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

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

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

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 M ij = M ji and the moment tensor is symmetric

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

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

16. 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 Implosion DC-CLVD+CLVD

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

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

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

26. Western US

27. 9 Oct 06 North Korea test

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

30. Can be implosion

31. Or shallow normal event

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

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

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

35. Hayward Fault

36. 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