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Modeling swarms: A path toward determining short-term 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 - PowerPoint PPT Presentation
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Modeling swarms:A path toward determining short-
term probabilities
Andrea LlenosUSGS Menlo Park
Workshop on Time-Dependent Models in UCERF38 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?
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Background seismicity rate
Observed seismicity rate
Aftershock sequences
Time-dependent background rates are needed to account for rate changes due to external (aseismic) processes
Daniel et al. (2011)
2003-2004 Ubaye swarm (fluid-flow)Lombardi et al. (2006)
2000 Izu Islands swarm (magma/fluids)2000 Vogtland/Bohemia swarm (fluids)
Hainzl and Ogata (2005)
Salton Trough
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Time-dependent background rate matches observed seismicity better than stationary ETAS model
Llenos and McGuire (2011)
Transformed Time
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 catalogSwarms associated with aseismic transients2005 Obsidian Buttes, CA (1985-2005, SCEDC)2005 Kilauea, HI (2001-2007, ANSS)2002, 2007 Boso, Japan (1992-2007, JMA)
Ozawa et al. (2007)
Lohman & McGuire (2007)
Wolfe et al. (2007)
Slow slip events on the subduction plate interface off of Boso, Japan observed by cGPS, tiltmeter
Shallow aseismic slip on a strike-slip fault in southern CA observed by InSAR and GPS
Slow slip events on southern flank of Kilauea volcano in HI observed by GPS
Data analysis: ETAS model optimization
• 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)
– 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 associated with aseismic transients2005 Obsidian Buttes, CA (1985-2005, SCEDC)2005 Kilauea, HI (2001-2007, ANSS)2002, 2007 Boso, Japan (1992-2007, JMA)
2005 Kilauea
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Swarms appear as anomalies relative to ETAS
2002, 2007 Boso, Japan
2005 Obsidian Buttes
2005 Kilauea
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,
0.0032005 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
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– Don’t fit empirical models of aftershock clustering, appear anomalous
• ETAS parameters change during swarms (primarily stationary background rate)
• How to implement this to calculate short-term probabilities?– Where we are now
• Detection (retrospective)• How they affect ETAS parameters
– Outstanding issues that need to be addressed– Data assimilation?