yan y. kagan dept. earth and space sciences, ucla, los angeles,
DESCRIPTION
Yan Y. Kagan Dept. Earth and Space Sciences, UCLA, Los Angeles, CA 90095-1567, [email protected] , http://eq.ess.ucla.edu/~kagan.html. Statistics of earthquake focal mechanisms. http://moho.ess.ucla.edu/~kagan/USC13 .ppt. Outline of the Talk (1). - PowerPoint PPT PresentationTRANSCRIPT
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Yan Y. Kagan
Dept. Earth and Space Sciences, UCLA, Los Angeles,
CA 90095-1567, [email protected], http://eq.ess.ucla.edu/~kagan.html
http://moho.ess.ucla.edu/~kagan/USC13.ppt
Statistics of earthquake focal mechanisms
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Outline of the Talk (1)• Symmetry of Double-Couple earthquake source: DC4 – four
rotations (fault-plane ambiguity); DC2 – two rotations (fault plane known); DC1 – one rotation.
• Statistical crystallographic texture studies: orientation, symmetry, Rodrigues space.
• Rotation theoretical probability distributions: Uniform, Cauchy, von Mises-Fisher.
• Statistical analysis of earthquake source properties in global seismicity.
• Kagan, Double-couple earthquake source: symmetry and rotation, GJI, 2013.
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World seismicity: 1976 – 2012 (GCMT)
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Schematic (beachball) diagram of the DC earthquake focalmechanism and its quadrupole radiation patterns.The null (B) axis is orthogonal to the T- and P-axes, or it is located on the intersection of fault and auxiliary planes, i.e., perpendicular to the paper sheet in this display. The N-axis is normal to the fault-plane; U is a slip
vector.
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Four schematic diagrams of earthquake focal mechanism withthe DC4 symmetry.The right-hand coordinate system is used.We show how three vectors can be arranged in a standard representation of a 3-D Cartesian coordinate system.
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Rodrigues transformation in crystallography
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Fundamental zone display for DC4 source.The B, P, and T-axes of the sourceare shown.The octant of the cube0 < x1 < 1; 0 < x2 < 1; 0 < x3 < 1; is called the `MacKenzie cell.'
\
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Fundamental zone display for DC4 source.Two opposite faces of the fundamental cube are shown. Colors show two face points corresponding to one source orientation with the angle Phi > 90 degree. The cyan central points correspond to two equivalent rotationsPhi = 90. When rotation point moves to the edge of one face an equivalent point on the opposite face also moves to another edge, resulting in rotation with an angle 109.5 degrees.
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DC4:Four sets for rotations with an angle 109.5 degrees.
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DC4:Two sets of rotations with an angle 120 degrees.
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Cumulative distributions of rotation angles for pairs of focalmechanisms of shallow earthquakes in the GCMTcatalog 1977-2011; Distance range 0-50 km, magnitude threshold 5.0,kappa=0.1.
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Distance 400-500 km, kappa=0.2
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Kappa=
0.075
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Randomly rotated DC4 sources in the central section of the fundamentalzone.
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Shallow earthquakes, distance 0-50 km, m>5.8. Shown in central section of the fundamentalzone.
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, The GCMT catalog 1977-2011. N is the total number of events with magnitude m >= m_t; N_p is the total number of event pairs; N_c is the number of event pairs in the central section; rho(pt, bp, bt) are the correlation coefficients for all points; rho’ is the correlation coefficient for all points within the central section; Phi is the average disorientation angle and its standard deviation.
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Outline of the Talk (2)• Forecasts of focal mechanisms for future earthquakes
(Kagan & Jackson, JGR, 1994): mechanisms and their uncertainty are forecasted. Because of spatial averaging the method does not work properly in polar areas.
• Difference in azimuth (bearing) needs to be taken into account in polar regions.
• We produce high-resolution forecast for the whole Earth, the forecast skill and source complexity is evaluated.
• Kagan & Jackson, Statistical earthquake focal mechanism forecasts, submitted to GJI.
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World seismicity: 1976 – 2012 (GCMT)
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Kagan & Jackson, GJI, 2000.
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Forecast:Long-term earthquake
rate based on GCMT catalog 1977-present.
0.1 x 0.1 degree,
Magnitude M>=5.8
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Focal mechanism forecast
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END
Thank you
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Kagan, Y. Y., and D. D. Jackson, 1995. New seismic gap hypothesis: Fiveyears after, J. Geophys. Res., 100, 3943-3959.
N test (events number) L test (events location likelihood)R test (likelihood comparison of models)
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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 south-western Pacific area
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Global earthquake long-term potential based on smoothed seismicity
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Forecast:Short-term earthquake
rate based on GCMT
catalog 1977-present.0.1 x 0.1 degree,
Magnitude M>=5.8
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http://bemlar.ism.ac.jp/wiki/index.php/Bird%27s_Zones