GROUND MOTION SCALING IN THE MARMARA REGION: ATTENUATION

OF SEISMIC WAVES

(1)M.B.SØRENSEN,(2) A. AKINCI, (2) L. MALAGNINI

and (3)R. B. HERRMANN

(1) Department of Earth Science, University of Bergen,

Allegaten 41, 5007 Bergen, Norway

(2) Istituto Nazionale di Geofisica e Vulcanologia

Via di Vigna Murata 605, 00143 Roma-Italy

(3) Earth and Atm. Sci. Dept., Saint Louis University,

3507 Laclede Ave. St. Louis MO, USA

WHY THIS STUDY...?

In Seismic Hazard calculations, attenuation is an important input;

Since regional variations in the high-frequency crustal attenuation may be significant, studies on the ground-motion scaling at a regional scale must be performed in order to produce reliable hazard maps;

Tectonic Map of Turkey

A fundamental requirement for hazard studies

is the determination of the ground motion predictive relationships (Kramer, 1996).

Attenuation relationships have been developed for many regions of the world (Ambraseys, 1996; Boore and Joyner, 1991; Boore, 1983; Toro and McGuire, 1987; Atkinson and Boore, 1995; Atkinson and Silva, 1987; Campell, 1997; Sadigh, 1997) mainly by regressing strong-motion data.

Problem: Strong-motion waveforms are usually not available in

large numbers: can we use data from the background seismicity?

Solution: Yes, in this study, we deal mostly with ground

velocity data from a set of local recordings ..!

A general form for a predictive relationship may be:  

D(r,f) contains both the geometrical spreading and the anelastic attenuation experienced by the seismic waves all along their paths.

log A(M,r,f)=SOURCE(M,f) + D(r,f) + SITE(f)

For the evaluation of the sFor the evaluation of the seismic hazardeismic hazard we need we need a predictive relationship for the ground motion:a predictive relationship for the ground motion:

Source spectrum

Crustal attenuation

Surface geology and topography

Amplitude A(M,r,f) can be:

Time-domain quantities (peak ground accelerations, peak ground velocities, response spectra);

Frequency-domain quantities (Fourier spectra);

in this study, linear predictive relationships are obtained through regressions on data set of ground motion time histories

Time-domain processing Define a prototype narrow band-pass

filter; For each seismogram, at each

frequency: Apply the filter Take the peak value:

PEAK(f)=SRC(f) + D(r,f) + SITE (f)PEAK(f)=log [ Observed Peak ]

Frequency-domain processing

At the same set of central frequencies: on the original seismograms, compute the Fourier

amplitude spectrum on a time window of length T, starting at the S-wave onset. Window length varies with central frequency;

for each central frequency, compute the RMS value of the Fourier amplitude within the corners of the corresponding bandpass filter

AMP(f) = SRC(f) + D(r,f) + SITE(f)

AMP(f) = log [ rms Fourier amplitude ]

we are able to arrange all our observations (K observations from J earthquakes recorded at I stations) in a large matrix

Ok(rij,f) = SRCj(f) + D(rij,f) + SITEi(f)

k = 1,2,....,K ; j = 1,2,...,J ; i = 1,2,...,I

Invert for:

D(r,f)=lplDl pl=(r – Rl)/(Rl+1-Rl)

SITEi (f)

SRCj (f) Constraints :

j SITEi (f) = 0

D(r=rref, f)=0

(Use an L1- norm regression technique)

(Use an L1- norm regression technique)

After the inversion is run at a set of central frequencies, random vibration theory is used to model the empirical estimates of D(r, rref, f) and SRC(r, rref)

RVT combines a random, stationary time history with its Fourier amplitude spectrum and duration to predict its peak value in the time domain.

Theory is taken from Cartwright and Longuet-Higgins (1956);

The regional propagation term (normalized)

10D(ri, rref f)=[g (rij) / g (rref)] exp[-f (rij – rref) / Q(f)

g(r) = Geometrical spreading function Q(f) = Qo(f/fref) n Crustal quality factor = Shear – wave velocity rref= Arbitrary reference distance

Let data define crustal attenuation:for the inversion, D(r,rref,f) is parameterised as a piece-wise linear function with many nodes: no a priori assumptions

The last step in the processing is the modelling of the inverted excitation terms

Horizontal Velocity Spectrum at reference distance

10EXCj(rref, f)=sj(f) g(rref) exp(-frref /Q(f)v(f)exp(-f)>avg

exc(f,rref)= C(2f)Mos(f)(f)p(rref,f) expf

s(f) = (1- ) / (1 + (f/fa)2) + / (1 + (f/fb)2)

C = (0.55) (0.707)(2.0)/4

(f) = generic site amplification factor relative to hard rock

p (r, f) = [ g(r) exp ( -fr/Q(f) ) ]

MARMARA REGION

264 Horizontal waveforms (1 station)

100 horizontal waveforms (2 stations)

80 horizontal waveforms (15 stations)

Distribution is bad……!

Distance range and magnitudes should be well distributed...

Duration of the ground motion as a function of

central frequency and hypocentral

distance, used as input in RVT

Duration of the ground motion as a function of

central frequency and hypocentral

distance, used as input in RVT

•Horizontal lines represent a 1/r decay with hypocentral distance.

• Peak values are modeled through the use of Random Vibration Theory (RVT), given an arbitrary spectral model and an empirical functional form to quantify the duration of ground shaking at each hypocentral distance.

•g(r) is forced to be ~ 1/r at short distances and ~ 1/sqrt(r) at large distances. At intermediate r’s, crustal bounces may interfere with direct arrivals, giving rise to complex attenuation patterns.

•Horizontal lines represent a 1/r decay with hypocentral distance.

• Peak values are modeled through the use of Random Vibration Theory (RVT), given an arbitrary spectral model and an empirical functional form to quantify the duration of ground shaking at each hypocentral distance.

•g(r) is forced to be ~ 1/r at short distances and ~ 1/sqrt(r) at large distances. At intermediate r’s, crustal bounces may interfere with direct arrivals, giving rise to complex attenuation patterns.

D(r, rref,f)=log g(r) – log(rref) – [f(r – rref)/Q(f)]log e

Regional crustal attenuation of ground motion due to geometrical spreading and

Q(f)

Regional crustal attenuation of ground motion due to geometrical spreading and

Q(f)

Modelling the ground motion: geometrical spreading and Q(f)

D(r, rref,f)=log g(r) – log(rref) – [f(r – rref)/Q(f)]log e

g(r)= r-1.0, r < 30 km r-0.6, 30 < r < 40 km r-1.0, 40 < r < 50 km

r-0.7, 50 < r < 70 km r-2.0, r > 70 km…?

Q(f)= 300(f/1.0)0.3…………..?

Trade-off:

Since the range of distances is finite, a

tradeoff exists between Q0 and g(r).

How to minimize it:

Force geometrical spreading to describe body-waves at short

distances, and surface-waves beyond a critical

distance.

Trade-off:

Since the range of distances is finite, a

tradeoff exists between Q0 and g(r).

How to minimize it:

Force geometrical spreading to describe body-waves at short

distances, and surface-waves beyond a critical

distance.

Single corner-frequency Brune’s spectral model:

=20 Mpa…..?

0=0.06 sec……?

(f)=1.0

Single corner-frequency Brune’s spectral model:

=20 Mpa…..?

0=0.06 sec……?

(f)=1.0

Vertical excitation terms at 40 km hypocentral distance

Vertical excitation terms at 40 km hypocentral distance

Vertical site terms are forced to be zero-average at

each single frequency: as a consequence of this constraint,

possible systematic effects

acting on every station are

automatically forced over the

empirical, vertical excitation terms.

Vertical site terms are forced to be zero-average at

each single frequency: as a consequence of this constraint,

possible systematic effects

acting on every station are

automatically forced over the

empirical, vertical excitation terms.

TURKEY (ERZINCAN)170 recorded earthquakes

743 horizontal waveforms

6 three-component stations

Q(f) = 45 (f/1.0) 0.45

g (r) = r –1.1 r < 25 km r-0.5 r > 25 km

D(r, rref,f)=log g(r) – log(rref) – [f(r – rref)/Q(f)]log e

=0.02 sec=100 bar(f)=1.0

SUMMARY

Region Q0 n (sec)

(bar)

rmax

Colfiorito-Italy 130 0.10 0.04 200 50

Apennines-Italy 130 0.10 0.00 200 400

Friuli-Italy 300 0.43 0.03 600 200

Central Europe 400 0.42 0.08-.05 30 600

Greece 180 0.30 0.06 56 500

Crete 280 0.25 0.04 100 200

S. California 180 0.45 0.04 70 500

Erzincan –Turkey 45 0.45 0.02 100 40

How do we use these results?

We can calibrate linear predictive relationships (LPR) for the ground motion on the regions of interest (examples are next...);

We can integrate them into procedures of hazard analysis (coming up!);

We make engineers a little happier, by significantly reducing uncertainties in our predictions;

Peak Horizontal Ground Acceleration (g)Squares KOCAELI ERTHQUAKE, 1999, M=7.4

Other CURVES M=7.0

PHA’s and PHV’s were computed in each specific region through the use of Random

Vibration Theory (RVT), given the attenuation characteristics of the crust, the

specific source spectral model, and a functional form which predicts duration of

the ground shaking at each epicentral distance (and frequency)

Squares KOCAELI ERTHQUAKE, 1999, M=7.4

Other CURVES M=7.0

PHA’s and PHV’s were computed in each specific region through the use of Random

Vibration Theory (RVT), given the attenuation characteristics of the crust, the

specific source spectral model, and a functional form which predicts duration of

the ground shaking at each epicentral distance (and frequency)

CONCLUSIONS

Regionalization shows substantial variations in the attenuation parameters, even within a relatively small country like Italy;

Variations must be taken into account in order to produce reliable hazard maps;

Regional ground motion scaling can be properly defined by using the background seismicity;

and trade off

Since small events are insensitive to in the frequency band of our interest, they can be used to calibrate. Spectra of radiated

energy of large earthquakes, on the other hand, must be used to calibrate the stress parameter. Of

course, is expected to change as a

function of magnitude.

Since small events are insensitive to in the frequency band of our interest, they can be used to calibrate. Spectra of radiated

energy of large earthquakes, on the other hand, must be used to calibrate the stress parameter. Of

course, is expected to change as a

function of magnitude.

Peak amplitudes: residuals at all central

frequencies (fc=0.25 – 14.0 Hz)

Peak amplitudes: residuals at all central

frequencies (fc=0.25 – 14.0 Hz)

In the L-1 norm, we no longer need the distributions of residuals to be symmetrically

distributed around zero. Since a large number of

residuals always characterize the data

sets, the medians of the distributions are always very stable quantities, even in cases like the

ones shown below.

In the L-1 norm, we no longer need the distributions of residuals to be symmetrically

distributed around zero. Since a large number of

residuals always characterize the data

sets, the medians of the distributions are always very stable quantities, even in cases like the

ones shown below.