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Sessione 3.3 - Metodi e Tecnologie Innovative

Cite: Dal Moro G., 2022. Determination of the VS profile in a noisy industrial site: further
evidences about the importance of Love waves and the opportunities of the group velocity
analysis. Proceedings of the 40th GNGTS (Gruppo Nazionale di Geofisica della Terra Solida)
National Congress, Trieste (Italy), June 27-29 2022

Determination of the VS profile in a noisy industrial site: further

evidences about the importance of Love waves and the
opportunities of the group velocity analysis

Giancarlo Dal Moro

Institute of Rock Structure and Mechanics - Academy of Sciences of the Czech Republic
Prague, Czech Republic

dalmoro@irsm.cas.cz / gdm@winmasw.com

keywords: Surface waves; Rayleigh waves; Love waves; ESAC (Extended Spatial
AutoCorrelation); MAAM (Miniature Array Analysis of Microtremors) ; FVS (Full Velocity
Spectrum); joint analysis; phase velocity; group velocity, surface waves; HVSR; HS (Holistic
analysis of Surface waves); RPM (Rayleigh-wave Particle Motion)
Introduction
In the last decade, the analysis of surface-wave propagation has become extremely popular
especially in the framework of seismic-hazard studies although, as a matter of fact, the
determination of the shear-wave velocity (VS) profile is useful for any geotechnical or
geological application that requires the knowledge of the subsurface conditions.
In it well known that the accuracy of the VS profile depends on the number of observables
considered in the inversion process and on the kind of analyses actually put in place. In fact,
in spite of the popularity of the approach based on the interpretation of the modal dispersion
curves of the vertical component of Rayleigh waves (MASW – Multichannel Analysis of
Surface Waves), a wide range of further options are possible and capable of providing better
results, free from major ambiguities and pitfalls that characterize the standard MASW
approach.
For the present illustrative study, we considered a set of multi-component active and passive
data gathered in a NE-Italy heavily-industrialised area home to many industries related to
metalworking and therefore characterized by an extremely-high level of microtremors.

Data and analyses

With the goal of defining the best procedures necessary to unambiguously define the
subsurface model in a very noisy industrial area in NE Italy, we collected a comprehensive
series of active and passive seismic data. Active data were recorded by means of a single
3-component sensor in order to work with the Holistic analysis of Surface waves (HS) (Dal
Moro et al., 2019; Dal Moro, 2018; 2020) while passive data were recorded so to define the
HVSR (Horizontal-to-Vertical Spectral Ratio), the dispersion curve of the vertical (Z)
component of Rayleigh waves via Miniature Array Analysis of Microtremors (MAAM - Cho
et al., 2006a; 2006b; 2013; Tada et al., 2007; Dal Moro et al., 2015a; 2018) and the Love-
wave dispersion curve via ESAC (Extended Spatial AutoCorrelation - Ohori et al., 2002).
MAAM was accomplished considering a triangular geometry with a radius of 1.7 m while
data for the ESAC were collected considering various multi-offset linear arrays with total
lengths ranging from 44 to 60 m and with different orientations (for a series of clarifications
about the performances of the MAAM and ESAC techniques see Dal Moro, 2020).
Since it was systematically observed that Rayleigh-wave phenomenology is extremely
complex and therefore prone to significant ambiguities and pitfalls (Safani et al., 2005; Dal
Moro et al., 2015b; Dal Moro, 2020), first of all we accomplished the joint inversion of the
HVSR together with the effective dispersion curves of the Z and T components (i.e. the
vertical component of Rayleigh waves and Love waves) as obtained from MAAM and ESAC,
respectively (see data and results shown in Fig. 1).

GIANCARLO DAL MORO 2

Figure 1. Purely passive data: shear-wave velocity profile (c plot) obtained through the joint
analysis of the phase-velocity effective dispersion curves of the Z (a plot) and T (b plot)
components together with the HVSR curve (d plot). In the a and b plots, the background
colours represent the field data while the overlaying white curves are the effective dispersion
curves of the identified subsurface model. In the d plot, the α value (0.2) in the legend
represents the amount of Love waves in the microtremor field (Arai and Tokimatsu, 2004;
Dal Moro, 2020).

Since a more common approach is based on the joint analysis of Rayleigh-wave dispersion
and HVSR (e.g. Arai and Tokimatsu, 2005), in order to compare the outcomes we also
accomplished this kind of simpler approach (in other words, unlike before, now we are not
considering the Love-wave dispersion). Fig. 2 shows the obtained results. Although the
overall misfits appear quite good and would inevitably represent a very satisfactory result,
the comparison with the solution obtained while considering both Rayleigh and Love waves
(see Fig. 1 and related text) demonstrates that the use of Rayleigh waves alone can lead to
erroneous solution which are necessarily associated to higher VS values. This is easily and
plainly demonstrated if we compute the Love-wave dispersion from the VS profile shown in
Fig. 2c and compare it with the field data (i.e. the velocity spectrum shown in Fig. 1b): the
Love-wave phase velocities of the model are significantly higher than the observed ones.
This is a very common problem (mistake) due to the intrinsic ambiguity of the Rayleigh-wave
effective curve which, whether considering active or passive data, can be explained by a
large variety of energy distribution and therefore models (Dal Moro, 2020) which cannot be
solved by the HVSR (which, in turn, suffers from major non-uniqueness issues). In this case,
as in other previously-published (e.g. Dal Moro, 2019; 2020), only the presence of Love
waves can properly channel the inversion procedure towards the correct solution.

GIANCARLO DAL MORO 3

It should be clearly underlined that in both the accomplished procedures reported in Fig. 1
and 2, the observed dispersion curves were not interpreted in terms of modal curves but
modelled according to the mathematics of the effective curve (Tokimatsu et al., 1992; Ikeda
et al., 2012).

Figure 2. Result of the joint analysis of the phase-velocity effective dispersion curve of the
Z component (a plot) and the HVSR (b plot). The ambiguities of the Rayleigh-wave effective
dispersion curve (and HVSR) are such that the obtained shear-wave velocities (VS profile
shown in the c plot) overestimate the actual values. Compare with the result presented in
Fig. 1 and see text for comments.

A different approach to surface-wave analysis is possible through the computation of the

group velocities and their holistic analysis jointly with the Rayleigh-wave Particle Motion
(RPM) curve (describing the actual particle motion due to the Rayleigh-wave propagation
and quite useful in further constraining the subsurface model) and, in case we intend to
investigate deeper strata, the HVSR (Dal Moro et al., 2017; 2019; Dal Moro, 2018; 2020).
Group velocities are computed via frequency-time analysis (Levshin et al., 1972) and can
be obtained both from passive (e.g. Fang et al., 2010) and active data (Ritzwoller and
Levshin, 1998; 2002; Dal Moro et al., 2019). Differently than phase velocities, group
velocities can be obtained considering a very limited field equipment which is fundamentally
based on just one or two 3-component geophones, depending on whether we are
considering passive or active data.
Data considered in the present study were recorded by means of a 3-component geophone
deployed at a distance of 44 m from the source (a 10-kg sledgehammer). Due to the high

GIANCARLO DAL MORO 4

noise level, stack was fixed to 25. Fig. 3 shows both the extracted data (group velocity
spectra of the Z and R components as well as the RPM curve) and the solution of the holistic
analysis of surface waves (HS), i.e. the joint analysis of multi-component group velocities
together with the RPM and the HVSR (this latter is useful to extend the investigated profile
in depth). It should be underlined that in the HS approach, dispersion data (group-velocity
spectra) are not analysed through the interpretation of the dispersion curves but through the
multi-component Full-Velocity Spectrum (FVS) approach (Dal Moro et al., 2015a; 2015b;
2019; Dal Moro, 2019; 2020).
The result (VS profile shown in Fig. 3e) is apparently very similar to the one obtained by
considering the joint analysis of the phase velocities of the Z and T components together
with the HVSR (see Fig. 1).

Figure 3. Holistic analysis of the group velocities of the vertical (Z) (a plot) and radial (R) (b
plot) components (FVS approach – background colours represent the field data while the
overlying black contour lines the obtained model) jointly with the RPM (c plot) and HVSR (d
plot) curves. The obtained VS profile (e plot) is entirely similar to the one obtained while
considering the joint analysis of the phase velocities of the Z and T components (see Fig.
1).

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Conclusions
Accomplished analyses allow to highlight the following evidences:
1) Rayleigh-wave modelling cannot be performed considering an approach based on the
modal dispersion curves and the use of the effective curves (for passive data) or the FVS
(for active data) is crucial;
2) Because of the intrinsic (i.e. inevitable) ambiguity of the dispersion curve, Rayleigh-wave
modelling based on the effective curve does not ensure the correctness of the obtained VS
profile even when performed jointly with the HVSR;
3) Especially when analysing phase velocities, the acquisition and analysis of Love waves
reveal decisive to constrain an inversion procedure capable of providing a robust solution
free from significant ambiguities;
4) Love-wave dispersion can be effectively obtained from passive data via ESAC even
while considering linear arrays (data and analyses are not affected by significant directivity
issues);
5) The holistic analysis of multi-component group velocities and RPM curves based on the
FVS approach reveals an effective way to obtain robust shear-wave velocity profiles.

Since a solution needs to be of general validity, it is therefore clear that phase velocity
analyses based just on Rayleigh waves are not recommended because, due to the complex
contribution of different modes, they can lead to overestimated Vs values even if the
analyses are accomplished jointly with the HVSR. Due to their simpler phenomenology,
Love waves represent an essential tool to properly constrain an inversion procedure.
On the other side, the holistic analysis of multi-component group velocities and RPM data
appear an extremely efficient alternative both because it requires a simpler acquisition
setting, both because, thanks to the possibility to deal with a large number of observables,
it leads to a VS profile free from major ambiguities.

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