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SuRFACE wAvE ANALySIS FOR LOOSE SOIL ChARACTERIZATIONM. Papadopoulou, L.V. Socco1, C. Comina2

1 Politecnico di Torino, Italy2 Università degli Studi di Torino, Italy

Introduction. �he characterization of loose sand formations in terms of seismic velocities and thickness is relevant in man� engineering applications, ranging from seismic hazard identification and environmental studies to estimation of liquefaction potential and desertification phenomena. In oil and gas, the stud� of these materials is particularl� interesting in static corrections, especiall� in sand dune environments. �he use of surface wave anal�sis in these formations has �een proven to �e a ver� powerful tool that, in several cases, can overcome the limitations of other seismic methods. �he dispersion curve (DC) can �e experimentall� retrieved �� computing wavefield transforms of the raw seismic records and picking the energ� maxima. �nce the DC is estimated it can �e inverted to provide a local 1D �-wave velocit� model. For the inversion, the su�soil is modeled as a stack of homogeneous linear elastic la�ers which are characterized �� four parameters: V�, VP, ρ (densit�) and H (thickness). �he dispersion curve

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shows high sensitivit� towards �-wave velocit� so usuall� the unknowns of the inversion are V� and thickness while the value of the VP, or Poisson’s ratio (ν), and densit� are assumed a priori.

�he poor sensitivit� of �W to the Poisson’s ratio has �een addressed �� several authors. For instance Nazarian (1984), showed that the variation of the phase velocit� due to a variation of Poisson’s ratio is small. However, Foti and �tro��ia (2002) showed that a wrong a priori assumption on the value of can significantl� affect the inversion results� it has also �een shown that the investigation depth of surface waves depends on (see for example Pelekis and Athanasopoulos, 2011). �occo and Comina (2017�) demonstrated that the relationship �etween the depth of investigation and the wavelength of propagation of �W is sensitive to and this sensitivit� increases with depth.

�he mechanical properties of loose soils, and hence their seismic velocities, depend on the over�urden load according to a power-law relationship (�assmann, 1951). When dr� granular materials are concerned, this results in a depth dependenc� in the form:

�P = γP (ρgz)ap �� = γ� (ρgz)as (1)where g is the gravit� acceleration, z is the depth, ρ is the �ulk densit�, γp and γs are depth-independent coefficients mainl� related to the elastic properties of the grains for P- and �-wave respectivel�, and αp and αs are the power-law exponents for P- and �-wave respectivel�.

�he dispersion of �W propagation in loose granular media is also characterized �� a power law that can �e formulated as:

c = bλαs (2)where λ is the wavelength, c is the phase velocit� and b is a proportionalit� coefficient (see for example �usev et al., 2006). Bergamo and �occo (2013, 2016) exploited this �ehavior for a ro�ust inversion of �W. �he� retrieved the 1D V� profile within the sand formation and, assuming that for shallow investigation depths the propagating wavelength is equal to the depth, the� o�tained an estimation of the sand �ottom depth. �he� also concluded that if higher modes are availa�le, the� can �e included in the inversion process and allow the estimation of the Poisson’s ratio and consequentl�, the 1D VP profile can also �e estimated.

Here we aim to improve the accurac� of estimation of the sand �ottom depth and to estimate the value of the Poisson’s ratio �� including in the inversion a method proposed �� �occo and Comina (2017a) that relates the wavelength of propagation of �W with the depth of investigation.

Method. We use a s�nthetic model and its relevant dispersion curve to illustrate the method. In Fig. 1a we show the velocit� model that simulates a loose sand formation having thickness equal to 30 m over a stiff �edrock. We consider a V� gradient (Eq. 1) for the loose sand and a constant V� value for the �edrock. �he power-law parameters for the V� in the sand are γs = 18.31 and αs = 0.231 (Zimmer et al., 2007). Poisson’s ratio (v = 0.2) and densit� (ρ = 1560 kg/m3) are considered constant. �he s�nthetic DC is computed using Haskell and �homson forward operator (Maraschini, 2008) and it is presented in phase velocit�-wavelength domain (Fig. 1a). �o isolate the part of the DC that refers to the propagation inside the sand onl�, we define a threshold wavelength, λb, �elow which the power law is not an� more valid. According to this, we select the data points that �elong to the sand and with a power law fitting we o�tain the value of αs equal to 0.229 (estimation error 2.42%). �he selected data points are used in a Monte Carlo inversion where the unknown is γs and its value is estimated as 18.44 (the error is 1.5%). �ince also the 1st higher mode is availa�le, the estimation of v is possi�le and VP can �e computed. �he Poisson’s ratio value estimation was 0.2102, approximating the true value with an error of 5.1%.

For the estimation of the sand thickness we use the wavelength-depth (W/D) relationship methodolog� proposed �� �occo et al. (2017). Based on our s�nthetic dispersion curve (fundamental mode) and the inverted �-wave velocit� profile, we can compute the time-average velocit� V�z:

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(3)

where n is the num�er of la�ers down to depth z, and hi and ��i are the thickness and the velocit� of the ith la�er, respectivel�. We o�tain couples of wavelength and depth for which the �W phase velocit� is equal to V�z and these couples are then interpolated (Fig. 1�). �he W/D curve of the simulated model is a straight line in the depth range that �elongs to the sand and it presents a �reak point at the wavelength λb and at the depth of the sand �ottom. Another important o�servation is that the deviation from linearit� starts at a wavelength shallower than

Fig. 1 - a) V� (�lue solid) models and the corresponding �W dispersion curve (�lue dots) plotted as a function of wavelength. �he DC follows a power law until a threshold value of wavelength, λ�. �) W/D corresponding to the model of Fig. 1. �he curve deviates from linearit� at wavelength λd and presents a �reak point at wavelength λ�. �he �reak point corresponds to the sand �ottom depth.

Fig. 2 - a) V� (green solid) and VP (various color solid) models. V� model is kept the same and VP is updated according to Poisson’s ratio that increases from 0.18 to 0.38 with steps of 0.02. �) W/D corresponding to the various velocit� models of Fig. 2a.

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λb, which we note in Fig. 1� as λd. �aking this �ehavior into consideration, we simulate models of sand having the estimated V� and VP gradients and various thicknesses in order to o�tain the W/D curve that presents a deviation from linearit� at wavelength equal to λd and a �reak point at a wavelength equal to λb. �he depth coordinate of the �reak point gives us an accurate estimation of the sand �ottom depth. �he o�tained value is 30.01 m, approximating the true one with an error of 1%.

Another interesting point is the sensitivit� of the W/D on the Poisson’s ratio. In Fig. 2a we present the effect of variation of the Poisson’s ratio. V� is kept constant and VP varies in the sand, corresponding to the increase in v from 0.18 to 0.38 in steps of 0.02 (Poisson’s ratio for dr� sand usuall� ranges �etween 0.2 and 0.3). �he corresponding W/Ds are plotted with the same color scale in Fig. 2�. We o�serve that the W/D presents a quasi linear sensitivit� to Poisson’s ratio that increases with depth and can therefore �e used, once the V� gradient parameters have �een estimated, to estimate the Poisson’s ratio value in the sand, without the need of higher modes.

Conclusions. We showed with s�nthetic modeling that it is possi�le to use �W to characterize loose soils in terms of V� and VP. B� including in the inversion procedure the W/D relationship we are a�le to estimate with accurac� the thickness of the loose soil. �his relationship presents also an important sensitivit� to Poisson’s ratio which can �e used to estimate VP using onl� the fundamental mode of the DC. ReferencesBergamo P., and L.V. �occo, 2013, Estimation of P- and �-wave velocit� of unconsolidated granular materials

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Foti, �., and C. �tro��ia, 2002, �ome notes on model parameters for surface wave data inversion: ��mposium on the Application of �eoph�sics to Engineering and Environmental Pro�lems �A�EEP, �EI6� doi:10.4133/1.2927179.

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dissertation, Politecnico di �orino.Nazarian, �., 1984, In situ determination of elastic moduli of soil deposits and pavement s�stems �� �pectral-Anal�sis-

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