Powerpoint materials for conference on "earthquake predictability and timedependent forecasting"

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Yan Y. Kagan Dept. Earth and Space Sciences,
UCLA, Los Angeles, CA 90095-1567,
ykagan_at_ucla.edu, http//scec.ess.ucla.edu/ykagan.h
tml
EARTHQUAKE PREDICTABILITY AND TIME-DEPENDENT
FORECASTING
http//scec.ess.ucla.edu/ykagan/zurich_index.html
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(1) Frequency-moment distribution

• Kagan, Y. Y., 1997. Seismic moment-frequency
  relation for shallow earthquakes Regional
  comparison, J. Geophys. Res., 102, 2835-2852.

Kagan, Y. Y., 2002. Seismic moment distribution
revisited I. Statistical results, Geophys. J.
Int., 148, 521-542.
Bird, P., and Y. Y. Kagan, 2004. Plate-Tectonic
Analysis of Shallow Seismicity Apparent Boundary
Width, Beta, Corner Magnitude, Coupled
Lithosphere Thickness, and Coupling in Seven
Tectonic Settings, Bull. Seismol. Soc. Amer.,
94(6), 2380-2399 (plus electronic supplement).
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Using the Harvard CMT catalog of 15,015 shallow
events
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Review of results on spectral slope, b
Although there are variations, none is
significant with 95-confidence. Kagans 1999
hypothesis of uniform b still stands.
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Long-term forecast 1977-today
Spatial smoothing kernel is optimized by using
the first part of a catalog to forecast its
second part.
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Cumulative event curve interpreted here as
cumulative seismic moment for a realization of
the branching process model with an illustration
of the filtered signal (using the theoretical
seismogram in the middle) from which events and
their seismic moments can be determined (Kagan
and Knopoff, JGR, 1981).
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Kagan, Y. Y., and Knopoff, L., 1984. A stochastic
model of earthquake occurrence, Proc. 8-th Int.
Conf. Earthq. Eng., 1, 295-302.
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(3) Stochastic models of earthquake occurrence
and forecasting

• Long-term models for earthquake occurrence,
  optimization of smoothing procedure and its
  testing (Kagan and Jackson, 1994, 2000).

• Empirical branching models (Kagan, 1973a,b
  Kagan and Knopoff, 1987 Ogata, 1988, 1998
  Kagan, 2006).
• Physical branching models propagation of
  earthquake fault is simulated (Kagan and Knopoff,
  1981 Kagan, 1982).

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(a) Earthquake catalog data
(b) Point process Branching along magnitude
axis, introduced by Kagan (1973ab)
(c) Point process Branching along time axis
(Hawkes, 1971 Kagan Knopoff, 1987 Ogata, 1988)
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Time history of long-term and hybrid (short-term
plus 0.8 long-term) forecast for a point at
latitude 39.47 N., 143.54 E. northwest of Honshu
Island, Japan. Blue line is the long-term
forecast red line is the hybrid forecast.
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Short-term forecast uses Omori's law
to extrapolate present seismicity. Forecast one
day before the recent M8.3 Kuril Islands
earthquake.
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Short-term forecast uses Omori's law
to extrapolate current seismicity. Red spot east
of the Kuril Islands is the consequence of two
Mgt8 2006/2007 earthquakes.
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(4) Forecast Efficiency Evaluation

• We simulate synthetic catalogs using smoothed
  seismicity map.
• Likelihood function for simulated catalogs and
  for real earthquakes in the time period of
  forecast is computed.
• If the real earthquakes likelihood value is
  within 2.597.5 of synthetic distribution, the
  forecast is considered successful.
• Kagan, Y. Y., and D. D. Jackson, 2000.
  Probabilistic forecasting of earthquakes,
  Geophys. J. Int., 143, 438-453.

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Here we demonstrate forecast effectiveness dis
played earthquakes occurred after smoothed
seismicity forecast had been calculated.
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Kossobokov, 2006. Testing earthquake prediction
methods The West Pacific short-term forecast
of earthquakes with magnitude MwHRV \ge 5.8",
Tectonophysics, 413(1-2), 25-31. See also Kagan
Jackson, TECTO, 2006, pp. 33-38.
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(5) EARTHQUAKE PREDICTABILITY MEASUREMENTINFORMA
TION SCORE AND ERROR DIAGRAM
Two methods for measuring the effectiveness of
earthquake prediction algorithms are discussed
the information score based on the likelihood
ratio and error diagrams. For both of these
methods, closed form expressions are obtained for
the renewal process based on the gamma and
lognormal distributions. The error diagram is
more informative than the likelihood ratio and
uniquely specifies the information score. We
derive expressions connecting the information
score and error diagrams. http//scec.ess.ucla.ed
u/ykagan/eqpred_index.html
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Basic equations
Information score in bits Calculation from
likelihood ratio
Calculation from error diagram
Calculation of error diagram lower bound given
info score
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Molchan, G. M., and Y. Y. Kagan, 1992. Earthquake
prediction and its optimization, J. Geophys.
Res., 97, 4823-4838.
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(6) Power-law distributions new paradigms in
statistics

• Almost all statistical distributions in
  earthquake seismology are power-laws
  Gutenberg-Richter relation, Omoris law, the
  fractal pattern of earthquake spatial
  distribution.
• These distributions are drastically different
  from Gaussian-type laws that were used in
  mathematical statistics for over two centuries.

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Non-linear increase of sums of heavy-tailed
distributions.
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Holt, W. E., Chamot-Rooke, N., Le Pichon, X.,
Haines, A. J., Shen-Tu, B., and Ren, J., 2000.
Velocity field in Asia inferred from Quaternary
fault slip rates and Global Positioning System
observations, J. Geophys. Res., 105,
19,185-19,209.
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(7) Application to insurance

• The power-law distributions governing earthquake
  occurrence mean that very rare extreme events
  contribute a major part of total losses.
• The theory of stable distributions needs to be
  applied for appropriate loss calculation.

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Kagan, Y. Y., 1997. Earthquake size distribution
and earthquake insurance, Communications in
Statistics Stochastic Models, 13(4), 775-797.
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END