Yan Y. Kagan
Dept. Earth and Space Sciences, UCLA, Los Angeles,
CA 90095-1567, kagan@moho.ess.ucla.edu,
http://eq.ess.ucla.edu/~kagan.html
EARTHQUAKES: Statistics,
Models, Testable Forecasts
http://moho.ess.ucla.edu/~kagan/Extr13.ppt
Outline of the Talk
• Tohoku M9 2011 earthquake -- extreme disaster.
• Long- and short-term seismicity rate forecasts in
NW Pacific (Tohoku area) region.
• Statistical analysis of earthquake occurrence –
earthquake numbers, spatial scaling, earthquake
size, time, space, and focal mechanism
orientation statistical distributions.
• Current global earthquake forecasts and their
testing.
Earthquake Phenomenology
1. Modern earthquake catalogs include origin
time, hypocenter location, and second-rank
seismic moment tensor for each earthquake.
2. The moment tensor is symmetric, traceless,
with zero determinant: it has only four
degrees of freedom -- the norm of the
tensor and the 3-D orientation of the focal
mechanism (quaternions are used to model).
3. An earthquake occurrence is controlled by
power-law (stable) distributions.
Seismicity:
Turbulence
of Solids,
Nonlinear
Science
Today, 2, 113, 1992.
World seismicity: 1976 – 2012
(Global Centroid Moment Tensor catalog)
http://bemlar.ism.ac.jp/wiki/index.php/Bird%27s_Zones
Losses from 2011 Tohoku (Japan) M9
earthquake
• Close to 20,000 dead and more than $300 billion
(perhaps close to one trillion – $10^12) in economic
losses.
• However, the number of casualties is more than 10
times fewer than for the 2004 Sumatra earthquake of
similar magnitude.
• If an appropriate alarm has been issued in the first
few minutes after the earthquake, the casualties may
be reduced by a factor of 10 (Kanamori, 2011).
Tohoku M9 earthquake and tsunami
Lay, T., and Kanamori, H.,
2011. Insights from the
great 2011 Japan
earthquake, Phys. Today,
64, 33-39.
Geller, R. J., 2011.
Shake-up time for
Japanese
seismology,
Nature, 472(7344),
407-409
Simons, M.
et al., 2011.
The 2011
magnitude
9.0 TohokuOki
earthquake:
mosaicking
the
megathrust
from
seconds to
centuries,
Science,
332(6036),
1421-1425
2011 Tohoku earthquake
Maximum size estimates for subduction zones
relevant for Tohoku (Japan) M9 earthquake:
1. Historical/instrumental seismicity record
(M7.7 maximum magnitude predicted).
2. Statistical method (likelihood optimization).
3. Moment-conservation method (tectonic versus
seismic moment rates) -- calculations for
Flinn-Engdahl zones.
Long- and short-term seismicity rate forecasts
in Tohoku region.
not to be
taken
literally!
(“a large
number”)
threshold
magnitude
95%-confidence
upper limit
95%-confidence
lower limit
95%-confidence
lower limit
Review of results on spectral slope, b:
Although there are variations, none is significant with 95%-confidence.
Kagan’s [1999] hypothesis of uniform b still stands.
Flinn-Engdahl seismic regions
Why select them? Regions were defined before GCMT catalog started (no selection
bias), and it is easier to replicate our results (programs and tables available).
DETERMINATION OF MAXIMUM
(CORNER) MAGNITUDE: AREA-SPECIFIC
MOMENT CONCERVATION PRINCIPLE
Seismic moment rate depends on 3 variables -1.The number of earthquakes in a region (N),
2.The beta-value (b-value) of G-R relation,
3.The value of maximum (corner) magnitude.
Tectonic moment rate depends on 3 variables -1. Width of seismogenic zone (W – 30-104 km),
2. Seismic efficiency coefficient (50 -- 100%),
3. Value of shear modulus (30GPa -- 49GPa).
Kagan, Seismic moment-frequency relation for shallow earthquakes:
Regional comparison, J. Geophys. Res., 102, 2835-2852 (1997).
Tectonic rate for 1977-1995/6/30 period is calculated by using parameters: W=30 km,
mu=30 GPa, chi=1.0.
Tectonic rate for 1977-2011 period is calculated by using Bird & Kagan
(2004) parameters: W=104 km, mu=49 GPa, chi=0.5
Beta values for 1977-2011 in Flinn-Engdahl zones
For the Tohoku area the
approximate recurrence
interval for magnitude
M>=9.0 earthquakes is on
the order of 350 years
For the Tohoku area the
approximate recurrence
interval for magnitude
M>=9.0 earthquakes is on
the order of 350 years
Log aftershock zone length against magnitude, 1977-2000
Log aftershock zone length against magnitude, 1977-2013
Jackson, D. D., and
Y. Y. Kagan, 1999.
Testable earthquake
forecasts for 1999,
Seism. Res. Lett., 70,
393-403.
Combined long- and
short-term forecast for
north- and southwestern Pacific area
Focal mechanism forecast
Error diagram tau,
nu for global longterm seismicity (M
> 5.0) forecast.
Solid black line -the strategy of
random guess.
Solid thick red
diagonal line is a
curve for the
global forecast.
Blue line is
earthquake
distribution from
the PDE catalog in
2004-2006
(forecast);
magenta line
corresponds to
earthquake
distribution from
the PDE catalog in
1969-2003
Earthquake forecast conclusions
• We present an earthquake forecast program
which quantitatively predicts both long- and
short-term earthquake probabilities.
• The program is numerically and rigorously
testable both retrospectively and prospectively as
done by CSEP (Collaboratory for the Study of
Earthquake Predictability) worldwide, as well as
in California, Italy, Japan, New Zealand, etc.
• It is ready to be implemented as a technological
solution for earthquake hazard forecasting and
early warning.
END
Thank you
Abstract
The aim of this work is the comprehensive and methodologically rigorous analysis of
earthquake occurrence. Models based on the theory of the stochastic multidimensional
point processes were employed to approximate the earthquake occurrence pattern and
evaluate its parameters. We show that most of these parameters have universal values.
These results help explain the classical earthquake distributions (Omori's law and the
Gutenberg-Richter relation) and the fractal correlation dimension for spatial
distributions of earthquake hypocenters was determined. We also investigated the
disorientation of earthquake focal mechanisms and showed that it follows the
rotational Cauchy distribution. These statistical and mathematical advances made it
possible to produce quantitative forecasts of earthquake occurrence.
As an illustration of extreme consequences of earthquakes and the possibility of their
forecasting we consider three problems related to the 2011 Tohoku, Japan megaearthquake: (1) how to evaluate the earthquake maximum size especially in
subduction zones and why the event size was so grossly under-estimated for the
Tohoku area; (2) what is the repeat time for the largest earthquakes in this region; (3)
what are the possibilities of numerical long- and short-term forecasts during the 2011
earthquake sequence in the Tohoku area. We discuss the quantitative methods which
are available to answer these questions. We show that for all the subduction zones the
maximum moment magnitude is of the order 9.0--9.7, and for major subduction zones
the maximum earthquake size is statistically indistinguishable.
Kagan, Y. Y., and
D. D. Jackson, 1995.
New seismic gap
hypothesis: Five
years after,
J. Geophys. Res., 100,
3943-3959.
N test (events number)
L test (events location
likelihood)
R test (likelihood
comparison of models)