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Forecasting, Prediction, and Testing David D. Jackson, UCLA. Thanks to Yan Kagan, Yufang Rong, Zheng-kang Shen, Ned Field, Daniel Schorlemmer, Matt Gerstenberger, John Rundle, Don Turcotte, Volodya Kossobokov, Ilya Zaliapin. Definitions.

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forecasting prediction and testing david d jackson ucla
Forecasting, Prediction, and TestingDavid D. Jackson, UCLA
  • Thanks to Yan Kagan, Yufang Rong, Zheng-kang Shen, Ned Field, Daniel Schorlemmer, Matt Gerstenberger, John Rundle, Don Turcotte, Volodya Kossobokov, Ilya Zaliapin
definitions
Definitions
  • Forecast: specification of the probability per unit area, magnitude, time, focal mechanism, etc.
  • Prediction: special case of forecasting in which the probability in some region is much higher than normal, and high enough to justify exceptional .
  • Notes: a prediction must be temporary; it also requires a definition of normal (i.e., a null hypothesis).
why forecast and test
Why forecast and test
  • Test hypotheses of earthquake physics
    • Quasiperiodic characteristic earthquakes
    • Magnitudes limited by fault geometry
    • Moment balance (tectonic in = seismic out)
    • Earthquake rate proportional to stress rate
  • Inform decisions about earthquake risk
    • Facility locations, building codes, insurance rates, retrofit, etc.
  • Inspire envy
some testable statements
Some testable statements
  • At least one event will occur within given region, time interval, and magnitude interval with probability p.
    • For many small intervals, this is RELM type forecast
    • Replace region by “segment” and have WG88 type forecast. But “earthquake on segment” is subjective.
  • N events will occur within given region, time interval, and magnitude interval with probability p(N).
  • The largest event in given region and time interval will be m, with probability p(m). My recommendation for a usable and stable forecast.
  • If an event occurs in region 1, time interval 1, and magnitude interval 1, it will be in the included region 2, time interval 2, and magnitude interval 2 with probability p. (KB type forecast)
  • The next earthquake in a given region and magnitude interval will not be before time t with probability p(t). Replace region by “segment” and have WG88 type forecast.
what we can and can t do now
What we can and can’t do now
  • Can
    • Forecast 90% of quakes in 10% of area.
    • Predict aftershocks
    • Forecast mag-freq relationship for N(m)>10.
  • Maybe can
    • Forecast earthquake rate from deformation rate.
    • Establish earthquake rate for “normal” conditions
    • Forecast Mmax
  • Can’t
    • Predict times of individual earthquakes
likelihood testing
Likelihood Testing
  • Simulate catalogs using L(lat,lon)
  • Compute log likelihood function for observed and simulated catalogs
  • Sort L values in increasing order, plot order vs L.
practical problems in testing
Practical problems in testing
  • Many users: many criteria
  • Earthquakes not independent
  • Testing should be rigorous, but also “feel good.”
  • Data on rupture lengths, endpoints of rupture, slip distribution, etc., not formalized
slide12

Ten-year Prospective Test of Seismic Gap and Null (Poissonian Smoothed Seismicity) models

Rank zones by decreasing probability of characteristic earthquake; accumulate area, predicted earthquake number, and actual earthquake number.

properties of test methods
Properties of test methods
  • Likelihood ratio test
    • Includes absolute rates
    • Useful for marked point process: lat, lon, mag, etc.
    • As used, assumes independent events;
      • Adaptable to time varying forecasts
      • Could use declustered catalog
    • Gives scalar “score”
  • Likelihood ratio test on largest event in zone, time interval
    • Reduces effect of dependent events
    • May respond to long-term users: investors, planners
  • Molchan diagram
    • Based on relative rates, as normally used
    • Needs a scalar measure to reject a hypothesis
    • Not convenient for marked point processes; need to commit to magnitude threshold, e.g.
    • Does not avoid problem of dependent events
conclusions
Conclusions
  • Many users => Many criteria for optimality
    • Absolute rate vs. relative rate
    • Short time vs. long time
    • Big events vs. smaller ones
  • Biggest problem is interdependence of quakes
    • Long term users want stability: unconditional probabilities
    • Scientists care about interactions: conditional probabilities
  • Solutions to interdependence
    • Decluster catalog: needs model
    • Test using conditional probabilities updated automatically
    • Test only largest earthquake in zone.