Comparison of Empirical and Numerical Site Responses at the Tito ...

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Bulletin of the Seismological Society of America, Vol. 97, No. 5, pp. 1413–1431, October 2007, doi: 10.1785/0120060223

Comparison of Empirical and Numerical Site Responses at the Tito

Test Site, Southern Italy

by S. Parolai, M. Mucciarelli, M. R. Gallipoli, S. M. Richwalski, and A. Strollo

Abstract The town of Potenza (Southern Italy) is one of the test sites for preparingground-motion scenarios within the framework of the Italian Dipartimento ProtezioneCivile–Instituto Nazionale di Geofisica e Vulcanologia (DPC-INGV) 2004–2006 pro-jects. An area in the neighboring village of Tito was selected to evaluate differenttechniques for estimating site effects involving a 40-m-deep instrumented borehole.This two-sensor vertical array records teleseismic, regional, and local seismicity.

Close to the borehole, three seismological microarrays (utilizing short-period sen-sors and digitizers with a high dynamic range) were installed in May 2005 to recordseismic noise. Differing acquisition geometries allowed the checking of any depen-dency in the derived dispersion curves based on the adopted analysis method (ex-tended spatial autocorrelation [ESAC] and frequency wave-number [F-K]). In gen-eral, the ESAC method appears to provide more reliable results in the low-frequencyrange.

Furthermore, the soil-velocity profiles obtained from the microarray data werecompared with the S-wave velocity profile derived from down-hole measurements.A good agreement was observed in the depth range well constrained by the data.Finally, empirical site responses were compared with those calculated numericallyfrom the S-wave velocity profiles obtained from the microarray data. Although thiscomparison did not resolve a preference among the derived models, it showed theimportance of downgoing waves in modifying the site response at the Tito site.

Introduction

In the past decades, seismologists and earthquake en-gineers have focused on estimating the amplification ofearthquake ground motion due to local geology. In particu-lar, the introduction of nonreference site techniques like thehorizontal-to-vertical (H/V) spectral ratio method, which canbe both applied to noise (Nakamura, 1989; Field and Jacob,1993; Lermo and Chavez-Garcia, 1994) and earthquake re-cordings (Lermo and Chavez-Garcia, 1993), has stimulatedan ever-increasing number of studies. Moreover, improve-ments in the quality of instrumentation and in computingpower have enabled seismologists to redirect their attentiontoward analyzing seismic noise recorded by arrays (e.g.,Horike, 1985; Hough et al., 1992; Ohori et al., 2002; Okada,2003; Scherbaum et al. 2003; Parolai et al., 2005), a methodoriginally proposed by Aki (1957). The objective of suchstudies is the (local) shear-wave velocity profile. However,only a few studies have included attempts to compare nu-merical site responses based on local velocity profiles withempirical ones (e.g., Satoh et al., 2001, 2004; Ohrnberger etal., 2004; Parolai et al., 2006), due to the lack of informationfor several parameters.

Within the framework of the Dipartimento Protezione

Civile-Istituto Nazionale di Geofisica e Vulcanologia 2004–2006 projects (http://www.ingv.it/progettiSV/), which aimto calculate seismic-shaking scenarios in areas of strategicand/or priority interest in Italy, the town of Potenza(Southern Italy) was chosen as one of the test sites. Specif-ically, an area in the neighboring village of Tito was selectedfor evaluating different techniques to estimate site effects.The site was also selected because of a current project deal-ing with the long-term (years) monitoring of possible tem-poral variations in site response (Mucciarelli et al., 2003).Therefore, a 40-m-deep borehole was drilled and down-holemeasurements to obtain the S-wave velocity were carriedout. Then, a Kinemetrics Shallow Borehole EpiSensor con-nected to a �114 dB (K2) digital recorder was placed in theborehole at 35 m. In addition, an STS2 triaxial seismometerconnected to a �135-dB (Q330) digitizer was installed atthe surface for recording teleseismic, regional, and localevents. In June 2005, this equipment was replaced with anEpisensor triaxial force-balance accelerometer at the surface,linked to a six-channel K2 digital recorder. Furthermore,three microarrays utilizing short-period sensors and digitiz-ers with high dynamic range were installed in May 2005 to

1414 S. Parolai, M. Mucciarelli, M. R. Gallipoli, S. M. Richwalski, and A. Strollo

Figure 1. Location of the Tito test site. The epicentral locations of the earthquakesanalyzed in this study are indicated by filled circles.

record seismic noise. Different acquisition geometries wereused to check any dependency in the derived dispersioncurves on the adopted analysis method (extended spatial au-tocorrelation [ESAC] and frequency wave-number [F-K]).The results of the analyses carried out on this high-qualitydata set are presented in the following. In particular, thecomparison of the soil-velocity profiles obtained from themicroarray data with the S-wave velocity profiles derivedfrom down-hole measurements will be illustrated. Finally,emphasis will be given to the comparison between the em-pirical site responses and those calculated numerically fromthe S-wave velocity profiles obtained from the microarraydata, aiming at evaluating the possibility of obtaining reli-able site responses from array noise measurements.

Geology and Geotechnical Measurements

The Tito test site is located in the Saint Loja Plain insouthern Italy, along the axial zone of Southern Apennines(Fig. 1). Previous geological studies (Pescatore et al., 1999)and geophysical investigations indicated that at the site ashallow layer of clay is interbedded with detritus and lensesof sand, and overlies a Flysch formation that can be consid-ered the engineering bedrock. A borehold of 40-m depth wasdrilled down to the Flysch formation and a seismometer wasinstalled at 35-m depth to record local, regional, and tele-seismic events. Nearby, a shallower borehole (20-m depth)was also drilled and a Casagrande piezometer installed in-side it.

The drilling survey showed quite homogeneous geologydown to 37 m, mainly characterized by clays with interbed-ded lenses of silt, sand, and detritus. The amount of detritusincreases with depth down to 37 m, with the grain size ofthe detritus varying between a few millimeters to some cen-timeters. Below 37 m, only coarse-slope detritus was found.The water level was encountered just few meters below thesurface.

During the survey, four undisturbed samples of 0.5-mlength were taken and subjected to geotechnical testing (oed-ometer and triaxial). The first was collected at 7-m depth,where a layer of very plastic clays with silt inclusions wasencountered. The second sample was taken from 9.5 m andconsisted of plastic clay. The third was collected at 20.5 mand consisted of gray clays. The last sample, taken at 27.5 m,consisted of overconsolidated clay. Table 1 shows some ofthe main geomechanical characteristics of the investigatedsoils.

Finally, Gallipoli (2004) derived a two-layered S-wavevelocity model using the results of the triaxial tests underthe assumption that for small strains, the stress-strain curvecan be assumed to be a straight line. Above 15 m the velocityis in the range 100 to 120 m/sec. Between 15 and 35 m itincreases to values between 180 and 225 m/sec.

Down-Hole Measurements

To obtain in situ shear-wave velocities, S waves gen-erated by a surface source were recorded at 1-m intervalsdown to a depth of 30 m. The measurements were not per-formed at greater depths due to signal-to-noise ratios thatwere too low. One single three-component down-hole geo-phone with a natural frequency of 10 Hz was used. It wasclamped to the PVC casing of the borehole by a hydraulicssystem that provided good coupling. S waves were generatedon the surface by a sledge hammer (7 kg) striking horizon-tally a steel plate. For each depth the direction of the hammerblow was also reversed to obtain two opposite polarities tofacilitate the picking of first arrivals. The use of a referencegeophone allowed the checking of the repeatability of theblows. The sampling rate was fixed to 4000 samples/sec.The acquisition system was equipped with a 16-bit digitizer.The measurements were performed by a service companythat also provided an S-wave velocity profile.

The data set collected during this experiment was rean-

Comparison of Empirical and Numerical Site Responses at the Tito Test Site, Southern Italy 1415

Table 1Geotechnical Parameters of Soil Samples from the Tito Test Site Borehole

Geotechnical Parameters1st Sample

(7–7.50 m depth)2nd Sample

(9.50–10 m depth)3rd Sample

(20.50–21 m depth)4th Sample

(27.50–28 m depth)

C unit weight (g/cm3) 1.97 1.78 1.96 1.87cs unit weight of solid particles (g/cm3) 2.71cd dry unit weight (g/cm3) 1.58 1.24 1.54 1.40w water content 25% 43% 27% 34%WL liquid limit 0.559 0.675Wp plastic limit 0.236 0.316Ip � (WL � WP) plasticity index 0.323 0.359

alyzed to check the reliability of the velocity profile providedby the service company and to estimate the S-wave qualityfactor Qs. First, the fast Fourier transform (FFT) was calcu-lated for each signal window starting from a preliminarypicking of the S-wave arrival and ending when 80% of theenergy was reached. Second, the frequency band with suf-ficient shot-related energy content was identified (30–100 Hz) after an inspection of the amplitude spectra. Therecordings were filtered successively using an eight-poleButterworth bandpass filter with low- and high-cutoff fre-quencies of 10 and 120 Hz, respectively. Figure 2 shows thefiltered recordings for the two horizontal components indi-cated as east–west and north–south. The orientation of thesensor changed while it was lowered down in the borehole,as seen for example, over the depth range 9 to 14 m, wheresudden changes in amplitude occur.

For the S-wave arrival-time calculation, the two hori-zontal components at each depth were rotated into the azi-muth that maximizes the horizontal ground motion (parallelto the beam strike) (Fig. 2). The horizontal components attwo different depths were then cross-correlated and the timelag was assumed to represent the travel-time difference be-tween the different depths. Intersensor distances of 3 and5 m were considered, and the operation repeated for reversedblows. The analysis was done by using nonoverlapping mov-ing windows, resulting in a total of 10 interval velocitycurves. For the smaller intersensor distances, the S-wave ve-locity estimation is very sensitive to small timing errors.

From Figure 3 it can be seen that the S-wave velocitystructure provided by the service company is in good agree-ment with our calculations. The greater variability of the S-wave velocity structure in the uppermost 5 m might indicatea larger influence of small triggering errors and source ef-fects, suggesting that interpreting linear segments of down-hole travel-time curves should be preferred to the estimationof interval velocities.

To estimate the effective quality factor Qs, the squareroot of the sum of the squares of the amplitude spectra onthe two horizontal components was used. Spectra were cal-culated as described. In addition, the selected windows weretapered with a 5% cosine function at both ends and the am-plitude spectra smoothed using a Konno and Ohmachi(1998) window fixing the parameter b to 40.

The spectral amplitudes were corrected considering afactor G(z), where z indicates depth. This factor accounts forthe geometrical spreading and the change in amplitude dueto variations in seismic impedance along the ray path (Gibbset al., 1994). For this correction, the velocity profile pro-vided by the service company was used. The quality factorwas determined by looking at the depth dependence of spec-tral values at individual frequencies (Gibbs et al., 1994).This analysis assumes that there is no depth dependence ei-ther on the source or the quality factor. The analysis wascarried out for 11 frequencies in the range 30 to 90 Hz dueto the signal-to-noise (S/N) ratio and the limitation imposedby the FFT because of the usage of short-signal windows.Similarly to Gibbs et al. (1994), the corrected spectral am-plitudes of the analyzed frequencies were plotted against thetravel times between the source and receivers. The slope ofthe straight line fitted to the data points provides an estimateof Qs at frequency f.

Figure 4a shows the results obtained for four frequen-cies. The scattering of the data might be due to Qs variationswith depth, source effects, and measurement errors. Never-theless, a clear trend showing the quality factor increasingwith frequency is observed, with a minimum of 7 at 30 Hz(Fig. 4b). Because it was observed that, especially for higherfrequencies, the S/N ratio was decreasing, the straight-linefitting was repeated for all the frequencies after removingthe data corresponding to larger travel times (down to0.15 sec corresponding to 25-m depth). The results (Fig. 4b)were not affected by the selected travel-time interval for fre-quencies below 70 Hz, whereas the results for higher fre-quencies showed that the strong increase in the Qs factormight be due to noise affecting the data. The Qs factor be-tween 50 and 80 Hz seems to be nearly 20–30. This effectivequality factor at low frequencies is consistent with the damp-ing estimated by Mucciarelli and Gallipoli (2006) using anonparametric damping analysis of earthquake recordings.Furthermore, estimates of the quality factor carried out usingthe spectral ratio method (Gibbs et al., 1994) between the25- and 5-m down-hole signals and fitting the 15–40 Hz andthe 15–70 Hz frequency band (not shown here) resulted inQs values between 10 and 20, consistent with those obtainedby spectral amplitude decay analysis.


Figure 2. Shear-wave data from the down-hole experiment, corrected by using adepth-dependent factor. Shear waves from positive and negative pulses of the shearsource are superimposed for the identification of shear-wave arrivals. All data areshown using a common scale.

Microarray Measurements

The installation of microarrays in urban areas is obvi-ously guided strongly by practical restrictions. Dependingon the conditions, it is often difficult to configure the arraygeometry optimally for certain techniques. The ESACmethod (Ohori et al., 2002; Okada, 2003; Parolai et al.,2006) performs in this aspect better than methods based onF-K analysis (Okada, 2003), because for the same maximuminterstation distance it provides reliable results even forlower frequencies; that is, larger depths can be investigatedby the same array size. Moreover, considering that Parolaiet al. (2005), Picozzi et al. (2005), and Arai and Tokimatsu(2005) showed that a joint inversion of dispersion curvesand H/V spectral ratio of noise might increase the depth ofinvestigation, the potential of microarrays can now be evenbetter exploited. Recently, Chavez-Garcia et al. (2006) con-firmed that the spatial correlation method, for the case ofisotropic distribution of noise, does not need an azimuthalaveraging to estimate the phase velocity, thus overcomingone of the major drawbacks from a practical point of view.

In fact, a regular geometry with sufficient azimuthal cover-age might be difficult to obtain in urban areas and may re-quire a large number of stations. However, F-K-based meth-ods allow the identification of not only the direction of thenoise sources, but also allow differentiating between differ-ent modes that exist in the wave field.

To evaluate the advantages/disadvantages of both meth-ods in a typical urban environment, three different arrayswere installed around the borehole in Tito. The array ge-ometries varied from a simple T-shaped to more complicatedones (Fig. 5a–c). All the geometries were planned to providea sufficient azimuth and interstation distance coverage, al-lowing the retrieval of information about the Rayleigh wave-phase velocity in the frequency band between 2 and 10 Hz.This range was expected to be sufficient for characterizingthe sedimentary cover. The actual station positions were alsoconstrained by the distribution of buildings in the area.

The stations operated simultaneously for more than1 hour for each array, recording noise at 500 samples/sec,which is adequate for the short interstation distance consid-ered. Every station was equipped with a 24-bit digitizer con-


Figure 3. S-wave velocity profiles (black lines)determined in this work. The S-wave velocity struc-ture provided by the service company is shown by thegray line.

nected to a Mark L-4C-3D 1 Hz sensor and Global Posi-tioning System (GPS) timing. For the analysis, the datarecorded by each station of each array were divided in 60-sec windows. A total of 44 nonoverlapping windows wereconsidered. Only the vertical component was analyzed. Re-cordings were corrected for the instrumental response con-sidering the calibration parameters of each sensor.

Figure 5d–f shows respective responses of the arrays.The array response does not only depend on the slowness ofthe seismic phases observed within the array, but is also afunction of the wavenumber k of the observed signal and ofthe array geometry. It provides insights about the limits, interms of k, of the valid array output. Note the different re-sponse of the arrays in terms of wavenumber. The F-K re-sponse of array 1 shows a major aliasing peak at wave-number 0.18 rad/m (kmax). This peak does not reach themidheight of the central peak, a value that was suggested by

Wathelet (2005) to define the threshold for the aliasing andresolution limits of the array response. A rough estimate ofthe minimum wavenumber kmin (that define the resolutionlimit) of about 0.03 rad/m was deduced from the width ofthe central peak, measured at its midheight. The same esti-mate was obtained for the other two arrays, whereas kmax is0.23 and 0.135 for arrays 2 and 3, respectively. Please notethat in those cases the peaks also do not reach the midheightof the central peak.

ESAC Method

Following Ohori et al. (2002), Okada (2003), and Par-olai et al. (2006), the space correlation function �(x) wascalculated in the frequency domain for every pair of stationsby:

M1Re( S (x))� m jnM m�1

�(x) � ,M M1 (1)

S (x) S (x)� m jj � m nn�M m�1 m�1

where mSjn is the cross-spectrum for the mth segment of databetween the jth and the nth station, and M is the total numberof used segments. The power spectra of the mth segments atstation j and station n are mSjj and mSnn, respectively. Thespace-correlation function obtained for every pair of stationswas smoothed using a Konno and Ohmachi window (Konnoand Ohmachi, 1998) with the coefficient b, which determinesthe bandwidth, fixed to 40. The space-correlation values forevery frequency were then plotted as a function of distance.An iterative grid-search procedure was then performed usingthe equation (Aki, 1957)

x0�(r, x ) � J r , (2)0 0� �c(x )0

to find the value of the phase velocity c(x0), that gives thebest fit to the data, with c(x0) varied between 50 and 3000 m/sec in steps of 1 m/sec. In equation (2), �(r,x0) is the space-correlation function for the angular frequency x0, r is theinterstation distance and J0 is the zero-order Bessel function.The best fit was achieved by minimizing the root-mean-square (rms) of the differences between the values calculatedusing equations (1) and (2). Data points that differed by morethan two standard deviations from the value obtained withthe minimum-misfit velocity were removed before the nextiteration of the grid search. A maximum of three grid-searchiterations was allowed.

Further details about the procedure can be found in Par-olai et al. (2006).

F-K Methods

Two different methods for F-K analysis have been con-sidered: the beam-forming method (BFM) (Lacoss et al.,


Figure 4. (a) Spectral amplitude values versus travel timefor selected frequencies (black dots). The best-fitting linesin a least-squares sense considering the whole travel-timeinterval are shown in black. The gray lines are the least-squares fit if the interval is limited to 0.17 sec, while thedashed line is obtained if the fit is performed considering amaximum travel time of 0.15 sec. Note that the vertical scalefor the plot showing f � 80 Hz differs from the others.(b) Qs-factor estimates versus frequency. Open circles indi-cate estimates obtained by fitting the whole available dataset. Triangles show the values obtained by limiting the fit tospectral amplitudes corresponding to travel times smallerthan 0.17 sec. Filled circles show the values obtained bylimiting the fit to spectral amplitudes corresponding to traveltimes smaller than 0.15 sec. Vertical lines indicate the un-certainties estimated from the standard errors of the fit.

1969) and the maximum likelihood method (MLM) (Capon,1969). The estimate of the F-K spectra Pb(f, k) by the BFMis given by:

n

P ( f, k) � � exp{ik(X � X }, (3)b � lm l ml,m�1

where f is the frequency, k is the two-dimensional horizontalwavenumber vector, n is the number of sensors, �lm is theestimate of the cross-power spectra between the lth and themth data, and Xi and Xm are the coordinates of the lth andthe mth sensors, respectively.

The MLM gives the estimate of the F-K spectra Pm(f, k)as:

n �1�1P ( f, k) � � exp{ik(X � X } . (4)m � lm l m� �

l,m�1

Capon (1969) showed that the resolving power of the MLMis higher than that of the BFM, but the MLM is more sensitiveto measurements errors.

From the peak in the F-K spectrum occurring at coor-dinates kxo and kyo for a certain frequency f0, the phase ve-locity c0 can be calculated by:

2pf0c � . (5)0 2 2k � k� xo yo

An extensive description of these methods can be found inHorike (1985) and Okada (2003).

H/V Spectral Ratio Method

H/V spectral ratios (Nakamura, 1989) from the 44 win-dows of noise recordings at each station of each array were


Figure 5. (top) Microarray configurations. (a) Array 1; (b) array 2; (c) array 3. Thegray-filled circle indicates the borehole location. (bottom) Microarray responses:(d) Array 1; (e) array 2; (f) array 3.

also calculated. Their Fourier spectra were computed andsmoothed by using a Konno and Ohmachi (1998) windowwith the coefficient b fixed to 40. For every station a meanH/V curve was calculated using a logarithmic average of theindividual H/V curves. Figure 6 shows the mean H/V curveat the different stations for each array, together with an array-averaged H/V curve (thick gray curve).

The frequency of the first peak in the H/V spectral ratiois consistent between the different arrays. However, the am-plitude of the peak for array 3 is clearly larger. Array 3 wasoperational during a Monday morning, but arrays 1 and 2were operational during Sunday morning; hence, the varia-tion in amplitude is clearly related to the amount of anthro-pogenic noise, because the Tito array is located in an indus-trial area. However, the presence of high-noise transientsdoes not adversely affect the HVRS if a sufficient numberof signal windows is used (as shown by Parolai and Galiana-Merino [2006]). On the contrary, the amplification level ap-proaches the one derived from earthquakes, as already ob-served for this site by Mucciarelli et al. (2003).

Results: Array 1

Figure 7a (left) shows the space-correlation coefficientsderived from equation (1) compared with those obtained forthe best-fitting phase velocities of equation (2) (Fig. 7a,right). Clearly, the latter allows a satisfactory retrieval of the

observed space-correlation coefficients and reproduces themain features displayed in the frequency-distance plain. InFigure 7b, examples of F-K MLM (upper panel) and BFM(lower panel) analyses are shown for three different fre-quencies, selected from all those analyzed. Both methodsshow low resolution for the lowest frequency depicted(2.5 Hz). However, they allow a clear identification of themaxima at 3.9 and at 6.5 Hz. Although both methods suggesta nearly isotropic distribution of the noise sources, MLMseems to have a higher resolving power than BFM, consistentwith the conclusion of Horike (1985).

The apparent dispersion curves obtained by the threedifferent analysis methods are shown in Figure 7c. They looknormally dispersive, that is, they seem to be dominatedmainly by the fundamental mode. In general, there is a goodagreement between the phase velocities between 3.5 and10 Hz. However, at lower frequencies, the F-K methods pro-vide a larger estimate of the phase velocity than ESAC. Thisresult is consistent with Okada (2003), who concluded thatthe F-K method is able to use wavelengths up to two to threetimes the largest interstation distance, whereas with theESAC method, one may investigate the subsurface by usingwavelengths up to 10 to 20 times the largest interstationdistance, being therefore more reliable in the low-frequencyrange. For frequencies from about 11 Hz onward the phasevelocity increases nearly linearly. This effect is due to spatial


Figure 6. Mean H/V spectral ratio at each station(black lines) and array-averaged H/V spectral ratio(gray line) for all three microarrays: (a) array 1; (b)array 2; (c) array 3.

aliasing and limits the upper bound of the usable frequencyband. At very low frequencies, that is, below 2.37 Hz forthis test site, the phase velocity curve obtained using ESACstarts to diminish. This is probably due to the filtering effectof the sediments on the vertical component (Scherbaum etal., 2003), because this frequency is close to the resonancefrequency of the site (Fig. 6).

On the basis of these results, the joint inversion of thedispersion curve and the H/V spectral ratio curve was per-formed considering the phase-velocity values obtained bythe ESAC method (between 2.37 and 10.6 Hz), followingParolai et al. (2005) and using the modified Genetic Algo-rithm (GA) proposed by Yamanaka and Ishida (1996).

To evaluate the most suitable parameterization of themodel (finally made of eight layers), several tests (not shownhere) were performed. The first test demonstrated that thedeeper crustal velocity structure had a minor influence onthe inversion. Therefore, only a shallow crustal structure wasconsidered. Then, the influence of the P-wave velocity on

the final results was tested, the result being that there waslittle influence, and hence the relationship of Kitsunezaki etal. (1990) was used: Vp (m/sec) � 1290 � 1.11 Vs [m/sec].In the upper 30 m this provided values in agreement withthose computed by the service company from down-holemeasurements. Finally, once it was verified that the costfunction, that is, equation (2) in Parolai et al. (2005), did notallow a solution that similarly balanced the dispersion andthe H/V curve contribution to be obtained, a cost functionsimilar to Herrmann et al. (1999) was adopted:

N 2(1 � p) c ( f ) � c( f )ocost � [(1 � p)N � pK ] �� N c ( f )� j�1 o (6)

K 2p hv ( f ) � hv( f )o� ,�� K hv ( f ) �j�1 o

where the subscript o indicates the observed phase velocity(c(f)) and H/V (hv(f)) data, and N and K are the number ofdata points in the dispersion and H/V ratio curves, respec-tively. The relative influence of both data sets is controlledby the parameter p that was finally fixed to 0.01. We per-formed several tests that showed that this value yields a goodfit of both the dispersion curve and the H/V spectral ratio.

The probability of crossover and mutation, that is, thevalue below which the crossover and the mutation operation(Goldberg, 1989) take place, were fixed to 0.7 and 0.01,respectively (Yamanaka and Ishida, 1996). The scheme ofYamanaka and Ishida (1996) was followed for the elite se-lection and the dynamic mutation. The inversion was thenperformed following Parolai et al. (2005).

The minimum-misfit model, together with the modelslying inside the minimum cost �10%, are shown in Figure8 (left). All models tested by the inversion procedure arealso depicted, showing that a large solution space was in-vestigated. The dispersion curve constrains the model onlydown to �60–90 m. The deeper part is constrained by theH/V data alone. All models lying inside the minimum cost�10% show little variability down to 200-m depth. Below200 m, the large variability indicates that the trade-off be-tween velocity and thickness of the layers is not fully solvedby the H/V inversion. This hints that the S-wave velocitystructure of the best-fit model below 200-m depth is alsoonly weakly constrained. Figure 8 (right, top) shows that theaverage cost function of each generation may show largevariations. This indicates that the inversion generates verydifferent models while trying to escape from a possible localminimum in the solution. However, for the seed numberleading to the minimum misfit model, the minimum costfunction of each generation decreases from 0.162 at the firstgeneration to 0.049 by the 89th generation, when the bestmodel is found, a reduction in the misfit of �70%. Figure 8(right middle and below) shows the fit of the calculated dis-persion and H/V curves to the observed data, respectively.


Figure 7. (a) Spatial correlation coefficient from observeddata (left) and from a grid search (right) for array 1.(b) F-K analysis results for 2.5 Hz, 3.9 Hz, and 6.5 Hz. Whitedots indicate the position of the maximum used to estimatethe phase velocity. The white circle joins points with thesame k value. (c) Apparent phase-velocity curve obtained bythe ESAC method (black line). Circles show the frequenciesused for the joint inversion. The gray area indicates velocityvalues for a certain frequency determining a misfit within10% of the minimum in the grid-search procedure. Thephase-velocity curves from MLM (dashed line) and BFM(dotted line) are also shown.

Results: Array 2

Analyses for array 2 were performed by using the sameparameters as for array 1 and the results are presented in thesame way. Figure 9a shows that the empirical and fittedspace-correlation coefficients exhibit good agreement. BothF-K results are similar to those for array 1 (Fig. 9b). A com-

parison of the dispersion curves from the three methods(Fig. 9c) leads to the same conclusions as for array 1 re-garding the ability of ESAC to produce a reliable estimate ofthe phase velocity at low frequencies. Here, the low-frequency filtering effect of the site sets the lowest usable


Figure 8. (left) Joint inversion for array 1: all tested models (dark gray), the min-imum misfit model (white), and models lying inside the minimum misfit �10% range(black). The inset shows the P-wave velocity model using equation (6) in the joint-inversion procedure. (right top) Minimum misfit (black dots) and average misfit (grayline) versus number of generations for the seed number leading to the best model. (rightmiddle) Observed (gray circles) and calculated (white circles) H/V spectral ratio. (rightbottom) Observed (gray circles) and calculated (white circles) apparent phase velocities.

frequency to 2.17 Hz and aliasing becomes an issue beyond14 Hz.

The inversion was carried out by using apparent phase-velocity values between 2.17 and 9.7 Hz. Again, the disper-sion curve allows the model to be constrained only to depthsof 60 to 90 m, below which the H/V alone guides the inver-sion. For this array, small variations exist down to 250 m(Fig. 10). Below, a large variability indicates that the trade-off between velocity and thickness of the layers is not fullysolved by the H/V inversion. The minimum cost function ofeach generation decreases from 0.3982 for the first genera-tion to 0.046 by the 83rd generation when the best model isfound.

Results: Array 3

Again, there is a good agreement between empirical andfitted space-correlation coefficients (Fig. 11a). However, the

geometry obviously hampers the application of F-K meth-ods. Both methods (MLM and BFM) show low resolution forthe lowest depicted frequency (2.5 Hz) as well as for manyazimuthal directions. Only one maximum can be clearlyidentified at 3.9 Hz, whereas at 6.5 Hz the results are am-biguous. The agreement for the three methods is thereforeonly good between 3 and 6 Hz (Fig. 11b). The low-frequency filtering effect is observed at 1.9 Hz, whereas al-iasing in the ESAC analysis plays a role from 14 Hz on. Theapparent dispersion curve is very similar to that obtained bythe previous arrays, apart from slightly higher velocities atlow frequencies.

The joint inversion was performed for phase velocitiesin the range 1.9 to 9.7 Hz, which constrain the model downto depths of 85 to 125 m, with little variability down to650 m (Fig. 12). The large depth variability of the last in-terface clearly indicates that the trade-off between velocityand thickness of the deepest layer is not fully solved by the


Figure 9. The same as Figure 7 for array 2.

H/V inversion. The minimum cost function of each genera-tion decreases from 0.6067 for the first generation to 0.075by the last generation (100), when the best model is found.

Finally, Figure 13 shows the comparison of the threeminimum cost models for the uppermost 150 m (well con-strained in all inversions). The general trend of velocity is

similar for all models and is in agreement with the S-wavevelocity profile calculated by down-hole measurements inthe uppermost 30 m (compare with Fig. 3).

The best agreement is shown by models derived fromarrays 2 and 3, where the S-wave velocity decreases between6–13 m and 9–18 m, respectively. Both models also indicate



an increase in velocity at 35 and 39 m, respectively, consis-tent with the geotechnical investigations. Moreover, the S-wave velocities are also consistent with the estimates of Gal-lipoli (2004).

Empirical Site Response

Among the data recorded by the two stations (in theborehole and at the surface) six earthquakes with good S/Nratios were selected (see Fig. 1 and Table 2). Data wererecorded at 100 sample/sec. Figure 14 shows the three-component recordings of a local event (BA923 in Table 2),together with the pre-event and S-wave signal windows in-dicated. A clear amplification of the seismic signal from thebottom to the surface is evident, as well as larger amplitudeson the horizontal components with respect to the verticalones at both the borehole and surface stations. To estimatethe empirical site response, signal windows starting beforethe S-wave arrival and ending when 80% of the energy wasreached were selected. The signal windows were taperedwith a 5% cosine function at both ends and the associatedFFT calculated. The spectra were corrected for the instru-mental response and smoothed by using a Konno and Ohma-

chi (1998) window, fixing the parameter b to 40. Spectra ofpre-event signals were also calculated and used to estimatethe frequency-dependent S/N ratio of the recordings used.Figure 15 shows the average S/N ratios for each componentcalculated for the station at the surface and in the borehole.A sufficient (�3) S/N ratio is present between 0.5 and 20 Hz.

The H/V spectral ratios for both the surface and the bore-hole stations and the standard spectral ratios (SSRs) betweenthe horizontal (and vertical) components at the surface andin the borehole (SSR H and SSR Z, respectively) were com-puted. The logarithmic average of the H/V ratios, as well asof the SSR are depicted in Figure 16. Furthermore, in Figure16, the SSR for the horizontal components calculated by Gal-lipoli (2004) with respect to a reference station (SSR withreference site) 5 km way from the Tito test site and installedover limestone is also shown.

The H/V spectral ratio at the surface shows a main peakat about 1.2 Hz (consistent with that obtained by noise anal-ysis) and a secondary peak at about 3 Hz. The H/V spectralratio of the borehole station shows a main peak of amplifi-cation around 1.1 Hz with smaller secondary peaks at about3–4 Hz, 6–7 Hz, and 12.5 Hz.

The SSR H results differ from the H/V spectral ratios,



with a first broad peak shown at 1.7 Hz, while other narrowpeaks are depicted at about 4.6 and 8.6 Hz. The SSR Z resultsshow a main peak at about 12.5 Hz. Finally, the SSR ratiowith respect to the reference site shows the largest amplifi-cation at about 1.2 Hz and a general shape that stronglyagrees with the H/V ratio at the surface.

The discrepancies between SSR H and the other esti-mates of the site response (H/V spectral ratio of noise andearthquakes and SSR with reference site) suggest that theeffect of downgoing waves on the borehole recordings is notnegligible. Careful analysis of the amplitude spectra of therecordings of event BA924 provided useful insights into



explaining the observed behavior. Figure 17 shows thehorizontal-component spectra amplitudes of the surface re-cordings to be clearly larger than those of the borehole re-cordings at frequencies higher than 0.8 Hz, likely due to theimpedance becoming smaller toward the surface. However,the spectra of the horizontal components at the bottom sta-tion clearly show spectral troughs at about 2 Hz, 5 Hz, and8 Hz, mainly in correspondence with the peaks in the SSRH. A similar behavior is also seen in the vertical-component

spectra, showing amplification at the surface for frequencieshigher than 1.2 Hz and a clear spectral trough at nearly 12 Hzin the bottom recording. This trough is responsible for thepeak in the SSR Z. These troughs are considered to resultfrom destructive interference of upgoing and downgoingwaves at the borehole station.

Finally, although with slightly different magnitudes,both the surface and borehole recordings show larger am-plitudes on the horizontal component spectra with respect tothe vertical one in the frequency band 0.5–2 Hz (independentof the event magnitude and hypocentral distance), thus sug-gesting a deeper origin of the amplification observed at thesite.

Synthetic Seismogram Modeling

To evaluate the reliability of the S-wave velocity struc-tures obtained by the three different microarrays, syntheticseismograms were calculated by using a semianalyticalmethod that consists of an improved Thompson–Haskellpropagator matrix method that overcomes numerical insta-bilities by an orthonormalization technique (Wang, 1999).

Table 2Hypocentral Parameters of the Analyzed Earthquakes

ID No. Date

OriginTime

(UTC)Latitude

(�)Longitude

(�)Depth(km) ML

EpicentralDistance

(km)

BA923 7/1/06 4:27:12 40.618 15.805 9.1 2.3 7BA924 8/1/06 11:34:53 36.3 23.2 60 Mw 6.7 807BA967 5/2/06 17:02:59 40.789 15.22 10.5 3.2 48BA1175 17/4/06 2:44:05 39.572 17.14 10 4.3 167BA1208 24/4/06 9:59:41 40.567 15.578 10.8 2.6 13BA200 29/05/06 2:20:00 41.801 15.903 31.2 4.8 134


Figure 13. (left) S-wave velocity profiles obtained from the three different arraydata. (right) P-wave velocity profiles. The triangles indicate the depth of the boreholestation.

Figure 14. Vertical (Z), north–south (NS), and east–west (EW) component record-ings of the event BA923 (Table 2). The signal (S) and the pre-event noise (N) windowsused for the analysis are shown. (top) Surface station; (bottom) borehole station.


First, synthetic seismograms were generated consider-ing the upper-crustal structures of the three different modelsand a homogeneous half-space below. A source was locatedat a depth of 5 km and seismograms were computed forreceivers located at the surface and at a depth of 35 m (cor-responding to the depth of the borehole sensor) at distancesranging between 0.5 and 14.5 km. A total of 15 equallyspaced receivers were used, the complete records analyzed,and the results averaged. Different quality factors for theuppermost layers, consistent with those obtained by down-hole measurements, were tested (Qs � 10, Qs � 20, Qs �30). Because the results showed minor differences in theshape of the site responses with respect to the variability dueto the adopted models, in the following only the spectralratios obtained for Qs � 10, which provided results closestto the empirical ones, will be discussed.

Second, synthetic seismograms were also generatedconsidering a pure half-space model and using the parame-ters (P- and S-wave velocity and density) of the deepest layerof the model derived by using array 2. The same source andsurface receiver positions adopted in the first step were used.These synthetic seismograms were used to simulate the re-cording at a reference site.

Finally, FFT spectra of all the recordings were calcu-lated, and H/V, SSR H, SSR Z, and SSR with respect to thereference site spectral ratios computed.

Figure 16 shows that the models are able to capture themain trend (especially above 0.5 Hz) of all the different site-response estimate techniques. Differences in the amplitudeof the peaks (see, for example, the H/V at the borehole stationand the SSR H results) might come from the simplified, with

respect to reality, synthetic wave field that does not take intoaccount wave diffraction and scattering. Therefore, there isless redistribution of energy between the components ofground motion, and spectral troughs are more pronounced.The smaller amplitude of the SSR H between 5 and 20 Hzmight also indicate a slight overprediction of damping in theused models.

No single model was found to fully explain all obser-vations. For example, some models that reproduce the SSRresults very well may in turn be the worst for the H/V. Thus,deciding which of these quite similar models is the best onemay be more a matter of user preference than an objectivedecision.

The large peak at nearly 1 Hz in the SSR Z for the modelderived by array 1 is an artifact coming from a small troughin the synthetic spectrum. The variability of the syntheticSSR H with respect to the reference site reflects the uncer-tainty in the reference site S-wave velocity at the surface. Inthis case, the model derived from array 1 seems to be theone providing the impedance contrast closest to the actualone.

Conclusions

The availability of high-quality geophysical data fromthe Tito test site allowed the estimation of an S-wave veloc-ity structure down to 30-m depth from down-hole measure-ments. Furthermore, Qs was estimated for the uppermost30 m of the sedimentary cover. The Qs was determined forfrequencies higher than those generally of interest in engi-neering seismology, and represented an estimation of the

Figure 15. (top) Average S/N ratio of the vertical (Z), north–south (NS), and east–west (EW) components (black line) of all the analyzed earthquake events recorded atthe surface station. The gray area indicates the 95% confidence interval. (bottom) Samefor borehole station.


effective Qs (implying that the intrinsic Q might be larger).Nevertheless, a range of Qs values were used in numericalsimulations. Results showed that adopting a low Qs value,that agrees with the damping calculated by earlier studies,gave better numerical site responses, suggesting that this Qs

estimation might be considered for future numerical simu-lations of ground motion.

Different methods of analyzing microarray noise datawere evaluated while considering urban conditions (withtheir restrictions and limitations). Consistent with previousresults (Okada, 2003) the ESAC method provides phase ve-locities lower than those from the F-K analysis at low fre-

quencies. Okada (2003) showed that by increasing the arraysize, the F-K velocities at low frequencies become similarto those estimated by ESAC, indicating the latter is moresuitable for providing reliable dispersion curves over a widerfrequency range, especially toward lower frequencies(greater depths). Unfortunately, independent S-wave veloc-ity estimates at this test site for the depth range reached bythese low frequencies are not available, and the Okada(2003) results cannot be verified. Three S-wave velocity pro-files for the three different arrays were inferred. The consis-tency of the profiles, and even more important, the consis-tency of the numerical site responses based on such models,

Figure 16. (top left) H/V ratios at the surface station. (top right) SSR H spectralratios (surface to bottom). (middle left) H/V ratios at the borehole station. (middle right)SSR Z spectral ratios (surface to bottom). All figures show averaged results from earth-quake recordings (black line), and the gray area indicates the 95% confidence interval.Ratios from synthetic seismograms are shown considering the model obtained by array1 (dashed line), array 2 (dashed-dotted line), and array 3 (dotted-dashed line). (bottomleft) Array-averaged H/V spectral ratio of seismic noise for array 1 (continuous line),array 2 (dashed line), and array 3 (dotted line). (bottom right) SSR H spectral ratio withrespect to a reference site from earthquake recordings (black line). SSR H spectral ratiowith respect to a reference site from synthetic seismograms considering the modelobtained by array 1 (dashed line), array 2 (dashed-dotted line), and array 3 (dotted-dashed line).


shows the capability of the ESAC method to provide similarresults when the employed array geometries are fairly dif-ferent. This “independence” of the ESAC results with respectto the geometry of the array, under the condition that seismicnoise is stationary, is certainly a great advantage of the ESACmethod. In the case at hand, where there is a gradual increaseof impedance with depth, the joint inversion of dispersionand H/V curves seems to provide only marginal improve-ments in constraining the final model. This result differsfrom the observation of Picozzi et al. (2005), who investi-gated a site with a strong impedance contrast between sed-iment and bedrock.

The site response of the shallow crustal structure wasmodeled, but it did not allow us to resolve a preferenceamong the calculated velocity models. However, the mech-anism determining the differences between site responsescalculated by using both seismic noise and earthquake weak-motion recordings was identified. In particular, the impor-tance of downgoing waves affecting the borehole recordingstation at Tito was shown, as well as the existence of anamplification mechanism with a deeper origin than the depthof the borehole. This emphasizes the importance of not lim-iting ones investigation to only the uppermost tens of meters.Moreover, this result provides a warning about the use ofshallow-borehole recordings as input for numerical simula-tions.

The microarray data will also be used for future inves-tigations into the feasibility of applying other noise-analysistechniques, for example, the cross-correlation method (e.g.,Lobkis and Weaver, 2001) in urban areas and for studyingsoft-sediment S-wave velocity structure. The vertical arrayis still operational with the aim of enlarging the data set ofrecordings to include larger-magnitude events to performmore detailed site-response analysis, while also taking intoaccount soil nonlinearity.

Acknowledgments

K. Fleming kindly improved our English. Figures have been drawnusing the GMT (Wessel and Smith, 1991) software. Thanks to the fieldcrew E. Gunther and D. Di Giacomo. R. Milkereit improved the figures.Thanks to C. Di Maio and the soil dynamic lab of DiSGG for the geotech-

nical test and to I. Giano for the geological support at the drilling site. Thiswork was partially funded by project INGV-DPC S3. We are grateful to R.Wang for providing routines for forward calculation of the wavefield. Iden-tifying the name of manufactures is not meant to be an endorsement oftheir products. The comments by two anonymous reviewers and the As-sociate Editor Ivan Wong helped us to improve our manuscript.

References

Aki, K. (1957). Space and time spectra of stationary stochastic waves, withspecial reference to microtremors, Bull. Earthquake Res. Inst. 35,415–456.

Arai, H., and K. Tokimatsu (2005). S-wave velocity profiling by joint in-version of microtremor dispersion curve and horizontal-to-vertical(H/V) spectrum, Bull. Seism. Soc. Am. 95, 1766–1778.

Capon, J. (1969). High-resolution frequency-wavenumber spectral analysis,Proc. IEEE. 57, 1408–1419.

Chavez-Garcia, F. J., M. Rodriguez, and W. R. Stephenson (2006). Subsoilstructure using SPAC measurements along a line, Bull. Seism. Soc.Am. 96, 729–736.

Field, E. H., and K. Jacob (1993). The theoretical response of sedimentarylayers to ambient seismic noise, Geophys. Res. Lett. 20-24, 2925–2928.

Gallipoli, M. R. (2004). Tecniche geofisiche integrate in studi di micro-zonazione sismica, Ph.D. Thesis, University of Basilicata, 146 pp.

Gibbs, J. F., D. M. Boore, W. B. Joyner, and T. E. Fumal (1994). Theattenuation of seismic shear waves in Quaternary alluvium in SantaClara Valley, California, Bull. Seism. Soc. Am. 84, 76–90.

Goldberg, D. E. (1989). Genetic Algorithms in Search, Optimization, andMachine Learning, Addison-Wesley Pub. Co., Reading, Massachus-setts.

Herrmann, R. B., C. J. Ammon, J. Julia, and T. Mokhtar (1999). Jointinversion of receiver functions and surface-wave dispersion for crustalstructure, in Proc. 21st Seismic Research Symposium Technologiesfor Monitoring the Comprehensive Nuclear Test Ban Treaty 21–24September 1999, Las Vegas, Nevada, Los Alamos National Labora-tory, LA-UR-99 4700.

Horike, M. (1985). Inversion of phase velocity of long period microtremorsto the S-wave velocity structure down to the basement in urbanizedareas, J. Phys. Earth 33, 59–96.

Hough, S. E., L. Seeber, A. Rovelli, L. Malagnini, A. DeCesare, G. Sel-vaggi, and A. Lerner-Lam (1992). Ambient noise and weak motionexcitation of sediment resonances: results from the Tiber Valley, Italy,Bull. Seism. Soc. Am. 82, 1186–1205.

Kitsunezaki, C., N. Goto, Y. Kobayashi, T. Ikawa, M. Horike, T. Saito, T.Kurota, K. Yamane, and K. Okuzumi (1990). Estimation of P- and S-wave velocities in deep soil deposits for evaluating ground vibrationsin earthquake, J. JSNDS 9, 1–17 (in Japanese with English abstract).

Figure 17. (left) Horizontal-componentspectra of the recordings from the BA924 event(Table 2) at the surface (thick and thin blacklines for the north–south and the east–westcomponents, respectively) and the bottom sta-tions (thick and thin gray lines for the north–south and the east–west components, respec-tively). (right) Same as for the left panel butfor the vertical component.


Konno, K., and T. Ohmachi (1998). Ground-motion characteristic estimatedfrom spectral ratio between horizontal and vertical components ofmicrotremor, Bull. Seism. Soc. Am. 88, 228–241.

Lacoss, R. T., E. J. Kelly, and M. N. Toksoz (1969). Estimation of seismicnoise structure using array, Geophysics 29, 21–38.

Lermo, J., and F. J. Chavez-Garcia (1993). Site effect evaluation usingspectral ratios with only one station, Bull. Seism. Soc. Am. 83, 1574–1594.

Lermo, J., and F. J., Chavez-Garcia (1994). Are microtremors useful in siteresponse evaluation? Bull. Seism. Soc. Am. 84, 1350–1364.

Lobkins, O. I., and R. L. Weaver (2001). On the emergence of the Green’sfunction in the correlations of a diffusive field, J. Acoust. Soc. Am.110, 3011–3017.

Mucciarelli, M., and M. R. Gallipoli (2006). Estimate of frequency anddamping for large set of buildings in dense urban areas, Presented atFirst European Conference on Earthquake Engineering and seismol-ogy, Geneva, Switzerland, 3–8 September 2006, paper no. 211.

Mucciarelli, M., M. R. Gallipoli, and M. Arcieri (2003). The stability ofthe horizontal-to-vertical spectral ratio of triggered noise and earth-quake recordings, Bull. Seism. Soc. Am. 93, no. 3, 1407–1412.

Nakamura, Y. (1989). A method for dynamic characteristics estimations ofsubsurface using microtremors on the ground surface, Q. Rept. RTRIJapan 30, 25–33.

Ohori, M., Nobata, A., and Wakamatsu, K. (2002). A comparison of ESAC

and FK methods of estimating phase velocity using arbitrarily shapedmicrotremor analysis, Bull. Seism. Soc. Am. 92, 2323–2332.

Ohrnberger, M., F. Scherbaum, F. Kruger, R. Pelzing, and S.-K. Reamer(2004). How good are shear-wave velocity models obtained from in-version of ambient vibrations in the lower Rhine embayment (N.W.Germany)? Boll. Geofis. Teor. Appl. 45, 215–232.

Okada, H. (2003). The Microtremor Survey Method, Geophysical Mono-graph series 12, M. W. Asten (Editor), Society of Exploration Geo-physicists, Tulsa, Oklahoma.

Parolai, S., and J. J. Galiana-Merino (2006). Effect of transient seismicnoise on estimates of H/V spectral ratios, Bull. Seism. Soc. Am. 96,228–236.

Parolai, S., M. Picozzi, S. M. Richwalski, and C. Milkereit (2005). Jointinversion of phase velocity dispersion and H/V ratio curves from seis-mic noise recordings using a genetic algorithm, considering highermodes, Geophys. Res. Lett. 32, L01303, doi 10.1029/2004GL021115.

Parolai, S., S. M. Richwalski, C. Milkereit, and D. Fah (2006). S-wavevelocity profiles for earthquake engineering purposes for the Colognearea (Germany), Bull. Earth. Eng. 4, 65–94.

Pescatore, T., P. Renda, M. Schiattarella, and M. Tramutoli (1999). Strati-graphic and structural relationships between Meso-Cenozoic Lago-negro basin and coeval carbonate platforms in southern Apennines,Italy, Tectonophysics 315, 269–286.

Picozzi, M., S. Parolai, and S. M. Richwalski (2005). Joint inversion ofH/V ratios and dispersion curves from seismic noise: estimating theS-wave velocity of bedrock, Geophys. Res. Lett. 32, L11308, doi10.1029/2005GL022878.

Satoh, T., H. Kawase, T. Iwata, S. Higashi, T. Sato, and H.-C. Huang(2004). S-wave velocity structures of sediments estimated from arraymicrotremor records and site responses in the near-fault region of the1999 Chi-Chi, Taiwan earthquake, J. Seism. 4, 545–558.

Satoh, T., H. Kawase, and S. Matsushima (2001). Estimation of S-wavevelocity structures in and around the Sendai Basin, Japan, using arrayrecords of microtremors, Bull. Seism. Soc. Am. 91, 206–218.

Scherbaum, F., K.-G. Hinzen, and M. Ohrnberger (2003). Determinationof shallow shear wave velocity profiles in Cologne, Germany areausing ambient vibrations, Geophys. J. Int. 152, 597–612.

Wang, R. (1999). A simple orthonormalization method for stable and ef-ficient computation of Green’s functions, Bull. Seism. Soc. Am. 83,733–741.

Wathelet, M. (2005). Array recordings of ambient vibrations: surface-waveinversion, Ph.D. Thesis, Universite de Liege, Faculte des SciencesAppliquees.

Wessel, P., and W.H.F. Smith (1991). Free software helps map and displaydata, EOS Trans. AGU 72, no. 41, 441, 445–446.

Yamanaka, H., and H. Ishida (1996). Application of genetic algorithms toan inversion of surface-wave dispersion data, Bull. Seism. Soc. Am.86, 436–444.

GeoForschungsZentrum PotsdamTelegrafenberg14473 Potsdam, Germany

(S.P., S.M.R., A.S.)

Dipartimento di Strutture Geotecnica e Geologia applicata all’IngegneriaUniversita’ della Basilicata85100 Campus Macchia Romana, Potenza, Italy

(M.M., M.R.G.)

Istituto di Metodologie per l’Analisi Ambientale — CNR85050 Tito Scalo, Potenza, Italy

(M.R.G.)

Center for Disaster Management and Risk Reduction Technology76128 Karlsruhe, Germany

(S.M.R.)

Manuscript received 24 October 2006.

Comparison of Empirical and Numerical Site Responses at the Tito ...

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