Active and Passive Experiments for S-Wave Velocity Measurements in Urban Areas

The study of earthquakes combines science, technology and expertise in infrastructure and engineering in an effort to minimize human and material losses when their occurrence is inevitable. This book is devoted to various aspects of earthquake research and analysis, from theoretical advances to practical applications. Different sections are dedicated to ground motion studies and seismic site characterization, with regard to mitigation of the risk from earthquake and ensuring the safety of the buildings under earthquake loading. The ultimate goal of the book is to encourage discussions and future research to improve hazard assessments, dissemination of earthquake engineering data and, ultimately, the seismic provisions of building codes.


Methodologies
In the FTAN analysis, signal is passed through a set of narrow-band Gaussian filters with central frequencies varying in the frequency band of interest. The combination of all so filtered signals is a complex function S(ω c , t) of two variables, filter central frequency ω c and time, called frequency-time representation of a signal. A FTAN image is produced by displaying the logarithm of the square of the contour map of S(ω c , t) amplitude and, for ω fixed, it represents the signal envelope at the output of the relevant filter. The group arrival time as a function of the central frequency of the Gaussian filter is determined from the peak of the envelope function. Typically period replaces filter central frequency and, being known the source-receiver distance, group velocity replaces time. One example of the FTAN analysis on a signal recorded with active seismic experiment at Napoli (Italy) is given in Figs. 1a-e. An average dispersion curve of Rayleigh group velocities with errors is computed, from FTAN analysis made on a few (4-5 or more) signals, which can be inverted to determine V S profiles versus depth. A non-linear inversion is made with the Hedgehog method (Panza et al., 2007 and references therein) that is an optimized Monte Carlo non-linear search of velocity-depth distributions. In the inversion, the unknown Earth model is replaced by a set of parameters (V P , V S , density and thickness) and the definition of the structure is reduced to the determination of the numerical values of these parameters. In the inversion V S and thickness are variable parameters, while density is fixed and V P is dependent on V S through an assigned V P /V S ratio. In the inversion problem of V S modeling, the parameter function is the dispersion curve of group velocities of Rayleigh fundamental mode. Given the error of the experimental phase and/or group velocity data, it is possible to compute the resolution of the parameters, computing partial derivatives of the dispersion curve with respect to the parameters to be inverted (Panza, 1981). The parameterization for the inversion is defined so that the parameter steps are minima, subject to the condition where  is the standard deviation of measurements, V is phase or group velocity, T i is the i-th period, and P j is the j-th parameter; in this way each parameter step represents a satisfactory measure of the uncertainty affecting each parameter. The theoretical phase and/or group velocities computed during the inversion with normalmode summation are then compared with the corresponding experimental ones and the models are accepted as solutions if their dif f e r e n c e , a t e a c h p e r i o d , i s l e s s t h a n t h e measurement errors and if the r.m.s. (root mean square) of the differences, at all periods considered, is less than a chosen quantity (usually 60-70% of the average of the measurement errors). All the solutions of the Hedgehog inversion differ by no more than ±1 step from each other. A good rule of thumb is that the number of solutions is comparable with the number of the inverted parameters. From the set of solutions, we accept as a representative solution the one with the rms (root mean square) for phase and group velocities closest to the average rms for all the solutions, reducing in this way the projection of possible systematic errors into the structural model (Panza, 1981). Other selection criteria could be followed as described by Boyadzhiev et al. (2008). An example is shown in Fig. 2. Fig. 1. Example of FTAN analysis on a signal of active experiment at Napoli (Scampia, located in Fig. 3) with 120m offset: (a) the raw waveform (black line); (b) Fourier spectrum amplitude of the signal; (c) a raw group velocity curve (green dots) is chosen by the analyst by picking maxima on the FTAN map. This raw group velocity dispersion curve is back Fourier transformed to get the dispersed signal. Phase-matched (anti-dispersion) filtering is performed on the chosen period-band to remove dispersion. (d) The anti-dispersed signal will collapse into a single narrow spike. Such operation has the only effect to alter the initial phase of the resulting signal, so it can be shifted to a convenient instant of time, for example, to the midpoint of the record. The collapsed waveform is then cut (vertical lines) from the surrounding time-series and re-dispersed to give the clean waveform. (e) The FTAN image of the cleaned waveform is computed and, using the same process applied to the raw waveform, the cleaned group velocity curve (blue dots) and fundamental mode waveform (red line in (a)) are obtained. www.intechopen.com

Active experiments
FTAN measurements have been successfully performed, at engineering scale, in italian urban areas with different soil and rock environments (e.g. Nunziata et al., 2004;Nunziata, 2005). A weight drop of 30 kg is used as source and one or more low frequency 4.5-1 Hz vertical geophones are used as receivers for offsets less or greater than 50 m, respectively. Only one receiver is requested, or, alternatively, a seismic refraction spreading, in order to evaluate an average group velocity dispersion curve from 4-5 receivers or 4-5 sources. In the following some examples are reported at the neapolitan area to show the main advantages of FTAN method in complex geological settings of noisy urban areas.

FTAN measurements at Napoli
Several measurements have been performed at the urban area of Napoli for which, taking into account the stratigraphies, six geologically homogeneous zones have been recognized (Nunziata, 2004) (Fig. 3). The geological setting of Napoli is mainly characterized by pyroclastic materials, soil (pozzolana) and rock (tuff), produced by different eruptive centres at Campi Flegrei and Somma-Vesuvio volcanoes. The most widespread lithotype is the Neapolitan Yellow Tuff (NYT, 15 ka) which constitutes the skeleton of the historical urban area. FTAN-Hedgehog V S models represent average values over distances of 50-100m and are more suitable than down-hole (DH) and cross-hole (CH) point measurements for seismic response analysis. Beside this, the good agreement of FTAN-Hedgehog with CH measurements , has allowed to enrich database and to acquire experience enough to select, for each zone, some V S models for the evaluation of the spectral amplification (Nunziata, 2004). In fact, because of the lack of recordings of strong ground motion at Napoli, the only way to estimate site effects is to compute them. Starting from the good fit between the first strong event recorded close to Napoli (about 20km far), that is the 1980 earthquake (Ms=6.9), and seismograms computed with mode summation technique, the detailed geological and seismic information of the neapolitan subsoil were used to compute quite realistic ground motion at Napoli for the 1980 earthquake (Nunziata, 2004) and the 1688 scenario earthquake . The propagation of the waves from the source to the complex laterally varying structure is computed with the mode summation technique, and in the laterally heterogeneous structure, it is computed with the finite difference method (Panza et al., 2001 and references therein). Site amplification effects were estimated in terms of spectral amplification, defined as the response spectrum at a site in the 2-D structural model, normalized to the response spectrum computed for the 1-D average reference model. Average and maximum response spectra and spectral amplifications were computed for all V S models at each zone and proposed for zoning purposes. The need of doing robust V S measurements vs. depth in volcanic settings is strictly dependent on their wide ranges of variations. They are the consequence of the profound differences in the physical properties and textural conditions that can be found even in the same formation. An additional important factor responsible for the observed scatter in the V S values is the different hardening degree, due to the diagenetic process. As an example, V S measurements relative to NYT, both in soil and lithoid facies, are shown in Figure 4.

FTAN measurements at Portici (Somma-Vesuvio)
Somma-Vesuvio is a very densely populated area, and accurate V S measurements are requested for the volcanic and seismic hazards. FTAN measurements performed at the Royal Palace of Portici, famous town for the highest population density in Italy, have given detailed V S models for the shallower 40 m (Fig. 5). These results are important for seismic zoning and give precious volcanological information in terms of thickness of the erupted products. In fact, taking into account the stratigraphy of a close drilling, it resulted that a Vesuvio shallow lava (medieval or 1631 eruption) is characterized by V S of 500 m/s, which is higher than that of Somma lava at 30 m of depth, and that pyroclastic deposits have low V S velocities around 200-300 m/s.

Passive experiments
Passive methods are based on ambient vibrations or microtremors and can be used to infer V S profiles vs. depth. One method is the H/V method of Nakamura (1989), defined as the ratio between the mean of the Fourier spectra of the horizontal components and the spectrum of the vertical component, which has proven to be a convenient technique to estimate the fundamental frequency of soft deposits (e.g. Lermo & Chavez-Garcia, 1994). Another method is the Noise Cross-correlation Function (NCF) based on the cross correlation of simultaneous noise recordings at two sites, which allows to recover surface wave dispersion (Green function) over the site distance.

Single station
If V S models representative of average geological structures are available, the measured main peak of the average H/V spectral ratios is in agreement with the ellipticity computed, from the models, of the fundamental mode Rayleigh wave (Nunziata, 2007). The ellipticity at each frequency is defined as the ratio between the horizontal and vertical displacement eigenfunctions in the P-SV case, at the free surface. The ellipticity of the fundamental mode of Rayleigh waves computed for the V S velocity models obtained by FTAN-Hedgehog methods, integrated at greater depths, down to the seismic bedrock, both by geological information and eventual down-and cross-hole measurements, has been compared with the ambient noise H/V ratio (Nunziata, 2007). The interpretation of noise measurements, carried out with Kinemetrics Quanterra Q330 station and a 3 component Episensor broadband sensor, has been also done through the comparison with the computed SH wave spectral amplifications, both 2D (Nunziata, 2004) and simplified 1D with SHAKE program (Schnabel et al., 1972).
As an example, we show the interpretation of noise measurements performed at two sites, 2km apart, at Poggioreale quarter, zone 6 (Figs. 6 a-e). Site 1 is located at the Centro Direzionale area with many skyscrapers built after 1980 earthquake and very detailed geological and geophysical information. The area was a marsh recently drained both for urban development and for the reduction of water supply. The subsoil is mainly formed by man-made ground, alluvial soils (ashes, sands, peat), loose and slightly cemented pozzolanas, NYT tuff and marine sands (Fig. 6a). Taking into account several DH and CH measurements, a good agreement has resulted with FTAN measurements and it has been possible to attribute VS velocities at depths greater than 30m along a cross section through noise measurement site 1 (Nunziata, 2004 and references therein). Instead, at site 2, strong discrepancy resulted between the V S profiles vs depth obtained with FTAN-Hedgehog methods and the Down-hole measurements (Comune di Napoli, 1994) in a nearby drilling, despite the very good agreement between the representative Hedgehog solutions at the two sites since peat is characterized by similar velocities of host pyroclastics (Fig. 6b). At greater depth, average velocities increasing from 320 m/s, typical of tuff soils, up to 900 m/s, at 76m of depth, have been assigned on the basis of DH and CH measurements in the nearby Centro Direzionale (Fig. 6c). Hence, the seismic cross section through site 1 can be considered representative of site 2 as well. Two-dimensional spectral amplifications (5% damping) computed along the cross section are characterized by main peaks at about 1 Hz for the transverse component. H/V noise measurements show a good agreement with the average and maximum 2D spectral amplifications, while 1D amplifications have the first main peak at frequencies a little bit higher than H/V noise (Fig.  6d). Instead, the 1D amplification computed for the V S profile measured in the drilling close to site 2 has a very high frequency content with the main peak at about 7 Hz. Agreement is also observed between H/V noise and ellipticity computed for the V S models attributed at sites 1 and 2 as shown in Fig. 6c (Fig. 6e), whereas ellipticity computed for DH velocity profile has a peak at very high frequency (about 7 Hz). Where a n are the complex modal amplitudes and u n the real orthogonal mode shapes and  indicates the real part of a complex quantity. The cross correlation of the diffuse field at points x and y is: The basic idea of the method is that a time-average cross correlation of a random, isotropic wavefield computed between a pair of receivers will result in a waveform that diff ers only b y an am plitu de f actor f ro m the Green function between the receivers. Ambient seismic noise can be considered as a random and isotropic wavefield both because the distribution of the ambient sources responsible for the noise randomizes when averaged over long times and because of scattering from heterogeneities that occur within the Earth. Several researchers have used the noise cross correlation instead of the time derivative (e.g. Campillo & Paul, 2003;Shapiro & Campillo, 2004). This assumption is acceptable from the ambient noise recorded on broadband seismic stations, typically with relatively small bandwidth, being the difference between the cross correlation and its derivative a phase shift. The assertion that the impulse response (Green's function) can be retrieved from cross correlation of the diffused fields (noise) in two receiving points is based on the time-reversal symmetry of the Green's function (Derode et al., 2003). Thus, for a perfectly homogeneous distribution of sources surrounding the two points, fully immersed in the scattering medium, the exact impulse response can be recovered from either the causal (t>0) or the anticausal (t<0) part of the cross correlation stacked for all sources, that is the cross correlation is symmetric. However, considerable asymmetry in amplitude and spectral content is typically observed, which indicates differences in both the source process and distance to the source in the directions radially away from the stations (Larose et al., 2004;Bensen et al., 2007). Yet, in the seismic experiments described by Campillo and Paul (2003) and Sabra et al. (2005), the Green's function was reconstructed from one-sided cross correlation because of a preferential direction. Many authors, using the spatial reciprocity of the Green's functions (De Nisco & Nunziata, 2011 and references therein), average positive and negative parts of NCF and impose symmetry. In most cases, this procedure enhances the signal to noise ratio (SNR) and effectively mixes the signals coming from opposite directions, which helps to homogenize the source distribution. If the signature of the Green function is recognized in only one part of the NCF or if there is a large time shift between the positive and negative part, seismic noise could have a preferred orientation source, and it is not possible to design the geometry of the array so that correct wave velocity can be computed. If the possible preferred orientation source is identified and the array is installed perpendicular to it, the Green function is obviously seen only in one part of NCF. Experiments of noise cross correlation have been successfully conducted at Napoli over distances ranging from 50 m to about 4 km (Fig. 7). Two broadband Kinemetrics Quanterra Q330 stations equipped with 3-component Episensor broadband FBA (Force Balance Accelerometer) sensors have been employed. Fig. 7. Location of the seismic stations employed in the cross correlation experiments at the urban area of Napoli.

Signal analysis
The analysis of noise cross correlation consists of the steps that are illustrated in Figure 8 and refer to measurements at 4 km receiver spacing (path MERG-PORT located in Fig. 7). A one-bit normalization is applied to the vertical components of the recorded noise (Fig. 8A), which retains only the sign of the raw signal by replacing all positive amplitudes with a 1 and all negative amplitudes with a −1, in order to increase the signal-to-noise ratio. After average removal, power spectra are evaluated to discern the frequency band of interest (Fig.  8B). Signals are iteratively band-pass filtered (Butterworth filters) to enhance the dispersed wave trains in the cross correlation (Fig. 8C). The cross correlations are computed and then stacked with the Seismic Analysis Code (SAC) (Goldstein et al., 2003). One-sided cross correlations have generally resulted indicating differences in both the source process and distance to the source in the directions radially away from the stations (Larose et al., 2004;Bensen et al., 2007), or the presence of a preferential direction (Campillo & Paul, 2003;Sabra et al., 2005). Then FTAN analysis is performed to extract the fundamental mode of Rayleigh waves (Figs. 8 D-E). Three experiments have been conducted at the historical centre of Napoli (SMN, SOC and SLOR in Fig. 7) being one (SMN), permanently installed and continuously recording at the rock foundations of the SS. Marcellino and Festo monumental complex (www.geosism.unina.it). The other Q330 station was mobile and recorded ambient noise, for at least 1 hour, using a 100-Hz sampling frequency, at S. Lorenzo Maggiore basilica (SLOR) and the Sociology Faculty of University (SOC). The SMN-SOC and SMN-SLOR distances are 260 m and 400 m, respectively. The retrieved V S models (shown along the SMN-SLOR in Fig. 9) clearly show at 20-35 m below ground level a V S increase to about 600 m/s. According to stratigraphies and velocity ranges for NYT tuff (Fig. 4), it can be argued that such V S values are consistent with the presence of altered NYT tuff, typically found on the top of compact tuff and called "cappellaccio". Compact NYT tuff (V S of about 800 m/s) is found 10-15 m deeper. The average thickness of the NYT tuff formation is 50m. At greater depth, a further increment of V S is observed, to 970 m/s at 70-150 m of depth. This V S distribution versus depth is very consistent with the stratigraphy of a deep borehole (400 m) drilled in the Plebiscito square, in front of the Royal Palace, and close to the investigated area. In fact, in the shallower 160 m, layers of NYT tuff, 80 m thick, and Whitish tuff, 80 m thick, were found. Then an important stratigraphic result can be deduced: the thickening of the NYT tuff layer moving towards west, that is in the direction of the eruptive centre (Nunziata et al., 2009). Another experiment has been performed at the Partenope street (PART in Fig. 7), with highly chaotic traffic, by noise recordings with a 24 bit Geometrics StrataVisor seismograph and 1 Hz vertical geophones (Geospace GS-1), along a spreading with geophone distance of 180 m. The V S distribution vs. depth is very consistent with the stratigraphy of a deep borehole at Vittoria square (Fig. 7), close to the investigated area (Fig. 10). It turns out that the investigated area is characterized by fractured and compact tuffs below a shallow layer of man made ground material, laid to construct and protect the street from sea actions. Very recently, a further experiment has been performed over a distance of 4 km in order to define the thickness of the tuff cover. Two 24 bit digital tromographs with a wide frequency range (0.1-200 Hz) have simultaneously recorded noise for 1 hour at Mergellina (MERG) and harbour (PORT) (for their location see Fig. 7). The results are very important as, for the first time, structures have been defined below Napoli at 2 km of depth (Fig. 11). The obtained V S models are in agreement with V S velocities obtained by Nunziata (2010) along the Vesuvio-Campi Flegrei path, crossing Napoli and its gulf. The agreement with the data relative to Mofete (Campi Flegrei) drillings, that is V S computed from V P sonic log measurements (AGIP, 1987) by assuming a reasonable V P /V S ratio of 1.8, and ultrasonic measurements on saturated specimens (Zamora et al., 1994) is quite impressive and the following interpretative structural model can be formulated. The first 0.5 km consists of tuffs while tuffs and tuffites are present at 0.5-1.2 km depth; tuffs and tuffites with lava interbedding, probably thermometamorphic, might be present at depths of 1.2-2 km. At these depths, both the agreement with ultrasonic velocity measured on a conglomerate sample (Bernard & Zamora, 2003) and the stratigraphy at Plebiscito square ( Fig. 9), suggest that the presence of highly fractured sedimentary rocks cannot be escluded. The compact sedimentary horizon, with a V S of 3.6-3.7 km/s, has been found below the Neapolitan area at about 3 km of depth (Nunziata, 2010).  with geophone distance of 180 m. The statigraphy is relative to Vittoria square borehole (located in Fig. 7). The photo of the investigated area, the cross correlation of 1-Bit 6-25 Hz band-pass filtered signals, the fundamental mode Green function extracted with FTAN method (red line), and average dispersion curve of the fundamental mode, with error bars, are also shown. Legend: MS = Marine sands; F NYT = Fractured Neapolitan Yellow Tuff; C NYT = Compact Neapolitan Yellow Tuff. Fig. 11. The V S solutions and the chosen solution (red line) for the MERG-PORT path (Fig. 7) are shown together with the average dispersion curve of the fundamental mode, with error bars, and comparison between 1-Bit 0.3-0.7 Hz band-pass filtered signals cross correlation and the fundamental mode Green function extracted with FTAN method (red line). Ultrasonic measurements on specimens from Campi Flegrei (Zamora et al., 1994) and Vesuvio (Trecase drilling) (Bernard & Zamora, 2003) are reported together with V S values computed from V P sonic log measurements (AGIP, 1987).

Conclusions
The results obtained in Napoli metropolitan area, with the non linear inversion of Rayleigh wave group velocity dispersion curve of the fundamental mode extracted with FTAN method from both active seismic surveys and noise cross correlation, show that the procedure is a powerful and reliable instrument to get V S profiles versus depth in urban areas. The proposed methodology is low cost, as one (active experiments) or two (passive experiments) receivers are requested on ground surface and is particularly suitable for urban areas as doesn't require spreadings. The depth of penetration is mainly controlled by the distance and the soil velocities.