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

JiJiříří Zahradník Zahradník

Charles University, PragueCharles University, Prague

Colfiorito earthquake (Umbria-Marche, Central Italy)

• mainshock 26 September 1997 at 09:40 GMT

• Mw = 6.0

• strike 152o, 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)

Importance of an asperityfor 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

Fault and asperities in generalFault 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

Asperity modelAsperity modelEntire fault:

Average slip: D

Moment: Mo= D L2

Stress drop: MoL

Spectr. acc: A L

Asperity:

Slip 2D

Moment: Mo/2

Stress drop: 4Spectr. acc: 2A

Asperity size for ColfioritoAsperity 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

Moment (Nm) 0.5 e18Length x Width (km) 5 x 5Static Stress Drop (MPa) 10Average Slip (m) 0.8Rupture Veloc. (km/s) 2.6

Asperity model

the asperity slip 0.8 m is equivalent to the all-faultaverage slip of 0.4 m (cf. 0.37 m of Capuano et al.)

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

Moment (Nm) 0.4 e16Length x Width (km) 1 x 1Stress Drop (MPa) 10Duration (sec) 0.385Slip (m) 0.159

Subevent model asperity = 5x5 subevents like this:

subevent duration = its length / rupture velocity(a formal quantity, dependent on N)

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

Maximum slip velocity

Just changethe subevent duration(while keeping itsmoment and N).

It is a free parameter

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.

Fault geometry

strike 152o, 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

Stations

Crustal model

Thickness(km)

Vp(km/s)

Vs(km/s)

3.0 5.08 2.672.0 5.75 3.032.0 6.00 3.168.0 6.25 3.30

999. 6.50 3.42

M. Cocco, pers. comm.

(Qp=290, Qs=100)

Results: LF directivity in the

velocity synthetics

extreme station:2 = NOCR(Nocera Umbra)

Synthetic velocity, 3 components

Synthetic acceleration, 3 components

Synthetic acceleration: peak values

station ordering with increasing epic. distance

CLFRNOCR

Synthetic acceleration: peak values

Uncertaintyestimate ?

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

Extrapolation is a little bit “tricky”.

Instead of explaining the technique,

I present examples and compare them with deterministic (reference) results.

Example of a single realization, accelerationextrapolated

above 2.6 Hz

GTAD = Gualdo Tadino

... another station

CTOR = Cerreto Torre

The stochastic extrapolation is equivalent to perturbation of

the deterministic simulation

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.

From 8 stations to 64

“stations”

PGA map (average of 30 realizations) extrapolated from 2.6 to 5.0 Hz

area: 60 x 60 kmaround epicentre

PGA=max(NS,EW,Z)

of about 15 minuteson a PC

< 2 m/s2 ; too low ?

Incresing maximum slip velocity

old: 0.9 m/s

Incresing maximum slip velocity = a multiplication

constantonly

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.

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.

The extrapolation limit decreased from 2.6 to 1.0 Hz

GTAD increase, CTOR decrease...

GTAD

CTOR

Acc. increase for theforward directivitystation GTAD, and decrease for the backward station CTOR

rupture propag.

HF directivity increased, but

the overall maximum

decreased

directivity:note the asymmetry of red dots

By decreasing the extrapolation limit, PEXT produces a stronger HF directivity

(similar to kinematic methods).

extrapolated above 2.6 Hz extrapolated above 1.0 Hz

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 variationis implicitly included

Asperity 5x5 km, equal-sizesubsources

Entire fault 12.0 x 7.5 km,

fractal subsources(Jan Burjánek)

average of 100 realizations

Asperity 5x5 km, equal-sizesubsources

Entire fault 12.0 x 7.5 km,

fractal subsources(Jan Burjánek)

a single realization

... and for peak values

Engineering need of f > 5 Hz:

Absorption treatment ?

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.

Preferred results of this study

PGA maps for the extrapolation limit of 2.6 Hz (HF directivity is weak)

max slip vel. 0.9m/s, kappa=0f < 5 Hz

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

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

PGV map in two versions:without (left) and with (right)

a LF perturbation

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

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).

SummarySummary• We investigated synthetic composite models of a We investigated synthetic composite models of a

finite-extent source.finite-extent source.• Input data: stations, 1D crustal structure, Mw, focal Input data: stations, 1D crustal structure, Mw, focal

mechanism, position of asperity. A free parameter is mechanism, position of asperity. A free parameter is maximum slip velocity. maximum slip velocity.

• Variations of the HF spectral level due to source Variations of the HF spectral level due to source complexities do not require repeated source complexities do not require repeated source calculation. Instead, we use a (randomized) calculation. Instead, we use a (randomized) extrapolation of the LF acceleration spectrum. extrapolation of the LF acceleration spectrum.

and finally ... and finally ...

• Since the HF directivity of true ground motions is Since the HF directivity of true ground motions is questionable we propose composite modeling with questionable we propose composite modeling with variable extrapolation limit, hence with a variable extrapolation limit, hence with a high/intermediate/low HF directivity. high/intermediate/low HF directivity.

• The pronounced LF directivity remains unchanged The pronounced LF directivity remains unchanged unless we want to account for uncertain slip unless we want to account for uncertain slip distribution. distribution.

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

ENDEND

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.

• 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.

• 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.

• 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.

• 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.

• 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.

How the summation works ?

• a formal exercise (parametric study)a formal exercise (parametric study)

• summation of N2 wavelets of equal duration summation of N2 wavelets of equal duration in a given time windowin a given time window

• varying window length simulates directivityvarying window length simulates directivity

• arrival times subjected to a perturbation arrival times subjected to a perturbation

HF incoherence (e4.gif)

HF incoherence (sum8.gif)

LF coherence & directivity (f2.gif)

Effect of duration (f6.gif)

Effect of duration (f8.gif)

No HF directivity (d1.gif) and artificial

HF directivity (d3.gif)

d4 and d5

d6 and d7

Fixed and perturbed duration (t3 and t4.gif)

!!!!!!!!!!!!

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”

PEXT method: time domain

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 Aave |A(f)| by

averaging |A(f)| between fstart, fstop

• Aave G(f) for f>fstop, i.e. extrapolation; note that

G(f) is normalized, thus it is affecting only duration, not amplitude

PEXT method: frequency domain

fstart fstop

PEXT method: time domain

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