Forecasting prediction and testing david d jackson ucla
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Forecasting, Prediction, and Testing David D. Jackson, UCLA PowerPoint PPT Presentation

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

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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


Scec csep jackson se gt

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


Scec csep jackson se gt

Testing scheme for elements of risk model


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.


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