UQtRNEHP6BW9Obnz4rw7H8vWklPMnKI/cD5/AG5Ykto=</latexit><latexit sha1_base64="WqBQsQOZhZGJhAo0wUUhhOBDIGI=">AAAB+XicbVBNS8NAEN3Ur1q/oh69LBbBU0mkoMeiF48V7Ac0oWy2k3bp7ibubgol9J948aCIV/+JN/+N2zYHbX0w8Hhvhpl5UcqZNp737ZQ2Nre2d8q7lb39g8Mj9/ikrZNMUWjRhCeqGxENnEloGWY4dFMFREQcOtH4bu53JqA0S+SjmaYQCjKULGaUGCv1XTcgPB2RQDMBT9ir1ftu1at5C+B14hekigo0++5XMEhoJkAayonWPd9LTZgTZRjlMKsEmYaU0DEZQs9SSQToMF9cPsMXVhngOFG2pMEL9fdEToTWUxHZTkHMSK96c/E/r5eZ+CbMmUwzA5IuF8UZxybB8xjwgCmghk8tIVQxeyumI6IINTasig3BX315nbSvar5X8x/q1cZtEUcZnaFzdIl8dI0a6B41UQtRNEHP6BW9Obnz4rw7H8vWklPMnKI/cD5/AG5Ykto=</latexit><latexit sha1_base64="WqBQsQOZhZGJhAo0wUUhhOBDIGI=">AAAB+XicbVBNS8NAEN3Ur1q/oh69LBbBU0mkoMeiF48V7Ac0oWy2k3bp7ibubgol9J948aCIV/+JN/+N2zYHbX0w8Hhvhpl5UcqZNp737ZQ2Nre2d8q7lb39g8Mj9/ikrZNMUWjRhCeqGxENnEloGWY4dFMFREQcOtH4bu53JqA0S+SjmaYQCjKULGaUGCv1XTcgPB2RQDMBT9ir1ftu1at5C+B14hekigo0++5XMEhoJkAayonWPd9LTZgTZRjlMKsEmYaU0DEZQs9SSQToMF9cPsMXVhngOFG2pMEL9fdEToTWUxHZTkHMSK96c/E/r5eZ+CbMmUwzA5IuF8UZxybB8xjwgCmghk8tIVQxeyumI6IINTasig3BX315nbSvar5X8x/q1cZtEUcZnaFzdIl8dI0a6B41UQtRNEHP6BW9Obnz4rw7H8vWklPMnKI/cD5/AG5Ykto=</latexit><latexit sha1_base64="WqBQsQOZhZGJhAo0wUUhhOBDIGI=">AAAB+XicbVBNS8NAEN3Ur1q/oh69LBbBU0mkoMeiF48V7Ac0oWy2k3bp7ibubgol9J948aCIV/+JN/+N2zYHbX0w8Hhvhpl5UcqZNp737ZQ2Nre2d8q7lb39g8Mj9/ikrZNMUWjRhCeqGxENnEloGWY4dFMFREQcOtH4bu53JqA0S+SjmaYQCjKULGaUGCv1XTcgPB2RQDMBT9ir1ftu1at5C+B14hekigo0++5XMEhoJkAayonWPd9LTZgTZRjlMKsEmYaU0DEZQs9SSQToMF9cPsMXVhngOFG2pMEL9fdEToTWUxHZTkHMSK96c/E/r5eZ+CbMmUwzA5IuF8UZxybB8xjwgCmghk8tIVQxeyumI6IINTasig3BX315nbSvar5X8x/q1cZtEUcZnaFzdIl8dI0a6B41UQtRNEHP6BW9Obnz4rw7H8vWklPMnKI/cD5/AG5Ykto=</latexit>
Catalog from Southern California
(Hainzl et al. 2015)
υ 1.35
short-ranged for induced earthquakes
υ 3
might depend on the structure
of the fault network ??
r/10↵m
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⇢⇥10↵m
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↵ ' 0.4<latexit sha1_base64="WqBQsQOZhZGJhAo0wUUhhOBDIGI=">AAAB+XicbVBNS8NAEN3Ur1q/oh69LBbBU0mkoMeiF48V7Ac0oWy2k3bp7ibubgol9J948aCIV/+JN/+N2zYHbX0w8Hhvhpl5UcqZNp737ZQ2Nre2d8q7lb39g8Mj9/ikrZNMUWjRhCeqGxENnEloGWY4dFMFREQcOtH4bu53JqA0S+SjmaYQCjKULGaUGCv1XTcgPB2RQDMBT9ir1ftu1at5C+B14hekigo0++5XMEhoJkAayonWPd9LTZgTZRjlMKsEmYaU0DEZQs9SSQToMF9cPsMXVhngOFG2pMEL9fdEToTWUxHZTkHMSK96c/E/r5eZ+CbMmUwzA5IuF8UZxybB8xjwgCmghk8tIVQxeyumI6IINTasig3BX315nbSvar5X8x/q1cZtEUcZnaFzdIl8dI0a6B41UQtRNEHP6BW9Obnz4rw7H8vWklPMnKI/cD5/AG5Ykto=</latexit><latexit sha1_base64="WqBQsQOZhZGJhAo0wUUhhOBDIGI=">AAAB+XicbVBNS8NAEN3Ur1q/oh69LBbBU0mkoMeiF48V7Ac0oWy2k3bp7ibubgol9J948aCIV/+JN/+N2zYHbX0w8Hhvhpl5UcqZNp737ZQ2Nre2d8q7lb39g8Mj9/ikrZNMUWjRhCeqGxENnEloGWY4dFMFREQcOtH4bu53JqA0S+SjmaYQCjKULGaUGCv1XTcgPB2RQDMBT9ir1ftu1at5C+B14hekigo0++5XMEhoJkAayonWPd9LTZgTZRjlMKsEmYaU0DEZQs9SSQToMF9cPsMXVhngOFG2pMEL9fdEToTWUxHZTkHMSK96c/E/r5eZ+CbMmUwzA5IuF8UZxybB8xjwgCmghk8tIVQxeyumI6IINTasig3BX315nbSvar5X8x/q1cZtEUcZnaFzdIl8dI0a6B41UQtRNEHP6BW9Obnz4rw7H8vWklPMnKI/cD5/AG5Ykto=</latexit><latexit sha1_base64="WqBQsQOZhZGJhAo0wUUhhOBDIGI=">AAAB+XicbVBNS8NAEN3Ur1q/oh69LBbBU0mkoMeiF48V7Ac0oWy2k3bp7ibubgol9J948aCIV/+JN/+N2zYHbX0w8Hhvhpl5UcqZNp737ZQ2Nre2d8q7lb39g8Mj9/ikrZNMUWjRhCeqGxENnEloGWY4dFMFREQcOtH4bu53JqA0S+SjmaYQCjKULGaUGCv1XTcgPB2RQDMBT9ir1ftu1at5C+B14hekigo0++5XMEhoJkAayonWPd9LTZgTZRjlMKsEmYaU0DEZQs9SSQToMF9cPsMXVhngOFG2pMEL9fdEToTWUxHZTkHMSK96c/E/r5eZ+CbMmUwzA5IuF8UZxybB8xjwgCmghk8tIVQxeyumI6IINTasig3BX315nbSvar5X8x/q1cZtEUcZnaFzdIl8dI0a6B41UQtRNEHP6BW9Obnz4rw7H8vWklPMnKI/cD5/AG5Ykto=</latexit><latexit sha1_base64="WqBQsQOZhZGJhAo0wUUhhOBDIGI=">AAAB+XicbVBNS8NAEN3Ur1q/oh69LBbBU0mkoMeiF48V7Ac0oWy2k3bp7ibubgol9J948aCIV/+JN/+N2zYHbX0w8Hhvhpl5UcqZNp737ZQ2Nre2d8q7lb39g8Mj9/ikrZNMUWjRhCeqGxENnEloGWY4dFMFREQcOtH4bu53JqA0S+SjmaYQCjKULGaUGCv1XTcgPB2RQDMBT9ir1ftu1at5C+B14hekigo0++5XMEhoJkAayonWPd9LTZgTZRjlMKsEmYaU0DEZQs9SSQToMF9cPsMXVhngOFG2pMEL9fdEToTWUxHZTkHMSK96c/E/r5eZ+CbMmUwzA5IuF8UZxybB8xjwgCmghk8tIVQxeyumI6IINTasig3BX315nbSvar5X8x/q1cZtEUcZnaFzdIl8dI0a6B41UQtRNEHP6BW9Obnz4rw7H8vWklPMnKI/cD5/AG5Ykto=</latexit>
⇠ ' 0.01 ⇥ 10↵m
(km)<latexit sha1_base64="eQaOol6DgV5HTA//ECpyEj2b76A=">AAACGHicbVC7TsMwFHXKq5RXgJHFokIqS0kQEowVLIxFog+pKZXjuq1VOwn2DWoV5TNY+BUWBhBi7cbf4LYZoOVIlo7OOVfX9/iR4Boc59vKrayurW/kNwtb2zu7e/b+QV2HsaKsRkMRqqZPNBM8YDXgIFgzUoxIX7CGP7yZ+o0npjQPg3sYR6wtST/gPU4JGKljn3kjjj3NJXvETtlxPTBUY9d5SDwiogHBMsUlD9gIkqFMTzt20cRmwMvEzUgRZah27InXDWksWQBUEK1brhNBOyEKOBUsLXixZhGhQ9JnLUMDYta3k9lhKT4xShf3QmVeAHim/p5IiNR6LH2TlAQGetGbiv95rRh6V+2EB1EMLKDzRb1YYAjxtCXc5YpREGNDCFXc/BXTAVGEgumyYEpwF09eJvXzsuuU3buLYuU6qyOPjtAxKiEXXaIKukVVVEMUPaNX9I4+rBfrzfq0vubRnJXNHKI/sCY/kjue3g==</latexit><latexit sha1_base64="eQaOol6DgV5HTA//ECpyEj2b76A=">AAACGHicbVC7TsMwFHXKq5RXgJHFokIqS0kQEowVLIxFog+pKZXjuq1VOwn2DWoV5TNY+BUWBhBi7cbf4LYZoOVIlo7OOVfX9/iR4Boc59vKrayurW/kNwtb2zu7e/b+QV2HsaKsRkMRqqZPNBM8YDXgIFgzUoxIX7CGP7yZ+o0npjQPg3sYR6wtST/gPU4JGKljn3kjjj3NJXvETtlxPTBUY9d5SDwiogHBMsUlD9gIkqFMTzt20cRmwMvEzUgRZah27InXDWksWQBUEK1brhNBOyEKOBUsLXixZhGhQ9JnLUMDYta3k9lhKT4xShf3QmVeAHim/p5IiNR6LH2TlAQGetGbiv95rRh6V+2EB1EMLKDzRb1YYAjxtCXc5YpREGNDCFXc/BXTAVGEgumyYEpwF09eJvXzsuuU3buLYuU6qyOPjtAxKiEXXaIKukVVVEMUPaNX9I4+rBfrzfq0vubRnJXNHKI/sCY/kjue3g==</latexit><latexit sha1_base64="eQaOol6DgV5HTA//ECpyEj2b76A=">AAACGHicbVC7TsMwFHXKq5RXgJHFokIqS0kQEowVLIxFog+pKZXjuq1VOwn2DWoV5TNY+BUWBhBi7cbf4LYZoOVIlo7OOVfX9/iR4Boc59vKrayurW/kNwtb2zu7e/b+QV2HsaKsRkMRqqZPNBM8YDXgIFgzUoxIX7CGP7yZ+o0npjQPg3sYR6wtST/gPU4JGKljn3kjjj3NJXvETtlxPTBUY9d5SDwiogHBMsUlD9gIkqFMTzt20cRmwMvEzUgRZah27InXDWksWQBUEK1brhNBOyEKOBUsLXixZhGhQ9JnLUMDYta3k9lhKT4xShf3QmVeAHim/p5IiNR6LH2TlAQGetGbiv95rRh6V+2EB1EMLKDzRb1YYAjxtCXc5YpREGNDCFXc/BXTAVGEgumyYEpwF09eJvXzsuuU3buLYuU6qyOPjtAxKiEXXaIKukVVVEMUPaNX9I4+rBfrzfq0vubRnJXNHKI/sCY/kjue3g==</latexit><latexit sha1_base64="eQaOol6DgV5HTA//ECpyEj2b76A=">AAACGHicbVC7TsMwFHXKq5RXgJHFokIqS0kQEowVLIxFog+pKZXjuq1VOwn2DWoV5TNY+BUWBhBi7cbf4LYZoOVIlo7OOVfX9/iR4Boc59vKrayurW/kNwtb2zu7e/b+QV2HsaKsRkMRqqZPNBM8YDXgIFgzUoxIX7CGP7yZ+o0npjQPg3sYR6wtST/gPU4JGKljn3kjjj3NJXvETtlxPTBUY9d5SDwiogHBMsUlD9gIkqFMTzt20cRmwMvEzUgRZah27InXDWksWQBUEK1brhNBOyEKOBUsLXixZhGhQ9JnLUMDYta3k9lhKT4xShf3QmVeAHim/p5IiNR6LH2TlAQGetGbiv95rRh6V+2EB1EMLKDzRb1YYAjxtCXc5YpREGNDCFXc/BXTAVGEgumyYEpwF09eJvXzsuuU3buLYuU6qyOPjtAxKiEXXaIKukVVVEMUPaNX9I4+rBfrzfq0vubRnJXNHKI/sCY/kjue3g==</latexit>
Peak interpretted as rupture size
Leonard (2010)
1<latexit sha1_base64="wqpTvg+N0fzv28Gf0Dl4QiuZwPw=">AAAB9HicbVBNS8NAEJ34WetX1aOXxSJ4KokIeix68VjBfkAbymYzaZduNnF3Uyihv8OLB0W8+mO8+W/ctjlo64OBx3szOzsvSAXXxnW/nbX1jc2t7dJOeXdv/+CwcnTc0kmmGDZZIhLVCahGwSU2DTcCO6lCGgcC28Hobua3x6g0T+SjmaTox3QgecQZNVbye/MXcoXhlHj9StWtuXOQVeIVpAoFGv3KVy9MWBajNExQrbuemxo/p8pwJnBa7mUaU8pGdIBdSyWNUfv5fOWUnFslJFGibElD5urviZzGWk/iwHbG1Az1sjcT//O6mYlu/JzLNDMo2WJRlAliEjJLgIRcITNiYgllitu/EjakijJjcyrbELzlk1dJ67LmuTXv4apavy3iKMEpnMEFeHANdbiHBjSBwRM8wyu8OWPnxXl3Phata04xcwJ/4Hz+AJ7Pkfs=</latexit><latexit sha1_base64="wqpTvg+N0fzv28Gf0Dl4QiuZwPw=">AAAB9HicbVBNS8NAEJ34WetX1aOXxSJ4KokIeix68VjBfkAbymYzaZduNnF3Uyihv8OLB0W8+mO8+W/ctjlo64OBx3szOzsvSAXXxnW/nbX1jc2t7dJOeXdv/+CwcnTc0kmmGDZZIhLVCahGwSU2DTcCO6lCGgcC28Hobua3x6g0T+SjmaTox3QgecQZNVbye/MXcoXhlHj9StWtuXOQVeIVpAoFGv3KVy9MWBajNExQrbuemxo/p8pwJnBa7mUaU8pGdIBdSyWNUfv5fOWUnFslJFGibElD5urviZzGWk/iwHbG1Az1sjcT//O6mYlu/JzLNDMo2WJRlAliEjJLgIRcITNiYgllitu/EjakijJjcyrbELzlk1dJ67LmuTXv4apavy3iKMEpnMEFeHANdbiHBjSBwRM8wyu8OWPnxXl3Phata04xcwJ/4Hz+AJ7Pkfs=</latexit><latexit sha1_base64="wqpTvg+N0fzv28Gf0Dl4QiuZwPw=">AAAB9HicbVBNS8NAEJ34WetX1aOXxSJ4KokIeix68VjBfkAbymYzaZduNnF3Uyihv8OLB0W8+mO8+W/ctjlo64OBx3szOzsvSAXXxnW/nbX1jc2t7dJOeXdv/+CwcnTc0kmmGDZZIhLVCahGwSU2DTcCO6lCGgcC28Hobua3x6g0T+SjmaTox3QgecQZNVbye/MXcoXhlHj9StWtuXOQVeIVpAoFGv3KVy9MWBajNExQrbuemxo/p8pwJnBa7mUaU8pGdIBdSyWNUfv5fOWUnFslJFGibElD5urviZzGWk/iwHbG1Az1sjcT//O6mYlu/JzLNDMo2WJRlAliEjJLgIRcITNiYgllitu/EjakijJjcyrbELzlk1dJ67LmuTXv4apavy3iKMEpnMEFeHANdbiHBjSBwRM8wyu8OWPnxXl3Phata04xcwJ/4Hz+AJ7Pkfs=</latexit><latexit sha1_base64="wqpTvg+N0fzv28Gf0Dl4QiuZwPw=">AAAB9HicbVBNS8NAEJ34WetX1aOXxSJ4KokIeix68VjBfkAbymYzaZduNnF3Uyihv8OLB0W8+mO8+W/ctjlo64OBx3szOzsvSAXXxnW/nbX1jc2t7dJOeXdv/+CwcnTc0kmmGDZZIhLVCahGwSU2DTcCO6lCGgcC28Hobua3x6g0T+SjmaTox3QgecQZNVbye/MXcoXhlHj9StWtuXOQVeIVpAoFGv3KVy9MWBajNExQrbuemxo/p8pwJnBa7mUaU8pGdIBdSyWNUfv5fOWUnFslJFGibElD5urviZzGWk/iwHbG1Az1sjcT//O6mYlu/JzLNDMo2WJRlAliEjJLgIRcITNiYgllitu/EjakijJjcyrbELzlk1dJ67LmuTXv4apavy3iKMEpnMEFeHANdbiHBjSBwRM8wyu8OWPnxXl3Phata04xcwJ/4Hz+AJ7Pkfs=</latexit>
⌫ ' 3<latexit sha1_base64="zuylTV8uQuP9Qz/b+zTqq1vxfJ4=">AAAB/3icbVDLSsNAFJ3UV62vqODGzWARXJVEBV0W3bisYB/QhDKZ3LZDJ5M4MxFK7MJfceNCEbf+hjv/xmmahbYeuHA45965c0+QcKa043xbpaXlldW18nplY3Nre8fe3WupOJUUmjTmsewERAFnApqaaQ6dRAKJAg7tYHQ99dsPIBWLxZ0eJ+BHZCBYn1GijdSzD7z8jUxCOPFE6ikWwT0+69lVp+bkwIvELUgVFWj07C8vjGkagdCUE6W6rpNoPyNSM8phUvFSBQmhIzKArqGCRKD8LN89wcdGCXE/lqaExrn6eyIjkVLjKDCdEdFDNe9Nxf+8bqr7l37GRJJqEHS2qJ9yrGM8DQOHTALVfGwIoZKZv2I6JJJQbSKrmBDc+ZMXSeu05jo19/a8Wr8q4iijQ3SETpCLLlAd3aAGaiKKHtEzekVv1pP1Yr1bH7PWklXM7KM/sD5/AE4tlkI=</latexit><latexit sha1_base64="zuylTV8uQuP9Qz/b+zTqq1vxfJ4=">AAAB/3icbVDLSsNAFJ3UV62vqODGzWARXJVEBV0W3bisYB/QhDKZ3LZDJ5M4MxFK7MJfceNCEbf+hjv/xmmahbYeuHA45965c0+QcKa043xbpaXlldW18nplY3Nre8fe3WupOJUUmjTmsewERAFnApqaaQ6dRAKJAg7tYHQ99dsPIBWLxZ0eJ+BHZCBYn1GijdSzD7z8jUxCOPFE6ikWwT0+69lVp+bkwIvELUgVFWj07C8vjGkagdCUE6W6rpNoPyNSM8phUvFSBQmhIzKArqGCRKD8LN89wcdGCXE/lqaExrn6eyIjkVLjKDCdEdFDNe9Nxf+8bqr7l37GRJJqEHS2qJ9yrGM8DQOHTALVfGwIoZKZv2I6JJJQbSKrmBDc+ZMXSeu05jo19/a8Wr8q4iijQ3SETpCLLlAd3aAGaiKKHtEzekVv1pP1Yr1bH7PWklXM7KM/sD5/AE4tlkI=</latexit><latexit sha1_base64="zuylTV8uQuP9Qz/b+zTqq1vxfJ4=">AAAB/3icbVDLSsNAFJ3UV62vqODGzWARXJVEBV0W3bisYB/QhDKZ3LZDJ5M4MxFK7MJfceNCEbf+hjv/xmmahbYeuHA45965c0+QcKa043xbpaXlldW18nplY3Nre8fe3WupOJUUmjTmsewERAFnApqaaQ6dRAKJAg7tYHQ99dsPIBWLxZ0eJ+BHZCBYn1GijdSzD7z8jUxCOPFE6ikWwT0+69lVp+bkwIvELUgVFWj07C8vjGkagdCUE6W6rpNoPyNSM8phUvFSBQmhIzKArqGCRKD8LN89wcdGCXE/lqaExrn6eyIjkVLjKDCdEdFDNe9Nxf+8bqr7l37GRJJqEHS2qJ9yrGM8DQOHTALVfGwIoZKZv2I6JJJQbSKrmBDc+ZMXSeu05jo19/a8Wr8q4iijQ3SETpCLLlAd3aAGaiKKHtEzekVv1pP1Yr1bH7PWklXM7KM/sD5/AE4tlkI=</latexit><latexit sha1_base64="zuylTV8uQuP9Qz/b+zTqq1vxfJ4=">AAAB/3icbVDLSsNAFJ3UV62vqODGzWARXJVEBV0W3bisYB/QhDKZ3LZDJ5M4MxFK7MJfceNCEbf+hjv/xmmahbYeuHA45965c0+QcKa043xbpaXlldW18nplY3Nre8fe3WupOJUUmjTmsewERAFnApqaaQ6dRAKJAg7tYHQ99dsPIBWLxZ0eJ+BHZCBYn1GijdSzD7z8jUxCOPFE6ikWwT0+69lVp+bkwIvELUgVFWj07C8vjGkagdCUE6W6rpNoPyNSM8phUvFSBQmhIzKArqGCRKD8LN89wcdGCXE/lqaExrn6eyIjkVLjKDCdEdFDNe9Nxf+8bqr7l37GRJJqEHS2qJ9yrGM8DQOHTALVfGwIoZKZv2I6JJJQbSKrmBDc+ZMXSeu05jo19/a8Wr8q4iijQ3SETpCLLlAd3aAGaiKKHtEzekVv1pP1Yr1bH7PWklXM7KM/sD5/AE4tlkI=</latexit>
CharacteristicSize
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static triggering
21
Gutenberg-
Richter Relation
Omori Relation
Spatial Density
Decay
Productivity
Relation
Induced
(Oklahoma)
Tectonic vs Induced seismicity
(southern California)
Gu et al. (2013)
p = 1.2 ± 0.05<latexit sha1_base64="oYQtIwXH3+ByfVBcJ8rdpL2axwE=">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</latexit><latexit sha1_base64="oYQtIwXH3+ByfVBcJ8rdpL2axwE=">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</latexit><latexit sha1_base64="oYQtIwXH3+ByfVBcJ8rdpL2axwE=">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</latexit><latexit sha1_base64="oYQtIwXH3+ByfVBcJ8rdpL2axwE=">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</latexit>
1 < ⌫ < 2<latexit sha1_base64="DVEcsiPRKgnuGOg8avWlCHjY4NM=">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</latexit><latexit sha1_base64="DVEcsiPRKgnuGOg8avWlCHjY4NM=">AAACpnicbVFdb9MwFHXC1whfBR55sagqlYdFcWBiQq00wQu8oPHRdVLTBcdxOm+2E+ybiirLT+NP8Ma/wW0zCTauZOn43nN8fc/NKiksRNFvz79x89btOzt3g3v3Hzx81Hv85MiWtWF8wkpZmuOMWi6F5hMQIPlxZThVmeTT7Pzduj5dcmNFqb/CquJzRRdaFIJRcKm093OQSMfOaZKXwL9jloBQ3GISnTS72VClYlel7EUbDHTaiLN2fEnf0i6SJWeNaR3tEp1dnDR5WrQdAzayrTyN14i9wQnwH9AsZJlRiSkDsRSwwoYCd3USvhy5B0Yk3AsGrvk4DveDQTUmYZxUCkdhtBeQUaLrUZz2+u66CXwdkA70UReHae+Xm5PVimtgklo7I1EF84YaEEy65klteUXZOV3wmYOauhHmzcbmFg9cJsdFadzRgDfZvxUNVdauVOaYisKpvVpbJ/9Xm9VQ7M8boasauGbbRkUtMZR4vTOcC8MZyJUDlBnh/orZKTXOOLfZwJlAro58HRzFIYlC8ulV/+BtZ8cOeoaeoyEi6DU6QO/RIZog5vW9D95n74s/9D/6E3+6pfpep3mK/gn/2x/vscuP</latexit><latexit sha1_base64="DVEcsiPRKgnuGOg8avWlCHjY4NM=">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</latexit><latexit sha1_base64="DVEcsiPRKgnuGOg8avWlCHjY4NM=">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</latexit>
b ' 1.1<latexit sha1_base64="n+VzsoLhzIjeLmIerNbSLWiZUIY=">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</latexit><latexit sha1_base64="n+VzsoLhzIjeLmIerNbSLWiZUIY=">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</latexit><latexit sha1_base64="n+VzsoLhzIjeLmIerNbSLWiZUIY=">AAACs3icbVHLbtQwFHXCq4TXAEs2FqNIZdEonlJRoRmpgg3LIjHTSpNpcBxn6tZOUvtmxCjND7Jkx99w51EJWq5k6eicc31fWa2Vgzj+7fn37j94+GjncfDk6bPnL3ovX01c1Vghx6LSlT3NuJNalXIMCrQ8ra3kJtPyJLv8vNJPFtI6VZXfYFnLmeHzUhVKcEAq7f0ME43unCd5BfKKigSUkY6y+Kzdy3ZNqvZMKt51QVimrbroRjf2je06WUjR2g5tN+ji+qzN06LbOmCdtklPByskPtIE5A9o57rKuKZcgFooWFLLQaLOov0hfjBk0UEQYvHRIDoMwnrEokFSGxpHMfJsmJTNcBBkicMyV5RFLO31UVsHvQvYFvTJNo7T3i8cWjRGliA0d27K4hpmLbeghMZOksbJmotLPpdThCXHeWbteucdDZHJaVFZfCXQNft3RsuNc0uTodNwOHe3tRX5P23aQHE4a1VZNyBLsSlUNJpCRVcHpLmyUoBeIuDCKuyVinNucYt45gCXwG6PfBdMBhGLI/b1ff/o03YdO+QNeUt2CSMfyBH5Qo7JmAgv9iZe6n33D/ypn/n5xup725zX5J/wzR/qG8/N</latexit><latexit sha1_base64="n+VzsoLhzIjeLmIerNbSLWiZUIY=">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</latexit>
b = 1.65 ± 0.07<latexit sha1_base64="fc0LCnPfxJT8pZz8zxx8iF5l2NA=">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</latexit><latexit sha1_base64="fc0LCnPfxJT8pZz8zxx8iF5l2NA=">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</latexit><latexit sha1_base64="fc0LCnPfxJT8pZz8zxx8iF5l2NA=">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</latexit><latexit sha1_base64="fc0LCnPfxJT8pZz8zxx8iF5l2NA=">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</latexit>
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p ' 0.7<latexit sha1_base64="u+xcoRBO3YV9JBoHt0logTHBq44=">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</latexit><latexit sha1_base64="u+xcoRBO3YV9JBoHt0logTHBq44=">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</latexit><latexit sha1_base64="u+xcoRBO3YV9JBoHt0logTHBq44=">AAACs3icbVHLbtQwFHXCq4TXAEs2FqNIZdEoHqhaoRmpgg3LIjHTSpNpcBxn6tZOUvtmxCjND7Jkx99w51EJWq5k6eicc31fWa2Vgzj+7fn37j94+GjncfDk6bPnL3ovX01c1Vghx6LSlT3NuJNalXIMCrQ8ra3kJtPyJLv8vNJPFtI6VZXfYFnLmeHzUhVKcEAq7f0ME43unCd5BfKKigSUkY6y+Kzdy3ZNqvZMKt51QVimrbroRjf2je06WUjR2g5tN+ji+qzN06LbOmCdtklPByskPtIE5A9o57rKuKZcgFooWFLLQaLOovdD/GDIov0gxOKjQXQYhPWIRYOkNjSOYuTZMCmb4SCoE4dlrpA9SHt91NZB7wK2BX2yjeO09wuHFo2RJQjNnZuyuIZZyy0oobGTpHGy5uKSz+UUYclxnlm73nlHQ2RyWlQWXwl0zf6d0XLj3NJk6DQczt1tbUX+T5s2UBzOWlXWDchSbAoVjaZQ0dUBaa6sFKCXCLiwCnul4pxb3CKeOcAlsNsj3wWTQcTiiH390D/6tF3HDnlD3pJdwsgBOSJfyDEZE+HF3sRLve/+vj/1Mz/fWH1vm/Oa/BO++QMHgM/g</latexit><latexit sha1_base64="u+xcoRBO3YV9JBoHt0logTHBq44=">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</latexit>
↵ ' 0.9<latexit sha1_base64="hKzn8coOf/qnEHDlqDw4n0ve7/Y=">AAACuHicbVHLattAFB2pr1R9Oe2ym6HGkC4iNEpDk2BDaDddplAnActRR6ORPcnokZkrU6PoGwvd9W96bSvQJr0wcDjn3LmvpNLKQhD8dtwHDx89frL11Hv2/MXLV73t16e2rI2QY1Hq0pwn3EqtCjkGBVqeV0byPNHyLLn6vNLPFtJYVRbfYFnJac5nhcqU4IBU3Ps5iDS6Ux6lJchrKiJQubSUBRfNbrKTx2o3j8X71hsUcaMu29GtfWO7iRZSNKZF2y26vLlo0jhrOwes0zbpcbhC4ohGIH9AM9NlwjXlAtRCwZIaDhJ15u8N8YMh8/e9ARYfhf6BN6hGzA+jKqeBHyDPhlFRD0Mv4rqa88hirWuUDuNeHw3roPcB60CfdHES937h5KLOZQFCc2snLKhg2nADSmhsJ6qtrLi44jM5QVhwHGrarBff0gEyKc1Kg68Aumb/zmh4bu0yT9CZc5jbu9qK/J82qSE7mDaqqGqQhdgUympNoaSrK9JUGSlALxFwYRT2SsWcG1wl3trDJbC7I98Hp6HPAp99/dA//tStY4u8Je/IDmHkIzkmX8gJGRPh7DsTJ3Wke+R+d2eu2lhdp8t5Q/4J1/wBGzDSBg==</latexit><latexit sha1_base64="hKzn8coOf/qnEHDlqDw4n0ve7/Y=">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</latexit><latexit sha1_base64="hKzn8coOf/qnEHDlqDw4n0ve7/Y=">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</latexit><latexit sha1_base64="hKzn8coOf/qnEHDlqDw4n0ve7/Y=">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</latexit>
N / 10↵m
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(t) / t p
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⇢(r) / r ⌫
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N / 10 bm
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↵ ' 0.7<latexit sha1_base64="7j1zccuFUGgdqgcIySc+Zk0oNpA=">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</latexit><latexit sha1_base64="7j1zccuFUGgdqgcIySc+Zk0oNpA=">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</latexit><latexit sha1_base64="7j1zccuFUGgdqgcIySc+Zk0oNpA=">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</latexit><latexit sha1_base64="7j1zccuFUGgdqgcIySc+Zk0oNpA=">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</latexit>
22
Ongoing Work
Why important: implications for
hazard assesment
Epidemic‐Type Aftershock Sequence (ETAS)
Model (Llenos and Michael, AGU, 2016)
use empirical relations
run your model
forcast future!
CAL PROPERTIES OF AFTERSHOCKS
ng rela-
by the
nificant
apin et
s j with
onsider
vents in
nted in
choice
ructure
2013].
mber of
ificant.
e k and
city in
depend on space and time such that the ETAS model falls
into the class of nonhomogeneous spatiotemporal Poisson
processes. The overall rate of activity is given by
(Er, t) = b(Er) +
X
tiÄt
mi (t – ti,Er – Eri), (3)
where ti, Eri, and mi refer to the time, location, and magnitude
of earthquake i, respectively. mi
(t – ti,Er – Eri) describes
the occurrence rate of earthquakes triggered by event i,
while b(Er) is the spatially varying background activity. For
the ETAS model, the occurrence rate is defined as
mi (t – ti,Er – Eri) = (mi)‰(t – ti)ˆmi (Er – Eri), (4)
(t ti) p
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|~r ~ri| v
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23
Ongoing Work
Background Ratio
Low High
LocalGlobal
Less Triggering in relative
sense
0 50 100
24
Ongoing Work
Background Ratio
Low High
Varying cfixed c
Less Triggering in relative
sense
Thank
You!
0 50 100
25
Temporal Properties
of Triggering
Time (day)
Rate(day-1)
?
Aftershock decay rate:
Omori-Utsu Relation
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Time
Magnitude
HourMin.
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r(t) /
1
(t + c)p
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t p
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Interevent triggering induced by wastewater injection in Oklahoma and southern Kansas

  • 1. 1 Interevent triggering induced by wastewater injection in Oklahoma and southern Kansas Kamran Karimi Joern Davidsen Department of Physics & Astronomy 10th Annual Sponsors Meeting, Banff, Nov7-8, 2019
  • 2. 2 Injection-Induced Seismicity Langenbruch & Zoback, Sci. Adv (2016) Monthly Rate of earthquakes M > 3 in Oklahoma
  • 3. 3 Injection-Induced Seismicity Question: + strong correlation but are there any secondary processes? https://maps.fractracker.org Earthquake Magnitude Injection Volume 0 50 100
  • 4. 4 Earthquake-earthquake Triggering well-established in natural seismicity but what about induced seismicity? Stresschange Kilb et al. (2000) Time Distancefromthe mainshock
  • 5. 5 Earthquake-earthquake Triggering Stacked instantaneous rates: aftershocks 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 FS AS 〈ρ〉 Hoadley FS AS Horn-River 0 0.25 0.5 0.75 1 FS AS FS AS FS AS 〈ρ〉 AS1 BS2 BS4 Maghsoudi et al. (2018) Our focus: spatial features of triggering cascades Tectonic Vs. Induced
  • 6. 6 Declustering Method Poisson Process With Gutenberg-Richter Rate earthquake : tj,~rj, mj ose events with ti < tj |~ri ~rj|df tij 10 bmi n⇤ ij = min{nij} ⌧⇤ ij . = t⇤ ij10 b mi 2 r⇤ ij . = r⇤ ij10 b mi 2 nij = ⇥ |~ri ~rj|df ⇥ tij<latexit sha1_base64="3bV7SThS3NOvZaNrlxWMXaq9Q/A=">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</latexit><latexit 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sha1_base64="3bV7SThS3NOvZaNrlxWMXaq9Q/A=">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</latexit> . = c ⇥ 10 b(mi mc) <latexit 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sha1_base64="Vy2g97mHCUEprZMr7oGO68uTUIQ=">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</latexit><latexit sha1_base64="Vy2g97mHCUEprZMr7oGO68uTUIQ=">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</latexit> Magnitude of Completeness mc = 2.8<latexit sha1_base64="G6xQrQ46Lt2ZPQBaExpvSh4QCBI=">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</latexit><latexit sha1_base64="G6xQrQ46Lt2ZPQBaExpvSh4QCBI=">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</latexit><latexit sha1_base64="G6xQrQ46Lt2ZPQBaExpvSh4QCBI=">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</latexit><latexit sha1_base64="G6xQrQ46Lt2ZPQBaExpvSh4QCBI=">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</latexit> Zaliapin et al. (2008), Zaliapin & Ben-Zion (2013), Gu et al. (2013) j i0 i1 i2 ni0 j <latexit sha1_base64="quaE706v+uYVFwF+IJel02M3SzY=">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</latexit> <latexit 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sha1_base64="W086uoUBAQIIvHo0KTlgnbBIgJ0=">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</latexit><latexit 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  • 7. 7 Suitable Null Model Of Uncorrelated Events Declustering Method Scaled Time ScaledDistance Density Plots Scaled Time Actual Data Shuffled Data
  • 8. 8 Suitable Null Model Of Uncorrelated Events Declustering Method Scaled Time ScaledDistance Background Triggered Density Plots Background Scaled Time Actual Data Shuffled Data
  • 9. 9 Identified Clusters Longitude Latitude -98.8° -98.7° 36.4° 36.5° 2016-01-13 2016-02-02 2016-02-22 2016-03-13 3 4 5 6 Magnitude -98° -97° -96° 0 1 2 3 4 10 0 10 1 10 2 10 3 10 4 2 3 4 510 7 10 8 10 9 m m Longitude N⇥10bm (c) 0 50 km 100 mc 1 0 10 20
  • 10. 10 Identified Clusters Longitude -98.8° -98.7° 36.4° 36.5° 2016-01-13 2016-02-02 2016-02-22 2016-03-13 3 4 5 6 Longitude Latitude Magnitude -98° -97° -96° 0 1 2 3 4 10 0 10 1 10 2 10 3 10 4 2 3 4 510 7 10 8 10 9 m m Longitude N⇥10bm (c) 0 50 km 100 mc 1 0 10 20
  • 11. 11 Identified Clusters Longitude -98.8° -98.7° 36.4° 36.5° 2016-01-13 2016-02-02 2016-02-22 2016-03-13 3 4 5 6 Longitude Latitude Magnitude -98° -97° -96° 0 1 2 3 4 10 0 10 1 10 2 10 3 10 4 2 3 4 510 7 10 8 10 9 m m Longitude N⇥10bm (c) 0 50 km 100 mc 1 0 10 20
  • 12. 12 Identified Clusters Longitude -98.8° -98.7° 36.4° 36.5° 2016-01-13 2016-02-02 2016-02-22 2016-03-13 3 4 5 6 Longitude Latitude Magnitude -98° -97° -96° 0 1 2 3 4 10 0 10 1 10 2 10 3 10 4 2 3 4 510 7 10 8 10 9 m m Longitude N⇥10bm (c) 0 50 km 100 mc 1 0 10 20
  • 13. 13 Identified Clusters Longitude -98.8° -98.7° 36.4° 36.5° 2016-01-13 2016-02-02 2016-02-22 2016-03-13 3 4 5 6 Longitude Latitude Magnitude -98° -97° -96° 0 1 2 3 4 10 0 10 1 10 2 10 3 10 4 2 3 4 510 7 10 8 10 9 m m Longitude N⇥10bm (c) 0 50 km 100 mc 1 0 10 20
  • 14. 14 Identified Clusters Longitude -98.8° -98.7° 36.4° 36.5° 2016-01-13 2016-02-02 2016-02-22 2016-03-13 3 4 5 6 Longitude Latitude Magnitude -98° -97° -96° 0 1 2 3 4 10 0 10 1 10 2 10 3 10 4 2 3 4 510 7 10 8 10 9 m m Longitude N⇥10bm (c) 0 50 km 100 mc 1 0 10 20
  • 15. 15 Identified Clusters Longitude -98.8° -98.7° 36.4° 36.5° 2016-01-13 2016-02-02 2016-02-22 2016-03-13 3 4 5 6 Longitude Latitude Magnitude -98° -97° -96° 0 1 2 3 4 10 0 10 1 10 2 10 3 10 4 2 3 4 510 7 10 8 10 9 m m Longitude N⇥10bm (c) 0 50 km 100 mc 1 0 10 20
  • 16. 16 Identified Clusters Longitude -98.8° -98.7° 36.4° 36.5° 2016-01-13 2016-02-02 2016-02-22 2016-03-13 3 4 5 6 Longitude Latitude Magnitude -98° -97° -96° 0 1 2 3 4 10 0 10 1 10 2 10 3 10 4 2 3 4 510 7 10 8 10 9 m m Longitude N⇥10bm (c) 0 50 km 100 mc 1 0 10 20
  • 17. 17 Identified Clusters Longitude -98.8° -98.7° 36.4° 36.5° 2016-01-13 2016-02-02 2016-02-22 2016-03-13 3 4 5 6 Longitude Latitude Magnitude -98° -97° -96° 0 1 2 3 4 10 0 10 1 10 2 10 3 10 4 2 3 4 510 7 10 8 10 9 m m Longitude N⇥10bm (c) 0 50 km 100 mc 1 0 10 20
  • 18. 18 Identified Clusters Longitude -98.8° -98.7° 36.4° 36.5° 2016-01-13 2016-02-02 2016-02-22 2016-03-13 3 4 5 6 Longitude Latitude Magnitude -98° -97° -96° 0 1 2 3 4 10 0 10 1 10 2 10 3 10 4 2 3 4 510 7 10 8 10 9 m m Longitude N⇥10bm (c) 0 50 km 100 mc 1 0 10 20
  • 19. 19 Spatial Properties of Triggering r<latexit sha1_base64="D+vIjYIYiuYBqfGNJBmXYbUZJb0=">AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqMeiF48t2A9oQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ3dzvPKHSPJYPZpqgH9GR5CFn1FipqQblilt1FyDrxMtJBXI0BuWv/jBmaYTSMEG17nluYvyMKsOZwFmpn2pMKJvQEfYslTRC7WeLQ2fkwipDEsbKljRkof6eyGik9TQKbGdEzVivenPxP6+XmvDGz7hMUoOSLReFqSAmJvOvyZArZEZMLaFMcXsrYWOqKDM2m5INwVt9eZ20r6qeW/Wa15X6bR5HEc7gHC7BgxrU4R4a0AIGCM/wCm/Oo/PivDsfy9aCk8+cwh84nz/dIYz2</latexit> <latexit sha1_base64="D+vIjYIYiuYBqfGNJBmXYbUZJb0=">AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqMeiF48t2A9oQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ3dzvPKHSPJYPZpqgH9GR5CFn1FipqQblilt1FyDrxMtJBXI0BuWv/jBmaYTSMEG17nluYvyMKsOZwFmpn2pMKJvQEfYslTRC7WeLQ2fkwipDEsbKljRkof6eyGik9TQKbGdEzVivenPxP6+XmvDGz7hMUoOSLReFqSAmJvOvyZArZEZMLaFMcXsrYWOqKDM2m5INwVt9eZ20r6qeW/Wa15X6bR5HEc7gHC7BgxrU4R4a0AIGCM/wCm/Oo/PivDsfy9aCk8+cwh84nz/dIYz2</latexit> <latexit sha1_base64="D+vIjYIYiuYBqfGNJBmXYbUZJb0=">AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqMeiF48t2A9oQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ3dzvPKHSPJYPZpqgH9GR5CFn1FipqQblilt1FyDrxMtJBXI0BuWv/jBmaYTSMEG17nluYvyMKsOZwFmpn2pMKJvQEfYslTRC7WeLQ2fkwipDEsbKljRkof6eyGik9TQKbGdEzVivenPxP6+XmvDGz7hMUoOSLReFqSAmJvOvyZArZEZMLaFMcXsrYWOqKDM2m5INwVt9eZ20r6qeW/Wa15X6bR5HEc7gHC7BgxrU4R4a0AIGCM/wCm/Oo/PivDsfy9aCk8+cwh84nz/dIYz2</latexit> <latexit sha1_base64="D+vIjYIYiuYBqfGNJBmXYbUZJb0=">AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqMeiF48t2A9oQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ3dzvPKHSPJYPZpqgH9GR5CFn1FipqQblilt1FyDrxMtJBXI0BuWv/jBmaYTSMEG17nluYvyMKsOZwFmpn2pMKJvQEfYslTRC7WeLQ2fkwipDEsbKljRkof6eyGik9TQKbGdEzVivenPxP6+XmvDGz7hMUoOSLReFqSAmJvOvyZArZEZMLaFMcXsrYWOqKDM2m5INwVt9eZ20r6qeW/Wa15X6bR5HEc7gHC7BgxrU4R4a0AIGCM/wCm/Oo/PivDsfy9aCk8+cwh84nz/dIYz2</latexit> Distance (km) m<latexit sha1_base64="uIbhaxHObW9k+KtpSlNLCo0J2X4=">AAAB6HicbVDLSgNBEOz1GeMr6tHLYBA8hV0R9Bj04jEB84BkCbOT3mTMzOwyMyuEkC/w4kERr36SN//GSbIHTSxoKKq66e6KUsGN9f1vb219Y3Nru7BT3N3bPzgsHR03TZJphg2WiES3I2pQcIUNy63AdqqRykhgKxrdzfzWE2rDE/VgxymGkg4Ujzmj1kl12SuV/Yo/B1klQU7KkKPWK311+wnLJCrLBDWmE/ipDSdUW84ETovdzGBK2YgOsOOoohJNOJkfOiXnTumTONGulCVz9ffEhEpjxjJynZLaoVn2ZuJ/Xiez8U044SrNLCq2WBRngtiEzL4mfa6RWTF2hDLN3a2EDammzLpsii6EYPnlVdK8rAR+Jahflau3eRwFOIUzuIAArqEK91CDBjBAeIZXePMevRfv3ftYtK55+cwJ/IH3+QPVjYzx</latexit><latexit sha1_base64="uIbhaxHObW9k+KtpSlNLCo0J2X4=">AAAB6HicbVDLSgNBEOz1GeMr6tHLYBA8hV0R9Bj04jEB84BkCbOT3mTMzOwyMyuEkC/w4kERr36SN//GSbIHTSxoKKq66e6KUsGN9f1vb219Y3Nru7BT3N3bPzgsHR03TZJphg2WiES3I2pQcIUNy63AdqqRykhgKxrdzfzWE2rDE/VgxymGkg4Ujzmj1kl12SuV/Yo/B1klQU7KkKPWK311+wnLJCrLBDWmE/ipDSdUW84ETovdzGBK2YgOsOOoohJNOJkfOiXnTumTONGulCVz9ffEhEpjxjJynZLaoVn2ZuJ/Xiez8U044SrNLCq2WBRngtiEzL4mfa6RWTF2hDLN3a2EDammzLpsii6EYPnlVdK8rAR+Jahflau3eRwFOIUzuIAArqEK91CDBjBAeIZXePMevRfv3ftYtK55+cwJ/IH3+QPVjYzx</latexit><latexit sha1_base64="uIbhaxHObW9k+KtpSlNLCo0J2X4=">AAAB6HicbVDLSgNBEOz1GeMr6tHLYBA8hV0R9Bj04jEB84BkCbOT3mTMzOwyMyuEkC/w4kERr36SN//GSbIHTSxoKKq66e6KUsGN9f1vb219Y3Nru7BT3N3bPzgsHR03TZJphg2WiES3I2pQcIUNy63AdqqRykhgKxrdzfzWE2rDE/VgxymGkg4Ujzmj1kl12SuV/Yo/B1klQU7KkKPWK311+wnLJCrLBDWmE/ipDSdUW84ETovdzGBK2YgOsOOoohJNOJkfOiXnTumTONGulCVz9ffEhEpjxjJynZLaoVn2ZuJ/Xiez8U044SrNLCq2WBRngtiEzL4mfa6RWTF2hDLN3a2EDammzLpsii6EYPnlVdK8rAR+Jahflau3eRwFOIUzuIAArqEK91CDBjBAeIZXePMevRfv3ftYtK55+cwJ/IH3+QPVjYzx</latexit><latexit sha1_base64="uIbhaxHObW9k+KtpSlNLCo0J2X4=">AAAB6HicbVDLSgNBEOz1GeMr6tHLYBA8hV0R9Bj04jEB84BkCbOT3mTMzOwyMyuEkC/w4kERr36SN//GSbIHTSxoKKq66e6KUsGN9f1vb219Y3Nru7BT3N3bPzgsHR03TZJphg2WiES3I2pQcIUNy63AdqqRykhgKxrdzfzWE2rDE/VgxymGkg4Ujzmj1kl12SuV/Yo/B1klQU7KkKPWK311+wnLJCrLBDWmE/ipDSdUW84ETovdzGBK2YgOsOOoohJNOJkfOiXnTumTONGulCVz9ffEhEpjxjJynZLaoVn2ZuJ/Xiez8U044SrNLCq2WBRngtiEzL4mfa6RWTF2hDLN3a2EDammzLpsii6EYPnlVdK8rAR+Jahflau3eRwFOIUzuIAArqEK91CDBjBAeIZXePMevRfv3ftYtK55+cwJ/IH3+QPVjYzx</latexit> ProbabilityDensity(km-1) Triggered Earthquakesuncertainties
  • 20. 20 Spatial Properties of Triggering ↵ ' 0.4<latexit sha1_base64="WqBQsQOZhZGJhAo0wUUhhOBDIGI=">AAAB+XicbVBNS8NAEN3Ur1q/oh69LBbBU0mkoMeiF48V7Ac0oWy2k3bp7ibubgol9J948aCIV/+JN/+N2zYHbX0w8Hhvhpl5UcqZNp737ZQ2Nre2d8q7lb39g8Mj9/ikrZNMUWjRhCeqGxENnEloGWY4dFMFREQcOtH4bu53JqA0S+SjmaYQCjKULGaUGCv1XTcgPB2RQDMBT9ir1ftu1at5C+B14hekigo0++5XMEhoJkAayonWPd9LTZgTZRjlMKsEmYaU0DEZQs9SSQToMF9cPsMXVhngOFG2pMEL9fdEToTWUxHZTkHMSK96c/E/r5eZ+CbMmUwzA5IuF8UZxybB8xjwgCmghk8tIVQxeyumI6IINTasig3BX315nbSvar5X8x/q1cZtEUcZnaFzdIl8dI0a6B41UQtRNEHP6BW9Obnz4rw7H8vWklPMnKI/cD5/AG5Ykto=</latexit><latexit 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sha1_base64="WqBQsQOZhZGJhAo0wUUhhOBDIGI=">AAAB+XicbVBNS8NAEN3Ur1q/oh69LBbBU0mkoMeiF48V7Ac0oWy2k3bp7ibubgol9J948aCIV/+JN/+N2zYHbX0w8Hhvhpl5UcqZNp737ZQ2Nre2d8q7lb39g8Mj9/ikrZNMUWjRhCeqGxENnEloGWY4dFMFREQcOtH4bu53JqA0S+SjmaYQCjKULGaUGCv1XTcgPB2RQDMBT9ir1ftu1at5C+B14hekigo0++5XMEhoJkAayonWPd9LTZgTZRjlMKsEmYaU0DEZQs9SSQToMF9cPsMXVhngOFG2pMEL9fdEToTWUxHZTkHMSK96c/E/r5eZ+CbMmUwzA5IuF8UZxybB8xjwgCmghk8tIVQxeyumI6IINTasig3BX315nbSvar5X8x/q1cZtEUcZnaFzdIl8dI0a6B41UQtRNEHP6BW9Obnz4rw7H8vWklPMnKI/cD5/AG5Ykto=</latexit><latexit sha1_base64="WqBQsQOZhZGJhAo0wUUhhOBDIGI=">AAAB+XicbVBNS8NAEN3Ur1q/oh69LBbBU0mkoMeiF48V7Ac0oWy2k3bp7ibubgol9J948aCIV/+JN/+N2zYHbX0w8Hhvhpl5UcqZNp737ZQ2Nre2d8q7lb39g8Mj9/ikrZNMUWjRhCeqGxENnEloGWY4dFMFREQcOtH4bu53JqA0S+SjmaYQCjKULGaUGCv1XTcgPB2RQDMBT9ir1ftu1at5C+B14hekigo0++5XMEhoJkAayonWPd9LTZgTZRjlMKsEmYaU0DEZQs9SSQToMF9cPsMXVhngOFG2pMEL9fdEToTWUxHZTkHMSK96c/E/r5eZ+CbMmUwzA5IuF8UZxybB8xjwgCmghk8tIVQxeyumI6IINTasig3BX315nbSvar5X8x/q1cZtEUcZnaFzdIl8dI0a6B41UQtRNEHP6BW9Obnz4rw7H8vWklPMnKI/cD5/AG5Ykto=</latexit> Catalog from Southern California (Hainzl et al. 2015) υ 1.35 short-ranged for induced earthquakes υ 3 might depend on the structure of the fault network ?? r/10↵m <latexit 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static triggering
  • 21. 21 Gutenberg- Richter Relation Omori Relation Spatial Density Decay Productivity Relation Induced (Oklahoma) Tectonic vs Induced seismicity (southern California) Gu et al. 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  • 22. 22 Ongoing Work Why important: implications for hazard assesment Epidemic‐Type Aftershock Sequence (ETAS) Model (Llenos and Michael, AGU, 2016) use empirical relations run your model forcast future! CAL PROPERTIES OF AFTERSHOCKS ng rela- by the nificant apin et s j with onsider vents in nted in choice ructure 2013]. mber of ificant. e k and city in depend on space and time such that the ETAS model falls into the class of nonhomogeneous spatiotemporal Poisson processes. The overall rate of activity is given by (Er, t) = b(Er) + X tiÄt mi (t – ti,Er – Eri), (3) where ti, Eri, and mi refer to the time, location, and magnitude of earthquake i, respectively. mi (t – ti,Er – Eri) describes the occurrence rate of earthquakes triggered by event i, while b(Er) is the spatially varying background activity. For the ETAS model, the occurrence rate is defined as mi (t – ti,Er – Eri) = (mi)‰(t – ti)ˆmi (Er – Eri), (4) (t ti) p <latexit sha1_base64="ld6/P7fuQgLNui2y1dPvida5nKc=">AAAB83icbVDLSgNBEOyNrxhfUY9eBoMQDwm7Iugx6MVjBPOAZA2zk0kyZHZ3mOkVwpLf8OJBEa/+jDf/xkmyB00saCiquunuCpQUBl3328mtrW9sbuW3Czu7e/sHxcOjpokTzXiDxTLW7YAaLkXEGyhQ8rbSnIaB5K1gfDvzW09cGxFHDzhR3A/pMBIDwShaqVvGCvbE+WNaUdNeseRW3TnIKvEyUoIM9V7xq9uPWRLyCJmkxnQ8V6GfUo2CST4tdBPDFWVjOuQdSyMacuOn85un5MwqfTKIta0IyVz9PZHS0JhJGNjOkOLILHsz8T+vk+Dg2k9FpBLkEVssGiSSYExmAZC+0JyhnFhCmRb2VsJGVFOGNqaCDcFbfnmVNC+qnlv17i9LtZssjjycwCmUwYMrqMEd1KEBDBQ8wyu8OYnz4rw7H4vWnJPNHMMfOJ8/HhOREw==</latexit><latexit sha1_base64="ld6/P7fuQgLNui2y1dPvida5nKc=">AAAB83icbVDLSgNBEOyNrxhfUY9eBoMQDwm7Iugx6MVjBPOAZA2zk0kyZHZ3mOkVwpLf8OJBEa/+jDf/xkmyB00saCiquunuCpQUBl3328mtrW9sbuW3Czu7e/sHxcOjpokTzXiDxTLW7YAaLkXEGyhQ8rbSnIaB5K1gfDvzW09cGxFHDzhR3A/pMBIDwShaqVvGCvbE+WNaUdNeseRW3TnIKvEyUoIM9V7xq9uPWRLyCJmkxnQ8V6GfUo2CST4tdBPDFWVjOuQdSyMacuOn85un5MwqfTKIta0IyVz9PZHS0JhJGNjOkOLILHsz8T+vk+Dg2k9FpBLkEVssGiSSYExmAZC+0JyhnFhCmRb2VsJGVFOGNqaCDcFbfnmVNC+qnlv17i9LtZssjjycwCmUwYMrqMEd1KEBDBQ8wyu8OYnz4rw7H4vWnJPNHMMfOJ8/HhOREw==</latexit><latexit sha1_base64="ld6/P7fuQgLNui2y1dPvida5nKc=">AAAB83icbVDLSgNBEOyNrxhfUY9eBoMQDwm7Iugx6MVjBPOAZA2zk0kyZHZ3mOkVwpLf8OJBEa/+jDf/xkmyB00saCiquunuCpQUBl3328mtrW9sbuW3Czu7e/sHxcOjpokTzXiDxTLW7YAaLkXEGyhQ8rbSnIaB5K1gfDvzW09cGxFHDzhR3A/pMBIDwShaqVvGCvbE+WNaUdNeseRW3TnIKvEyUoIM9V7xq9uPWRLyCJmkxnQ8V6GfUo2CST4tdBPDFWVjOuQdSyMacuOn85un5MwqfTKIta0IyVz9PZHS0JhJGNjOkOLILHsz8T+vk+Dg2k9FpBLkEVssGiSSYExmAZC+0JyhnFhCmRb2VsJGVFOGNqaCDcFbfnmVNC+qnlv17i9LtZssjjycwCmUwYMrqMEd1KEBDBQ8wyu8OYnz4rw7H4vWnJPNHMMfOJ8/HhOREw==</latexit><latexit sha1_base64="ld6/P7fuQgLNui2y1dPvida5nKc=">AAAB83icbVDLSgNBEOyNrxhfUY9eBoMQDwm7Iugx6MVjBPOAZA2zk0kyZHZ3mOkVwpLf8OJBEa/+jDf/xkmyB00saCiquunuCpQUBl3328mtrW9sbuW3Czu7e/sHxcOjpokTzXiDxTLW7YAaLkXEGyhQ8rbSnIaB5K1gfDvzW09cGxFHDzhR3A/pMBIDwShaqVvGCvbE+WNaUdNeseRW3TnIKvEyUoIM9V7xq9uPWRLyCJmkxnQ8V6GfUo2CST4tdBPDFWVjOuQdSyMacuOn85un5MwqfTKIta0IyVz9PZHS0JhJGNjOkOLILHsz8T+vk+Dg2k9FpBLkEVssGiSSYExmAZC+0JyhnFhCmRb2VsJGVFOGNqaCDcFbfnmVNC+qnlv17i9LtZssjjycwCmUwYMrqMEd1KEBDBQ8wyu8OYnz4rw7H4vWnJPNHMMfOJ8/HhOREw==</latexit> |~r ~ri| v <latexit sha1_base64="c4SMSEQDFb0EQToMDrBwH5SIctc=">AAACAXicbVDLSsNAFJ3UV62vqBvBzWAR3LQkIuiy6MZlBfuANobJ9KYdOnkwMymUNG78FTcuFHHrX7jzb5y2WWjrgcs9nHMvM/d4MWdSWda3UVhZXVvfKG6WtrZ3dvfM/YOmjBJBoUEjHom2RyRwFkJDMcWhHQsggceh5Q1vpn5rBEKyKLxX4xicgPRD5jNKlJZc82jSHQFNRVbJu8smD2lllLlm2apaM+BlYuekjHLUXfOr24toEkCoKCdSdmwrVk5KhGKUQ1bqJhJiQoekDx1NQxKAdNLZBRk+1UoP+5HQFSo8U39vpCSQchx4ejIgaiAXvan4n9dJlH/lpCyMEwUhnT/kJxyrCE/jwD0mgCo+1oRQwfRfMR0QQajSoZV0CPbiycukeV61rap9d1GuXedxFNExOkFnyEaXqIZuUR01EEWP6Bm9ojfjyXgx3o2P+WjByHcO0R8Ynz98AZeJ</latexit><latexit sha1_base64="c4SMSEQDFb0EQToMDrBwH5SIctc=">AAACAXicbVDLSsNAFJ3UV62vqBvBzWAR3LQkIuiy6MZlBfuANobJ9KYdOnkwMymUNG78FTcuFHHrX7jzb5y2WWjrgcs9nHMvM/d4MWdSWda3UVhZXVvfKG6WtrZ3dvfM/YOmjBJBoUEjHom2RyRwFkJDMcWhHQsggceh5Q1vpn5rBEKyKLxX4xicgPRD5jNKlJZc82jSHQFNRVbJu8smD2lllLlm2apaM+BlYuekjHLUXfOr24toEkCoKCdSdmwrVk5KhGKUQ1bqJhJiQoekDx1NQxKAdNLZBRk+1UoP+5HQFSo8U39vpCSQchx4ejIgaiAXvan4n9dJlH/lpCyMEwUhnT/kJxyrCE/jwD0mgCo+1oRQwfRfMR0QQajSoZV0CPbiycukeV61rap9d1GuXedxFNExOkFnyEaXqIZuUR01EEWP6Bm9ojfjyXgx3o2P+WjByHcO0R8Ynz98AZeJ</latexit><latexit sha1_base64="c4SMSEQDFb0EQToMDrBwH5SIctc=">AAACAXicbVDLSsNAFJ3UV62vqBvBzWAR3LQkIuiy6MZlBfuANobJ9KYdOnkwMymUNG78FTcuFHHrX7jzb5y2WWjrgcs9nHMvM/d4MWdSWda3UVhZXVvfKG6WtrZ3dvfM/YOmjBJBoUEjHom2RyRwFkJDMcWhHQsggceh5Q1vpn5rBEKyKLxX4xicgPRD5jNKlJZc82jSHQFNRVbJu8smD2lllLlm2apaM+BlYuekjHLUXfOr24toEkCoKCdSdmwrVk5KhGKUQ1bqJhJiQoekDx1NQxKAdNLZBRk+1UoP+5HQFSo8U39vpCSQchx4ejIgaiAXvan4n9dJlH/lpCyMEwUhnT/kJxyrCE/jwD0mgCo+1oRQwfRfMR0QQajSoZV0CPbiycukeV61rap9d1GuXedxFNExOkFnyEaXqIZuUR01EEWP6Bm9ojfjyXgx3o2P+WjByHcO0R8Ynz98AZeJ</latexit><latexit sha1_base64="c4SMSEQDFb0EQToMDrBwH5SIctc=">AAACAXicbVDLSsNAFJ3UV62vqBvBzWAR3LQkIuiy6MZlBfuANobJ9KYdOnkwMymUNG78FTcuFHHrX7jzb5y2WWjrgcs9nHMvM/d4MWdSWda3UVhZXVvfKG6WtrZ3dvfM/YOmjBJBoUEjHom2RyRwFkJDMcWhHQsggceh5Q1vpn5rBEKyKLxX4xicgPRD5jNKlJZc82jSHQFNRVbJu8smD2lllLlm2apaM+BlYuekjHLUXfOr24toEkCoKCdSdmwrVk5KhGKUQ1bqJhJiQoekDx1NQxKAdNLZBRk+1UoP+5HQFSo8U39vpCSQchx4ejIgaiAXvan4n9dJlH/lpCyMEwUhnT/kJxyrCE/jwD0mgCo+1oRQwfRfMR0QQajSoZV0CPbiycukeV61rap9d1GuXedxFNExOkFnyEaXqIZuUR01EEWP6Bm9ojfjyXgx3o2P+WjByHcO0R8Ynz98AZeJ</latexit>
  • 23. 23 Ongoing Work Background Ratio Low High LocalGlobal Less Triggering in relative sense 0 50 100
  • 24. 24 Ongoing Work Background Ratio Low High Varying cfixed c Less Triggering in relative sense Thank You! 0 50 100
  • 25. 25 Temporal Properties of Triggering Time (day) Rate(day-1) ? Aftershock decay rate: Omori-Utsu Relation t<latexit sha1_base64="fInOqGTCCrWkRGJFOZWK1l6FLBY=">AAAB6HicbVBNS8NAEJ34WetX1aOXYBE8lUQEPRa9eGzBfkAbymY7adduNmF3IpTSX+DFgyJe/Une/Ddu2xy09cHA470ZZuaFqRSGPO/bWVvf2NzaLuwUd/f2Dw5LR8dNk2SaY4MnMtHtkBmUQmGDBElspxpZHEpshaO7md96Qm1Eoh5onGIQs4ESkeCMrFSnXqnsVbw53FXi56QMOWq90le3n/AsRkVcMmM6vpdSMGGaBJc4LXYzgynjIzbAjqWKxWiCyfzQqXtulb4bJdqWIneu/p6YsNiYcRzazpjR0Cx7M/E/r5NRdBNMhEozQsUXi6JMupS4s6/dvtDISY4tYVwLe6vLh0wzTjabog3BX355lTQvK75X8etX5eptHkcBTuEMLsCHa6jCPdSgARwQnuEV3pxH58V5dz4WrWtOPnMCf+B8/gDgKYz4</latexit><latexit 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