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Differential wave equation and seismic events

Differential wave equation and seismic events . Sean Ford & Holly Brown Berkeley Seismological Laboratory. Outline. Holly and Sean 101 Quick intro: Wave equation Monitoring nuclear tests Predicting ground motion for a future event on the Hayward Fault Hayward Fault tour. Introduction.

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Differential wave equation and seismic events

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  1. Differential wave equation and seismic events Sean Ford & Holly Brown Berkeley Seismological Laboratory

  2. Outline • Holly and Sean 101 • Quick intro: Wave equation • Monitoring nuclear tests • Predicting ground motion for a future event on the Hayward Fault • Hayward Fault tour

  3. Introduction • Seismic sources • Earthquake • Explosion Slip on a plane Pressure pulse on a sphere

  4. Seismic wave equation • Start with Newton • Add ‘constitutive equation’ to relate stress to strain to displacement

  5. Seismic wave equation • Can decompose to P and S wave solutions of the form • Wave equation can be solved by plane-wave

  6. Finite differences • The wave equation is solved on a computer by using a discrete representation of the differential equation

  7. Possible project: Sumatra earthquake Time (sec)

  8. Possible project Time (sec)

  9. Possible project T Time (sec)

  10. Seismic sources • Earthquake - slip on a plane • Explosion - pressure pulse on a sphere Compressional (P-wave) radiation pattern Shear (S-wave) radiation pattern No volume change Compressional (P-wave) radiation constant No Shear (S-wave) radiation Volume change

  11. From Walter et al. (2008)

  12. North Korea Nuclear Test From Walter et al. (2008)

  13. Seismic moment tensors M represents all possible force couple components due to a seismic source in a cartesian coordinate system Necessary to have two force couples (double couple, DC), so that angular momentum is conserved in the source sphere, which leads to Mij = Mji and the moment tensor is symmetric

  14. Seismic moment tensors Model Source M Couples Focal Mechanism Double-couple (DC) x Strike-slip y z Compensated linear vector dipole (CLVD) x y Ring Fault z x Isotropic Explosion y z

  15. Moment tensor inversion in matrix form d = Gm m = vector of 6 independent moment tensor elements m = (GTG)-1GTd

  16. Western US

  17. Western US

  18. Western US

  19. Western US

  20. Source-type plot We calculate source-type plot parameters (Hudson et al., 1989)

  21. Source-type plot We calculate source-type plot parameters (Hudson et al., 1989) Explosion Implosion

  22. Source-type plot We calculate source-type plot parameters (Hudson et al., 1989) Explosion +CLVD DC -CLVD Implosion

  23. Source-type plot We calculate source-type plot parameters (Hudson et al., 1989) Explosion HOYA +CLVD DC -CLVD Little Skull Implosion

  24. Source-type plot We calculate source-type plot parameters (Hudson et al., 1989) Explosion HOYA HOYA +CLVD DC -CLVD Little Skull Little Skull Implosion

  25. Source-type plot We calculate source-type plot parameters (Hudson et al., 1989) Explosion HOYA HOYA +CLVD DC -CLVD Little Skull Little Skull Implosion

  26. Western US

  27. 9 Oct 06 North Korea test

  28. Crandall Canyon, Utah Site of 6 Aug 08 Mine Collapse

  29. Can be implosion

  30. Or shallow normal event

  31. Use method for nuclear test explosions to find source at Crandall Canyon

  32. Crandall Canyon event plotted near where a closing crack or collapse source should plot Dominantly implosional Crandall Canyon

  33. Crandall Canyon event plotted near where a closing crack or collapse source should plot Dominantly implosional But also some shear portion

  34. Hayward Fault

  35. Hayward fault • GoogleEarth tour • 1868 Hayward event M6.8 • Scenario events from USGS http://earthquake.usgs.gov/regional/nca/simulations/hayward/ • San Pablo epicenter • Fremont epicenter • View from Concord

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