Spatio-temporal evolution of seismic clusters
in southern and central California
Ilya Zaliapin
Department of Mathematics and Statistics
University of Nevada, Reno
Yehuda Ben-Zion
Department of Earth Sciences
University of Southern California
SAMSI workshop “Dynamics of Seismicity”
Thursday, October 10, 2013
Outline
1
Earthquake clusters: existence, detection, stability
2
Clusters in southern California
o
o
Main types of clusters
Topological cluster characterization
3
Cluster type vs. physical properties of the lithosphere
4
Evolution of clustering with relation to large events
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)
Distance from an earthquake j to an earlier earthquake i :
Definition:
(Fractal) dimension of epicenters
   r 10
d
Intercurrence time
 bmi
Spatial distance
,  0
Gutenberg-Richter law
Property:
  TR, log  log T  log R
Rescaled time T   10bmi /2 , Rescaled distance R  r d 10bmi /2
[M. Baiesi and M. Paczuski, PRE, 69, 066106 (2004)]
[Zaliapin et al., PRL, 101, 018501 (2008)]
Separation of clustered and background parts in southern California
Earthquake j
Zaliapin et al., PRL (2008)
Zaliapin and Ben-Zion, JGR (2012)
Background and clustered parts in models
Homogeneous Poisson process
ETAS model
Zaliapin et al., PRL (2008)
Zaliapin and Ben-Zion, JGR (2013)
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 et al., PRL (2008)
Zaliapin and Ben-Zion, JGR (2013)
Identification of clusters: data driven
Cluster #3
Cluster #1
Cluster #2
weak link
strong link
Time
Identification of event types: problem driven
Foreshocks
Mainshock
Single
Aftershocks
Time
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).
Swarm vs. burst like clusters:
Topologic representation
M5.51
M5.75
L= 417, tree depth = 9, ave. depth = 3.8
Swarm-like
M5.75
Time
M5.51
Time
Burst-like
L= 572, tree depth = 44, ave. depth = 30.3
Average leaf depth (number of generations from a leaf to the root):
Bimodal structure
ETAS model
Large topological depth:
Swarm-like clusters
Small topological depth:
Burst-like clusters
HYS (2012), mM ≥ 2
Heat flow in southern California
http://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
Space
Statistical analysis of premonitory patterns: zero-level approach
D-zone
X-zone
D-zone
X-zone
N-zone
Time
Topological depth (average leaf depth)
All mainshocks
D = 2 years, X = 1 year, R = 200 km, M=6.5
mainshocks with m>3 are examined
Topological depth (average leaf depth)
ANOVA p =7x10-7 : Significant difference
Large families, N > 20
Δ = X = 3 years, R = 100km
m > 3, N > 20
Proportion of families
All mainshocks
Δ = X = 2 years, R = 100km
m>3
Proportion of large families (N>=5)
Families (N > 1)
Δ = X = 2 years, R = 100km
m > 3, N >1
Large earthquakes in California, M6.5
4) Hector Mine, M7.1, 1999
3) Northridge, M6.7, 1994
1) Superstition Hills, M6.6, 1987
5) El Mayor Cucapah, M7.2, 2010
2) Landers, M7.3, 1992
L
L
EMC
“San Jacinto Fault”
HM
L
N
SH
EMC
“San Jacinto Fault”
EMC
SH
Families with size L > 10
L
N
HM
Families with 3 < m < 4
100 km from Superstition Hills, M6.6 of 1987
SH
L
N
HM
Topological depth d > 6, mainshock m< 5
EMC
Salton Trough
Salton Trough
SH
L
N
HM
Average leaf depth > 1, Family size > 5
EMC
Baja California
Baja California
SH
L
N
HM
Average leaf depth > 1, Family size > 5
EMC
El Mayor Cucapah, M7.2
R < 5 km
R < 20 km
R < 100 km
R < 300 km
Average leaf depth > 1, Family size > 5
20 km from Landers, M7.3 of 1992
SH
L
N
HM
EMC
Landers, M7.3 of 1992
Remote foreshock to Hector
Mine, M7.1 of 1999
Remote aftershock of
Superstition Hill, M6.6 of 1987
Topological depth d > 5
In this region: 613 mainshocks; 139 families;
11 mainshocks/10 families with m>3.5
Summary
1
Seismic clusters in southern California
o Four types of clusters:
• Burst-like clusters
• Swarm-like clusters
• Singles
• Largest regional clusters
o Topological cluster characterization
2
Spatial variability: Relation to physical properties of the crust
o
o
3
Swarm-like clusters <-> decreased effective viscosity
Burst-like clusters <-> increased effective viscosity
Temporal variability: Relation to large events