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

Day 1

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

Time-Dependent Background seismicity

• Particularly useful for earthquake swarms where background seismicity differs from 'normal' rate
  • Could determine rate from previous swarms
  • 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
  • Hydro mechanical models for stressing-rate can be used for induced seismicity
  • rate-and-state framework
• Testing strategy:
  • Given a swarm; how long should we provide forecasts?

Day 2

UCERF3

• Three models
  • 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)
  • Time-dependent
    • Based on reed renewal statistics
    • Additional logic tree branches added
  • 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
  • Need to create ucerf3 style ruptures
  • 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
  • Also: repeat times and short period ground motions
  • but starts to disagree at longer spectral periods
• interesting conditional probs:
  • 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
  • i.e., incorp. South America
  • retrospective testing experiments
  • time-dependence
  • extend authoritative data sets
• issue 2: primitive models based on point-based models (ie, hypocentral/nucleation)
  • need: simulation- , fault-, and physics-based models
  • 3d models
  • Need to account for non-poissonian & correlation structures
  • [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)
  • How to go from logic tree to continuous pdf?
  • Need to consider correlations within tree
• Issue 4: testing fault-based models
  • Lots of work to be done
  • '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
  • Secondary sequences
  • Faster adaptation
  • Spatial forecasts
  • Better estimates of the range of outcomes
• CSEP 1day forecasts begin at start of day; lose some power
• Challenges for USGS testing:
  • Overlapping windows
  • Update forecasts within window
  • New RJ89 method no longer Poissonian
  • ETAS forecasts are not Poissonian
  • All violate CSEP testing methods
• Likelihood based on Poisson distribution using standard statistical test
• CSEP strategy:
  • 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
  • Non-Poissonian behavior
  • Simulation based forecasts could address some issues
  • Will also handle overlapping time windows
  • 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:
  • Adjusted likelihood simulations (in other words, remove likelihood)
  • Normal approximation
  • 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
  • General approach is to compare statistic computed from simulated catalog with same statistics from observed catalog
  • For example, inter-event time distribution
  • P-values should be uniform on [0,1]
• Interesting in improving models: looking at information gained
  • Not obvious way to transparently estimate without gridding
  • 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
  • Establishing discrepancies/agreement with observations
    • E.g., number of earthquakes
    • Likelihood
  • Comparing against other models
    • How much better or worse does one model do
• Installed methods
  • Number test: compares number of epicenter forecasts in bin
  • 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.
  • Conditional likelihood test: set simulated = observed, and place sim eqs in bins according to relative rates
  • 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
  • Magnitude test:
    • Same as S test but integrating over space.
    • Not particularly powerful, could be using a more powerful KS test.
  • Information gain per earthquake: is "rate-corrected" information gain significane 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:
  • Residual: difference between local forecast and observation
  • Raw residual: bin-wise difference between observed # and forecast
  • Pearson residuals: normalized cell-wise difference between rate and observed number
  • Deviance residuals: difference between (point-process) log-likelihood Scores.
• Hit&miss tests
  • Receiver-operating characteristic
  • Molchan error diagram
  • 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.
  • 1 day forecasting for California.
  • Over 200 eqs for New Zealand, lots of science to be done here. Kaikoura and Christchurch…
  • Curated dataset valuable resource for the scientific community.
• Next steps:
  • 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
  • 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
  • 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
  • Known magnitude distribution
  • Known scaling between mw and length
  • 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
  • Aleatory variability -> frequentist
  • Epistemic uncertainty -> Bayesian methods
  • 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
  • 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:
  • Describe epistemic uncertainty
  • Significantly increases the skill of forecast
• Hybrid models to increase information gain
  • Additive hybrid
    • Best fitting linear combination of models
  • Maximum hybrid
  • 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.

Day 3

Milestones for UCERF3 Testing Program (U3-TP)

1. Goals:
   • Verify
   • Validate
   • 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
   • Exploratory testing: Turing
   • Comparatively: T and W tests
   • Mean-Hazard testing: null hypothesis significance testing
   • Ontological testing: including epistemic uncertainty
   • 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.
• UCERF3 drivers of CSEP2
  • Datasets used in prospective testing must be versioned and archived. Should include analyzed datasets and raw catalogs
  • Testing on simulated event catalogs
• Benefits of UCERF3-TP to the USGS
  • Scientific value
  • Software infrastructure

List of Possible milestones

• CSEP1.0. What products would be useful?
  • Do we need to keep operationalizing CSEP1.0?
  • New models necessary?
    • [Max] CSEP1 big achievement/success was incorporating new models.
    • [Ned] Should support new models but need to be more selective.
    • [Max] Wants to published the CA 1-day forecast results.
    • [Morgan] Value in providing CSEP1.0 data set publicly.
    • [Mike B.] Need some clear scientific findings and be 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.
    • [Peter] Need products that are digestible by the public.
• Simulation based testing
  • Methods:
    • ETAS, U3-ETAS,
  • Need: Process for defining timelines, and which models we would be evaluating.
• Event-triggered/sequence specific testing
• Comparative valuations
  • Turing tests
  • Verification
  • 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
• UCERF3-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 about SRL special issue

• 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.