Published on October 30, 2007
Slide1: 100 Years after the San Francisco Earthquake of 1906 Earthquake Forecasting and Forecast Verification Status, Prospects, Promise John B. Rundle Center for Computational Science & Engineering University of California, Davis Image of the destroyed City Hall, 1906, from Museum of San Francisco collection Collaborators: Collaborators US Scientists Andrea Donnellan, Division of Earth and Space Science, JPL James Holliday, Dept. of Physics and CSE, University of California, Davis Bill Klein, Professor of Physics and Engineering, Boston University. John Rundle, Professor of Physics and Geology, University of California, Davis. Kristy Tiampo, Professor of Earth Science, University of Western Ontario, London, Ontario Don Turcotte, Professor of Geology, University of California, Davis. International Partners Chien-chih Chen, Professor of Earth Sciences, National Central University, Taipei, Taiwan Mitsuhiro Matsu'ura, Professor of Earth Science, University of Tokyo, Japan Peter Mora, Professor or Earth Science, University of Queensland, Australia Kazuyoshi Nanjo, Institute of Statistical Mathematics, Tokyo, Japan Xiang-chu Yin, Professor of Seismology, Chinese Seismological Bureau, China Slide3: 100 Years After the San Francisco Earthquake It is now known that the M ~ 7.9 San Francisco earthquake and fire of April 18, 1906 killed more than 3000 persons. Estimates are that if such an event were to happen again today, damages could easily total well in excess of $500 Billion, with potential fatalities of many thousands of lives. Ruins of financial district (Museum of San Francisco collection) Slide4: Example of an Official Earthquake Forecast - Based on Statistical Renewal Models Slide5: Another Example of an Official Forecast: 24 hour Forecasts of Ground Shaking USGS STEP Forecast Wheeler Ridge Earthquake of April 16, 2005; M =5.2 Slide6: Russian Group Forecasts – California V. Keilis-Borok, V. Kossobokov, P. Shebalin, I Zaliapin et al. Successful Unsuccessful Slide7: An Earthquake Forecast – Published Feb 19, 2002, in PNAS. ( JB Rundle et al., PNAS, v99, Supl 1, 2514-2521, Feb 19, 2002; KF Tiampo et al., Europhys. Lett., 60, 481-487, 2002; JB Rundle et al.,Rev. Geophys. Space Phys., 41(4), DOI 10.1029/2003RG000135 ,2003. http://quakesim.jpl.nasa.gov ) Color Scale Decision Threshold D.T. => “false alarms” vs. “failures to predict” CL#03-2015 Plot of Log10 (Seismic Potential) Increase in Potential for significant earthquakes, ~ 2000 to 2010 Eighteen significant earthquakes (M > 4.9; blue circles) have occurred in Central or Southern California. Margin of error of the anomalies is +/- 11 km; Data from S. CA. and N. CA catalogs: After the work was completed 1. Big Bear I, M = 5.1, Feb 10, 2001 2. Coso, M = 5.1, July 17, 2001 After the paper was in press ( September 1, 2001 ) 3. Anza I, M = 5.1, Oct 31, 2001 After the paper was published ( February 19, 2002 ) 4. Baja, M = 5.7, Feb 22, 2002 5. Gilroy, M=4.9 - 5.1, May 13, 2002 6. Big Bear II, M=5.4, Feb 22, 2003 7. San Simeon, M = 6.5, Dec 22, 2003 8. San Clemente Island, M = 5.2, June 15, 2004 9. Bodie I, M=5.5, Sept. 18, 2004 10. Bodie II, M=5.4, Sept. 18, 2004 11. Parkfield I, M = 6.0, Sept. 28, 2004 12. Parkfield II, M = 5.2, Sept. 29, 2004 13. Arvin, M = 5.0, Sept. 29, 2004 14. Parkfield III, M = 5.0, Sept. 30, 2004 15. Wheeler Ridge, M = 5.2, April 16, 2005 16. Anza II, M = 5.2, June 12, 2005 17. Yucaipa, M = 4.9 - 5.2, June 16, 2005 18. Obsidian Butte, M = 5.1, Sept. 2, 2005 Slide8: Comparing the PI Hotspot Map with the USGS National Seismic Hazard Map Information Content is Different USGS National Hazard Map http://earthquake.usgs.gov/hazmaps/products_data/2002/2002April03/WUS/WUSpga500v4.pdf PI Hotspot Map: http://hirsute.cse.ucdavis.edu/~rundle/EQ_FORECASTS/CURRENT_SCORECARDS/ScoreCard_Original_Sept_2_2005.pdf Slide9: PI Maps can be Compared to Relative Intensity Maps PI maps are obtained by computing average squared changes in RI Figures Courtesy of James Holliday Log10 (Normalized Intensity with M 3) [ Intensity normalized to maximum value ] Start with raw seismicity data Define spatial coarse-grained grid at a size of .1o x .1o (.1o ~ linear size of an M ~ 6 earthquake) Compute and contour the relative seismic intensity I(x,t0,t) over the time interval (t0,t). Units are ( Number / NumberMAX ) Slide10: Binary Forecasts – Testing and Verification Receiver (Relative) Operating Characteristic (ROC) Diagrams An Application of Signal Detection Theory “Success” is defined if epicenter of large event falls within the area enclosed by dashed line Signal Dectection Theory => Decision Threshold Defines Fraction of Probability Map Appearing as Hotspots x (position) Probability Decision Threshold Success EQ Likely EQ Unlikely Slide11: Testing and Verification of Binary Forecasts Bounds on confidence limits were computed by a Bayesian statistical procedure developed by J Zechar and T Jordan (2005) A series of contingency tables is constructed by progressively lowering the decision threshold, thereby revealing progressively more hotspot pixels. For each contingency table, we compute the number of earthquakes successfully forecast, by noting whether there is a hotspot within the Moore neighborhood of each observed earthquake. Similarly, we observe the number of pixels with no large earthquake present, and note whether any hotspots are within their Moore neighborhood. Slide12: Enhanced PI Method Applied to California Earthquakes JR Holliday et al., Nonlin. Proc. Geophys., 2005; CC Chen et al., Geophys. Res. Lett., in press, 2005 We have developed a new enhancement of the original PI method whose starting point is a forecast based on the RI map, and then improves upon it (CC Chen et al., 2005). At right are maps based on this enhancement corresponding to the forecast for 2000 - 2010. Details: We use only the top 10% most active sites, and normalize all time series in the remaining boxes to have the same statistics. The new algorithm weights the change maps made using longer time series more heavily than change maps made using shorter time series. Here t0 = 1950, t1 = 1985, t2 = 1999. Here we use M > 2.8 events to forecast M > 4.8 earthquakes. ANSS Catalog Slide13: Simulation based methods: Virtual California Virtual California 2001 Includes All the Major Active Strike Slip Faults in California (JB Rundle et al., PNAS, 102: 15363-15367, 2005) Faults in RED are shown superposed on a LandSat image of California. Geologic data are used to set the model parameters. (Image courtesy of Peggy Li, JPL) Fault model has 650 segments, 10 km x 15 km. Slide14: The Virtual California Simulation Characteristics & Properties Backslip model – Topology of fault system does not evolve. Stress accumulation occurs as a result of negative slip, or “backslip”. Linear interactions (stress transfer) -- At the moment, interactions are purely elastic, but viscoelastic interactions can easily be added. Arbitrarily complex 3D fault system topologies -- At the moment, all faults are vertical strike-slip faults. Boundary element mesh is ~ 10 km horizontal, 15 km vertical. Faults are embedded in an elastic half space, but layered media are possible as well. Friction laws -- are based on laboratory experiments of Tullis-Karner-Marone, with additive stochastic noise. Method of solution for stochastic equations is therefore via Cellular Automaton methods. Friction laws based on general theoretical law obtained by Klein et al. (1997). Both TKM and Rate-and-State friction can be derived as special cases. Slide15: Activity on the San Francisco Segment of the San Andreas Fault San Francisco Bay section of the San Andreas fault is shown by the yellow fault line. Slide16: Waiting Time Statistics -- A New Method to Forecast the Next Major San Francisco Earthquake on the Northern San Andreas Fault We compute (measure) the conditional cumulative probability that an event with magnitude M > m will occur prior to a time t from the present, given that it has not occurred during the elapsed time to since the last event. From this, we compute the median waiting time until the next event, and the 25% - 75% envelope (yellow band). The yellow region is .25 Pm(t<T) .75, the middle 50%. The red diamond represents the value for today, 99 years after the great 1906 San Francisco earthquake. These curves can be fit well by the statistics of Weibull distributions (JBR, DL Turcotte, R Shcherbakov, G. Morein et al.) Slide17: Optimizing Numerical Forecasts using “Data-Scoring” Slide18: Summary: According to the late K. Aki, we are presently embarked on a “new and exciting era of earthquake forecasting research”. The methods used in weather and climate forecasting can be adapted to earthquake forecasting as well (State vectors, Principal Component Analysis, Numerical simulations) We can move from long term hazard maps (shaking on > ~50 year time scales; probabilities on ~30 year time scales) to event locations in significantly shorter time windows (months to a few years). Numerical simulations of complex interacting fault systems are playing an increasingly important role in understanding earthquake physics and forecasting. We are developing objective methods to verify forecasts; this is a critical field of research if progress in forecasting is to continue. Slide19: 1. Original Map: Anomaly associated with lower left corner of box 2. Shifted Map: Anomaly associated with center of box Minor Note: Shifting the Original Map Produces Better Agreement 1. Big Bear I, M = 5.1, Feb 10, 2001 2. Coso, M = 5.1, July 17, 2001 3. Anza I, M = 5.1, Oct 31, 2001 4. Baja, M = 5.7, Feb 22, 2002 5. Gilroy, M=4.9 - 5.1, May 13, 2002 6. Big Bear II, M=5.4, Feb 22, 2003 7. San Simeon, M = 6.5, Dec 22, 2003 8. San Clemente Island, M = 5.2, June 15, 2004 9. Bodie I, M=5.5, Sept. 18, 2004 10. Bodie II, M=5.4, Sept. 18, 2004 11. Parkfield I, M = 6.0, Sept. 28, 2004 12. Parkfield II, M = 5.2, Sept. 29, 2004 13. Arvin, M = 5.0, Sept. 29, 2004 14. Parkfield III, M = 5.0, Sept. 30, 2004 15. Wheeler Ridge, M = 5.2, April 16, 2005 16. Anza II, M = 5.2, June 12, 2005 17. Yucaipa, M = 4.9 - 5.2, June 16, 2005 18. Obsidian Butte, M=5.1, Sept. 2, 2005
· Rundle, J.B., Turcotte, D.L., Holliday, J.R., Rundle, P.B., ... (52), Fall Meet. Suppl., Abstract NG21A-07.)
· 楠城一嘉, Holliday, J.R., Chen, C.-c., Rundle, J.B. and Turcotte, D.L. (2006). ... (52), Fall Meet. Suppl., Abstract NG21A-07. ...
100 Years after the San Francisco Earthquake of 1906: Earthquake ... Turcotte, D. L.; Holliday, J. R.; Rundle, P ... abstract #NG21A-07:
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