CSEP Powell Center 2018

CSEP2 Challenges

• Testing fault and simulation-based models
• Care about low prob. events
• Should we be testing something other nucleation?
• Is UCERF3-ETAS more valuable given the alternatives?
• Epistemic Uncertainties

Reasenberg & Jones for USGS OAF

• Rate of ≥M aftershocks at time t after mainshock with given magnitude
• Improvements made to reasenberg & jones model to update generic parameters for California
• Aftershock forecast for Mw ≥ 5 using improved R&J model
• Automating aftershock forecasts for the US (in progress w/ code development challenges)
• Moving past R&J in favor of ETAS, but could be useful for UCERF3-ETAS testing
• Testability challenges:
  • Overlapping, non-independent forecasts
  • EQ prob. Dist. Not necessarily Poissonian
  • Temporal forecasts with poorly defined spatial area
  • R&J not great with substantial triggering (e.g., swarms)

Update on ETAS Forecasting

• GUI interface to compute manual forecasts for external uses.
• AIC prefers ETAS, however more complicated models not favored over simple 3 param model
• Performs better than R&J
• Issues with "supercriticality"
  • Could solve by fitting mainshock separately
• For global problem (and local): estimating magnitude of completeness and b-value
• Need to limit supercriticality before OEF can be given to non-experts
• "Similarity forecast" can be implemented as mask/failsafe to reduce surprises
  • Defined as having "similar number of earthquakes in binned magnitudes"
  • ETAS has ½ the surprise rate of R&J
  • Or could be included in ensemble

Spatial ETAS

" ETAS type models can zero in on aftershock hot-spots o Using spatial omori type o Need some spatial kernel " Moving from spatial rates to hazards o Couple forecasts with GMPE to produce ground motions o MMI regression-based models " Testability o Challenges associated with incorporating hazard, because it eliminates some granularity in the forecast model o Worried about Type II error

Time-Dependent Background seismicity " Particularly useful for earthquake swarms where background seismicity differs from 'normal' rate o Could determine rate from previous swarms o Potential issues: " Swarm duration " Considerable variability in swarm durations " Solving using "life expectancy" table, but limited data in southern California " Likely need some physical constraints on distribution functions " Using STETAS to use standard catalog without needing declustering o Hydro mechanical models for stressing-rate can be used for induced seismicity o rate-and-state framework " Testing strategy: o Given a swarm; how long should we provide forecasts?

UCERF3 " Three models o Time-independent " Fault-based approach that splits faults into subsections " Rate of rupture computed from Grand Inversion (see pub for details) " Add gridded off-fault seismicity " Logic tree used to capture the epistemic uncertainty " Fault participation most important. (ie., what is the prob. of a particular fault hosting an eq ≥ Mw) o Time-dependent " Based on reed renewal statistics " Additional logic tree branches added o ETAS " Ignoring faults gives rise to discrepancy between ETAS and elastic rebound type models " Combines UCERF3-TD with an ETAS model and produces synthetic catalog " Issues: " Variability of MFD throughout CA " GR not consistent with data " Main question: what is the conditional prob of observing large eq given an observed small eq? " Determined that elastic rebound necessary " Rate of small events not always consistent with rate of expected aftershocks " Operationalizable, but needs significant resources " Major question: Does it have value? " HayWired scenario recently published in SRL " Shows value if interested in severe shaking. " Faults important for low prob high ground motions. " Testing UCERF3-ETAS " Fault participation, not nucleation " Logic-tree branches " Elastic rebound/aperiodicity " Characteristic behavior near faults " Retrospective testing " Aleatory variability and sequence specific etas parameters

RSQSim Rate-State earthquake Simulator " Physics-based forecasting model based on R&S statistics " Using RSQsim ruptures in hazard assessments o Need to create ucerf3 style ruptures o Do RSQSim ruptures pass ucerf3 plausibility criteria? " Surprisingly, most RSQsim ruptures didn't pass the coulomb criterion. ~17.5% did not pass. " Multi-fault ruptures tend to agree between UCERF3 and RSQsim " RSQsim agrees well with UCERF3 without specific tuning of recurrence intervals o Also: repeat times and short period ground motions o but starts to disagree at longer spectral periods " interesting conditional probs: o what is the prob of having 2 mw 7 on the Mojave within 1 week? " 4.5% in UCERF3 and 5.6% in RSQSim " Could look at two-point statistics pairwise difference between centroids " CSEP2 needs to be able to compare synthetic catalogs coming from RSQSim, ie., the ability to handle non-standard catalog sources.

Objectives & Challenges of Model Testing " Not enough data " Expand data sources in space and time o i.e., incorp. South America o retrospective testing experiments o time-dependence o extend authoritative data sets " issue 2: primitive models based on point-based models (ie, hypocentral/nucleation) o need: simulation- , fault-, and physics-based models o 3d models o Need to account for non-poissonian & correlation structures o DJ: expand ucerf3 approach to new locations to understand principal components " Issue 3: need to build complete prob. models accounting for ontological error (unknown unknowns) o How to go from logic tree to continuous pdf? o Need to consider correlations within tree " Issue 4: testing fault-based models o Lots of work to be done o 'Turing' style testing can help… Page (2018)

Turing Tests of UCERF3 " properly accounting for spatial diffusivity " Inter-sequence aftershock productivity " Foreshock and aftershock productivity as function of differential magnitude " Nearest neighbor separations " Analysis of clusters " Paleo hiatus " NF: what are the possible explanations of hiatus? " Super cycle: extreme clustering over extreme period " CSEP testing should be more visual and include into CSEP2

Comparing R&J with ETAS " R&J -> ETAS o Secondard sequences o Faster adaptation o Spatial forecasts o Better estimates of the range of outcomes " CSEP 1day forecasts begin at start of day; lose some power " Challenges for USGS testing: o Overlapping windows o Update forecasts within window o New RJ89 method no longer Poissonian o ETAS forecasts are not Poissonian o All violate CSEP testing methods " Likelihood based on Poisson distribution using standard statistical test " CSEP strategy: o Poisson numbers based on RJ forecasts " Strategy: 1. Want dist. Of events in window that starts at t with duration d 2. Using R&J and ETAS to simulate "real" observations 3. Fit R&J to ETAS model: fit is the mode of the individual ETAS runs " Using overlapping windows CSEP assumptions on independence fail; solved by incorporating R&J simulations, forecast, and observations " ETAS observations fails bc they are not Poisson distributed " R&J fails when considering large magnitude main shock " Solution: all ETAS all the time " Takeaway: forecasts and observations must be consistent " Conclusion o Non-Poissonian behavior o Simulation based forecasts could address some issues o Will also handle overlapping time windows o RJ will fail assuming that the world is like ETAS " CSEP must take the forecasts in as simulations in order to test

Moving past Poisson " Poisson likelihood does not allow for clustering " Three-ways to eliminate: o Adjusted likelihood simulations (in other words, remove likelihood) o Normal approximation o K-S test (could work with Turing style tests too) " N-test could be fixed by using negative binomial if dispersion is supplied " Accommodating simulation-based models better solution " Simulations can preserve space-time clustering " (CSEP needs to separate forecasting from modelling) " Consistency tests of simulation-based tests o General approach is to compare statistic computed from simulated catalog with same statistics from observed catalog o For example, inter-event time distribution o P-values should be uniform on [0,1] " Interesting in improving models: looking at information gained o Not obvious way to transparently estimate without gridding o Standard CSEP information not restricted to Poisson " CSEP needs to be able to retroactively evaluate new tests, in other words become a testing center. " Moving past parametric distribution functions in favor of non-parametric simulation-based models " CSEP could support individual testing, will be more straightforward with agreed upon simulated catalog formats

Current CSEP Testing Approaches " Two approaches o Establishing discrepancies/agreement with observations " E.g., number of earthquakes " Likelihood o Comparing against other models " How much better or worse does one model do " Installed methods o Number test: compares number of epicenter forecasts in bin o Likelihood test: based on RELM model setup using mainshock and mainshock+aftershock class, mainshocks declusted using reasenberg. Assume that the model is the data generating process. o Conditional likelihood test: set simulated = observed, and place sim eqs in bins according to relative rates o Space test: collapses forecast into spatial domain. Integrate over magnitude and set simulated = observed. Use relative rates. Calculate simulated LL scores " One of the more interesting tests o Magnitude test: " Same as S test but integrating over space. " Not particularly powerful, could be using a more powerful KS test. o Information gain per earthquake: is "rate-corrected" information gain significant greater than 0. " Paired t-test (T-test) " Differences must be approximately independent " If differences are not iid normal, CLT! " Wilcoxon signed rank test (W-test) " Less powerful " Require symmetric data " Differences are proportional to error bounds, ie., large difference -> large error bounds " Error bounds only apply to forecast pairs " Residuals based: o Residual: difference between local forecast and observation o Raw residual: bin-wise difference between observed # and forecast o Pearson residuals: normalized cell-wise difference between rate and observed number o Deviance residuals: difference between (point-process) log-likelihood Scores. " Hit&miss tests o Receiver-operating characteristic o Molchan error diagram o Area-skill-score " Goal is to evaluate different aspects of the forecasting model " Interpreting results requires going back to the models. A shortcoming of CSEP results is that not enough scientific discussion about the evaluations within context of models. " 10 years of data collected by testing centers @ SCEC and GNS science. Need more results. o 1 day forecasting for California. o Over 200 eqs for New Zealand, lots of science to be done here. Kaikoura and Christchurch… o Curated dataset valuable resource for the scientific community. " Next steps: o Ensemble modeling " Marzochi et al, 2012 " BMA: averaged based on previously best performing model, which makes it better for selecting models " Using additive or multiplicative models for combining models o Simulated-based forecasts " See previous lecture from Morgan Page and David Rhoades " NSIM: number of target eqs " Earthquake rate distribution " Inter-event time distribution " Inter-event distance distribution o External forecasts and predictions " Quakefinder type predictions. " No implemented evaluation method. " Critical for real-time forecast and predictions that are generated externally to CSEP platform.

Testing Fault Based Models " Association problem: mapping an eq to the ucerf3 fault model " Need to understand the stopping probabilities associated with stopping between fault segments " Proposed Procedure: 1. Separate linear fault into sections 2. For each section: estimate nucleation rate for eqs of interest 3. Estimate conditional probabilities of earthquake stopping 4. Evaluate frequency of eqs for each pair of section " Could rely on aftershocks to determine the extent of the rupture plane or maybe a finite-fault inversion " Fault participation is the most important this to test for fault-based models. " Null-hypothesis can be established using the following assumptions o Known magnitude distribution o Known scaling between mw and length o Uniform distribution of rupture locations on fault

Considering Epistemic Uncertainty " Aleatory variability: inherent complexity or randomness in some physical process " Epistemic uncertainty: comes from our lack of knowledge about the process " An exchangeable event allow testing of Bayesian models in frequentist framework " Modifying experimental concept allows for ontological testing of exchangeable sequences " Hierarchy of uncert. Necessary for testing o Aleatory variability -> frequentist o Epistemic uncertainty -> Bayesian methods o Ontological error -> rejection of 'ontological' null hypothesis " States that the true hazard is a realization of the extended experts distribution (EED) " Rejection of this null hypothesis implies ontological error o Ontological tests requires 'experimental concept' that conditions the aleatory variability of the natural system.

Ensemble Modeling and Hybrid model " Definition: inferring the extended expert's distribution from the sample provided by any set of models that sample the epistemic uncertainty " Combining models allows the ensemble to perform only slightly worse than the best performing model. Useful when not sure what is 'correct' model. " Two main features: o Describe epistemic uncertainty o Significantly increases the skill of forecast " Hybrid models to increase information gain o Additive hybrid " Best fitting linear combination of models o Maximum hybrid o Multiplicative hybrids " Exploit independent information ie., GPS and smoothed seismicity " Form hybrids for better information gain " Does not require a choice of best model but leverages all models " Could be a target for CSEP to help gain hybrid models -> improve collaborations

Event based testing " Could move to solution where you can make updates to forecast during the forecast period. Likely more important for long-term models " Might want to update forecast when event happens and when event doesn't happen.

Milestones for UCERF3 Testing Program (U3-TP) 1. Goals: o Verify o Validate o Valuate 2. Milestones " Develop infrastructure " Retrospective testing of UCERF3 " Prospective testing of UCERF3 " Comparatively evalulate U3 against empirical models and physics-based models 3. 5 types of testing o Exploratory testing: Turing o Comparatively: T and W tests o Mean-Hazard testing: null hypothesis significance testing o Ontological testing: including epistemic uncertainty o Sequence-specific testing: testing U3-ETAS against observed aftershock sequences " Guiding principal: all OEF models should be under continual prospective testing, put ETAS under operational testing. Need to find the value for UCERF3-ETAS testing. " Could possibly find out what aspects of U3 are superfluous and could simplify the model for using in other locales. " Slip-rate data are special for California data sets " Important to compare against physics-based earthquake simulations such as RSQsim to evaluate certain assumptions in the model. " U3 drivers of CSEP2 o Datasets used in prospective testing must be versioned and archived. Should include analyzed datasets and raw catalogs o Testing on simulated event catalogs " Benefits of U3-TP to the USGS o Scientific value o Software infrastructure

List of Possible milestones " CSEP1.0. What products would be useful? o Do we need to keep operationalizing CSEP1.0? " [Matt] Mistake to shutdown CSEP1.0 o New models necessary? " [Max] CSEP1 big achievement/success was incorporating new models. " [Ned] Should support new models but need to be more selective. o [Max] Wants to published the CA 1-day forecast results. o [Morgan] Value in providing CSEP1.0 data set publicly. o [Mike B.] Need some clear scientific findings and provocative about this. Need to find models that can be rejected and not worth pursuing. Need to curated in such a way that allows scientists to access and work. Would build community. o [Peter] Need products that are digestible by the public. " Simulation based testing o Methods: " ETAS, U3-ETAS, o Need: Process for defining timelines, and which models we would be evaluating. " Event-triggered/sequence specific testing " Comparative valuations o Turing tests o Verification o Inter-comparison of models " Modeling catalog completeness " Modeling epistemic uncertainties: Important, but IT challenges. " Fault/cell participation " [Ned] Testing usefulness! " Rupture association problem " Fault characteristics " U3-TD elastic-rebound testing " [Peter] Declustering work could help with the USGS. Lots of ambiguity on different declustering models. " [Phil] CSEP Should expose its methods so users could leverage the algorithm " [Mike B.] Valuation question most important. Should physics-based simulations be used for Hazard? " [Kevin] Errors need to be propagated moving forward! " [Phil] Need to figure out how the data will be provided to the scientist. " [All] Web based interface would be valuable.

Notes: Targeting publication for July/August issue of SRL. Have some time to develop the webpage. " Expect Press material surrounding the SRL release, so need to be prepared with digestible figures. " Schedule IT call with Peter, Ned, Phil, Bill, Max, Fabio