1. Numerical prediction of strong motions for a hypothetical M w 6.5 earthquake Jiří Zahradník Charles University, Prague

2. Numerical simulation of strong motions for 1997 Colfiorito Mw 6.0 earthquake: method Jiří Zahradník Charles University, Prague

3. Colfiorito earthquake (Umbria-Marche, Central Italy) mainshock 26 September 1997 at 09:40 GMT Mw = 6.0 strike 152 o, dip 38 o, rake -118 o fault size 12 x 7.5 km, bottom depth 8 km slip average 0.37 m (a heterogeneous model) Capuano et al., J. of Seismology (2000)

4. Importance of an asperity for the Colfiorito earthquake entire fault (incl. geodetic data): 12 x 9 km,  = 3 MPa asperity (strong motion data): 6 x 6 km, 13 MPa modelled with subevents of 20 MPa Castro et al., BSSA (2001) previous stress drop estimates from strong-motion accelerograms (Rovelli et al., 1988): 20 MPa

5. Another example: 1995 (Mw=6.4) Dinar, Turkey entire fault (incl. geodetic data): 13 x 17 km,  = 3.6 MPa two asperities, each one of about 5 x 5 km, 6 MPa J. G. Anderson et al., BSSA (2001)

6. Fault and asperities in general Somerville et al. (1999): a self-similar empirical scaling, relating Mw-L and asperity slip / average slip = 2 (slip contrast) asperity area / entire fault area = 0.25 Mw=6: fault area = 104 km 2 asperity area = 23 km 2

7. Asperity model Entire fault: Average slip: D Moment: Mo=  D L 2 Stress drop:  Mo  L  Spectr. acc: A   L Asperity: Slip 2D Moment: Mo/2 Stress drop: 4  Spectr. acc: 2A

8. Asperity size for Colfiorito Capuano et al. (2000): fault area = 90 km 2 Hunstad et al. (1999) and Salvi et al. (2000): fault area = 108 km 2 my asperity model = 1/4 fault: a square 5 x 5 km with 1/2 moment rupture outside asperity is neglected

9. Asperity model the asperity slip 0.8 m is equivalent to the all-fault average slip of 0.4 m (cf. 0.37 m of Capuano et al.)

10. Ground motion simulation: deterministic composite method asperity = N 2 equal-sized subevents (N=L/l) summation of the subevents with a constant rupture velocity (+ a perturbation), as in EGF subevents = point-source synthetics, DW HF incoherence: A = N a LF coherence: D = N 2 d, insufficient LF enhancement (Frankel): D = N 3 d

11. And what about C ? C = the stress-drop ratio: event/subevent here it is unimportant since subevents are synthetic (their stress drop is optional) therefore, C=1

12. Subevent model asperity = 5x5 subevents like this : subevent duration = its length / rupture velocity (a formal quantity, dependent on N)

13. Slip velocity (independent on N) average slip velocity = subevent slip / subevent duration =0.41 m/s (same for any Mw; self-similarity) maximum slip velocity depends on wavelet e.g., for Brune’s wavelet: = average slip velocity * 2.3 = 0.9 m/s

14. Maximum slip velocity Just change the subevent duration (while keeping its moment and N). It is a free parameter

15. maximum slip velocity depends on wavelet e.g., for Brune’s wavelet: = average slip velocity * 2.3 = 0.9 m/s We try this and also 1.8 m/s.

16. Fault geometry strike 152 o, dip 38 o, rake -118 o nucleation point at the hypocentre (43.03 N, 12.86 E, depth 7.1 km); this is the right bottom corner of the asperity the asperity top is at the depth of 4 km

17. Stations

18. Crustal model M. Cocco, pers. comm. (Qp=290, Qs=100)

19. Results: LF directivity in the velocity synthetics extreme station: 2 = NOCR (Nocera Umbra)

20. Synthetic velocity, 3 components

21. Synthetic acceleration: a small perturbation of rupture-time is helpful

22. Synthetic acceleration, 3 components

23. Synthetic acceleration: peak values station ordering with increasing epic. distance CLFR NOCR

24. Synthetic acceleration: peak values Uncertainty estimate ?

25. Deterministic-stochastic method Keep the LF motion unchanged, and perturb the HF motion (to reflect the source complexities) Get the perturbed HF motion by extrapolating the LF motion (PEXT method) see a paper in the present ESC proceedings

26. Extrapolation is a little bit “tricky”. Instead of explaining the technique, I present examples and compare them with deterministic (reference) results.

27. Example of a single realization, acceleration extrapolated above 2.6 Hz GTAD = Gualdo Tadino

28. ... another station CTOR = Cerreto Torre

29. Nocera Umbra station

30. The stochastic extrapolation is equivalent to perturbation of the deterministic simulation

31. Advantages of PEXT method It includes the requested ground-motion variability at HF due to uncertain source complexities (rupture and rise time variation...). Discrete wavenumber calculation is limited to LF only, thus PEXT is very fast. Easy to simulate many “stations”, i.e. to produce simulated ground-motion maps.

32. From 8 stations to 64 “stations”

33. PGA map (average of 30 realizations) extrapolated from 2.6 to 5.0 Hz area: 60 x 60 km around epicentre PGA=max(NS,EW,Z) of about 15 minutes on a PC < 2 m/s 2 ; too low ?

34. Incresing maximum slip velocity old: 0.9 m/s

35. Incresing maximum slip velocity = a multiplication constant only old: 0.9 m/s new: 1.8 m/s Be aware of the filter ! Here we consider f < 5 Hz. True new slip velocity is just about 1.2 m/s.

37. Where’s the limit beyond which we should extrapolate the acceleration spectrum ? The above experiment was for 2.6 Hz = the subevent corner frequency. In such a case, the HF directivity was low. Now we arbitrarily decrease from 2.6 Hz to 1.6 Hz.

39. Stations

40. Result: acc. increase for the forward directivity station GTAD and decrease for the backward station CTOR CTOR GTAD

43. From 2.6 Hz (left) to 1.6 Hz (right)

44. The HF directivity increased (focusing into a single location)

46. Where’s the limit beyond which we should extrapolate the acceleration spectrum ? The above experiment was for 2.6 Hz = the subevent corner frequency. In such a case, the HF directivity was low. Now we arbitrarily decrease from 2.6 Hz to 1.0 Hz.

47. The extrapolation limit decreased from 2.6 to 1.0 Hz

48. GTAD increase, CTOR decrease...

49. GTAD CTOR Acc. increase for the forward directivity station GTAD, and decrease for the backward station CTOR rupture propag.

50. HF directivity increased, but the overall maximum decreased directivity: note the asymmetry of red dots

51. By decreasing the extrapolation limit, PEXT produces a stronger HF directivity (similar to kinematic methods). extrapolated above 2.6 Hzextrapolated above 1.0 Hz

52. The same with identical scales:

53. Compare the homogeneous asperity with a more realistic model: Entire fault with a random slip heterogeneity (fractal distribution of subevent size) the rise-time and rupture-time variation is implicitly included

54. Asperity 5x5 km, equal-size subsources Entire fault 12.0 x 7.5 km, fractal subsources (Jan Burjánek) average of 100 realizations

55. Asperity 5x5 km, equal-size subsources Entire fault 12.0 x 7.5 km, fractal subsources (Jan Burjánek) a single realization

56. ... and for peak values

57. A summary plot

58. Engineering need of f > 5 Hz: Absorption treatment ?

59. Additional absorption correction exp(-  f) exp (-  R f / Vs / Q(f)) Q(f)=77 f 0.6 At distance R< 30 km the Q(f) effect is small.  = 0.06 The “kappa effect” is significant.

60. Kappa effect

61. Amplification due to increased slip velocity and de-amplification due to increased kappa

63. Preferred results of this study

64. PGA maps for the extrapolation limit of 2.6 Hz (HF directivity is weak) max slip vel. 0.9m/s, kappa=0 f < 5 Hz max slip vel. 1.8m/s, kappa=0.06 f < 10 Hz

65. PGA average of 30 realizations (left) and a single realization (right)

66. From acceleration to velocity Primary PEXT calculation is always acceleration (easy extrapolation on the flat plateau); then FFT from acc. to veloc. Velocity is only weakly dependent on the particular choice of the extrapolation limit To simulate uncertain slip distribution, velocity modeling may include a LF perturbation. Caution at very low frequency: slip outside asperity becomes important

67. PGV map max slip vel. 1.8m/s, kappa=0.06 f < 10 Hz

68. PGV map in two versions: without (left) and with (right) a LF perturbation max slip vel. 1.8m/s, kappa=0.06 f < 10 Hz

69. Validation on strong-motion records ? Not yet, since the Colfiorito recordings have been extremely complicated by local site effects (to be included as a next modeling step).

70. Summary We investigated synthetic composite models of a finite-extent source.We investigated synthetic composite models of a finite-extent source. Input data: stations, 1D crustal structure, Mw, focal mechanism, position of asperity. A free parameter is maximum slip velocity.Input data: stations, 1D crustal structure, Mw, focal mechanism, position of asperity. A free parameter is maximum slip velocity. Variations of the HF spectral level due to source complexities do not require repeated source calculation. Instead, we use a (randomized) extrapolation of the LF acceleration spectrum.Variations of the HF spectral level due to source complexities do not require repeated source calculation. Instead, we use a (randomized) extrapolation of the LF acceleration spectrum. and finally... and finally...

71. Since the HF directivity of true ground motions is questionable we propose composite modeling with variable extrapolation limit, hence with a high/intermediate/low HF directivity.Since the HF directivity of true ground motions is questionable we propose composite modeling with variable extrapolation limit, hence with a high/intermediate/low HF directivity. The pronounced LF directivity remains unchanged unless we want to account for uncertain slip distribution.The pronounced LF directivity remains unchanged unless we want to account for uncertain slip distribution. As the extrapolated composite method is very fast it allows easy construction of the PGA and PGV simulation maps.As the extrapolated composite method is very fast it allows easy construction of the PGA and PGV simulation maps. END

73. Summary in detail We investigated synthetic composite models of a finite-extent source. Input data: stations, 1D crustal structure, Mw, focal mechanism, position of the main asperity with respect to hypocentre (or the latter parameter is varied). The basic free parameter is maximum slip velocity.

74. Deterministic composite modeling yields a clear LF directivity. It is caused by station- dependent spectral level and duration. The HF directivity is weaker since the HF spectral level (given by the subevent size) does not vary with station position, but the duration does.

75. Variation of rupture time and rise time on the fault (and/or variation of the crustal model) yield variation of the HF spectral level. Effects like that do not require repeated source calculation. Instead, we use a (randomized) extrapolation of the acceleration spectrum.

76. If the extrapolation starts at (or above) the corner frequency of the subevent, the HF directivity is as small as in the deterministic composite model. If, however, we decrease the extrapolation limit, the HF directivity increases. The radiation becomes similar to kinematic source models.

77. Since the HF directivity of true ground motions is questionable we propose composite modeling with variable extrapolation limit, hence with a high/intermediate/low HF directivity. It is easy to do that, since the extrapolated composite method is very fast.

78. The LF perturbation can be also included to account for the uncertainty of the slip distribution. As the extrapolated composite method is very fast it allows easy construction of the PGA and PGV maps.

80. How the summation works ? a formal exercise (parametric study)a formal exercise (parametric study) summation of N2 wavelets of equal duration in a given time windowsummation of N2 wavelets of equal duration in a given time window varying window length simulates directivityvarying window length simulates directivity arrival times subjected to a perturbationarrival times subjected to a perturbation

81. HF incoherence (e4.gif)

82. HF incoherence (sum8.gif)

83. LF coherence & directivity (f2.gif)

84. Effect of duration (f6.gif)

85. Effect of duration (f8.gif)

86. No HF directivity (d1.gif) and artificial HF directivity (d3.gif)

87. d4 and d5

88. d6 and d7

89. Fixed and perturbed duration (t3 and t4.gif) !!!!!!!!!!!!

91. PEXT method composite DW accel. a(t) up to f = fstop; fstop is the so-called extrapolation limit, well above the apparent corner frequency of the target event time window w(t) obtained from a(t); w(t) is assumed to be basically affected by the apparent source duration windowed Gaussian noise g(t)=n(t)w(t), normalization, i.e., |G(f)|=1 “on average”

92. PEXT method: time domain

93. PEXT method (cont.) |A(f)| G(f) for f<fstop, i.e. perturbation; this step can be omitted to keep deter. LF estimation of spectral plateau A ave |A(f)| by averaging |A(f)| between fstart, fstop A ave G(f) for f>fstop, i.e. extrapolation; note that G(f) is normalized, thus it is affecting only duration, not amplitude

94. PEXT method: frequency domain fstart fstop

95. PEXT method: time domain

96. Meaning of fstart, fstop DW solution calculated: 0 < f < fstop (+ time window obtained there) accel. spectral plateau averaged: fstart < f < fstop accel. plateau extrapolated: f > fstop