Applications of Earthquake Simulators to Assessment of Earthquake Probabilities Jim Dieterich

Some issues/limitations with current UCERF approach Sometimes I lie awake at night, and I ask, "Where have I gone wrong?” Then a voice says to me, "This is going to take more than one night."   (Charles M. Schultz/Charlie Brown, in "Peanuts”) Models have become exceedingly complex. 2. Probability density distributions for recurrence of slip in large earthquakes are not known. Statistics of large earthquakes very poorly defined. Poisson, quasi-periodic, clustered? Magnitude and position dependence of pdfs. 3. Interpretation of empirical model. 4. Strict use of characteristic earthquakes and segmentation is problematic 5. Point characterizations of segments. Properties governing recurrence and slip are not constant along segments. Stress interactions, clock reset. 6. Non-linear loading processes. viscoelasticity, fault creep, off-fault relaxation 7. Integration with spatiotemporal clustering 8. Fault to fault jumps and rupture branching. Quote perhaps not too gross of an overstatement with respect to issues with UCERF Model has become rather ad hoc Contributing problem: Current approaches tend to treat these items independently, when in fact they are often coupled

Ned’s Priorities: Relax segmentation Incorporate spatiotemporal clustering

Inputs to simulators

Simulators directly produce earthquake rate models for A- and B- type faults. Catalogs ~106 events. Moment-balanced Segmentation is not assumed or enforced Multiple realizations ® effect of parameter uncertainties Multiple models Tuned to be consistent with paleoseismic recurrence Rupture jumps and branching Uncertainties in moment-area relations are largely avoided Major effort in UCERF2

Direct prediction of conditional probabilities Sufficient number of events in catalogs to generate empirical pdfs for all fault sub-sections No apriori assumptions about clustering vs Poisson vs quasi-periodic. Multiple realizations – evaluate effect of parameter uncertainties Multiple models

Subsection approach to determining conditional probabilities: Steps Probability density for recurrence of slip on fault sub-section k CPk = conditional probability of event M≥6.5 on section k Sub-catalog of n events for a section that occur in the interval Dt for used to determine CPk This catalog may be quite different for different times

Weighted participation rate of event i Sub-catalog of n events for a section that occur in the interval Dt for used to determine CPk

Weighted participation rate of event i Total probability of event i in the conditional interval Dt

Spatiotemporal clustering with RSQSim Stacked rate of seismicity relative to mainshocks 6>M<7 Bottom line – reached the limits of useful development Unified approach – built on physics which we can expect to improve with time Decay of aftershocks follows Omori power law t -p with p = 0.77 Foreshocks (not shown) follow an inverse Omori decay with p = 0.92 Dieterich and Richards-Dinger, PAGEOPH, 2010

Inter-event Waiting Time Distributions California catalog 1911-2010

Space – Time Distributions

Earthquake cluster along San Andreas Fault M7.3 43 aftershocks in 18.2days About 10% of M>7 , All-Cal model – SCEC Simulator Comparison Project 13

Earthquake cluster along San Andreas Fault M6.9 Followed by 6 aftershocks in 4.8 minutes All-Cal model – SCEC Simulator Comparison Project 14

Earthquake cluster along San Andreas Fault M7.2 All-Cal model – SCEC Simulator Comparison Project 15

Clusters of Large Earthquakes Rates of M≥7 Earthquakes following M≥7 Earthquakes Robs is the total number of clusters M≥7, divided by the number of isolated M≥7 earthquakes Rate is n

Cumulative probability of earthquake (on San Jacinto fault segment of the San Jacinto fault) From random time From time of M≥6.5 on adjacent Anza segment From random time From time of M≥6.5 on distant Calaveras segment M≥6.5 on San Jacinto Segment M≥6.5 on San Jacinto Segment Fault interaction probabilities – If pick times at random this red is the CPF for event M≥6.5 on Events on the SanJacinto segment of SanJacinto Flt. Red is waiting time dist for randomly selected time, what is waiting time for next M>6.5 on SanJacinto segment Black is waiting time for following an Anza event M>6.5 for an event M>6.5 on the San Jacinto Segment At 10^-1 yr prob is less than .01

Cumulative probability of earthquakes (on San Jacinto fault segment of the San Jacinto fault) From random time From time of M≥6.5 on adjacent Anza segment From random time From time of M≥6.5 on adjacent Anza segment M≥6.5 on San Jacinto Segment M≥5.5 on San Jacinto Segment Bottom plot is for events on the SanJacinto segment of SanJacinto Flt. Red is waitind time dist for randomly selected time, what is waiting time for next M>6.5 on SanJacinto segment Black is waiting time for following an Anza event M>6.5 for an event M>6.5 on the San Jacinto Segment

Summary of some advantages of simulators relative to current UCERF methods Integrated self-consistent framework for generating an earthquake rate model Properly captures intrinsic relations between stress and fault slip in 3D systems and avoids the dubious use of point characterizations of spatially varying properties (stress, slip, time since last slip, clock reset) Clustering is modeled deterministically and tied to constitutive parameters and evolving stress conditions Framework for characterizing regional fluctuations of seismicity rates – interpretation of empirical model Non-linear stressing from interactions with deep creeping zone and viscoelasticity in some models Moment balancing issues are eliminated No assumptions are made regarding characteristic earthquakes (pro or con) Rupture jumps and branching occur spontaneously Coupling factor and aseismic creep reduction of moment

Summary of Possible Near-Term Applications Earthquake rate models for A and B faults (no a priori segmentation) Conditional probabilities on A and B faults (Poisson, clustering and quasi-periodic are seen) Clustering probabilities for moderate and large earthquakes (Pre-calculate look-up table for near real-time response) Some other applications Develop and/or test algorithms and models used with current methods Interpretation of empirical model and regional rate fluctuations (Tullis talk) Relative weighting appropriate for quasi-periodic, clustering, and Poisson probability models Evolution of b-values Evaluate fault rupture scenarios (“Stringing Pearls” of Biasi and Weldon – Goal: reduce number of possible models)