Ilya Zaliapin Department of Mathematics and Statistics University of Nevada, Reno SAMSI workshop Dynamics of Seismicity Thursday, October 10, 2013 Yehuda Ben-Zion Department 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 Outline o Main types of clusters o Topological cluster characterization Evolution of clustering with relation to large events 44 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

Baiesi and Paczuski, PRE, 69, (2004) Zaliapin et al., PRL, 101, (2008) Zaliapin and Ben-Zion, GJI, 185, 1288–1304 (2011) Zaliapin and Ben-Zion, JGR, 118, (2013) Zaliapin and Ben-Zion, JGR, 118, (2013)

(Fractal) dimension of epicenters Intercurrence timeSpatial distanceGutenberg-Richter law [M. Baiesi and M. Paczuski, PRE, 69, (2004)] [Zaliapin et al., PRL, 101, (2008)] Distance from an earthquake j to an earlier earthquake i : Definition: Property:

Separation of clustered and background parts in southern California Earthquake j Parent (nearest neighbor) 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 processETAS 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 #3Cluster #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

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. 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. Singles Highly numerous in all regions; some but not all are related to catalog resolution. 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 M5.75 L= 417, tree depth = 9, ave. depth = 3.8L= 572, tree depth = 44, ave. depth = 30.3 Swarm vs. burst like clusters: Topologic representation Burst-likeSwarm-like Time

Average leaf depth (number of generations from a leaf to the root): Bimodal structure HYS (2012), m M 2 Large topological depth: Swarm-like clusters Small topological depth: Burst-like clusters ETAS model

Heat flow in southern California

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-zone D-zone Time Space N-zone Statistical analysis of premonitory patterns: zero-level approach

D = 2 years, X = 1 year, R = 200 km, M=6.5 mainshocks 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, ) Hector Mine, M7.1, ) Superstition Hills, M6.6, ) El Mayor Cucapah, M7.2, ) Northridge, M6.7, 1994

L EMC L

San Jacinto Fault SH EMC L N HM

Families with 3 < m < 4 Families with size L > 10 San Jacinto Fault SH EMC LNHM

Topological depth d > 6, mainshock m< km from Superstition Hills, M6.6 of 1987 SHEMCLNHM

Salton Trough

Average leaf depth > 1, Family size > 5 SHEMCLNHM Salton Trough

Baja California

Average leaf depth > 1, Family size > 5 Baja California SHEMCLNHM

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 Landers, M7.3 of 1992 Remote foreshock to Hector Mine, M7.1 of 1999 SHEMCLNHM

Seismic clusters in southern California 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 viscosity o Burst-like clusters increased effective viscosity Spatial variability: Relation to physical properties of the crust Temporal variability: Relation to large events