Modeling swarms:
A path toward determining shortterm probabilities
Andrea Llenos
USGS Menlo Park
Workshop on Time-Dependent Models in UCERF3
8 June 2011
Outline
• Motivation: Why are
swarms important for
UCERF?
• Where things stand now
– Characteristics of
swarms
– Detecting swarms
(retrospectively)
• What needs to be done
– Detecting swarms
(prospectively)
– Implementation
• As ETAS add-on?
• As a data assimilation
application?
Observed
seismicity rate
Ke ( mi  mc )
R(t )    
p
ti t (t  ti  c )
Background
seismicity rate
Aftershock
sequences
Time-dependent background rates are needed to account for rate
changes due to external (aseismic) processes
2000 Vogtland/Bohemia swarm (fluids)
Hainzl and Ogata (2005)
2000 Izu Islands swarm (magma/fluids)
Lombardi et al. (2006)
2003-2004 Ubaye swarm (fluid-flow)
Daniel et al. (2011)
Salton Trough
Time-dependent background rate matches
observed seismicity better than stationary
ETAS model
Transformed Time
Llenos and McGuire (2011)
ti
 i  (ti )    (s)ds
0
Characteristics of swarms
•
•
Increase in seismicity rate above background without clear
mainshock
Don’t follow empirical aftershock laws
– Bath’s Law
– Omori’s Law
•
These characteristics make them appear anomalous to ETAS
Holtkamp and Brudzinski (2011)
Detecting swarms in an earthquake catalog
Swarms associated with aseismic transients
2005 Obsidian Buttes, CA (1985-2005, SCEDC)
2005 Kilauea, HI (2001-2007, ANSS)
2002, 2007 Boso, Japan (1992-2007, JMA)
Shallow aseismic slip
on a strike-slip fault
in southern CA
observed by InSAR
and GPS
Slow slip events on the
subduction plate interface off
of Boso, Japan observed by
cGPS, tiltmeter
Lohman & McGuire (2007)
Slow slip events on
southern flank of
Kilauea volcano in HI
observed by GPS
Wolfe et al.
(2007)
Ozawa et al.
(2007)
Data analysis: ETAS model optimization
Swarms associated with aseismic transients
2005 Obsidian Buttes, CA (1985-2005, SCEDC)
2005 Kilauea, HI (2001-2007, ANSS)
2002, 2007 Boso, Japan (1992-2007, JMA)
•
•
Ke ( mi  mc )
R(t )    
p
(
t

t

c
)
ti t
i
Optimize ETAS model to fit
catalog prior to swarm and
extrapolate fit through
remainder of catalog
Calculate transformed times
(~ ETAS predicted number of
events in a time interval)
ti
 i  (ti )   R(s)ds
0
2005 Kilauea
– Cumulative number of events
vs. transformed time should
be linear if seismicity
behaving as a point process
– Positive deviations occur
when more seismicity is being
triggered in a time interval
than ETAS can explain
Swarms appear as anomalies relative to ETAS
2005 Obsidian Buttes
Swarm
Pre-swarm MLE
(K, , , p, c)
Swarm MLE
(K, , , p, c)
2002
Boso
0.13, 0.022, 0.56,
1.11, 0.096
0.07, 2.09, 0.09,
1.0, 0.0005
2005
Kilauea
0.28, 0.16, 1.24,
1.21, 0.002
0.96, 0.89, 0.61,
0.92, 0.003
2005
Obs
Buttes
0.61, 0.031, 0.88,
1.1, 0.001
1.4, 225, 1.05,
1.0, 0.001
2007
Boso
0.20, 0.013, 0.55,
0.88, 0.0004
0.61, 2.4, 1.37,
1.0, 0.0008
2002, 2007 Boso, Japan
2005 Kilauea
A path toward determining short-term
probabilities
• Build off of ETAS-based forecasts
– Detect that a swarm is occurring
• Has been done retrospectively
• Prospectively?
– During the swarm
• Re-estimate the background rate (and other parameters?)
• Re-calculate short-term probabilities
• How often? 1x? 2x? Every 5 days? 10 days?
– Identify when the swarm is over
• Return to pre-swarm background rate?
• More sophisticated approaches (e.g., data
assimilation)?
Data Assimilation Algorithms
•
•
•
Combines dynamic model with noisy data (e.g. seismicity rates) to estimate the
temporal evolution of underlying physical variables (states)
Examples: Kalman filters, particle filters
Applications in navigation, tracking, hydrology
Welch & Bishop (2001)
Data Assimilation Example
•
•
•
•
State-space model based on rate-state equations
States: stressing rate, rate-state state variable g
Algorithm: Extended Kalman Filter
Approach: Optimize ETAS for the catalog, subtract ETAS predicted
aftershock rate to obtain time-dependent background rate, use
data assimilation algorithm to estimate stressing rate and detect
transients that trigger swarms
Llenos and McGuire (2011)
A path toward determining short-term
probabilities
• Build off of ETAS-based forecasts
– Detect that a swarm is occurring
• Has been done retrospectively
• Prospectively?
– During the swarm
• Re-estimate the background rate (and other parameters?)
• Re-calculate short-term probabilities
• How often? 1x? 2x? Every 5 days? 10 days?
– Identify when the swarm is over
• Return to pre-swarm background rate?
• More sophisticated approaches (e.g., data
assimilation)?
Outline
•
Why are swarms important for UCERF?
– Need time-dependent background rate (mu) to model earthquake rates
observed in catalogs accurately
•
•
•
•
Salton Trough
Ubaye France
Campei Flagrei
Vogtland Bohemia
– Swarms prevalent in Salton Trough, volcanic regions like Long Valley,
places where M>6 events have occurred
•
Characteristics of swarms
•
ETAS parameters change during swarms (primarily stationary
background rate)
How to implement this to calculate short-term probabilities?
•
– Don’t fit empirical models of aftershock clustering, appear anomalous
– Where we are now
•
•
Detection (retrospective)
How they affect ETAS parameters
– Outstanding issues that need to be addressed
– Data assimilation?