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 – Detecting swarms (retrospectively) What needs to be done – Detecting swarms (prospectively) – Implementation As ETAS add-on? As a data assimilation application? 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) 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 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 catalog Swarms associated with aseismic transients 2005 Obsidian Buttes, CA ( , SCEDC) 2005 Kilauea, HI ( , ANSS) 2002, 2007 Boso, Japan ( , 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 transients 2005 Obsidian Buttes, CA ( , SCEDC) 2005 Kilauea, HI ( , ANSS) 2002, 2007 Boso, Japan ( , JMA) 2005 Kilauea

Swarms appear as anomalies relative to ETAS 2002, 2007 Boso, Japan 2005 Obsidian Buttes 2005 Kilauea SwarmPre-swarm MLE (K, , , p, c) Swarm MLE (K, , , p, c) 2002 Boso 0.13, 0.022, 0.56, 1.11, , 2.09, 0.09, 1.0, Kilauea 0.28, 0.16, 1.24, 1.21, , 0.89, 0.61, 0.92, Obs Buttes 0.61, 0.031, 0.88, 1.1, , 225, 1.05, 1.0, Boso 0.20, 0.013, 0.55, 0.88, , 2.4, 1.37, 1.0,

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  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?