Ilya Zaliapin Department of Mathematics and Statistics University of Nevada, Reno SAMSI workshop Dynamics of Seismicity Thursday, October 10, 2013 Yehuda.

Ilya ZaliapinDepartment of Mathematics and Statistics

University of Nevada, Reno

SAMSI workshop “Dynamics of Seismicity”Thursday, October 10, 2013

Yehuda Ben-ZionDepartment of Earth Sciences

University of Southern California

Spatio-temporal evolution of seismic clusters in southern and central California

Earthquake clusters: existence, detection, stability

Clusters in southern California

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3

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Outline

o Main types of clusterso Topological cluster characterization

Evolution of clustering with relation to large events44

Cluster type vs. physical properties of the lithosphere

Data

•Southern California catalog: Hauksson, Yang, Shearer (2012) available from SCEC data center; 111,981 earthquakes with m ≥ 2

•Heat flow data from www.smu.edu/geothermal

Baiesi and Paczuski, PRE, 69, 066106 (2004)Zaliapin et al., PRL, 101, 018501 (2008)

Zaliapin and Ben-Zion, GJI, 185, 1288–1304 (2011)Zaliapin and Ben-Zion, JGR, 118, 2847-2864 (2013)Zaliapin and Ben-Zion, JGR, 118, 2865-2877 (2013)

10 , 0ibmdr

(Fractal) dimension of epicenters

Intercurrence time Spatial distance Gutenberg-Richter law

[M. Baiesi and M. Paczuski, PRE, 69, 066106 (2004)]

/2 /2Rescaled time 10 , Rescaled distance 10i ibm bmdT R r

[Zaliapin et al., PRL, 101, 018501 (2008)]

, log log logTR T R

Distance from an earthquake j to an earlier earthquake i :

Definition:

Property:

Separation of clustered and background parts in southern California

Earthquake j

Pare

nt (n

eare

st n

eigh

bor)

i

Zaliapin and Ben-Zion, JGR (2012)

Zaliapin et al., PRL (2008)

Background and clustered parts in models

Zaliapin and Ben-Zion, JGR (2013)

Zaliapin et al., PRL (2008)

Homogeneous Poisson process ETAS model

Separation of clustered and background parts in southern California

Background = weak links(as in stationary,

inhomogeneous Poisson process)

Clustered part = strong links (events are much closer to each

other than in the background part)

Zaliapin and Ben-Zion, JGR (2013)

Zaliapin et al., PRL (2008)

weak link

strong link

Cluster #3

Cluster #2

Cluster #1

Identification of clusters: data driven

Time

Foreshocks

Aftershocks

Mainshock

Identification of event types: problem driven

Time

Single

ETAS declustering: Example

29,671 events

9,536 mainshocks

① Burst-like clusters Represent brittle fracture. Large b-value (b=1), small number of events,

small proportion of foreshocks, short duration, small area, isotropic spatial distribution.

Tend to occur in regions with low heat flow, non-enhanced fluid content, relatively large depth => increased effective viscosity.

② Swarm-like clusters Represent brittle-ductile fracture. Small b-value (b=0.6), large number of

events, large proportion of foreshocks, long duration, large area, anisotropic channel-like spatial pattern.

Tend to occur in regions with high heat flow, increased fluid content, relatively shallow depth => decreased effective viscosity.

③ Singles Highly numerous in all regions; some but not all are related to catalog

resolution.

④ Clusters of the largest events Most prominent clusters; object of the standard cluster studies. Not

representative of the majority of clusters (mixture of types 1-2).

M5.75

M5.51

M5.51 M5.75

L= 417, tree depth = 9, ave. depth = 3.8 L= 572, tree depth = 44, ave. depth = 30.3

Swarm vs. burst like clusters:Topologic representation

Burst-like Swarm-like

Tim

e

Tim

e

Average leaf depth (number of generations from a leaf to the root):Bimodal structure

HYS (2012), mM ≥ 2

Large topological depth:Swarm-like clusters

Small topological depth:Burst-like clusters

ETAS model

Heat flow in southern Californiahttp://www.smu.edu/geothermal

Preferred spatial location of burst/swarm like clusters 195 clusters with m ≥ 4, N ≥ 10; spatial average within 50 km

Moment of foreshocks relative to that of mainshock 195 clusters with m ≥ 4, N ≥ 10; spatial average within 50 km

Family size 112 Δ- clusters with m ≥ 4, N ≥ 10; spatial average within 50 km

X-zoneX-zone

X-zoneX-zone

D-zoneD-zone

D-zoneD-zone

Time

Spa

ce

N-zone

Statistical analysis of premonitory patterns: zero-level approach

D = 2 years, X = 1 year, R = 200 km, M=6.5mainshocks with m>3 are examined

All mainshocks

Topological depth (average leaf depth)

Δ = X = 3 years, R = 100km m > 3, N > 20

ANOVA p =7x10-7 : Significant difference

Large families, N > 20

Topological depth (average leaf depth)

Δ = X = 2 years, R = 100km m > 3

All mainshocks

Proportion of families

Δ = X = 2 years, R = 100km m > 3, N >1

Families (N > 1)

Proportion of large families (N>=5)

Large earthquakes in California, M6.5

2) Landers, M7.3, 1992

2) Landers, M7.3, 1992

4) Hector Mine, M7.1, 1999

4) Hector Mine, M7.1, 1999

1) Superstition Hills, M6.6, 1987

1) Superstition Hills, M6.6, 1987

5) El Mayor Cucapah, M7.2, 2010

5) El Mayor Cucapah, M7.2, 2010

3) Northridge, M6.7, 1994

3) Northridge, M6.7, 1994

L

EMCL

“San Jacinto Fault”

SH

EMC

LN

HM

Families with 3 < m < 4

Families with size L > 10

“San Jacinto Fault”

SH EMC

L N HM

Topological depth d > 6, mainshock m< 5

100 km from Superstition Hills, M6.6 of 1987

SH EMCL N HM

Salton Trough

Average leaf depth > 1, Family size > 5

SH EMCL N HM

Salton Trough

Baja California

Average leaf depth > 1, Family size > 5

Baja California

SH EMCL N HM

Average leaf depth > 1, Family size > 5

R < 5 km

R < 20 km

R < 100 km

R < 300 km

El Mayor Cucapah, M7.2

Topological depth d > 5

20 km from Landers, M7.3 of 1992

In this region: 613 mainshocks; 139 families; 11 mainshocks/10 families with m>3.5

Remote aftershock of Superstition Hill, M6.6 of 1987

Remote aftershock of Superstition Hill, M6.6 of 1987

Landers, M7.3 of 1992Landers, M7.3 of 1992

Remote foreshock to Hector Mine, M7.1 of 1999

Remote foreshock to Hector Mine, M7.1 of 1999

SH EMCL N HM

Seismic clusters in southern California1

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Summary

o Four types of clusters:• Burst-like clusters• Swarm-like clusters• Singles• Largest regional clusters

o Topological cluster characterization

o Swarm-like clusters <-> decreased effective viscosityo Burst-like clusters <-> increased effective viscosity

Spatial variability: Relation to physical properties of the crust

Temporal variability: Relation to large events