**3. Derivation of shear-wave velocities in Maltese rocks using joint inversion of H/V and ESAC curves**

Twenty sites have been chosen for this investigation (14 in Malta, 5 in Gozo and 1 in Comino, shown in **Figure 1a**), all of which are characterised by the full sedimentary sequence i.e. the Blue Clay is embedded between the Upper Coralline Limestone above and the Globigerina Limestone below. Since the sites all have similar stratigraphy, any spatial geophysical variations within a particular stratum can also be investigated.

At each site, single-station ambient noise measurements were conducted jointly with geophone array measurements. The sites were chosen not to have any major topographical slopes or irregularities so as to fulfil the 1-D assumption of the array methods. For reasons of clarity, the more detailed results in the next sub-sections are presented only for eight representative sites with a range of stratigraphical characteristics.

### **3.1 Single-station measurements**

Single-station measurements were used to obtain the Horizontal-to-Vertical Spectral Ratio (H/V) for ambient seismic noise. The H/V curve is known to give a peak that matches the S-wave resonance frequency of a site, *f*0, which is linked to the S-wave velocity (*V*S) of the sedimentary layer and its thickness *H* by:

Auto-Correlation (ESAC) technique and the curves automatically picked by the

*Assessing Seismic Site Response at Areas Characterized by a Thick Buried Low-Velocity Layer*

The ESAC method outputs an effective (or apparent) dispersion curve which in the presence of higher modes, will include a combination of the dispersion curves relative to the relevant modal components [23]. The results for the eight chosen

The curves, except in the Mellieha case, exhibit "normal" dispersion characteristics in the low frequency range whereby the effective Rayleigh-wave phase velocity decreases with increasing frequency. At higher frequencies, this trend changes to an inversely dispersive one. This represents an increase in velocity with increasing frequency or decreasing depth. This shape of the effective curves is indicative of the presence of higher modes of surface waves and has been attributed to the presence of a stiff layer overlying a softer one (i.e. UCL and BC, in this case) by various authors (e.g. [23, 24]). In Mellieha, only an inversely dispersive curve was obtained suggesting that the combined thickness of the UCL and BC layers is too high for the

The H/V and effective dispersion curves were jointly inverted using a Genetic Algorithm (GA; [25]) approach to obtain one-dimensional *V*<sup>S</sup> profiles. The range of allowed values of the most important parameters in the inversion, namely layer thickness and shear-wave velocity, for each site inversion were guided by previous knowledge of the site geology, from geological maps or previous publications. However, the shear-wave velocity in each layer was allowed to vary over a wide range of values, and no indication of where the low-velocity layer is found was given. This was done to assess the ability of the GA to correctly identify and characterize the shear-wave velocity inversion. Up to 10 higher modes were taken

Initially 100 models were randomly generated on which genetic operators (cross-over, mutation and elite selection) are applied for the selection and creation of a second generation of models. The processes were repeated through 150 iterations. For each site, ten separate inversions were run outputting 10 different bestfitting profiles, one from each inversion run. The one profile with the least misfit value from the best 10 profiles was then chosen as the representative profile for the site. The other 9 profiles are useful to estimate the variability and robustness of the final result. **Figures 4** and **5** shows the results of the joint inversion for the eight sites. The *V*S30 was also calculated for each site and is displayed in the figure.

*The effective dispersion curves (Rayleigh-wave vs. frequency) obtained at eight of the investigated sites.*

GL to be adequately sampled with the given array configuration.

provided code [19–22].

**3.3 Data inversion**

into account.

**Figure 3.**

**145**

sites are shown in **Figure 3**.

*DOI: http://dx.doi.org/10.5772/intechopen.95277*

$$f\_0 = \frac{V\_s}{4H}$$

Time-series of 20 minutes each, sampled at 128 Hz, were recorded using the Micromed Tromino™ and analysed using the software Grilla™ to obtain H/V curves in the frequency range of 0.5–64 Hz. The time-series were divided into 60 non-overlapping windows, each 20 s long, as suggested by the SESAME guidelines [10]. Before the analysis, windows which contain any spurious signals were removed to reduce the standard deviation. The H/V curve was obtained by averaging the horizontal spectra using the geometric mean and dividing the mean by the vertical spectrum for each time window. The curves for each window were then averaged to get the final H/V curve [11].

**Figure 2** shows the H/V curves obtained at eight representative sites. All curves exhibit a peak between 1 and 2 Hz, the amplitude of which varies between 2 and 5. Previous studies utilising H/V analysis in such areas have also obtained this peak [12–15], which is presumably associated with the boundary separating the BC and the GL [16]. This peak is immediately followed by a drop below 1 in the H/V spectrum over a wide frequency range. This feature has been attributed to the presence of a buried low-velocity layer by [17, 18] and is also evident and consistent in all previous studies of areas of similar lithostratigraphy on the islands.

#### **3.2 Array measurements**

The passive seismic array measurements were conducted using Micromed SoilSpy Rosina™ seismic digital acquisition system equipped with 4.5 Hz vertical geophones. The noise signals detected are interpreted as plane Rayleigh waves in their fundamental and higher propagation modes. The number of geophones used varied between 17 and 42 which were placed either in an L- or C-shaped configuration with a regular interstation distance of 5 m, for the majority of the cases. This decision depended on the space available and the expected thickness of the shallow layers. On average the total length of the array was around 150 m and the depth of exploration exceeded 100 m only at a couple of locations. The recordings, each 20 minutes long and sampled at 256 Hz, were analysed using the Extended Spatial

**Figure 2.** *The H/V curves obtained at eight of the investigated sites.*

*Assessing Seismic Site Response at Areas Characterized by a Thick Buried Low-Velocity Layer DOI: http://dx.doi.org/10.5772/intechopen.95277*

Auto-Correlation (ESAC) technique and the curves automatically picked by the provided code [19–22].

The ESAC method outputs an effective (or apparent) dispersion curve which in the presence of higher modes, will include a combination of the dispersion curves relative to the relevant modal components [23]. The results for the eight chosen sites are shown in **Figure 3**.

The curves, except in the Mellieha case, exhibit "normal" dispersion characteristics in the low frequency range whereby the effective Rayleigh-wave phase velocity decreases with increasing frequency. At higher frequencies, this trend changes to an inversely dispersive one. This represents an increase in velocity with increasing frequency or decreasing depth. This shape of the effective curves is indicative of the presence of higher modes of surface waves and has been attributed to the presence of a stiff layer overlying a softer one (i.e. UCL and BC, in this case) by various authors (e.g. [23, 24]). In Mellieha, only an inversely dispersive curve was obtained suggesting that the combined thickness of the UCL and BC layers is too high for the GL to be adequately sampled with the given array configuration.

#### **3.3 Data inversion**

**3.1 Single-station measurements**

*Earthquakes - From Tectonics to Buildings*

averaged to get the final H/V curve [11].

**3.2 Array measurements**

**Figure 2.**

**144**

*The H/V curves obtained at eight of the investigated sites.*

Single-station measurements were used to obtain the Horizontal-to-Vertical Spectral Ratio (H/V) for ambient seismic noise. The H/V curve is known to give a peak that matches the S-wave resonance frequency of a site, *f*0, which is linked to

> *<sup>f</sup>* <sup>0</sup> <sup>¼</sup> *Vs* 4*H*

Time-series of 20 minutes each, sampled at 128 Hz, were recorded using the Micromed Tromino™ and analysed using the software Grilla™ to obtain H/V curves in the frequency range of 0.5–64 Hz. The time-series were divided into 60 non-overlapping windows, each 20 s long, as suggested by the SESAME guidelines [10]. Before the analysis, windows which contain any spurious signals were removed to reduce the standard deviation. The H/V curve was obtained by averaging the horizontal spectra using the geometric mean and dividing the mean by the vertical spectrum for each time window. The curves for each window were then

**Figure 2** shows the H/V curves obtained at eight representative sites. All curves exhibit a peak between 1 and 2 Hz, the amplitude of which varies between 2 and 5. Previous studies utilising H/V analysis in such areas have also obtained this peak [12–15], which is presumably associated with the boundary separating the BC and the GL [16]. This peak is immediately followed by a drop below 1 in the H/V spectrum over a wide frequency range. This feature has been attributed to the presence of a buried low-velocity layer by [17, 18] and is also evident and consistent

in all previous studies of areas of similar lithostratigraphy on the islands.

The passive seismic array measurements were conducted using Micromed SoilSpy Rosina™ seismic digital acquisition system equipped with 4.5 Hz vertical geophones. The noise signals detected are interpreted as plane Rayleigh waves in their fundamental and higher propagation modes. The number of geophones used varied between 17 and 42 which were placed either in an L- or C-shaped configuration with a regular interstation distance of 5 m, for the majority of the cases. This decision depended on the space available and the expected thickness of the shallow layers. On average the total length of the array was around 150 m and the depth of exploration exceeded 100 m only at a couple of locations. The recordings, each 20 minutes long and sampled at 256 Hz, were analysed using the Extended Spatial

the S-wave velocity (*V*S) of the sedimentary layer and its thickness *H* by:

The H/V and effective dispersion curves were jointly inverted using a Genetic Algorithm (GA; [25]) approach to obtain one-dimensional *V*<sup>S</sup> profiles. The range of allowed values of the most important parameters in the inversion, namely layer thickness and shear-wave velocity, for each site inversion were guided by previous knowledge of the site geology, from geological maps or previous publications. However, the shear-wave velocity in each layer was allowed to vary over a wide range of values, and no indication of where the low-velocity layer is found was given. This was done to assess the ability of the GA to correctly identify and characterize the shear-wave velocity inversion. Up to 10 higher modes were taken into account.

Initially 100 models were randomly generated on which genetic operators (cross-over, mutation and elite selection) are applied for the selection and creation of a second generation of models. The processes were repeated through 150 iterations. For each site, ten separate inversions were run outputting 10 different bestfitting profiles, one from each inversion run. The one profile with the least misfit value from the best 10 profiles was then chosen as the representative profile for the site. The other 9 profiles are useful to estimate the variability and robustness of the final result. **Figures 4** and **5** shows the results of the joint inversion for the eight sites. The *V*S30 was also calculated for each site and is displayed in the figure.

**Figure 3.** *The effective dispersion curves (Rayleigh-wave vs. frequency) obtained at eight of the investigated sites.*

#### **Figure 4.**

*The joint inversion results and stratigraphic interpretation (lower panel) for Bahrija, Mdina, Mellieha and Mgarr sites. For each site, the best profiles from each of the 10 inversions are shown, with the red profile representing the one with the lowest misfit. The profiles in green are those characterized by a misfit which is within 50% of the best model's misfit value; the yellow ones are characterized by a misfit greater than 150% of the best model's misfit value. The GL layers are displayed in grey since the values are not reliably constrained by the data. Shown in the upper panel for each site are (from left to right) the effective dispersion and H/V curves. The blue curve is the experimental curve, the red curve shows the best-fitting theoretical curve while the rest (green and yellow) correspond to the other nine profiles. The calculated VS30 for each site is displayed in the top right corner. The colours used in the stratigraphic interpretation correspond to the colours in the geological map (Figure 1) [11].*

position and S-wave velocity of the low-velocity layer (the Blue Clay layer). Keeping in mind that broad exploration ranges were set in the parametrisations, such an agreement highlights the robustness of the inversion and the sensitivity of the curves to the presence and properties of the low-velocity layer. In addition, this justifies the use of global search methods, such as the GA, which are able to retrieve reasonable profiles without the need of an initial profile close to the solution. This consistency between the models for a particular site diminishes in the prediction of the velocity of the UCL and more so of the GL layer, where, for example, values between 700 and 1800/s were obtained for the latter. This

*Assessing Seismic Site Response at Areas Characterized by a Thick Buried Low-Velocity Layer*

*DOI: http://dx.doi.org/10.5772/intechopen.95277*

*The joint inversion results for Nadur, Selmun, Victoria 1 and Xemxija sites.*

**Figure 5.**

**147**

In general a good match between the theoretical and experimental effective dispersion curves and H/V peak can be observed in all cases. A significantly important feature is that all the final 10 profiles for each site, are in agreement on both the *Assessing Seismic Site Response at Areas Characterized by a Thick Buried Low-Velocity Layer DOI: http://dx.doi.org/10.5772/intechopen.95277*

**Figure 5.**

position and S-wave velocity of the low-velocity layer (the Blue Clay layer). Keeping in mind that broad exploration ranges were set in the parametrisations, such an agreement highlights the robustness of the inversion and the sensitivity of the curves to the presence and properties of the low-velocity layer. In addition, this justifies the use of global search methods, such as the GA, which are able to retrieve reasonable profiles without the need of an initial profile close to the solution.

This consistency between the models for a particular site diminishes in the prediction of the velocity of the UCL and more so of the GL layer, where, for example, values between 700 and 1800/s were obtained for the latter. This

In general a good match between the theoretical and experimental effective dispersion curves and H/V peak can be observed in all cases. A significantly important feature is that all the final 10 profiles for each site, are in agreement on both the

*The joint inversion results and stratigraphic interpretation (lower panel) for Bahrija, Mdina, Mellieha and Mgarr sites. For each site, the best profiles from each of the 10 inversions are shown, with the red profile representing the one with the lowest misfit. The profiles in green are those characterized by a misfit which is within 50% of the best model's misfit value; the yellow ones are characterized by a misfit greater than 150% of the best model's misfit value. The GL layers are displayed in grey since the values are not reliably constrained by the data. Shown in the upper panel for each site are (from left to right) the effective dispersion and H/V curves. The blue curve is the experimental curve, the red curve shows the best-fitting theoretical curve while the rest (green and yellow) correspond to the other nine profiles. The calculated VS30 for each site is displayed in the top right corner. The colours used in the stratigraphic interpretation correspond to the colours in the geological map*

**Figure 4.**

*Earthquakes - From Tectonics to Buildings*

*(Figure 1) [11].*

**146**

inconsistency can be attributed to different facts such as the available array conditions, especially length and resonance frequency of geophones which limit the observable depth and the soft BC layer acting as a high-pass filter.

The obtained ranges for *V*<sup>S</sup> and thickness for each layer from all the 20 tested sites are shown in **Table 1**. The *V*<sup>S</sup> profiles reveal a variation in the shear-wave velocities of the geological layers at the different sites. Variations in the UCL shearwave velocities are expected given the fact that the UCL exhibits considerable variation over the islands, ranging from very compact to highly fractured. The *V*<sup>S</sup> in clay varies between 350 and 600 m/s which contrasts with values obtained at sites with outcropping BC layer (between 300 and 400 m/s) [12, 14]. **Figure 6** shows the variation of BC shear-wave velocity with thickness of the overlying UCL considering all the 20 profiles. A trend is clearly visible whereby the higher the thickness of the UCL layer, the higher the shear-wave velocity of the BC layer. This phenomenon can presumably be related to the overburden of the hard UCL layer on the BC,

*Assessing Seismic Site Response at Areas Characterized by a Thick Buried Low-Velocity Layer*

increasing the compactness of the particles, and thus the *V*<sup>S</sup> of the layer.

inversely dispersive character [11].

*DOI: http://dx.doi.org/10.5772/intechopen.95277*

**4. Site-specific response analysis**

will be applied.

**149**

• the soil layer properties (namely the *V*<sup>S</sup> profile);

nical experts. The chosen curves are displayed in **Figure 9**.

• the modulus reduction and damping curves for each material;

Finally, in **Figure 7** we show the theoretical individual Rayleigh-wave dispersion

Numerical site-specific response analysis was carried out using the equivalent-linear earthquake site response analysis programme SHAKE2000 [26]. The SHAKE2000 software computes the propagation of shear waves incident vertically on a package of horizontal layers, in which the wave-field in each layer is composed of upward and downward moving waves, whose amplitudes are dependent on the reflectivity/ transmission matrices. The programme requires the following three main inputs:

• the ground motion time-history including the layer number to which the input

The *V*<sup>S</sup> profiles obtained from the ambient noise measurements (**Figures 4**, 5 and **8**) were used as input for the soil layer properties for each site. The GL layer was chosen as the bedrock reference layer given that its velocity is generally more than 800 m/s. The modulus reduction and damping curves were chosen from the set of available curves within the package itself after consulting with local geotech-

As for ground motion time-history, it is recommended that a suite of records is chosen which are compatible with the national seismic hazard parameters. From the probabilistic seismic hazard analysis conducted by [28], a plausible value for the mean peak ground acceleration (PGA) on rock sites corresponding to a 475-year return period is 0.08 *g.* [28] also note that from the study of historical seismicity and seismotectonic background it is indicated that the seismic hazard of the Maltese islands is related to both moderate magnitude events (M = 5.0–6.0) at short distances (d = 10–40 km) as well as high magnitude events (M = 6.5–8.0) at distances larger than 90 km. In this chapter, the far-field scenario of high magnitude events at

curves up to the second higher mode for the best fit models compared with the observed effective dispersion curve for the Bahrija and Mdina models. The computed theoretical effective dispersion curve is also plotted and it can be observed that it fits very well with the observed data. These plots confirm that the effective Rayleigh mode is indeed the superposition of different modes with the higher modes playing an important role in the frequency range when this curve shows an


#### **Table 1.**

*The VS ranges for each lithotype obtained from all the studied sites.*

#### **Figure 6.**

*A graph showing the variation of the BC shear-wave velocity with increasing UCL thickness.*

#### **Figure 7.**

*Comparison of the observed Rayleigh-wave phase velocities (black dots) with the theoretical effective phase velocities and the first three Rayleigh-wave modes for the Bahrija and Mdina sites [11].*

### *Assessing Seismic Site Response at Areas Characterized by a Thick Buried Low-Velocity Layer DOI: http://dx.doi.org/10.5772/intechopen.95277*

The obtained ranges for *V*<sup>S</sup> and thickness for each layer from all the 20 tested sites are shown in **Table 1**. The *V*<sup>S</sup> profiles reveal a variation in the shear-wave velocities of the geological layers at the different sites. Variations in the UCL shearwave velocities are expected given the fact that the UCL exhibits considerable variation over the islands, ranging from very compact to highly fractured. The *V*<sup>S</sup> in clay varies between 350 and 600 m/s which contrasts with values obtained at sites with outcropping BC layer (between 300 and 400 m/s) [12, 14]. **Figure 6** shows the variation of BC shear-wave velocity with thickness of the overlying UCL considering all the 20 profiles. A trend is clearly visible whereby the higher the thickness of the UCL layer, the higher the shear-wave velocity of the BC layer. This phenomenon can presumably be related to the overburden of the hard UCL layer on the BC, increasing the compactness of the particles, and thus the *V*<sup>S</sup> of the layer.

Finally, in **Figure 7** we show the theoretical individual Rayleigh-wave dispersion curves up to the second higher mode for the best fit models compared with the observed effective dispersion curve for the Bahrija and Mdina models. The computed theoretical effective dispersion curve is also plotted and it can be observed that it fits very well with the observed data. These plots confirm that the effective Rayleigh mode is indeed the superposition of different modes with the higher modes playing an important role in the frequency range when this curve shows an inversely dispersive character [11].
