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

Transcription

1 Bulletin of the Seismological Society of America, Vol. 97, No. 5, pp , October 2007, doi: / 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 preparing ground-motion scenarios within the framework of the Italian Dipartimento Protezione Civile Instituto Nazionale di Geofisica e Vulcanologia (DPC-INGV) projects. An area in the neighboring village of Tito was selected to evaluate different techniques 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 sensors and digitizers with a high dynamic range) were installed in May 2005 to record seismic noise. Differing acquisition geometries allowed the checking of any dependency in the derived dispersion curves based on the adopted analysis method (extended spatial autocorrelation [ESAC] and frequency wave-number [F-K]). In general, the ESAC method appears to provide more reliable results in the low-frequency range. Furthermore, the soil-velocity profiles obtained from the microarray data were compared 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 numerically from the S-wave velocity profiles obtained from the microarray data. Although this comparison did not resolve a preference among the derived models, it showed the importance of downgoing waves in modifying the site response at the Tito site. Introduction In the past decades, seismologists and earthquake engineers have focused on estimating the amplification of earthquake ground motion due to local geology. In particular, the introduction of nonreference site techniques like the horizontal-to-vertical (H/V) spectral ratio method, which can be both applied to noise (Nakamura, 1989; Field and Jacob, 1993; Lermo and Chavez-Garcia, 1994) and earthquake recordings (Lermo and Chavez-Garcia, 1993), has stimulated an ever-increasing number of studies. Moreover, improvements in the quality of instrumentation and in computing power have enabled seismologists to redirect their attention toward 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 method originally proposed by Aki (1957). The objective of such studies is the (local) shear-wave velocity profile. However, only a few studies have included attempts to compare numerical site responses based on local velocity profiles with empirical ones (e.g., Satoh et al., 2001, 2004; Ohrnberger et al., 2004; Parolai et al., 2006), due to the lack of information for several parameters. Within the framework of the Dipartimento Protezione Civile-Istituto Nazionale di Geofisica e Vulcanologia projects ( which aim to calculate seismic-shaking scenarios in areas of strategic and/or priority interest in Italy, the town of Potenza (Southern Italy) was chosen as one of the test sites. Specifically, an area in the neighboring village of Tito was selected for evaluating different techniques to estimate site effects. The site was also selected because of a current project dealing with the long-term (years) monitoring of possible temporal variations in site response (Mucciarelli et al., 2003). Therefore, a 40-m-deep borehole was drilled and down-hole measurements to obtain the S-wave velocity were carried out. Then, a Kinemetrics Shallow Borehole EpiSensor connected to a 114 db (K2) digital recorder was placed in the borehole at 35 m. In addition, an STS2 triaxial seismometer connected to a 135-dB (Q330) digitizer was installed at the surface for recording teleseismic, regional, and local events. In June 2005, this equipment was replaced with an Episensor triaxial force-balance accelerometer at the surface, linked to a six-channel K2 digital recorder. Furthermore, three microarrays utilizing short-period sensors and digitizers with high dynamic range were installed in May 2005 to 1413

2 1414 S. Parolai, M. Mucciarelli, M. R. Gallipoli, S. M. Richwalski, and A. Strollo record seismic noise. Different acquisition geometries were used to check any dependency in the derived dispersion curves on the adopted analysis method (extended spatial autocorrelation [ESAC] and frequency wave-number [F-K]). The results of the analyses carried out on this high-quality data set are presented in the following. In particular, the comparison of the soil-velocity profiles obtained from the microarray data with the S-wave velocity profiles derived from down-hole measurements will be illustrated. Finally, emphasis will be given to the comparison between the empirical site responses and those calculated numerically from the S-wave velocity profiles obtained from the microarray data, aiming at evaluating the possibility of obtaining reliable site responses from array noise measurements. Geology and Geotechnical Measurements The Tito test site is located in the Saint Loja Plain in southern 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 a shallow layer of clay is interbedded with detritus and lenses of sand, and overlies a Flysch formation that can be considered the engineering bedrock. A borehold of 40-m depth was drilled down to the Flysch formation and a seismometer was installed at 35-m depth to record local, regional, and teleseismic events. Nearby, a shallower borehole (20-m depth) was also drilled and a Casagrande piezometer installed inside it. The drilling survey showed quite homogeneous geology down to 37 m, mainly characterized by clays with interbedded lenses of silt, sand, and detritus. The amount of detritus increases with depth down to 37 m, with the grain size of the detritus varying between a few millimeters to some centimeters. Below 37 m, only coarse-slope detritus was found. The water level was encountered just few meters below the surface. During the survey, four undisturbed samples of 0.5-m length were taken and subjected to geotechnical testing (oedometer and triaxial). The first was collected at 7-m depth, where a layer of very plastic clays with silt inclusions was encountered. The second sample was taken from 9.5 m and consisted of plastic clay. The third was collected at 20.5 m and consisted of gray clays. The last sample, taken at 27.5 m, consisted of overconsolidated clay. Table 1 shows some of the main geomechanical characteristics of the investigated soils. Finally, Gallipoli (2004) derived a two-layered S-wave velocity model using the results of the triaxial tests under the assumption that for small strains, the stress-strain curve can be assumed to be a straight line. Above 15 m the velocity is in the range 100 to 120 m/sec. Between 15 and 35 m it increases to values between 180 and 225 m/sec. Down-Hole Measurements To obtain in situ shear-wave velocities, S waves generated by a surface source were recorded at 1-m intervals down to a depth of 30 m. The measurements were not performed at greater depths due to signal-to-noise ratios that were too low. One single three-component down-hole geophone with a natural frequency of 10 Hz was used. It was clamped to the PVC casing of the borehole by a hydraulics system that provided good coupling. S waves were generated on the surface by a sledge hammer (7 kg) striking horizontally a steel plate. For each depth the direction of the hammer blow was also reversed to obtain two opposite polarities to facilitate the picking of first arrivals. The use of a reference geophone allowed the checking of the repeatability of the blows. 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 company that also provided an S-wave velocity profile. The data set collected during this experiment was rean- Figure 1. Location of the Tito test site. The epicentral locations of the earthquakes analyzed in this study are indicated by filled circles.

3 Comparison of Empirical and Numerical Site Responses at the Tito Test Site, Southern Italy 1415 Table 1 Geotechnical Parameters of Soil Samples from the Tito Test Site Borehole Geotechnical Parameters 1st Sample ( m depth) 2nd Sample ( m depth) 3rd Sample ( m depth) 4th Sample ( m depth) C unit weight (g/cm 3 ) c s unit weight of solid particles (g/cm 3 ) 2.71 c d dry unit weight (g/cm 3 ) w water content 25% 43% 27% 34% W L liquid limit W p plastic limit I p (W L W P ) plasticity index alyzed to check the reliability of the velocity profile provided by the service company and to estimate the S-wave quality factor Q s. First, the fast Fourier transform (FFT) was calculated for each signal window starting from a preliminary picking of the S-wave arrival and ending when 80% of the energy was reached. Second, the frequency band with sufficient shot-related energy content was identified ( Hz) after an inspection of the amplitude spectra. The recordings were filtered successively using an eight-pole Butterworth bandpass filter with low- and high-cutoff frequencies of 10 and 120 Hz, respectively. Figure 2 shows the filtered recordings for the two horizontal components indicated as east west and north south. The orientation of the sensor changed while it was lowered down in the borehole, as seen for example, over the depth range 9 to 14 m, where sudden changes in amplitude occur. For the S-wave arrival-time calculation, the two horizontal components at each depth were rotated into the azimuth that maximizes the horizontal ground motion (parallel to the beam strike) (Fig. 2). The horizontal components at two different depths were then cross-correlated and the time lag was assumed to represent the travel-time difference between the different depths. Intersensor distances of 3 and 5 m were considered, and the operation repeated for reversed blows. The analysis was done by using nonoverlapping moving windows, resulting in a total of 10 interval velocity curves. For the smaller intersensor distances, the S-wave velocity estimation is very sensitive to small timing errors. From Figure 3 it can be seen that the S-wave velocity structure provided by the service company is in good agreement with our calculations. The greater variability of the S- wave velocity structure in the uppermost 5 m might indicate a larger influence of small triggering errors and source effects, suggesting that interpreting linear segments of downhole travel-time curves should be preferred to the estimation of interval velocities. To estimate the effective quality factor Q s, the square root of the sum of the squares of the amplitude spectra on the two horizontal components was used. Spectra were calculated as described. In addition, the selected windows were tapered with a 5% cosine function at both ends and the amplitude spectra smoothed using a Konno and Ohmachi (1998) window fixing the parameter b to 40. The spectral amplitudes were corrected considering a factor G(z), where z indicates depth. This factor accounts for the geometrical spreading and the change in amplitude due to variations in seismic impedance along the ray path (Gibbs et al., 1994). For this correction, the velocity profile provided by the service company was used. The quality factor was determined by looking at the depth dependence of spectral values at individual frequencies (Gibbs et al., 1994). This analysis assumes that there is no depth dependence either on the source or the quality factor. The analysis was carried out for 11 frequencies in the range 30 to 90 Hz due to the signal-to-noise (S/N) ratio and the limitation imposed by the FFT because of the usage of short-signal windows. Similarly to Gibbs et al. (1994), the corrected spectral amplitudes of the analyzed frequencies were plotted against the travel times between the source and receivers. The slope of the straight line fitted to the data points provides an estimate of Q s at frequency f. Figure 4a shows the results obtained for four frequencies. The scattering of the data might be due to Q s variations with depth, source effects, and measurement errors. Nevertheless, a clear trend showing the quality factor increasing with frequency is observed, with a minimum of 7 at 30 Hz (Fig. 4b). Because it was observed that, especially for higher frequencies, the S/N ratio was decreasing, the straight-line fitting was repeated for all the frequencies after removing the data corresponding to larger travel times (down to 0.15 sec corresponding to 25-m depth). The results (Fig. 4b) were not affected by the selected travel-time interval for frequencies below 70 Hz, whereas the results for higher frequencies showed that the strong increase in the Q s factor might be due to noise affecting the data. The Q s factor between 50 and 80 Hz seems to be nearly This effective quality factor at low frequencies is consistent with the damping estimated by Mucciarelli and Gallipoli (2006) using a nonparametric damping analysis of earthquake recordings. Furthermore, estimates of the quality factor carried out using the spectral ratio method (Gibbs et al., 1994) between the 25- and 5-m down-hole signals and fitting the Hz and the Hz frequency band (not shown here) resulted in Q s values between 10 and 20, consistent with those obtained by spectral amplitude decay analysis.

4 1416 S. Parolai, M. Mucciarelli, M. R. Gallipoli, S. M. Richwalski, and A. Strollo Figure 2. Shear-wave data from the down-hole experiment, corrected by using a depth-dependent factor. Shear waves from positive and negative pulses of the shear source are superimposed for the identification of shear-wave arrivals. All data are shown using a common scale. Microarray Measurements The installation of microarrays in urban areas is obviously guided strongly by practical restrictions. Depending on the conditions, it is often difficult to configure the array geometry optimally for certain techniques. The ESAC method (Ohori et al., 2002; Okada, 2003; Parolai et al., 2006) performs in this aspect better than methods based on F-K analysis (Okada, 2003), because for the same maximum interstation distance it provides reliable results even for lower frequencies; that is, larger depths can be investigated by the same array size. Moreover, considering that Parolai et al. (2005), Picozzi et al. (2005), and Arai and Tokimatsu (2005) showed that a joint inversion of dispersion curves and H/V spectral ratio of noise might increase the depth of investigation, the potential of microarrays can now be even better exploited. Recently, Chavez-Garcia et al. (2006) confirmed that the spatial correlation method, for the case of isotropic distribution of noise, does not need an azimuthal averaging to estimate the phase velocity, thus overcoming one of the major drawbacks from a practical point of view. In fact, a regular geometry with sufficient azimuthal coverage might be difficult to obtain in urban areas and may require a large number of stations. However, F-K-based methods allow the identification of not only the direction of the noise sources, but also allow differentiating between different modes that exist in the wave field. To evaluate the advantages/disadvantages of both methods in a typical urban environment, three different arrays were installed around the borehole in Tito. The array geometries varied from a simple T-shaped to more complicated ones (Fig. 5a c). All the geometries were planned to provide a sufficient azimuth and interstation distance coverage, allowing the retrieval of information about the Rayleigh wavephase velocity in the frequency band between 2 and 10 Hz. This range was expected to be sufficient for characterizing the sedimentary cover. The actual station positions were also constrained by the distribution of buildings in the area. The stations operated simultaneously for more than 1 hour for each array, recording noise at 500 samples/sec, which is adequate for the short interstation distance considered. Every station was equipped with a 24-bit digitizer con-

5 Comparison of Empirical and Numerical Site Responses at the Tito Test Site, Southern Italy 1417 Wathelet (2005) to define the threshold for the aliasing and resolution limits of the array response. A rough estimate of the minimum wavenumber k min (that define the resolution limit) of about 0.03 rad/m was deduced from the width of the central peak, measured at its midheight. The same estimate was obtained for the other two arrays, whereas k max is 0.23 and for arrays 2 and 3, respectively. Please note that in those cases the peaks also do not reach the midheight of the central peak. ESAC Method Following Ohori et al. (2002), Okada (2003), and Parolai et al. (2006), the space correlation function (x) was calculated in the frequency domain for every pair of stations by: M 1 Re( ms jn(x)) M m 1 (x), M M 1 (1) ms jj(x) ms nn(x) M m 1 m 1 Figure 3. S-wave velocity profiles (black lines) determined in this work. The S-wave velocity structure provided by the service company is shown by the gray line. nected to a Mark L-4C-3D 1 Hz sensor and Global Positioning System (GPS) timing. For the analysis, the data recorded by each station of each array were divided in 60- sec windows. A total of 44 nonoverlapping windows were considered. Only the vertical component was analyzed. Recordings were corrected for the instrumental response considering 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 of the seismic phases observed within the array, but is also a function of the wavenumber k of the observed signal and of the array geometry. It provides insights about the limits, in terms of k, of the valid array output. Note the different response of the arrays in terms of wavenumber. The F-K response of array 1 shows a major aliasing peak at wavenumber 0.18 rad/m (k max ). This peak does not reach the midheight of the central peak, a value that was suggested by where m S jn is the cross-spectrum for the mth segment of data between the jth and the nth station, and M is the total number of used segments. The power spectra of the mth segments at station j and station n are m S jj and m S nn, respectively. The space-correlation function obtained for every pair of stations was smoothed using a Konno and Ohmachi window (Konno and Ohmachi, 1998) with the coefficient b, which determines the bandwidth, fixed to 40. The space-correlation values for every frequency were then plotted as a function of distance. An iterative grid-search procedure was then performed using the equation (Aki, 1957) x c(x ) 0 (r, x ) J r, (2) to find the value of the phase velocity c(x 0 ), that gives the best fit to the data, with c(x 0 ) varied between 50 and 3000 m/ sec in steps of 1 m/sec. In equation (2), (r,x 0 ) is the spacecorrelation function for the angular frequency x 0, r is the interstation distance and J 0 is the zero-order Bessel function. The best fit was achieved by minimizing the root-meansquare (rms) of the differences between the values calculated using equations (1) and (2). Data points that differed by more than two standard deviations from the value obtained with the minimum-misfit velocity were removed before the next iteration of the grid search. A maximum of three grid-search iterations was allowed. Further details about the procedure can be found in Parolai et al. (2006). F-K Methods Two different methods for F-K analysis have been considered: the beam-forming method (BFM) (Lacoss et al.,

6 1418 S. Parolai, M. Mucciarelli, M. R. Gallipoli, S. M. Richwalski, and A. Strollo Figure 4. (a) Spectral amplitude values versus travel time for selected frequencies (black dots). The best-fitting lines in a least-squares sense considering the whole travel-time interval are shown in black. The gray lines are the leastsquares fit if the interval is limited to 0.17 sec, while the dashed line is obtained if the fit is performed considering a maximum travel time of 0.15 sec. Note that the vertical scale for the plot showing f 80 Hz differs from the others. (b) Q s -factor estimates versus frequency. Open circles indicate estimates obtained by fitting the whole available data set. Triangles show the values obtained by limiting the fit to spectral amplitudes corresponding to travel times smaller than 0.17 sec. Filled circles show the values obtained by limiting the fit to spectral amplitudes corresponding to travel times smaller than 0.15 sec. Vertical lines indicate the uncertainties estimated from the standard errors of the fit. 1969) and the maximum likelihood method (MLM) (Capon, 1969). The estimate of the F-K spectra P b (f, k) bythebfm is given by: n P (f, k) exp{ik(x X }, (3) b lm l m l,m 1 where f is the frequency, k is the two-dimensional horizontal wavenumber vector, n is the number of sensors, lm is the estimate of the cross-power spectra between the lth and the mth data, and X i and X m are the coordinates of the lth and the mth sensors, respectively. The MLM gives the estimate of the F-K spectra P m (f, k) as: n 1 1 P m(f, k) lm exp{ik(xl X m}. (4) l,m 1 Capon (1969) showed that the resolving power of the MLM is higher than that of the BFM, but the MLM is more sensitive to measurements errors. From the peak in the F-K spectrum occurring at coordinates k xo and k yo for a certain frequency f 0, the phase velocity c 0 can be calculated by: 2pf 0 c0. (5) 2 2 k k xo An extensive description of these methods can be found in Horike (1985) and Okada (2003). H/V Spectral Ratio Method H/V spectral ratios (Nakamura, 1989) from the 44 windows of noise recordings at each station of each array were yo

7 Comparison of Empirical and Numerical Site Responses at the Tito Test Site, Southern Italy 1419 Figure 5. (top) Microarray configurations. (a) Array 1; (b) array 2; (c) array 3. The gray-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 and smoothed by using a Konno and Ohmachi (1998) window with the coefficient b fixed to 40. For every station a mean H/V curve was calculated using a logarithmic average of the individual H/V curves. Figure 6 shows the mean H/V curve at the different stations for each array, together with an arrayaveraged H/V curve (thick gray curve). The frequency of the first peak in the H/V spectral ratio is consistent between the different arrays. However, the amplitude of the peak for array 3 is clearly larger. Array 3 was operational during a Monday morning, but arrays 1 and 2 were operational during Sunday morning; hence, the variation in amplitude is clearly related to the amount of anthropogenic noise, because the Tito array is located in an industrial area. However, the presence of high-noise transients does not adversely affect the HVRS if a sufficient number of signal windows is used (as shown by Parolai and Galiana- Merino [2006]). On the contrary, the amplification level approaches the one derived from earthquakes, as already observed for this site by Mucciarelli et al. (2003). Results: Array 1 Figure 7a (left) shows the space-correlation coefficients derived from equation (1) compared with those obtained for the 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 the main features displayed in the frequency-distance plain. In Figure 7b, examples of F-K MLM (upper panel) and BFM (lower panel) analyses are shown for three different frequencies, selected from all those analyzed. Both methods show low resolution for the lowest frequency depicted (2.5 Hz). However, they allow a clear identification of the maxima at 3.9 and at 6.5 Hz. Although both methods suggest a nearly isotropic distribution of the noise sources, MLM seems to have a higher resolving power than BFM, consistent with the conclusion of Horike (1985). The apparent dispersion curves obtained by the three different analysis methods are shown in Figure 7c. They look normally dispersive, that is, they seem to be dominated mainly by the fundamental mode. In general, there is a good agreement between the phase velocities between 3.5 and 10 Hz. However, at lower frequencies, the F-K methods provide a larger estimate of the phase velocity than ESAC. This result is consistent with Okada (2003), who concluded that the F-K method is able to use wavelengths up to two to three times the largest interstation distance, whereas with the ESAC method, one may investigate the subsurface by using wavelengths up to 10 to 20 times the largest interstation distance, being therefore more reliable in the low-frequency range. For frequencies from about 11 Hz onward the phase velocity increases nearly linearly. This effect is due to spatial

8 1420 S. Parolai, M. Mucciarelli, M. R. Gallipoli, S. M. Richwalski, and A. Strollo the final results was tested, the result being that there was little influence, and hence the relationship of Kitsunezaki et al. (1990) was used: V p (m/sec) V s [m/sec]. In the upper 30 m this provided values in agreement with those computed by the service company from down-hole measurements. Finally, once it was verified that the cost function, that is, equation (2) in Parolai et al. (2005), did not allow a solution that similarly balanced the dispersion and the H/V curve contribution to be obtained, a cost function similar to Herrmann et al. (1999) was adopted: j 1 N 2 (1 p) c o(f) c(f) cost [(1 p)n pk] N c (f) o (6) K 2 p hv o(f) hv(f) K j 1 hv o (f), 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 frequency band. At very low frequencies, that is, below 2.37 Hz for this test site, the phase velocity curve obtained using ESAC starts to diminish. This is probably due to the filtering effect of the sediments on the vertical component (Scherbaum et al., 2003), because this frequency is close to the resonance frequency of the site (Fig. 6). On the basis of these results, the joint inversion of the dispersion curve and the H/V spectral ratio curve was performed considering the phase-velocity values obtained by the ESAC method (between 2.37 and 10.6 Hz), following Parolai et al. (2005) and using the modified Genetic Algorithm (GA) proposed by Yamanaka and Ishida (1996). To evaluate the most suitable parameterization of the model (finally made of eight layers), several tests (not shown here) were performed. The first test demonstrated that the deeper crustal velocity structure had a minor influence on the inversion. Therefore, only a shallow crustal structure was considered. Then, the influence of the P-wave velocity on where the subscript o indicates the observed phase velocity (c(f)) and H/V (hv(f)) data, and N and K are the number of data points in the dispersion and H/V ratio curves, respectively. The relative influence of both data sets is controlled by the parameter p that was finally fixed to We performed several tests that showed that this value yields a good fit of both the dispersion curve and the H/V spectral ratio. The probability of crossover and mutation, that is, the value 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 of Yamanaka and Ishida (1996) was followed for the elite selection and the dynamic mutation. The inversion was then performed following Parolai et al. (2005). The minimum-misfit model, together with the models lying inside the minimum cost 10%, are shown in Figure 8 (left). All models tested by the inversion procedure are also depicted, showing that a large solution space was investigated. The dispersion curve constrains the model only down to m. The deeper part is constrained by the H/V data alone. All models lying inside the minimum cost 10% show little variability down to 200-m depth. Below 200 m, the large variability indicates that the trade-off between velocity and thickness of the layers is not fully solved by the H/V inversion. This hints that the S-wave velocity structure of the best-fit model below 200-m depth is also only weakly constrained. Figure 8 (right, top) shows that the average cost function of each generation may show large variations. This indicates that the inversion generates very different models while trying to escape from a possible local minimum in the solution. However, for the seed number leading to the minimum misfit model, the minimum cost function of each generation decreases from at the first generation to by the 89th generation, when the best model is found, a reduction in the misfit of 70%. Figure 8 (right middle and below) shows the fit of the calculated dispersion and H/V curves to the observed data, respectively.

9 Comparison of Empirical and Numerical Site Responses at the Tito Test Site, Southern Italy 1421 Figure 7. (a) Spatial correlation coefficient from observed data (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. White dots indicate the position of the maximum used to estimate the phase velocity. The white circle joins points with the same k value. (c) Apparent phase-velocity curve obtained by the ESAC method (black line). Circles show the frequencies used for the joint inversion. The gray area indicates velocity values for a certain frequency determining a misfit within 10% of the minimum in the grid-search procedure. The phase-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 same parameters as for array 1 and the results are presented in the same way. Figure 9a shows that the empirical and fitted space-correlation coefficients exhibit good agreement. Both F-K results are similar to those for array 1 (Fig. 9b). A comparison of the dispersion curves from the three methods (Fig. 9c) leads to the same conclusions as for array 1 regarding the ability of ESAC to produce a reliable estimate of the phase velocity at low frequencies. Here, the lowfrequency filtering effect of the site sets the lowest usable

10 1422 S. Parolai, M. Mucciarelli, M. R. Gallipoli, S. M. Richwalski, and A. Strollo Figure 8. (left) Joint inversion for array 1: all tested models (dark gray), the minimum 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 jointinversion procedure. (right top) Minimum misfit (black dots) and average misfit (gray line) versus number of generations for the seed number leading to the best model. (right middle) Observed (gray circles) and calculated (white circles) H/V spectral ratio. (right bottom) Observed (gray circles) and calculated (white circles) apparent phase velocities. frequency to 2.17 Hz and aliasing becomes an issue beyond 14 Hz. The inversion was carried out by using apparent phasevelocity values between 2.17 and 9.7 Hz. Again, the dispersion curve allows the model to be constrained only to depths of 60 to 90 m, below which the H/V alone guides the inversion. For this array, small variations exist down to 250 m (Fig. 10). Below, a large variability indicates that the tradeoff between velocity and thickness of the layers is not fully solved by the H/V inversion. The minimum cost function of each generation decreases from for the first generation to by the 83rd generation when the best model is found. Results: Array 3 Again, there is a good agreement between empirical and fitted space-correlation coefficients (Fig. 11a). However, the geometry obviously hampers the application of F-K methods. Both methods (MLM and BFM) show low resolution for the lowest depicted frequency (2.5 Hz) as well as for many azimuthal directions. Only one maximum can be clearly identified at 3.9 Hz, whereas at 6.5 Hz the results are ambiguous. The agreement for the three methods is therefore only good between 3 and 6 Hz (Fig. 11b). The lowfrequency filtering effect is observed at 1.9 Hz, whereas aliasing in the ESAC analysis plays a role from 14 Hz on. The apparent dispersion curve is very similar to that obtained by the previous arrays, apart from slightly higher velocities at low frequencies. The joint inversion was performed for phase velocities in the range 1.9 to 9.7 Hz, which constrain the model down to depths of 85 to 125 m, with little variability down to 650 m (Fig. 12). The large depth variability of the last interface clearly indicates that the trade-off between velocity and thickness of the deepest layer is not fully solved by the

11 Comparison of Empirical and Numerical Site Responses at the Tito Test Site, Southern Italy 1423 Figure 9. The same as Figure 7 for array 2. H/V inversion. The minimum cost function of each generation decreases from for the first generation to by the last generation (100), when the best model is found. Finally, Figure 13 shows the comparison of the three minimum cost models for the uppermost 150 m (well constrained in all inversions). The general trend of velocity is similar for all models and is in agreement with the S-wave velocity profile calculated by down-hole measurements in the uppermost 30 m (compare with Fig. 3). The best agreement is shown by models derived from arrays 2 and 3, where the S-wave velocity decreases between 6 13 m and 9 18 m, respectively. Both models also indicate

12 1424 S. Parolai, M. Mucciarelli, M. R. Gallipoli, S. M. Richwalski, and A. Strollo Figure 10. The same as Figure 8 for array 2. an increase in velocity at 35 and 39 m, respectively, consistent with the geotechnical investigations. Moreover, the S- wave velocities are also consistent with the estimates of Gallipoli (2004). Empirical Site Response Among the data recorded by the two stations (in the borehole and at the surface) six earthquakes with good S/N ratios were selected (see Fig. 1 and Table 2). Data were recorded at 100 sample/sec. Figure 14 shows the threecomponent recordings of a local event (BA923 in Table 2), together with the pre-event and S-wave signal windows indicated. A clear amplification of the seismic signal from the bottom to the surface is evident, as well as larger amplitudes on the horizontal components with respect to the vertical ones at both the borehole and surface stations. To estimate the empirical site response, signal windows starting before the S-wave arrival and ending when 80% of the energy was reached were selected. The signal windows were tapered with a 5% cosine function at both ends and the associated FFT calculated. The spectra were corrected for the instrumental response and smoothed by using a Konno and Ohmachi (1998) window, fixing the parameter b to 40. Spectra of pre-event signals were also calculated and used to estimate the frequency-dependent S/N ratio of the recordings used. Figure 15 shows the average S/N ratios for each component calculated 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 borehole stations and the standard spectral ratios (SSRs) between the horizontal (and vertical) components at the surface and in the borehole (SSR H and SSR Z, respectively) were computed. The logarithmic average of the H/V ratios, as well as of the SSR are depicted in Figure 16. Furthermore, in Figure 16, the SSR for the horizontal components calculated by Gallipoli (2004) with respect to a reference station (SSR with reference site) 5 km way from the Tito test site and installed over limestone is also shown. The H/V spectral ratio at the surface shows a main peak at about 1.2 Hz (consistent with that obtained by noise analysis) and a secondary peak at about 3 Hz. The H/V spectral ratio of the borehole station shows a main peak of amplification around 1.1 Hz with smaller secondary peaks at about 3 4 Hz, 6 7 Hz, and 12.5 Hz. The SSR H results differ from the H/V spectral ratios,

13 Comparison of Empirical and Numerical Site Responses at the Tito Test Site, Southern Italy 1425 Figure 11. The same as Figure 7 for array 3. with a first broad peak shown at 1.7 Hz, while other narrow peaks are depicted at about 4.6 and 8.6 Hz. The SSR Z results show a main peak at about 12.5 Hz. Finally, the SSR ratio with respect to the reference site shows the largest amplification at about 1.2 Hz and a general shape that strongly agrees with the H/V ratio at the surface. The discrepancies between SSR H and the other estimates of the site response (H/V spectral ratio of noise and earthquakes and SSR with reference site) suggest that the effect of downgoing waves on the borehole recordings is not negligible. Careful analysis of the amplitude spectra of the recordings of event BA924 provided useful insights into

14 1426 S. Parolai, M. Mucciarelli, M. R. Gallipoli, S. M. Richwalski, and A. Strollo Figure 12. The same as Figure 8 for array 3. ID No. Table 2 Hypocentral Parameters of the Analyzed Earthquakes Date Origin Time (UTC) Latitude ( ) Longitude ( ) Depth (km) explaining the observed behavior. Figure 17 shows the horizontal-component spectra amplitudes of the surface recordings to be clearly larger than those of the borehole recordings at frequencies higher than 0.8 Hz, likely due to the impedance becoming smaller toward the surface. However, the spectra of the horizontal components at the bottom station clearly show spectral troughs at about 2 Hz, 5 Hz, and 8 Hz, mainly in correspondence with the peaks in the SSR H. A similar behavior is also seen in the vertical-component M L Epicentral Distance (km) BA923 7/1/06 4:27: BA924 8/1/06 11:34: M w BA967 5/2/06 17:02: BA /4/06 2:44: BA /4/06 9:59: BA200 29/05/06 2:20: spectra, showing amplification at the surface for frequencies higher than 1.2 Hz and a clear spectral trough at nearly 12 Hz in the bottom recording. This trough is responsible for the peak in the SSR Z. These troughs are considered to result from destructive interference of upgoing and downgoing waves at the borehole station. Finally, although with slightly different magnitudes, both the surface and borehole recordings show larger amplitudes on the horizontal component spectra with respect to the vertical one in the frequency band Hz (independent of the event magnitude and hypocentral distance), thus suggesting a deeper origin of the amplification observed at the site. Synthetic Seismogram Modeling To evaluate the reliability of the S-wave velocity structures obtained by the three different microarrays, synthetic seismograms were calculated by using a semianalytical method that consists of an improved Thompson Haskell propagator matrix method that overcomes numerical instabilities by an orthonormalization technique (Wang, 1999).

15 Comparison of Empirical and Numerical Site Responses at the Tito Test Site, Southern Italy 1427 Figure 13. (left) S-wave velocity profiles obtained from the three different array data. (right) P-wave velocity profiles. The triangles indicate the depth of the borehole station. Figure 14. Vertical (Z), north south (NS), and east west (EW) component recordings of the event BA923 (Table 2). The signal (S) and the pre-event noise (N) windows used for the analysis are shown. (top) Surface station; (bottom) borehole station.

16 1428 S. Parolai, M. Mucciarelli, M. R. Gallipoli, S. M. Richwalski, and A. Strollo 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 at the surface station. The gray area indicates the 95% confidence interval. (bottom) Same for borehole station. First, synthetic seismograms were generated considering the upper-crustal structures of the three different models and a homogeneous half-space below. A source was located at a depth of 5 km and seismograms were computed for receivers located at the surface and at a depth of 35 m (corresponding to the depth of the borehole sensor) at distances ranging between 0.5 and 14.5 km. A total of 15 equally spaced receivers were used, the complete records analyzed, and the results averaged. Different quality factors for the uppermost layers, consistent with those obtained by downhole measurements, were tested (Q s 10, Q s 20, Q s 30). Because the results showed minor differences in the shape of the site responses with respect to the variability due to the adopted models, in the following only the spectral ratios obtained for Q s 10, which provided results closest to the empirical ones, will be discussed. Second, synthetic seismograms were also generated considering a pure half-space model and using the parameters (P- and S-wave velocity and density) of the deepest layer of the model derived by using array 2. The same source and surface receiver positions adopted in the first step were used. These synthetic seismograms were used to simulate the recording at a reference site. Finally, FFT spectra of all the recordings were calculated, and H/V, SSR H, SSR Z, and SSR with respect to the reference site spectral ratios computed. Figure 16 shows that the models are able to capture the main trend (especially above 0.5 Hz) of all the different siteresponse estimate techniques. Differences in the amplitude of the peaks (see, for example, the H/V at the borehole station and the SSR H results) might come from the simplified, with respect to reality, synthetic wave field that does not take into account wave diffraction and scattering. Therefore, there is less redistribution of energy between the components of ground motion, and spectral troughs are more pronounced. The smaller amplitude of the SSR H between 5 and 20 Hz might also indicate a slight overprediction of damping in the used models. No single model was found to fully explain all observations. For example, some models that reproduce the SSR results very well may in turn be the worst for the H/V. Thus, deciding which of these quite similar models is the best one may be more a matter of user preference than an objective decision. The large peak at nearly 1 Hz in the SSR Z for the model derived by array 1 is an artifact coming from a small trough in the synthetic spectrum. The variability of the synthetic SSR H with respect to the reference site reflects the uncertainty in the reference site S-wave velocity at the surface. In this case, the model derived from array 1 seems to be the one providing the impedance contrast closest to the actual one. Conclusions The availability of high-quality geophysical data from the Tito test site allowed the estimation of an S-wave velocity structure down to 30-m depth from down-hole measurements. Furthermore, Q s was estimated for the uppermost 30 m of the sedimentary cover. The Q s was determined for frequencies higher than those generally of interest in engineering seismology, and represented an estimation of the

17 Comparison of Empirical and Numerical Site Responses at the Tito Test Site, Southern Italy 1429 Figure 16. (top left) H/V ratios at the surface station. (top right) SSR H spectral ratios (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 earthquake recordings (black line), and the gray area indicates the 95% confidence interval. Ratios from synthetic seismograms are shown considering the model obtained by array 1 (dashed line), array 2 (dashed-dotted line), and array 3 (dotted-dashed line). (bottom left) 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 with respect to a reference site from earthquake recordings (black line). SSR H spectral ratio with respect to a reference site from synthetic seismograms considering the model obtained by array 1 (dashed line), array 2 (dashed-dotted line), and array 3 (dotteddashed line). effective Q s (implying that the intrinsic Q might be larger). Nevertheless, a range of Q s values were used in numerical simulations. Results showed that adopting a low Q s value, that agrees with the damping calculated by earlier studies, gave better numerical site responses, suggesting that this Q s estimation might be considered for future numerical simulations of ground motion. Different methods of analyzing microarray noise data were evaluated while considering urban conditions (with their restrictions and limitations). Consistent with previous results (Okada, 2003) the ESAC method provides phase velocities lower than those from the F-K analysis at low frequencies. Okada (2003) showed that by increasing the array size, the F-K velocities at low frequencies become similar to those estimated by ESAC, indicating the latter is more suitable for providing reliable dispersion curves over a wider frequency range, especially toward lower frequencies (greater depths). Unfortunately, independent S-wave velocity estimates at this test site for the depth range reached by these low frequencies are not available, and the Okada (2003) results cannot be verified. Three S-wave velocity profiles for the three different arrays were inferred. The consistency of the profiles, and even more important, the consistency of the numerical site responses based on such models,

18 1430 S. Parolai, M. Mucciarelli, M. R. Gallipoli, S. M. Richwalski, and A. Strollo Figure 17. (left) Horizontal-component spectra of the recordings from the BA924 event (Table 2) at the surface (thick and thin black lines for the north south and the east west components, respectively) and the bottom stations (thick and thin gray lines for the north south and the east west components, respectively). (right) Same as for the left panel but for the vertical component. shows the capability of the ESAC method to provide similar results when the employed array geometries are fairly different. This independence of the ESAC results with respect to the geometry of the array, under the condition that seismic noise is stationary, is certainly a great advantage of the ESAC method. In the case at hand, where there is a gradual increase of impedance with depth, the joint inversion of dispersion and H/V curves seems to provide only marginal improvements in constraining the final model. This result differs from the observation of Picozzi et al. (2005), who investigated a site with a strong impedance contrast between sediment and bedrock. The site response of the shallow crustal structure was modeled, but it did not allow us to resolve a preference among the calculated velocity models. However, the mechanism determining the differences between site responses calculated by using both seismic noise and earthquake weakmotion recordings was identified. In particular, the importance of downgoing waves affecting the borehole recording station at Tito was shown, as well as the existence of an amplification mechanism with a deeper origin than the depth of the borehole. This emphasizes the importance of not limiting ones investigation to only the uppermost tens of meters. Moreover, this result provides a warning about the use of shallow-borehole recordings as input for numerical simulations. The microarray data will also be used for future investigations into the feasibility of applying other noise-analysis techniques, for example, the cross-correlation method (e.g., Lobkis and Weaver, 2001) in urban areas and for studying soft-sediment S-wave velocity structure. The vertical array is still operational with the aim of enlarging the data set of recordings to include larger-magnitude events to perform more detailed site-response analysis, while also taking into account soil nonlinearity. Acknowledgments K. Fleming kindly improved our English. Figures have been drawn using the GMT (Wessel and Smith, 1991) software. Thanks to the field crew E. Günther and D. Di Giacomo. R. Milkereit improved the figures. Thanks to C. Di Maio and the soil dynamic lab of DiSGG for the geotechnical test and to I. Giano for the geological support at the drilling site. This work was partially funded by project INGV-DPC S3. We are grateful to R. 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