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Numerical simulation of strong motions for 1997 Colfiorito Mw 6.0 earthquake: method

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

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Numerical simulation of strong motions for 1997 Colfiorito Mw 6.0 earthquake: method

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

  2. Colfiorito earthquake (Umbria-Marche, Central Italy) • mainshock 26 September 1997 at 09:40 GMT • Mw = 6.0 • strike 152o, dip 38o, rake -118o • 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)

  3. Importance of an asperityfor the Colfiorito earthquake entire fault (incl. geodetic data): 12 x 9 km, Ds = 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

  4. 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 km2 asperity area = 23 km2

  5. Asperity model Entire fault: Average slip: D Moment: Mo=m D L2 Stress drop: DsMo/L3 Spectr. acc: A s L Asperity: Slip 2D Moment: Mo/2 Stress drop: 4Ds Spectr. acc: 2A

  6. Asperity size for Colfiorito Capuano et al. (2000): fault area = 90 km2 Hunstad et al. (1999) and Salvi et al. (2000): fault area = 108 km2 my asperity model = 1/4 fault: a square 5 x 5 km with 1/2 moment rupture outside asperity is neglected

  7. 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.)

  8. Ground motion simulation: deterministic composite method • asperity = N2 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 = N2 d, insufficient • LF enhancement (Frankel): D = N3 d

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

  10. 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

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

  12. 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.

  13. Fault geometry strike 152o, dip 38o, rake -118o 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

  14. Stations

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

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

  17. Synthetic velocity, 3 components

  18. Synthetic acceleration, 3 components

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

  20. Synthetic acceleration: peak values Uncertainty estimate ?

  21. 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

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

  23. Example of a single realization, accelerationextrapolated above 2.6 Hz GTAD = Gualdo Tadino

  24. ... another station CTOR = Cerreto Torre

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

  26. 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.

  27. From 8 stations to 64 “stations”

  28. PGA map (average of 30 realizations) extrapolated from 2.6 to 5.0 Hz area: 60 x 60 km around epicentre of about 15 minutes on a PC PGA=max(NS,EW,Z) < 2 m/s2 ; too low ?

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

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

  31. 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.

  32. The extrapolation limit decreased from 2.6 to 1.0 Hz

  33. GTAD increase, CTOR decrease...

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

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

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

  37. 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

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

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

  40. ... and for peak values

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

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

  43. Preferred results of this study

  44. 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

  45. 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

  46. 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

  47. 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).

  48. Summary • 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. • 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 ...

  49. 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. • As the extrapolated composite method is very fast it allows easy construction of the PGA and PGV simulation maps. END

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