100 Years after the San Francisco Earthquake of 1906

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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
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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

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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)
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Example of an Official Earthquake Forecast -
Based on Statistical Renewal Models
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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
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Russian Group Forecasts California V.
Keilis-Borok, V. Kossobokov, P. Shebalin, I
Zaliapin et al.
Successful
Unsuccessful
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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.n
asa.gov )
Eighteen significant earthquakes (M gt 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, M4.9 - 5.1, May 13, 2002 6. Big
Bear II, M5.4, 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, M5.5, Sept.
18, 2004 10. Bodie II, M5.4, 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
Color Scale ? Decision Threshold D.T. gt false
alarms vs. failures to predict
CL03-2015
Plot of Log10 (Seismic Potential) Increase in
Potential for significant earthquakes, 2000 to
2010
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Comparing the PI Hotspot Map with the USGS
National Seismic Hazard Map Information Content
is Different
USGS National Hazard Map http//earthquake.usgs.go
v/hazmaps/products_data/2002/2002April03/WUS/WUSpg
a500v4.pdf PI Hotspot Map http//hirsute.cse.ucd
avis.edu/rundle/EQ_FORECASTS/CURRENT_SCORECARDS/S
coreCard_Original_Sept_2_2005.pdf
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PI Maps can be Compared to Relative Intensity
Maps PI maps are obtained by computing average
squared changes in RI
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 )
Log10 (Normalized Intensity with M ? 3)
Intensity normalized to maximum value
Figures Courtesy of James Holliday
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Binary Forecasts Testing and Verification Receiv
er (Relative) Operating Characteristic (ROC)
Diagrams An Application of Signal Detection Theory
Signal Dectection Theory gt Decision Threshold
Defines Fraction of Probability Map Appearing as
Hotspots
Probability
Decision Threshold
EQ Likely
EQ Unlikely
x (position)
Success
Success is defined if epicenter of large event
falls within the area enclosed by dashed line
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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.
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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 gt 2.8 events to
forecast M gt 4.8 earthquakes.
ANSS Catalog
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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.
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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.
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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.
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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 gt 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(tltT) ? .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.)
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Optimizing Numerical Forecasts using
Data-Scoring
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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 gt 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.
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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, M4.9 - 5.1, May 13, 2002 6. Big Bear
II, M5.4, 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, M5.5, Sept. 18,
2004 10. Bodie II, M5.4, 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, M5.1, Sept. 2, 2005
1. Original Map Anomaly associated with lower
left corner of box 2. Shifted Map Anomaly
associated with center of box
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