The kinematic representation of seismic source

1. The kinematic representation of seismic source

2. The double-couple solution double-couple solution in an infinite, homogeneous isotropic medium. NF IT FF Radiation Pattern moment rate function

3. Far Field representation

4. Far Field representationhomogeneous, isotropic, elastic medium Neglecting all terms that attenuate with distance more rapidly than 1/r

5. Far Field representationhomogeneous, isotropic, elastic medium If the receiver is far enough away with respect to the linear dimension of fault L, we can assume that the distance and the direction cosines are approximately constant, independent of x. Thus, the constant or slowly variable factors can be moved outside the integral

6. Far Field Displacement pulse Final slip in following slides

7. Fraunhofer Approximation The error in this approximation is

8. DISPLACEMENT FOURIER SPECTRUM Acceleration The ground displacement Fourier spectrum is nearly flat at the origin displacement Corner frequency

9. Far Field representationinhomogeneous, isotropic, elastic medium If the receiver is far enough away with respect to the linear dimension of fault L, we can assume that the distance and the direction cosines are approximately constant, independent of x. Thus, the constant or slowly variable factors can be moved outside the integral

10. Aki – Richards, 2002, p.499 Unilateral Rupture propagation Source time function Y is the angle between the direction of rupture propagation and the direction of the receiver The integrand of this equation ranges between and The pulse is proportional to a moving average of taken over a time interval of duration

11. Unilateral Rupture propagation • Taking Fourier Transform The term sin(X)/X expresses the effect of fault finiteness on the amplitude spectrum. At high frequency this term is proportional to w-1. The smoothing effect is weakest in the direction of propagation (y=0) and strongest in the opposite direction (y=p). Thus, we observe more high-frequency in the direction of rupture propagation: that is DIRECTIVITY

12. Tr = rise time t The effect of finite rise time t < tr = x / vr Tr< t < T + tr t > T + tr The effect of finite rise time introduces an additional smoothing of the waveform: for high frequency it attenuates the spectrum proportional to w-1. Together with the effect of the term sin(X)/X, the spectrum decays asto w-2.

13. Some properties At w = 0 it is proportional to WLDmax, which is the seismic moment At frequency larger than the characteristic frequency given by 1/T or 1/L(1/v – cos(Y)/c) the spectrum attenuates as w-2 If the effect of finite width is taken into account, we have a high frequency spectral decay proportional to as w-3

14. An example from the 1997 Colfiorito earthquake sequence

16. A brief note on earthquake dynamic Slip, Slip velocity & Traction evolution

18. A brief note on earthquake dynamic The Slip Weakening mechanism

19. A case study: The 1997 Colfiorito Earthquake Normal faulting earthquakes Multiple main shocks of similar size Moderate magnitudes

20. Peak ground motionattenuationa) Colfiorito eventunilateral NW ruptureb) Sellano eventnearly unilateralSE propagation

21. Colfiorito earthquake • Some spectra

22. Comparison between predicted and observed PGA Colfiorito earthquake

23. PREDICTED PGA comparison with data & empirical law

24. Azimuthal variation

25. Comparison between predicted and observed data with empirical regression law

26. The 2007 Niigata-ken Chuetsu-oki earthquake KKNPP is the nuclear power plant

27. Waveform inversion to infer seismic source Seismic source models obtained by inverting seismograms and GPS displacements

29. Ground Motion Prediction through the inferred model

30. Some numbers

31. Spectral models Omega cube model Omega square model

32. Computing earthquake magnitude M = log (A/T) + F(h,R) + C A – amplitude T – dominant period F – correction for depth & distance C – regional scale factor

33. Seismic Moment & Magnitude From seismic moment we can compute an equivalent magnitude called the moment magnitude

34. Corner frequency shift with magnitude

35. Scaling of final slip with fault length Wells & Coppersmith 1994

36. STRESS DROP SCALING is a factor depending on fault’s shape For a circular fault with radius R

37. Magnitude & Energy

38. Stress and Radiated Energy Strain energy release Seismic efficiency Apparent stress

39. A slip weakening model Energy loss