Uncertainties in Seismicity Models: Towards Bayesian Earthquake Forecasting

Transcription

1 Ucertaities i Seismicity Models: Towards Bayesia Earthquake Forecastig Max Werer (UCLA) Kayo Ide (UCLA) Didier Sorette (ETHZ & UCLA) It is ot certai that everythig is ucertai. - Blaise Pascal

2 Outlie I) Motivatio: How do ucertaities impact earthquake forecasts? How ca we characterize magitude ucertaities? II) Magitude Noise i a Aftershock Model Impact o seismic rate estimates, forecasts ad tests III) Data assimilatio Framework for ucertaities Recursive Bayesia forecastig for temporal reewal process

3 Ucertaities: Pallett Creek Rhoades et al (1994) Ogata (1999, 2002)

4 ETAS Forecast STEP: ETAS Hidcast ERS :

5 Magitude Ucertaities What is the magitude ucertaity i forecast models? INTRA Ucertaity i measurig a particular magitude? Iversio process (e.g. hypoiverse - reports ucertaities) Velocity model, parameters, assumptios, istrumets Compare estimate of same type of magitude from differet methods or catalogs (e.g. CMT vs USGS momet magitude) For ANSS i Califoria, oly NCSN reports hypoiverse ucertaities INTER Ucertaity i the forecast magitude - Mf? Systematic ad radom differeces betwee differet magitudes reported i catalogs (e.g. CMT s Mw vs PDE mb ad Ms) CSEP s authorized data ANSS reports may differet magitudes E.g. NCSN reports two magitudes (Ms ad Md) Which is the forecast magitude?

6 Momet Magitude Ucertaity Kaga (2003)

7 Momet Magitude Ucertaities CMT vs USGS

8 ANSS: Magitude Ucertaity Withi Califoria, the oly (?) etwork i the ANSS that routiely reports ucertaities i magitude is the NCSN usig the hypoiverse format: Media Absolute Differece (MAD)

9 Forecast Magitude Ucertaity ANSS i CA reports may magitudes: Richter, momet, coda duratio, coda amplitude, S amplitude... NCSN reports amplitude magitude ad coda duratio magitude for the same evet (i the hypoiverse format): differeces up to 0.4 usually 0.1 to 0.2 CMT reports PDE mb ad/or Ms

10 Outlie I) Motivatio: How do ucertaities impact earthquake forecasts? How do we characterize magitude ucertaity? II) Magitude Noise i a Aftershock Model Impact o seismic rate estimates, forecasts ad tests III) Data assimilatio Framework for ucertaities Recursive Bayesia forecastig for temporal reewal process

11 Effects of Magitude Noise i a Aftershock Cluster Model Poisso Cluster Model: (maishock + aftershocks) Noisy magitudes: Queched weights: Radom variables: What are the fluctuatios i the seismic rate estimates?

12 Magitude Noise i Cluster Models What are the fluctuatios i the hazard due to oise? Sum of radom variables Strog fluctuatios i seismic rate estimates No cetral limit theorem for oise > 0.2 Queched weights strogly deped o catalog realizatio Averagig effects deped o parameter values

13 Simulatios of Perturbed Rates

14 Seismic Rate Estimatio: Power Law Tail Behavior

15 Noisy Forecasts i RELM Likelihood Tests Truth / Observatios : - simulate a sythetic catalog with the Poisso cluster model ad GR law - calculate (true) rate at time steps usig kow parameters - geerate 1000s of modified observatios cosistet with the rate assumig Poisso process (as i RELM likelihood tests) Models / Forecasts : - perturb magitudes of catalog 1000s of times - calculate seismic rate for each perturbed catalog based o Poisso cluster model equatio with kow parameters - for each such model, geerate 1000s of simulated observatios cosistet with its calculated rate from perturbed catalog RELM Likelihood test / Evaluatio : - perform N ad L tests o models agaist observatios

16 Fractio of Models Rejected by N, L Tests vs Time Because of magitude oise, a good model ca be rejected. What are the implicatios for log term testig? Which parameter regime is adequate?

17 Outlie I) Motivatio: How do ucertaities impact earthquake forecasts? II) III) Magitude Noise i a Aftershock Model Impact o seismic rate estimates, forecasts ad tests Data assimilatio Framework for ucertaities Mathematical set up for poit processes Recursive Bayesia forecastig for temporal reewal process

18 Data Assimilatio Talagrad (1997): The purpose of data assimilatio is to determie as accurately as possible the state of the atmospheric (or oceaic) flow, usig all available iformatio Statistical combiatio of observatios ad short-rage forecasts produce iitial coditios used i model to forecast. (Bayes theorem) Advatages: Geeral framework for ucertaities Ukow iitial coditio estimatio Accout for observatioal oise, system oise, parameter ucertaities

19 Data Assimilatio

20 Data Assimilatio

21 Data Assimilatio

22 Data Assimilatio

23 Data Assimilatio

24 Data Assimilatio

25 Data Assimilatio

26 Data Assimilatio

27 Temporal Reewal Processes Noise : Reewal process:... Forecast: Likelihood (observatio): Aalysis / Posterior: Werer, Ide ad Sorette (2007), i prep

28 Coclusios Ucertaities ad oise are importat Observatioal oise ca be large Magitude ucertaities ot straight forward. Seismic rate estimates i aftershock model fluctuate Forecasts suffer Testig ad evaluatig eed to be robust Data assimilatio ca help Geeric framework for dealig with ucertaities