Yan Y. Kagan Dept. Earth and Space Sciences, UCLA, Los Angeles,

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

http://moho.ess.ucla.edu/~kagan/USC13.ppt

Statistics of earthquake focal mechanisms

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.

World seismicity: 1976 – 2012 (GCMT)

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.

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.

Rodrigues transformation in crystallography

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.'

\

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.

DC4:Four sets for rotations with an angle 109.5 degrees.

DC4:Two sets of rotations with an angle 120 degrees.

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.

Distance 400-500 km, kappa=0.2

Kappa=

0.075

Randomly rotated DC4 sources in the central section of the fundamentalzone.

Shallow earthquakes, distance 0-50 km, m>5.8. Shown in central section of the fundamentalzone.

, 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.

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.

World seismicity: 1976 – 2012 (GCMT)

Kagan & Jackson, GJI, 2000.

Forecast:Long-term earthquake

rate based on GCMT catalog 1977-present.

0.1 x 0.1 degree,

Magnitude M>=5.8

Focal mechanism forecast

END

Thank you

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)

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

Global earthquake long-term potential based on smoothed seismicity

Forecast:Short-term earthquake

rate based on GCMT

catalog 1977-present.0.1 x 0.1 degree,

Magnitude M>=5.8

http://bemlar.ism.ac.jp/wiki/index.php/Bird%27s_Zones