Evaluation Study of Boundary and Depth of the Soil Structure for Geotechnical Site Investigation Using MASW

This study reviews the correlation between the experimental Rayleigh dispersion curve and the Vp & Vs ground model versus depth. Six samples of stations A , B , C , D ,  E  and  F  were used in the experiment.The geophone spacing used was set 1 m and total length of each line was 23 m. The result shows positive significance (best fit) of R2 that ranges from 0.80 to 0.90. The fk (frequency-wave number method) dispersion curves analysis confirmed that the soil structure investigated is divided into three zones: (1) Unsaturated soil zone (clay soil), in which the layer is dominated by soil with typically alluvial clayey silt and sand. The Vp ranges from 240 m/s to 255 m/s at a depth of 2 to 8 m. (2) The intermediate zone (stiff soil), in which the layer is dominated by sand, silt, clayey sand, sandy clay and clay of low plasticity. This structure is interpreted as partially saturated soil zone, the soil is typically very dense. It contains soft rock typically fill with cobble, sand, slight gravel and highly weathered at depth of 18 to 30 m with Vp of  255 to 300 m/s. (3) Saturated soil zone at a depth of  8 to 18 m with Vp of 300 to 390 m/s. There is a very good agreement between wave-number (k) and phase velocity (Vw)  produced. Both the two parameters shows similar pattern in the topsoil and subsurface layer, which constitute boundary field of soil structure. Moreover, relationship between phase velocity versus wave-length shows best fit of model from inversion with measured value (observed) in  implementation of the boundary and depth of each layer.

1. Int r oduct i on M ultichannel Analysis of Surface Wave (M ASW) survey is gaining popularity in geophysical/ geotechnical investigation due to the fact that it is non-destructive and provides accurate means of site characterization. It has been applied to delineate boundaries and depth of the target structure for geotechnical site investigation. Blake (2009) used M ASW to define the velocity of the structure and depth to bedrock. This survey gives information of sub surface structure, thickness of layers, w ave velocity of a body, and soil am plification parameters like Vs30; all of w hich are important in earthquake engineering. The utilization of MASW for soil characterization originates from the inherent nature of this kind of w ave. Tran (2008) studied surface w ave propagation along a free surface and associated motion, important information about the mechanical properties of the medium is revealed.
The objective of this study is t o characterize the boundary and depth of the soil structure using M ASW technique that substitute core drilling of sam ple (w hich is very expensive to perform), so necessitating geophysical technique as alt ernative means. Basically, geophysical method involve measuring the physical properties of the ground (or structure) and determining variations or Keary, et al.,2002).
Furthermore, the occurrence of anomalies can indicate the presence of features or changes in a material composition (Keary, et al.,2002). Dey (2015) reveals t hat unlike conventional borehole sounding test, geophysical method is less expensive and it provides the benefit of precision to estimate the subsurface compression and shear w ave velocity profile over a large area. It has been found to be better in some aspect compared to the ot her non-invasive methods such as the Ground Penetrating Radar (GPR) and Nuclear M agnetic Resonance (NM R) t echniques. A significant application of geophysical method in geotechnical engineering practice is determination of boundary, depth layer and insitu characterization of soil (Grandjean, 2009 andHiltunen et al., 2012). Critical analysis of the modeling observes w het her geophysical signatures can characterize the physical properties that affect the saturation of soil. This analysis focuses on the dispersion of surface w aves using M ASW method (the fact that w avelengths w ith different frequencies travel at different speeds). The basic principle is quite simple, the various components (frequencies) of the seismic signal travel at a speed that depends on the characteristics of the medium (Dey, 2015). To determine accurate dispersion information, multichannel data processing methods are required to discriminate against noise and enhance Rayleigh w ave signals (Tran, 2008 andChik et al., 2011). The Pattern of the relantionship of the layer s can be formulated mathematically as: Where the w avenumber (km) generated by equation (1) is inversely proportional to phase velocity (V Rm ) or equivalently proportional to the slow ness P m (). For a given frequency, surface w aves have uniquely defined w avenumbers k 0 (f), k 1 (f), k 2 (f) for different modes of propagation. In other w ords, the phase velocities V Rm = ω/k m are fixed for a given frequency. The f-k transform allow s separation of the modes of surface w aves by checking signals at different pairs of f-k.
The M ASW method uses this dispersive property to estimate P and S w ave velocities. It w as reported by Roy (2013) that the M ASW method has been developed w ith the assumption that the subsurface is vertically heterogeneous and laterally homogeneous (i.e. a layer-cakemodel). The M ASW used phase information of high-frequency Rayleigh w aves recorded on vertical component geophones to determine near-surface S-w ave velocities (Tran, 2008). The differences betw een M ASW result s and direct borehole measurements are approximately 15% or less. Studies show that inversion w ith higher modes and the fundam ental mode simultaneously can increase model resolution and depth of investigation (Xia , 2014).
The maximum depth of penetration is determined by the longest w avelength of the surface w aves. The longest w avelengths generated depend on the impact pow er of the source and physical properties of the subsurface (Pei,2007). The greater the impact pow er, the longer the w avelength and the greater w ill be the depth of penetration. Although the impact of t he source such as a heavy w eight drop can generate a longer w avelength of surface w aves, they are very costly and not convenient for field operation. Therefore, a controlled type of seismic source such as a sledge ham mer is used in an active survey (Dey, 2015).
The penetration depth of Rayleigh w aves is about 0.4 times the longest w avelength (Schuler, 2008). Therefore, the depth of investigation can be estimated by using the dispersion curve. Since w avelength is equal to velocity divi ded by frequency w e can estimate the depth of penetration using the equations: Where  is w avelength (m) ; D is depth of penetration (m), Vr is Rayleigh w ave velocity (m/sec) and f is Frequency (Hz).
On the other hand, the dispersion curve is an interpretation of the different modes or harmonics of the surface w ave as it propagates through a given media.

Si t e descr i pt i on and geology
The study w as carried out in Pedas, Negeri Sembilan, Peninsular M alaysia ( Figure 1). This area has a distinctive and unique geology than the surrounding areas because of the presence of hot springs. Hot spring is allegedly originates from the host rock, it is then migrated through the grounds and surrounding rock (limestone and sandstone) impregnated. Pedas is located in t he vicinity of Seremban Fault Zone that lies w ithin the West Belt Granite intrusion. Alexander (1968) revealed that the structural geology in the igneous rock of Pedas area w as dominated by granites w ith typically medium to coarse grained rocks, often porphyritic. Based on the Negeri Sembilan geological map, the location of site investigation is part of the main fault zone that is controlled by meta-sediment and granite rocks. Soil structure around hot spring w ith typically saturated soil. It comprises of sandstone, silty sandy gravel, and granite (bedrock), as w as confirmed by Ham izah (2016) on the study of Electrical resistivity imaging (2D and 3D) and Geochemical study in the hot spring area in Pedas.
Soil type depends on the parent rock type of the basin, although variations may occur over small distance due to differences in local condition. The bed rock in the study area is overlain by alluvial deposits of red and yellow lateritic clay, sand and gravel. The alluvium is quite deep in certain areas especially along the hills due to aggregation and tin mining activities. The alluvial deposits, especially along the rivers are composed of gray clay and peat. M ore areas under lat erite are found along the southw est ern coast of the stat e (Nather Khan and M ustafa, 2010). Geological genesis of hot spring formation at Pedas is still studied by experts.

Exper i m ent al W or k
The M ASW measurements w ere carried out along 52 stations in the study area. The stations w ere select ed based on data picking and frequencies to obtain best a curve fit. In this study, six sam ples w ere collected for use in M ASW dispersion Inversion. Figure 2 show s t he arrangement of 24 channels geophones using the spacing of 5 m and set 1 m inter-distance is used for recording data and the total length w as 23 m. The energy source w as set at 15 m offsets. The data w ere recorded using the sam pling rate of 1 ms. The data w ere recorded by Commercial Instruments (TERRA LOOK M K-8).
There are tw o main procedure involve in MASW data processing technique adopted in this study : generation of dispersion curves (frequency vs. phase velocity plots), and inversion of dispersion curves to estimate S-w ave velocities (Roy , 2013). The theoretical dispersion curve is calculated from random parameters given by the NA (forw ard problem) and then the number of layers to invert is chosen. There are four parameters to invert: P-w ave velocity (Vp), Poisson ratio, S-w ave velocity (Vs) and depth. Density w as held constant at 2000 kg/m3 (Table 1). It w as found that the choice of Vp did not have much influence on the inversion process.
Through trial-and-error, a three-layer model appeared to provide best fit to the data set. Finally, the misfit betw een the t heoretical dispersion curve and recorded data is evaluated. The depth to soil layer value is determined for each site as the depth to the boundary of layer 1 and layer 2. The best fit model of dispersion inversion for this study comprises of 3 layers (as seen in Table  1). Layer 1 and 2 of the model fit to the geological setting of soil structure around hot spring w ith typically saturated soil, comprises of sandstone, silty sandy gravel, and granite (bedrock).
All model inversions w ere conduct ed using Geopsypack w in32 v. 2.10.1. A neighbourhood algorithm applied in Dinver softw are is used to different models and finding the misfit of each one compared w ith the experimental dispersion curve.
Active-source experiments are processed w ith a fk technique. At the sam e location, the various shots available are stacked together w ith time. The various shot locations are combined to get standard deviations on dispersion curves usually picked w ithout error estimates (Wathelet, 2014). These uncertainties are analogous to those derived from am bient vibrations (stationary in time view ed as a random variation of source locations). Figure 3 show s that each dispersion curve have a chance in source effects of surface w aves. The signal to noise ratio is a measure of high am plitude w ave energy at a given frequency, w hich assist s in dispersion curve picking. The picking is automatically adjusted to the maximized the fk output.

Result and Di scussi on
By selecting the low est frequency on dispersion curve at six stations (Figure 3), this survey estimated approximately 15 to 59 m deep accurately (based on the equation 2) and the estimated results are show n in Table 2. Figures 4a and 4b show s linearity dispersion curve (relationship w ave number k w ith depth d and phase velocity Vw ), w hich caused by the homogeneity of the material beneath the surface, both the profiles above show s similar patterns. This can be observed w hen w e compare the upper soil layers (top soil) w ith low er layer (bedrock). In addition, the curve w hich gives the best fit to the measured data can provides information regarding maximum depth, and also interpretation at boundary inter-layers.
M oreover, both profiles show ed a significant correlation w ith R2 of each 0.954 and 0.939, in w hich the curve gives the best fit to the measured data to determine the boundary and depth of each layers. M oreover, it indicates that the similarity of material, specifically a soils layer around the survey area. The dependence phase velocity and depth distribution on w avenumber has been conducted by Chik et al. (2011). It show s t he linearity of frequency and phase velocity versusw ave-number relationship. The theoretical dispersion reveals consistent shear w ave velocity profile in the evaluation of near surface soil properties. Specifically to implement a w ide variety of geotechnical investigations, including pavements, solid w aste landfills, and sea beds profile.      Based on the refraction survey, dispersion curve (Figure 5a) show s the w ave velocity range from 255 m/s to 300 m/s in the unsaturated soil zone at the depth of 8m (w ater table level). Below t he w ater table, the w ave velocity continues to decrease till the depth of 18.0 m, due to the effect of critically refracted w aves. In the transition zone w hich is located below the w at er table, the velocity refers to an apparent velocity as w as studied by Godio et al. (2010). The data in joint inversion of fk analysis show s t hree different soil zones : the upper part of the unsaturated soil zone at a depth of 2 to 8 m w ith Vp of 240 to 255 m/s, saturated soil zone at a depth of 8 to 18 m w ith Vp of 255 to 300 m/s and in the intermediate zones (estimated as partially saturated soil zone) at a depth of 18 to 30 m w ith Vp of 300 to 390 m/s. In intermediate zone the response is very sensitive to different saturation conditions due to the groundw ater fluctuation and the different distribution of the w ater below the w ater table level.
The model (Figure 5b) show s a constant layer for at least 2 meters deep w ith phase velocity (Vp) of 255 m/s. In addition, Figure 5c agrees w ith a constant first layer up to around 8 meters deep. An increase in the dept h of the shear w ave velocity dispersion curves, particularly at a depth of 8 meters is caused by the presence of w ater table level and solid layers. Cross-section in Figure 5b show s overlapping of profile lines, this is due to noise interference around the survey area.
The tw o layers for P-and S-w ave velocities (Figures 6) of the inverted profile fit the model indicated by red colours. The possible param eter range is indicated by the region that is covered by models. The corresponding depth models are plotted in Figures 5 and 6. The compressional w ave velocities reach 500 m/s to 2000 m/s w ith a velocity at depths of 20 m. Discontinuity zone is found at about 30m deep. While, Shear w ave velocities range from200 m/s to 600 m/s and as w ell as at depths of approximately 20 m to 30 m, this is interpreted as a discontinuity zone. At depth of 30 m up to low er layer show s constant velocity, either Vp or Vs. These indicates that both Vp and Vs profiles has materials of homogeneities at depth dow n of 30 m.  Figure 7a and 7b show s Joint inversion of slow ness and ellipticity H/V (Slow ness indicates frequency dependent group and phase velocity) and ellipticity curves are then simultaneously invert ed to get the shear w ave velocities. Extracted ellipticities provided information w ithin the frequency band from 6 to 40 Hz, shear -w ave velocit ies are better constrained over larger depths than by using inversion of dispersion curve alone. How ever, even though such joint inversion provides the general shape of shear-w ave velocity structure w ithin sediments, bedrock depth is not constrained. In addition, the true ellipticity may also contain a smooth peak in case of gradual increase of the velocity w ith depth. Figure 7a show s slow ness drastically increase w ith frequency, particularly at frequency of 20 Hz. This relationship indicates the presence of low ervelocity layers overlying a zone w ith a significant velocity decrease w ith depth.
An additional contribution to the analysis can be provided by the inversion of the ellipticity curve obtained as the result of the seismic noise analysis by using the tool dinver available in Geopsy package. The important assumption of this technique is t hat the analyzed w ave field is mainly characterized by Rayleigh w aves.
The fundam ental and first higher mode in Figure  7b could be consistently explained w ith a common mode. Nguyen et al, 2009 opined that interpretation of the first higher mode is correct, since other associations to even higher modes could not be consistent ly fitted.
, generally is connected to deep penetration. As it w as reported by Babuska and Cara (1991) that longer w avelengths penetrat e deeper than shorter w avelengths for a given mode, generally exhibit greater phase velocity, and are more sensitive to the elastic properties of the deeper layer. Shorter w avelengths are sensitive to the physical properties of surficial layers. Correlation w as conducted in the w avelength rather than frequency domain, because w avelength is relat ed more closely to depth of interest (M artin and Diehl , 2004).
Figure 7 a) Contain the distribution curves for the fundamental Rayleigh mode and inversion results at array station D b) of the ellipticity inversion that is adopted from station D. Observed curves used in the inversion are in black and the colour distinguishes the misfit value. Red and yellow colours represent optimal models w ith smallest misfits. Figure 8 show s t he M ASW Rayleigh dispersion curve obtained for stations A to F as function of the phase velocity and the w avelength; as the w avelength reflects more closely at the dept h of penetration.
Curve of the model analysis in the phase velocity to w ave length could be a suitable approach to estimate the geometric specifications of the soil layers, especially for the soil layers w ith a clear contrast betw een t he sedimentary cover (Top soil) and bedrock. These allegation w as very strong w ith the result s of the correlation coefficient (R2) of a six stations by high significantly values w hich are 0.918, 0.904 ,0.867, 0.855 , 0.915 and 0.945, respectively. The result s obtained from the regression analysis are in agreement w ith dispersion curve interpretation in test site w ith low percentage error as show s in Table 3. M oreover, the similarities betw een the equations in the studied sites are good evidence for the utilization of this method in the geotechnical site investigation.
Correlation betw een the experimental Rayleigh dispersion curve (phase velocity versus w avelength) and the Vs ground model (shear w ave velocity versus depth) estimated from Rayleigh dispersion inversion w as observed, and they confirm that these non-invasive techniques are useful in evaluating the Vs ground profile.

Conclusi on
From the overview above, the M ASW dispersion curves have successfully applied on characterizing and evaluating boundaries and depth that have significant implication in both geotechnical and engineering applications. Particularly in comparison w ith conventional drilling, it is cheap and provides the benefit of precision. It is suitable for estimating the subsurface shear and compression w ave velocity profile over a large area.
The utilization of linear regression of tw o explicit empirical relationships for w avelength phase velocity and w ave number versus depth and phase velocity has a good matching (best fit curve) and both relationships w ere recommended for correcting and estimation Rayleigh dispersion curve of soil structure due to the higher value of R2.
This confirms that relationship pattern of fk (frequency w ave number) dispersion curves is a good interpretation method for understanding the soil layers of the investigated area. Acknow ledgem ent s First of all w e thank to the Directorate General of Higher Education (DGHE) of Indonesia w ho has giving us scholarship. The field support from colleague of Postgraduate student and technical staff of Geophysics Programme, School of Physics, Universiti Sains M alaysia is highly appreciated.