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?