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Modal analysis of Rayleigh waves using classical MASW-MAM approach: Site investigation in a reclaimed land
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Soil Dynamics and Earthquake Engineering journal homepage: http://www.elsevier.com/locate/soildyn
Modal analysis of Rayleigh waves using classical MASW-MAM approach: Site investigation in a reclaimed land Palanidoss Subramaniam a, Zhang Yunhuo a, b, Yannick C.H. Ng a, William Danovan c, Taeseo Ku a, * a b c
Department of Civil and Environmental Engineering, National University of Singapore, Singapore Geotechnical and Tunnel Division, Land Transport Authority of Singapore, Singapore Thomson-East Coast Line Group, Land Transport Authority of Singapore, Singapore
A R T I C L E I N F O
A B S T R A C T
Keywords: Multimodal joint inversion MASW MAM HVSR Cross-hole tomography
Surface wave tests such as the multi-channel analysis of surface waves (MASW) and microtremor array mea surements (MAM) offer a fast and convenient way of measuring the shear wave velocity (Vs) of the ground for geotechnical site investigation due to their non-intrusive nature. However, it has been widely reported that the accuracy and resolution of the Vs profile depend on the construction of the dispersion image and its interpre tation. While many advanced computational techniques have been proposed to process surface waves into a final Vs profile, we opted for the classical ‘picking and inverting’ approach in the current study. This is in view of the lower required computation power as well as the relatively uniform geology of the site. Surface wave tests (MASW, MAM and horizontal-to-vertical spectral ratio) were carried out at a remote reclaimed land in Singapore. A systematic methodology for the modal analysis of Rayleigh waves based on combined MASW and MAM tests is presented. The MAM dispersion image was constructed using the phase shift method, the extended spatial autocorrelation (ESAC), and the refraction microtremor (ReMi) method but a meaningful dispersion curve could only be obtained using the phase shift. Due to the modes of energy in the low frequency regime being unclear in the dispersion image, an idealized synthetic model of the site was set up to guide the mode identification process. The combined dispersion curve and HVSR profile were jointly inverted to construct the final Vs profile, which agreed quite well with the seismic cross-hole tomography experiments and bore-log information. It is also demonstrated that the inversion of the fundamental mode alone led to slight errors and low resolution in the final velocity profile, even for such a simple soil stratigraphy.
1. Introduction Shear wave velocity (Vs) is one of the important site assessment and design parameters in geotechnical and earthquake engineering. Invasive geophysical tests such as cross-hole experiments, seismic cone pene tration test, down-hole seismic test, and up-hole seismic test are commonly carried out to determine the Vs profile of the site. Noninvasive surface wave methods such as Multi Channel Analysis of Sur face Waves (MASW) and Microtremor Array Measurements (MAM) (traditionally known as Active and Passive MASW) are also widely used to evaluate the Vs of the ground due to their relatively fast deployment on site. Though the theoretical framework of surface wave propagation was established in the early 20th century, their engineering applications
were established in the 1950s [33]. In the 1980s, Rayleigh wave dispersion curves were used to determine the thickness of pavements, shear wave velocity of structure above the basement and pavement moduli [3,31,54]. With the advancements in computing power, MASW and MAM methods became popular among the geotechnical and geophysics community [50,60,74]. The MASW is a multichannel extension of a widely used surface wave method called the Spectral Analysis of Surface Waves that generally uses a two-receiver approach [55,68]. The merits and wider range of applications of the MASW and MAM methods in geotechnical & earthquake engineering have been well documented ([18,22,28,29,34,37,38,43,51–53,59,66]). The classical approach to MASW /MAM, which is the focus of the current study, consists of three main steps: (1) recording multichannel seismic data, (2)
* Corresponding author. E-mail addresses: [email protected] (P. Subramaniam), [email protected], [email protected] (Z. Yunhuo), [email protected] (Y.C.H. Ng), [email protected] (W. Danovan), [email protected] (T. Ku). https://doi.org/10.1016/j.soildyn.2019.105902 Received 18 July 2019; Received in revised form 9 October 2019; Accepted 11 October 2019 0267-7261/© 2019 Elsevier Ltd. All rights reserved.
Please cite this article as: Palanidoss Subramaniam, Soil Dynamics and Earthquake Engineering, https://doi.org/10.1016/j.soildyn.2019.105902
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Fig. 1. (a) Satellite view of the Changi East Reclamation Project, whose boundary is delineated in green, (b) Satellite view of the site for the field test. The data from three boreholes, namely #1, #2 and #3 was used for site investigation.
generating the dispersion image and extracting dispersion curves and finally, (3) inverting these dispersion curves into a 1D shear wave ve locity (Vs) profile [69]. Numerous recommendations are available on the use of various data acquisition system, geophone type, array shape, array size, and recording duration ([69,73]). The most common methods to construct dispersion images include phase shift method [62], Cross-correlation, Spatially Autocorrelation method (SPAC) [1], Extended or Modified Spatial Autocorrelation method (ESAC /ESPAC /MSPAC) ([5,58]), slowness-frequency (p–f) analysis i.e., Refraction Microtremor (ReMi) [39]. These dispersion images are often represented in frequency-wave number (f–k) domain ([10,20,35,70]), intercept time -slowness (τ–p) domain ([19,72]), slowness–frequency (p–f) domain [47], frequency– phase velocity (f–v) domain [62]. The imaging method and resolution quality significantly affect the final shear wave velocity profile [62]. For instance, Don (2011) [21] reported that the SPAC method provides higher resolution and a wider frequency range than the f–k method. The identification of the dispersion curve corresponding to various modes, i.e., the fundamental mode and the subsequent higher modes, is an essential part of the analysis as it directly influences the accuracy of the Vs profile. While many studies have focused on the inversion of the fundamental mode dispersion curve, it is less common to perform multimodal inversion due to the ambiguity in picking the various modes. Xia et al. (2000) [75] reported the benefits of computing the Vs profile from the inversion of Rayleigh wave data with higher modes, which includes a greater investigation depth, a more stable inversion process and an increase in the resolution of the final Vs model. They also showed that any incorrect picking or misidentification of the modes would lead to an overestimate of the inverted velocity model since higher modes have higher phase velocities. Luo et al. (2007) [42] also compared the inversion results of synthetic data and concluded that the simultaneous inversion of the fundamental mode and two higher modes could achieve an almost perfect match to the Vs model as compared to the inverted fundamental mode alone. The causes of incorrect mode identification such as leaky mode contribution, mode jumping, mode kissing and misidentification of P-waves as Rayleigh waves are also documented in the literature (e.g. [27,48,57]). It is well established that the solution of the inversion process is non-
unique ([25,41]) and the accuracy of the Vs profile can be improved by constraining the problem ([4,9,32]). One of the methods is to invert the extracted dispersion curves together with Horizontal to Vertical Spectral Ratio HVSR ([9,63]). In this case, a single cost objective function or two distinct objective functions (for HVSR and dispersion curve) are used to calculate the misfit. Arai and Tokimatsu (2005) [2] performed the joint inversion of f–k based dispersion curve and HVSR to compare the Vs with PS log. Similarly, Parolai et al. (2005) [63] proposed the genetic algo rithm based joint inversion of dispersion curve and HVSR. However, these methods were often described as problematic due to the single cost objective function [11]. In order to solve this issue, Dal Moro (2010) [11] developed a multi-objective evolutionary algorithm to perform the joint inversion. To further improve the inversion solution, more advanced inversion techniques have been proposed such as the joint inversion of Rayleigh waves and Love waves (e.g. [13,44,49,76]), joint inversion of surface waves and refracted body waves (e.g. [8,30,65]), joint inversion of multi-components of surface waves (e.g. [14,15]), inversion using multimodal algorithms (e.g. [24,40,45,46,71]) and inversion of the full velocity spectrum (e.g. [12]). Nevertheless, it should be noted that the above-mentioned techniques are computationally demanding and may not be easily accessible to the practising engineer. In this paper, a site investigation study is herein presented whereby the critical issues encountered in the construction of dispersion image are discussed, eventually to establish a robust and straightforward interpretation framework. A workflow is proposed to identify corre sponding higher modes where apparent dispersion curves are ambig uous. With the aid of forward modelling, theoretical dispersion curves (the fundamental and higher modes) are generated based on the bore hole information to guide the mode identification process. A joint inversion is performed using the dispersion curve and HVSR through using a multi-objective evolutionary algorithm and, the final Vs profiles are compared with the results of a cross-hole tomography experiment. 2. History and description of the test site The field test was conducted on reclaimed land in the Eastern part of the Republic of Singapore. The reclamation works were part of a large offshore project called the Changi East Reclamation Project, whose aim 2
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Fig. 2. (a) Stratigraphy of the site and the SPT-N profiles, based on the three boreholes; (b) Acquisition geometry of MAM survey (50 m � 50 m) and active MASW survey line of 34.5 m length.
was to cater for the extension of the Changi International Airport and other infrastructural expansion in the area [6]. The reclamation project started in 1991, and it created about 20 km2 of land (delineated in Fig. 1 (a) by the green outline). Before the reclamation works, a comprehen sive site investigation and characterization program was conducted and it consisted of a seismic reflection survey, borehole sampling, in-situ, and laboratory testing [6]. It was found that the ground at the project area consists of four main layers, namely the upper marine clay, an in termediate layer of stiff silty clay and/or silty sand, lower marine clay and the cemented clayey sand layer of the Old Alluvium (OA). The marine clays in Singapore are quaternary deposits of estuarine, alluvial, littoral, and marine sediments that typically lie in valleys of Bukit Timah
Granite, Jurong Formation and Old Alluvium [67]. The Old Alluvium, on the other hand, consists mainly of medium to very dense sand, with lenses of silt and clay and is the result of rapid deposition by a braided river system of weathered materials from slopes of granite and low-grade metamorphic rock from Malaysia [64]. Bo et al. (2005) [6] reported that the thickness of the marine clay at the project site was found to vary from about 5 m to 55 m due to the undulations of the underlying Old Alluvium formation and non-uniform self-weight consolidation of the marine clay. The reclamation works were carried out by the hydraulic placement of 272,000,000 m3 of marine dredged sand on the seabed. While the mechanical properties of the soft and compressible marine clay layer were improved by a combination of 3
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middle of the geophone array coincides with the central borehole (#2). The impact energy was generated using a 7 kg sledgehammer at a source offset of 5.5 m from both ends of the geophones array. The data were acquired at a sampling frequency of 2 kHz for a duration of 2 s. The vertical stack shot gathered is shown in Fig. 3. For the MAM test, an Lshaped array of 11 geophones with a spacing of 10 m was formed and one leg of the L-shaped array coincided with the MASW test configu ration. The ambient noise was recorded for duration of about 1 h as shown in Fig. 4(a). In order to calculate the Horizontal-to-Vertical Spectral Ratio (HVSR), a three-component 4.5 Hz geophone (two hori zontal geophones each at East-West and North-South direction, one vertical component geophone) was placed closer to borehole #2. The stacked microtremor signals for each component are shown in Fig. 4(b).
Table 1 Properties of the Singapore marine clay collected from the site. Soil properties Permeability (m/s) by falling head method Plastic limit (%) Liquid Limit (%) Over-consolidation ratio Compression index Cc Recompression index Cr Undrained shear strength (kPa)
Borehole reference #1
#2
#3
2.25E-05
–
–
29.6–32.6 68.6–85.3 0.7–2.3 0.108–0.514 0.014–0.101 80.4–153.9
25.4–32.6 62.9–74.4 1.1–1.7 0.171–0.757 0.025–0.106 68.2–109.8
19.3–31.5 60.8–79.3 1.1–1.5 0.149–0.717 0.026–0.227 75.1–153.7
prefabricated vertical drains (PVD) installation and surcharge loading, the densification of the overlying sand fill layer was conducted by dy namic compaction, Müller resonance compaction, and vibroflotation. A satellite view of the test site is shown in Fig. 1(b). Boreholes were drilled at three locations (#1, #2, #3) to a depth of 120 m and with a centre-to-centre spacing of 25 m each along a straight line. The standard penetration test (SPT) was carried out up to a depth of 100 m and the SPT-N values were recorded at every 2.5 m. After drilling, a 75 mminner diameter polyvinyl chloride (PVC) casing was lowered in each borehole and grouted in place to facilitate the cross-hole tomography test. Based on the bore-log information, the soil profile along section XX’ and the SPT-N profile are shown in Fig. 2 (a). While the soft marine clay layer is about 35–40 m thick and interspersed by stiffer fluvial sand layers, the Old Alluvium (OA) layer is located at a depth of ~65 m. The SPT-N values generally increase with depth, with values less than 20 in the marine clay and reaching an SPT-N of 100 in the OA; local increases in SPT-N values are also observed in the fluvial sand layers. A summary of the marine clay properties is presented in Table 1.
3.2. Seismic cross-hole tomography Seismic cross-hole tomography was carried out by triggering an impact source inside borehole #1 and ‘listening’ to the propagated signal in borehole #2. The impact source was a Geotomographie BIS-SHDS electro-mechanical probe capable of producing both compression waves and horizontally polarized shear waves. It is powered by a Geo tomographie impulse generator IPG800 that supplies energy of 1000 J at a voltage of 800 V. The acquisition system consists of a Geotomographie Multi-station Borehole Acquisition System (MBAS) that is connected directly to a notebook via a USB interface. The MBAS comprises of a string of eight 30 Hz geophone stations, each individual station con taining three geophones in a triaxial orthogonal arrangement and a digitizer for the analog-to-digital conversion. For each shot, the signals were recorded for 1 s. The acquisition design for the cross-hole test is illustrated in Fig. 5. Basically, it comprises of several tomography blocks up to a depth of 40 m, overlapping each other by 4 m. Each tomography block consists of eight different shot positions, at an interval of 1 m depth, for a given position of the string of geophones. The acquisition depth was stopped at a depth of 40 m due to site constraints.
3. Test program 3.1. MASW test, MAM and HVSR The field data acquisition for the MASW and MAM tests was carried out using a 24-channel Geometrics Geode seismograph and 24 spiketype 4.5 Hz vertical-component geophones. The MAM array configura tion along with the borehole locations is shown in Fig. 2 (b). The MASW survey location (34.5 m length) is also indicated in Fig. 2 (b). The detailed testing configuration for the MASW test is shown in Fig. 3. The
4. Processing of measured seismic signals 4.1. Dispersion analysis of MASW and MAM test results For processing the seismic signals, we have opted for the traditional approach of picking and inverting the dispersion curve. A holistic
Fig. 3. Schematic for the MASW test. The source offset is 5.5 m and a constant geophone spacing of 1.5 m was used. A typical shot gather for the test is shown for a recording time of 2s. 4
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Fig. 4. Geophone signals corresponding to the (a) Microtremor Array Mea surements (b) three-component geophones (Vertical, North South and East West).
Fig. 6. Adopted multimodal approach for the processing of MASW and MAM raw signals.
Fig. 5. Schematic of seismic cross-hole test. One tomography block comprises of 8 different shot positions, at an interval of 1 m depth, for a given position of the receiver array. 5
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Fig. 7. MAM dispersion images obtained from (a) ReMi analysis (b) ESAC method.
Fig. 8. Dispersion images correspond to the (a) MASW test (b) MAM, obtained by phase-shift method (Park et al., 1999). The fundamental mode and possible higher modes are marked as white dots.
approach for the processing of MASW and MAM data is summarised in Fig. 6. Mainly, the work flow involves combining the MASW test and MAM dispersion curve and thereafter identifying the mode number through forward modelling. After the mode picking, a joint inversion is carried out to compute the final 1D velocity profile. During the initial analysis, MAM were processed by ReMi and ESAC methods to construct the dispersion image (Fig.7a–b). For ReMi analysis, each linear leg of Lshaped array was analysed separately in both forward and reverse di rection. Fig. 7(a) shows the average (forward and reverse direction) ReMi spectrum corresponding to the linear leg parallel to the line of boreholes. Similarly, the same geophone signals were used to construct the dispersion image by ESAC method. However, interestingly, both the ReMi and ESAC methods did not provide proper dispersion curves at this site, as shown in Fig. 7. The test site was located far from the road traffic /any cultural noise and the only considerable noise source was the nearby Changi Airport. Similarly, Gamal and Pullammanappallil (2011) [26] reported that at calm sites, the ReMi method did not provide good dispersion image to infer the dispersion curves, especially for shallow
surface investigations. The dominant unidirectional wave field might be the reason for the poor estimation by ESAC method. So, the geophone signals (MASW and MAM) were processed using the phase shift method proposed by Park et al. (1999) [60] to construct the dispersion image. The procedure essentially involves transforming the geophone signals from the time domain into the frequency domain using the Fast Fourier Transform and then calculating the phase velocity by applying an offset-dependent phase shift. Mathematically, the signals in the fre quency domain are integrated over the geophone offsets with respect to all apparent velocities. The constructed dispersion images for the MASW test and MAM are shown in Fig. 8(a)–(b) respectively. They are plotted in the RGB scale, with the amount of ‘redness’ being proportional to the energy distribution of the Rayleigh wave. The high-energy features are marked as white dots on the dispersion image. As expected, the range of frequencies with high-energy content is lower for the MAM (1–11 Hz) than for the MASW test (6–35 Hz) due to the low frequency content of microtremors that are generated from natural sources. The two disper sion images were then combined vertically by cutting off at 8 Hz, to 6
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whether they belong to the same mode because of mode jumping or, belong to two different modes such as the fundamental mode M0 and first mode M1. From the bore-log information, it was found that the Old Alluvium layer has a much higher SPT-N value than the overlying soft marine clay layer. This significant velocity contrast could potentially reduce the accuracy of mode identification and picking due to the overwhelming energy of higher modes or mode jumping [57] and ‘mode-kissing’ [27]. Due to these concerns, we resorted to forward modelling as a guide for mode identification, which is explained in section 5.1. 4.2. Horizontal to vertical spectral ratio (HVSR) The time-domain ambient noise signals are converted to Fourier spectra and the ratio of horizontal-to-vertical spectra is calculated as follows ([17,23]): sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�ffiffi S2NS þ S2EW H (1) ¼ V 2S2Z where, SNS, SEW and SZ are amplitude spectra of north-south, east-west and vertical component respectively. The calculated HVSR is shown in Fig. 10 and the resonant frequency of the ground is 0.88 Hz. This HVSR profile will be used together with the dispersion curve to perform the joint inversion.
Fig. 9. Combined MASW and MAM dispersion curve with a cut-off frequency at 8 Hz.
broaden the bandwidth of the dispersion curves and for more accurate model identification [61]. From Fig. 9, two very distinct bands of high energy can be observed: 1–6 Hz and 6–40 Hz. However, it is uncertain
Fig. 10. HVSR profile of test location in the reclaimed land at Changi.
Fig. 11. (a) Typical results of the seismic cross-hole test showing horizontal component-geophone signals for a shot triggered at a depth of 10 m. The first arrival times of P-waves and S-waves are labelled with a cross. (b) Final shear wave velocity tomogram after inversion. 7
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Fig. 12. (a) Idealized 4-layer representation of the site, with the Vs based on local geotechnical site investigation experience; (b) Synthetic traces obtained from forward modelling; (c) Synthetic dispersion image with the theoretical dispersion curves M0 to M3 superimposed; (d) Experimental dispersion image with the theoretical dispersion curves superimposed as dotted lines.
4.3. Tomography analysis for cross-hole test results
model are shown in different coloured lines in Fig. 12(c) and are also superimposed on the experimental velocity spectrum in Fig. 12(d) for comparison and mode identification. Fig. 12(c) and (d) show similar patterns, whereby the apparent dispersion curve is ambiguous at low frequencies whereas it becomes clearer and unique in the high frequency band i.e., above 10 Hz. The prominent feature of the synthetic model is that the four modes correspond to different distinct lines in the low frequency regime and start to merge beyond a frequency of about 20 Hz. The first band of energy (1–6 Hz) of the experimental dispersion curve coincides with the theoretical fundamental mode, and the second band (6–40 Hz) is closer to the theoretical 3rd higher mode and is labelled as M3. As demonstrated by the synthetic model, neither mode jumping nor mode kissing could be observed for this soil layer configuration. How ever, the higher mode M3 is found to be more overwhelming than M1 and M2, in terms of energy content. This is not surprising due to the strong velocity contrast of the underlying OA layer. The subsequent step is the inversion of the modes into a 1D-shear wave velocity profile.
An example of the geophone signals is shown in Fig. 11(a) for the cross-hole seismic source located at a depth of 10 m. It can be observed that for each signal, two sets of waves could be identified, that is P-wave and S-wave. The first arrival travel-time tomography technique was used to interpret the seismic signals. The first arrival times for P-waves and S-waves were picked manually (denoted by ‘ � ’ in Fig. 11(a)) and were compiled for inversion analysis. This was conducted using com mercial software GeoTomCG. The inversion process minimizes the dif ference between the assumed velocity model and the true velocity model through the root mean square (RMS) residual. More details about the inversion steps are available in Ng et al. (2018) [56]. The software adopts the simultaneous iterative reconstruction technique (SIRT) to perform inversions. In our study, it was found that the RMS residual reached a stable value after the 7th iteration, after which the velocity model did not change significantly. The final Vs tomogram is shown in Fig. 11(b). 5. Analysis and discussion
5.2. Multimodal joint inversion
5.1. Forward modelling based on borelog data
Based on the insight from the forward modelling output, joint inversion of the modes M0 and M3 was conducted through the Win MASW. The MATLAB based code uses a genetic algorithm (GA) devel oped by Dal Moro et al. (2007) [16] for the inversion analysis. In short, the proposed inversion approach involves performing several pre liminary and independent “parallel” runs and selecting the best indi vidual model results as the initial population for the final run. The Vs profile that corresponds to the lowest misfit (i.e., the best model in the final run) is selected. The final 1D Vs profile is shown in Figure 13. The 1D velocity profile obtained from MASW survey is the best representa tive of the ground conditions below the middle of the geophones array. This is based on the assumption that the ground stratigraphy does not
An idealized layered Vs model was setup in the aim to investigate the distribution of the theoretical dispersion energy. A sketch of the model with the assumed parameters is shown in Fig. 12(a). While the depths of the soil layers are obtained from the borehole information, the assumed shear wave velocities are typical values of Singapore soils based on local knowledge in geotechnical site investigations. Forward modelling was carried out using the software WinMASW. From the synthetic traces (shown in Fig. 12(b)), a velocity spectrum is produced and shown in Fig. 12(c). The theoretical dispersion curves obtained from the synthetic 8
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Fig. 13. (a) The 1D Vs profile obtained from the combined MASW and MAM, though the joint inversion of the modes M0 and M3. Also shown is the (1) inversion of the M0 mode, (2) sectional view Y–Y0 of the velocity model computed from the seismic cross-hole test, (3) extrapolated SPT-N profile and (4) geological profile of the middle borehole #2; (b) close-up view of the 1D Vs profile up to the depth of cross-hole test.
vary significantly in the lateral direction.
distribution of the ground because the whole region between the sourceborehole and receiver borehole is fully scanned by the seismic waves. As shown in Figure 13, there is generally a good agreement between the Vs profiles of the combined MASW - MAM test and cross-hole test for the first 40 m. Some minor discrepancies are observed around 24 m where the M0þM3 joint inversion and M0 inversion do not capture the decrease in the Vs that corresponds to the slow marine clay layer. However, the joint inversion seems to provide a hint on the low velocity layer. The overall trend that can be discerned from the M0þM3 joint inversion and M0 inversion is that the variation in Vs over the first 70 m is small (~80 m/s), with a significant increase of about 400 m/s occur ring thereafter due to the faster Old Alluvium layer. The mismatch be tween the depth of this significant increase in Vs and the start of the OA layer (as indicated by borehole #2) can be attributed to the assumption of 1D laterally homogenous profile whereas the actual interface of OA and soft marine clay might vary. It is thus possible that the MASW test and MAM are returning an average depth of the OA layer under the array of geophones. Site investigation results reported by Bo et al. (2012) [7] in the same region revealed severe undulations of the OA layer, indi cating that local variations in the OA could be present between our three boreholes. Lateral variations in a medium could lead to a false-depth related dispersion if a horizontally layered medium is assumed for the dispersion analysis, as reported by Lin & Lin (2007) [36]. The MASW profile is now qualitatively compared to the SPT-N pro file of borehole #2. It is observed in Fig. 2 (a) that the SPT-N value is equal to 100 at a depth of 75 m and beyond. By definition, the SPT-N value refers to the number of blows required to reach a penetration of 300 mm. When a blow count of 100 is achieved at a penetration less than 300 mm (which is often the case in very stiff soils like OA), it is a common practice to report a limiting value of 100 alongside the
5.3. Joint inversion of dispersion curve and HVSR The apparent dispersion curve obtained from the combined MASW and MAM dispersion image together with the HVSR, was inverted to generate a Vs profile. The joint inversion was performed in the win MASW [11]. The multi-objective evolutionary algorithm code uses the Pareto dominance criterion to perform the joint inversion [11]. In order to minimize the computational time, the HVSR curve was limited to the bell-shaped portion around the fundamental frequency. In the present study, 100 numbers of individual models and 100 numbers of genera tions were considered in the GA. However, it should be noted that the GA parameters need to be adjusted during the next run based on the misfit between the experimental dispersion curve and the dispersion curve after inversion. The Vs profile corresponding to the best GA model (corresponds to the lowest misfit) is plotted in Fig. 13. The Vs profile is selected based on the misfit calculated at each generation in the chosen population in the genetic algorithm. This involves considerable degree of uncertainty in the generation of final Vs profile. At each run, it may be difficult to obtain repeatable results. 5.4. Validation of MASW and MAM tests Borehole #2 was thus selected for validation purposes since it is the nearest borehole to the centre of the geophone array. Similarly, a 1D section Y–Y’ of the cross-hole test velocity model (shown in Fig. 11) was extracted due to its close proximity. The cross-hole test velocity profile is used herein to evaluate the accuracy of the MASW test in terms of the Vs values; the intrusive technique, would offer a more accurate Vs 9
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corresponding penetration depth (i.e., SPT refusal). For consistency, the values of SPT-N ¼ 100 in this study were extrapolated to a penetration depth of 300 mm. It must, however, be highlighted that while this approach is not ideal in itself, it does provide an indication of the rela tive penetration resistance. The final extrapolated profile (shown in Fig. 13) reveals the heterogeneous nature of the OA, which seems to be well captured by all the inversion methods. In general, the Vs profile seems to be quite consistent with the overall trend in the SPT-N. How ever, while the standard penetration test can identify the soft marine clay layers (as shown by the very low values of SPT-N), it is observed that the surface wave measurements are not so effective in detecting this change in soil type. This is probably due to the low impedance contrast between the fluvial sand and the marine clay layer, to which the active MASW measurements are not very sensitive. This is consistent with the flat dispersion curve at high frequencies, as shown in Fig. 8. Lastly, the importance of identifying and inverting the higher modes of the dispersion curve is highlighted: the experimental dispersion curve in Fig. 12(d) is inverted solely as the fundamental mode M0 for the sake of discussion and plotted in Fig. 13. While the overall trend in Vs closely resembles that of the M0-M3 joint inversion but with a lower resolution, it is noted in Fig. 13(b) that the M0 inversion underestimates the ve locity of the reclaimed sand by about 20% at the top 20 m. The joint inversion of an effective dispersion with HVSR method can therefore be used as a complementary method to confirm the mode identification.
the Land Transport Authority of Singapore and from Ryobi Geo technique Singapore for their logistical support in planning for this field test as well as during the testing phase. We are also grateful to Dr. Moon Sung Woo and Mr. Vinoth Ganapathiraman for their help during the field test. This project is supported by the Ministry of National Devel opment (MND) under its Land and Liveability National Innovation Challenge (L2 NIC) Awards No. (L2NICCFP2-2015-2). References [1] Aki K. Space and time spectra of stationary stochastic waves, with special reference to microtremors. Bull Earthq Res Inst 1957;35:415–56. [2] Arai H, Tokimatsu K. S-wave velocity profiling by joint inversion of microtremor dispersion curve and horizontal-to-vertical (H/V) spectrum. Bull Seismol Soc Am 2005;95(5):1766–78. https://doi.org/10.1785/0120040243. [3] Asten MW, Henstridge JD. Array estimators and the use of microseisms for reconnaissance of sedimentary basins. 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6. Summary and conclusion This paper presented the results of a geophysical site investigation that was carried out on reclaimed land in the Eastern part of Singapore. The case study was centred on the combined use of MASW test, MAM and HVSR technique; with the joint inversion of the dispersion curves and HVSR profile to produce the final 1D Vs profile. Meaningful dispersion images were successfully constructed using the phase shift method where ESAC and ReMi methods fail due to the remote location and unidirectional wave field. Simple work flow was proposed to identify the relevant modes of energy from the combined dispersion image. From the dispersion image, it was observed that the maximum spectral energy is better defined at high frequencies than at the lower frequencies. Two modes with high-energy content could be distin guished in the low frequency region, but, it was difficult to ascertain their modal identity due to the presence of a high velocity contrast layer; i.e., Old Alluvium that underlies the test site. Based on a synthetic elastic model of the site stratigraphy, theoretical dispersion curves were generated to give an indication of the different modes. Then, the fundamental mode M0 and 3rd higher mode M3 were identified suc cessfully from the dispersion image and were jointly inverted into a 1D Vs profile. The latter agreed well with the bore-log information and the results of a seismic cross-hole tomography test conducted at the same site. The experimental dispersion curves were also inverted as the fundamental mode to highlight the importance of higher mode picking. Joint inversion of effective dispersion curve and HVSR provides a similar Vs profile as obtained from the combined M0-M3 inversion, but with the additional information on low velocity layers. Despite the simple geol ogy of the site, it was shown that the sole inversion of the fundamental mode leads to slight inaccuracies and low resolution in the 1D Vs profile. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements We sincerely thank our collaborators from the Geotechnical and Tunnels Division of the Infrastructure Design and Engineering Group at 10
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Modal analysis of Rayleigh waves using classical MASW-MAM approach: Site investigation in a reclaimed land Palanidoss Subramaniam a, Zhang Yunhuo a, b, Yannick C.H. Ng a, William Danovan c, Taeseo Ku a, * a b c
Department of Civil and Environmental Engineering, National University of Singapore, Singapore Geotechnical and Tunnel Division, Land Transport Authority of Singapore, Singapore Thomson-East Coast Line Group, Land Transport Authority of Singapore, Singapore
A R T I C L E I N F O
A B S T R A C T
Keywords: Multimodal joint inversion MASW MAM HVSR Cross-hole tomography
Surface wave tests such as the multi-channel analysis of surface waves (MASW) and microtremor array mea surements (MAM) offer a fast and convenient way of measuring the shear wave velocity (Vs) of the ground for geotechnical site investigation due to their non-intrusive nature. However, it has been widely reported that the accuracy and resolution of the Vs profile depend on the construction of the dispersion image and its interpre tation. While many advanced computational techniques have been proposed to process surface waves into a final Vs profile, we opted for the classical ‘picking and inverting’ approach in the current study. This is in view of the lower required computation power as well as the relatively uniform geology of the site. Surface wave tests (MASW, MAM and horizontal-to-vertical spectral ratio) were carried out at a remote reclaimed land in Singapore. A systematic methodology for the modal analysis of Rayleigh waves based on combined MASW and MAM tests is presented. The MAM dispersion image was constructed using the phase shift method, the extended spatial autocorrelation (ESAC), and the refraction microtremor (ReMi) method but a meaningful dispersion curve could only be obtained using the phase shift. Due to the modes of energy in the low frequency regime being unclear in the dispersion image, an idealized synthetic model of the site was set up to guide the mode identification process. The combined dispersion curve and HVSR profile were jointly inverted to construct the final Vs profile, which agreed quite well with the seismic cross-hole tomography experiments and bore-log information. It is also demonstrated that the inversion of the fundamental mode alone led to slight errors and low resolution in the final velocity profile, even for such a simple soil stratigraphy.
1. Introduction Shear wave velocity (Vs) is one of the important site assessment and design parameters in geotechnical and earthquake engineering. Invasive geophysical tests such as cross-hole experiments, seismic cone pene tration test, down-hole seismic test, and up-hole seismic test are commonly carried out to determine the Vs profile of the site. Noninvasive surface wave methods such as Multi Channel Analysis of Sur face Waves (MASW) and Microtremor Array Measurements (MAM) (traditionally known as Active and Passive MASW) are also widely used to evaluate the Vs of the ground due to their relatively fast deployment on site. Though the theoretical framework of surface wave propagation was established in the early 20th century, their engineering applications
were established in the 1950s [33]. In the 1980s, Rayleigh wave dispersion curves were used to determine the thickness of pavements, shear wave velocity of structure above the basement and pavement moduli [3,31,54]. With the advancements in computing power, MASW and MAM methods became popular among the geotechnical and geophysics community [50,60,74]. The MASW is a multichannel extension of a widely used surface wave method called the Spectral Analysis of Surface Waves that generally uses a two-receiver approach [55,68]. The merits and wider range of applications of the MASW and MAM methods in geotechnical & earthquake engineering have been well documented ([18,22,28,29,34,37,38,43,51–53,59,66]). The classical approach to MASW /MAM, which is the focus of the current study, consists of three main steps: (1) recording multichannel seismic data, (2)
* Corresponding author. E-mail addresses: [email protected] (P. Subramaniam), [email protected], [email protected] (Z. Yunhuo), [email protected] (Y.C.H. Ng), [email protected] (W. Danovan), [email protected] (T. Ku). https://doi.org/10.1016/j.soildyn.2019.105902 Received 18 July 2019; Received in revised form 9 October 2019; Accepted 11 October 2019 0267-7261/© 2019 Elsevier Ltd. All rights reserved.
Please cite this article as: Palanidoss Subramaniam, Soil Dynamics and Earthquake Engineering, https://doi.org/10.1016/j.soildyn.2019.105902
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Fig. 1. (a) Satellite view of the Changi East Reclamation Project, whose boundary is delineated in green, (b) Satellite view of the site for the field test. The data from three boreholes, namely #1, #2 and #3 was used for site investigation.
generating the dispersion image and extracting dispersion curves and finally, (3) inverting these dispersion curves into a 1D shear wave ve locity (Vs) profile [69]. Numerous recommendations are available on the use of various data acquisition system, geophone type, array shape, array size, and recording duration ([69,73]). The most common methods to construct dispersion images include phase shift method [62], Cross-correlation, Spatially Autocorrelation method (SPAC) [1], Extended or Modified Spatial Autocorrelation method (ESAC /ESPAC /MSPAC) ([5,58]), slowness-frequency (p–f) analysis i.e., Refraction Microtremor (ReMi) [39]. These dispersion images are often represented in frequency-wave number (f–k) domain ([10,20,35,70]), intercept time -slowness (τ–p) domain ([19,72]), slowness–frequency (p–f) domain [47], frequency– phase velocity (f–v) domain [62]. The imaging method and resolution quality significantly affect the final shear wave velocity profile [62]. For instance, Don (2011) [21] reported that the SPAC method provides higher resolution and a wider frequency range than the f–k method. The identification of the dispersion curve corresponding to various modes, i.e., the fundamental mode and the subsequent higher modes, is an essential part of the analysis as it directly influences the accuracy of the Vs profile. While many studies have focused on the inversion of the fundamental mode dispersion curve, it is less common to perform multimodal inversion due to the ambiguity in picking the various modes. Xia et al. (2000) [75] reported the benefits of computing the Vs profile from the inversion of Rayleigh wave data with higher modes, which includes a greater investigation depth, a more stable inversion process and an increase in the resolution of the final Vs model. They also showed that any incorrect picking or misidentification of the modes would lead to an overestimate of the inverted velocity model since higher modes have higher phase velocities. Luo et al. (2007) [42] also compared the inversion results of synthetic data and concluded that the simultaneous inversion of the fundamental mode and two higher modes could achieve an almost perfect match to the Vs model as compared to the inverted fundamental mode alone. The causes of incorrect mode identification such as leaky mode contribution, mode jumping, mode kissing and misidentification of P-waves as Rayleigh waves are also documented in the literature (e.g. [27,48,57]). It is well established that the solution of the inversion process is non-
unique ([25,41]) and the accuracy of the Vs profile can be improved by constraining the problem ([4,9,32]). One of the methods is to invert the extracted dispersion curves together with Horizontal to Vertical Spectral Ratio HVSR ([9,63]). In this case, a single cost objective function or two distinct objective functions (for HVSR and dispersion curve) are used to calculate the misfit. Arai and Tokimatsu (2005) [2] performed the joint inversion of f–k based dispersion curve and HVSR to compare the Vs with PS log. Similarly, Parolai et al. (2005) [63] proposed the genetic algo rithm based joint inversion of dispersion curve and HVSR. However, these methods were often described as problematic due to the single cost objective function [11]. In order to solve this issue, Dal Moro (2010) [11] developed a multi-objective evolutionary algorithm to perform the joint inversion. To further improve the inversion solution, more advanced inversion techniques have been proposed such as the joint inversion of Rayleigh waves and Love waves (e.g. [13,44,49,76]), joint inversion of surface waves and refracted body waves (e.g. [8,30,65]), joint inversion of multi-components of surface waves (e.g. [14,15]), inversion using multimodal algorithms (e.g. [24,40,45,46,71]) and inversion of the full velocity spectrum (e.g. [12]). Nevertheless, it should be noted that the above-mentioned techniques are computationally demanding and may not be easily accessible to the practising engineer. In this paper, a site investigation study is herein presented whereby the critical issues encountered in the construction of dispersion image are discussed, eventually to establish a robust and straightforward interpretation framework. A workflow is proposed to identify corre sponding higher modes where apparent dispersion curves are ambig uous. With the aid of forward modelling, theoretical dispersion curves (the fundamental and higher modes) are generated based on the bore hole information to guide the mode identification process. A joint inversion is performed using the dispersion curve and HVSR through using a multi-objective evolutionary algorithm and, the final Vs profiles are compared with the results of a cross-hole tomography experiment. 2. History and description of the test site The field test was conducted on reclaimed land in the Eastern part of the Republic of Singapore. The reclamation works were part of a large offshore project called the Changi East Reclamation Project, whose aim 2
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Fig. 2. (a) Stratigraphy of the site and the SPT-N profiles, based on the three boreholes; (b) Acquisition geometry of MAM survey (50 m � 50 m) and active MASW survey line of 34.5 m length.
was to cater for the extension of the Changi International Airport and other infrastructural expansion in the area [6]. The reclamation project started in 1991, and it created about 20 km2 of land (delineated in Fig. 1 (a) by the green outline). Before the reclamation works, a comprehen sive site investigation and characterization program was conducted and it consisted of a seismic reflection survey, borehole sampling, in-situ, and laboratory testing [6]. It was found that the ground at the project area consists of four main layers, namely the upper marine clay, an in termediate layer of stiff silty clay and/or silty sand, lower marine clay and the cemented clayey sand layer of the Old Alluvium (OA). The marine clays in Singapore are quaternary deposits of estuarine, alluvial, littoral, and marine sediments that typically lie in valleys of Bukit Timah
Granite, Jurong Formation and Old Alluvium [67]. The Old Alluvium, on the other hand, consists mainly of medium to very dense sand, with lenses of silt and clay and is the result of rapid deposition by a braided river system of weathered materials from slopes of granite and low-grade metamorphic rock from Malaysia [64]. Bo et al. (2005) [6] reported that the thickness of the marine clay at the project site was found to vary from about 5 m to 55 m due to the undulations of the underlying Old Alluvium formation and non-uniform self-weight consolidation of the marine clay. The reclamation works were carried out by the hydraulic placement of 272,000,000 m3 of marine dredged sand on the seabed. While the mechanical properties of the soft and compressible marine clay layer were improved by a combination of 3
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middle of the geophone array coincides with the central borehole (#2). The impact energy was generated using a 7 kg sledgehammer at a source offset of 5.5 m from both ends of the geophones array. The data were acquired at a sampling frequency of 2 kHz for a duration of 2 s. The vertical stack shot gathered is shown in Fig. 3. For the MAM test, an Lshaped array of 11 geophones with a spacing of 10 m was formed and one leg of the L-shaped array coincided with the MASW test configu ration. The ambient noise was recorded for duration of about 1 h as shown in Fig. 4(a). In order to calculate the Horizontal-to-Vertical Spectral Ratio (HVSR), a three-component 4.5 Hz geophone (two hori zontal geophones each at East-West and North-South direction, one vertical component geophone) was placed closer to borehole #2. The stacked microtremor signals for each component are shown in Fig. 4(b).
Table 1 Properties of the Singapore marine clay collected from the site. Soil properties Permeability (m/s) by falling head method Plastic limit (%) Liquid Limit (%) Over-consolidation ratio Compression index Cc Recompression index Cr Undrained shear strength (kPa)
Borehole reference #1
#2
#3
2.25E-05
–
–
29.6–32.6 68.6–85.3 0.7–2.3 0.108–0.514 0.014–0.101 80.4–153.9
25.4–32.6 62.9–74.4 1.1–1.7 0.171–0.757 0.025–0.106 68.2–109.8
19.3–31.5 60.8–79.3 1.1–1.5 0.149–0.717 0.026–0.227 75.1–153.7
prefabricated vertical drains (PVD) installation and surcharge loading, the densification of the overlying sand fill layer was conducted by dy namic compaction, Müller resonance compaction, and vibroflotation. A satellite view of the test site is shown in Fig. 1(b). Boreholes were drilled at three locations (#1, #2, #3) to a depth of 120 m and with a centre-to-centre spacing of 25 m each along a straight line. The standard penetration test (SPT) was carried out up to a depth of 100 m and the SPT-N values were recorded at every 2.5 m. After drilling, a 75 mminner diameter polyvinyl chloride (PVC) casing was lowered in each borehole and grouted in place to facilitate the cross-hole tomography test. Based on the bore-log information, the soil profile along section XX’ and the SPT-N profile are shown in Fig. 2 (a). While the soft marine clay layer is about 35–40 m thick and interspersed by stiffer fluvial sand layers, the Old Alluvium (OA) layer is located at a depth of ~65 m. The SPT-N values generally increase with depth, with values less than 20 in the marine clay and reaching an SPT-N of 100 in the OA; local increases in SPT-N values are also observed in the fluvial sand layers. A summary of the marine clay properties is presented in Table 1.
3.2. Seismic cross-hole tomography Seismic cross-hole tomography was carried out by triggering an impact source inside borehole #1 and ‘listening’ to the propagated signal in borehole #2. The impact source was a Geotomographie BIS-SHDS electro-mechanical probe capable of producing both compression waves and horizontally polarized shear waves. It is powered by a Geo tomographie impulse generator IPG800 that supplies energy of 1000 J at a voltage of 800 V. The acquisition system consists of a Geotomographie Multi-station Borehole Acquisition System (MBAS) that is connected directly to a notebook via a USB interface. The MBAS comprises of a string of eight 30 Hz geophone stations, each individual station con taining three geophones in a triaxial orthogonal arrangement and a digitizer for the analog-to-digital conversion. For each shot, the signals were recorded for 1 s. The acquisition design for the cross-hole test is illustrated in Fig. 5. Basically, it comprises of several tomography blocks up to a depth of 40 m, overlapping each other by 4 m. Each tomography block consists of eight different shot positions, at an interval of 1 m depth, for a given position of the string of geophones. The acquisition depth was stopped at a depth of 40 m due to site constraints.
3. Test program 3.1. MASW test, MAM and HVSR The field data acquisition for the MASW and MAM tests was carried out using a 24-channel Geometrics Geode seismograph and 24 spiketype 4.5 Hz vertical-component geophones. The MAM array configura tion along with the borehole locations is shown in Fig. 2 (b). The MASW survey location (34.5 m length) is also indicated in Fig. 2 (b). The detailed testing configuration for the MASW test is shown in Fig. 3. The
4. Processing of measured seismic signals 4.1. Dispersion analysis of MASW and MAM test results For processing the seismic signals, we have opted for the traditional approach of picking and inverting the dispersion curve. A holistic
Fig. 3. Schematic for the MASW test. The source offset is 5.5 m and a constant geophone spacing of 1.5 m was used. A typical shot gather for the test is shown for a recording time of 2s. 4
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Fig. 4. Geophone signals corresponding to the (a) Microtremor Array Mea surements (b) three-component geophones (Vertical, North South and East West).
Fig. 6. Adopted multimodal approach for the processing of MASW and MAM raw signals.
Fig. 5. Schematic of seismic cross-hole test. One tomography block comprises of 8 different shot positions, at an interval of 1 m depth, for a given position of the receiver array. 5
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Fig. 7. MAM dispersion images obtained from (a) ReMi analysis (b) ESAC method.
Fig. 8. Dispersion images correspond to the (a) MASW test (b) MAM, obtained by phase-shift method (Park et al., 1999). The fundamental mode and possible higher modes are marked as white dots.
approach for the processing of MASW and MAM data is summarised in Fig. 6. Mainly, the work flow involves combining the MASW test and MAM dispersion curve and thereafter identifying the mode number through forward modelling. After the mode picking, a joint inversion is carried out to compute the final 1D velocity profile. During the initial analysis, MAM were processed by ReMi and ESAC methods to construct the dispersion image (Fig.7a–b). For ReMi analysis, each linear leg of Lshaped array was analysed separately in both forward and reverse di rection. Fig. 7(a) shows the average (forward and reverse direction) ReMi spectrum corresponding to the linear leg parallel to the line of boreholes. Similarly, the same geophone signals were used to construct the dispersion image by ESAC method. However, interestingly, both the ReMi and ESAC methods did not provide proper dispersion curves at this site, as shown in Fig. 7. The test site was located far from the road traffic /any cultural noise and the only considerable noise source was the nearby Changi Airport. Similarly, Gamal and Pullammanappallil (2011) [26] reported that at calm sites, the ReMi method did not provide good dispersion image to infer the dispersion curves, especially for shallow
surface investigations. The dominant unidirectional wave field might be the reason for the poor estimation by ESAC method. So, the geophone signals (MASW and MAM) were processed using the phase shift method proposed by Park et al. (1999) [60] to construct the dispersion image. The procedure essentially involves transforming the geophone signals from the time domain into the frequency domain using the Fast Fourier Transform and then calculating the phase velocity by applying an offset-dependent phase shift. Mathematically, the signals in the fre quency domain are integrated over the geophone offsets with respect to all apparent velocities. The constructed dispersion images for the MASW test and MAM are shown in Fig. 8(a)–(b) respectively. They are plotted in the RGB scale, with the amount of ‘redness’ being proportional to the energy distribution of the Rayleigh wave. The high-energy features are marked as white dots on the dispersion image. As expected, the range of frequencies with high-energy content is lower for the MAM (1–11 Hz) than for the MASW test (6–35 Hz) due to the low frequency content of microtremors that are generated from natural sources. The two disper sion images were then combined vertically by cutting off at 8 Hz, to 6
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whether they belong to the same mode because of mode jumping or, belong to two different modes such as the fundamental mode M0 and first mode M1. From the bore-log information, it was found that the Old Alluvium layer has a much higher SPT-N value than the overlying soft marine clay layer. This significant velocity contrast could potentially reduce the accuracy of mode identification and picking due to the overwhelming energy of higher modes or mode jumping [57] and ‘mode-kissing’ [27]. Due to these concerns, we resorted to forward modelling as a guide for mode identification, which is explained in section 5.1. 4.2. Horizontal to vertical spectral ratio (HVSR) The time-domain ambient noise signals are converted to Fourier spectra and the ratio of horizontal-to-vertical spectra is calculated as follows ([17,23]): sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�ffiffi S2NS þ S2EW H (1) ¼ V 2S2Z where, SNS, SEW and SZ are amplitude spectra of north-south, east-west and vertical component respectively. The calculated HVSR is shown in Fig. 10 and the resonant frequency of the ground is 0.88 Hz. This HVSR profile will be used together with the dispersion curve to perform the joint inversion.
Fig. 9. Combined MASW and MAM dispersion curve with a cut-off frequency at 8 Hz.
broaden the bandwidth of the dispersion curves and for more accurate model identification [61]. From Fig. 9, two very distinct bands of high energy can be observed: 1–6 Hz and 6–40 Hz. However, it is uncertain
Fig. 10. HVSR profile of test location in the reclaimed land at Changi.
Fig. 11. (a) Typical results of the seismic cross-hole test showing horizontal component-geophone signals for a shot triggered at a depth of 10 m. The first arrival times of P-waves and S-waves are labelled with a cross. (b) Final shear wave velocity tomogram after inversion. 7
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Fig. 12. (a) Idealized 4-layer representation of the site, with the Vs based on local geotechnical site investigation experience; (b) Synthetic traces obtained from forward modelling; (c) Synthetic dispersion image with the theoretical dispersion curves M0 to M3 superimposed; (d) Experimental dispersion image with the theoretical dispersion curves superimposed as dotted lines.
4.3. Tomography analysis for cross-hole test results
model are shown in different coloured lines in Fig. 12(c) and are also superimposed on the experimental velocity spectrum in Fig. 12(d) for comparison and mode identification. Fig. 12(c) and (d) show similar patterns, whereby the apparent dispersion curve is ambiguous at low frequencies whereas it becomes clearer and unique in the high frequency band i.e., above 10 Hz. The prominent feature of the synthetic model is that the four modes correspond to different distinct lines in the low frequency regime and start to merge beyond a frequency of about 20 Hz. The first band of energy (1–6 Hz) of the experimental dispersion curve coincides with the theoretical fundamental mode, and the second band (6–40 Hz) is closer to the theoretical 3rd higher mode and is labelled as M3. As demonstrated by the synthetic model, neither mode jumping nor mode kissing could be observed for this soil layer configuration. How ever, the higher mode M3 is found to be more overwhelming than M1 and M2, in terms of energy content. This is not surprising due to the strong velocity contrast of the underlying OA layer. The subsequent step is the inversion of the modes into a 1D-shear wave velocity profile.
An example of the geophone signals is shown in Fig. 11(a) for the cross-hole seismic source located at a depth of 10 m. It can be observed that for each signal, two sets of waves could be identified, that is P-wave and S-wave. The first arrival travel-time tomography technique was used to interpret the seismic signals. The first arrival times for P-waves and S-waves were picked manually (denoted by ‘ � ’ in Fig. 11(a)) and were compiled for inversion analysis. This was conducted using com mercial software GeoTomCG. The inversion process minimizes the dif ference between the assumed velocity model and the true velocity model through the root mean square (RMS) residual. More details about the inversion steps are available in Ng et al. (2018) [56]. The software adopts the simultaneous iterative reconstruction technique (SIRT) to perform inversions. In our study, it was found that the RMS residual reached a stable value after the 7th iteration, after which the velocity model did not change significantly. The final Vs tomogram is shown in Fig. 11(b). 5. Analysis and discussion
5.2. Multimodal joint inversion
5.1. Forward modelling based on borelog data
Based on the insight from the forward modelling output, joint inversion of the modes M0 and M3 was conducted through the Win MASW. The MATLAB based code uses a genetic algorithm (GA) devel oped by Dal Moro et al. (2007) [16] for the inversion analysis. In short, the proposed inversion approach involves performing several pre liminary and independent “parallel” runs and selecting the best indi vidual model results as the initial population for the final run. The Vs profile that corresponds to the lowest misfit (i.e., the best model in the final run) is selected. The final 1D Vs profile is shown in Figure 13. The 1D velocity profile obtained from MASW survey is the best representa tive of the ground conditions below the middle of the geophones array. This is based on the assumption that the ground stratigraphy does not
An idealized layered Vs model was setup in the aim to investigate the distribution of the theoretical dispersion energy. A sketch of the model with the assumed parameters is shown in Fig. 12(a). While the depths of the soil layers are obtained from the borehole information, the assumed shear wave velocities are typical values of Singapore soils based on local knowledge in geotechnical site investigations. Forward modelling was carried out using the software WinMASW. From the synthetic traces (shown in Fig. 12(b)), a velocity spectrum is produced and shown in Fig. 12(c). The theoretical dispersion curves obtained from the synthetic 8
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Fig. 13. (a) The 1D Vs profile obtained from the combined MASW and MAM, though the joint inversion of the modes M0 and M3. Also shown is the (1) inversion of the M0 mode, (2) sectional view Y–Y0 of the velocity model computed from the seismic cross-hole test, (3) extrapolated SPT-N profile and (4) geological profile of the middle borehole #2; (b) close-up view of the 1D Vs profile up to the depth of cross-hole test.
vary significantly in the lateral direction.
distribution of the ground because the whole region between the sourceborehole and receiver borehole is fully scanned by the seismic waves. As shown in Figure 13, there is generally a good agreement between the Vs profiles of the combined MASW - MAM test and cross-hole test for the first 40 m. Some minor discrepancies are observed around 24 m where the M0þM3 joint inversion and M0 inversion do not capture the decrease in the Vs that corresponds to the slow marine clay layer. However, the joint inversion seems to provide a hint on the low velocity layer. The overall trend that can be discerned from the M0þM3 joint inversion and M0 inversion is that the variation in Vs over the first 70 m is small (~80 m/s), with a significant increase of about 400 m/s occur ring thereafter due to the faster Old Alluvium layer. The mismatch be tween the depth of this significant increase in Vs and the start of the OA layer (as indicated by borehole #2) can be attributed to the assumption of 1D laterally homogenous profile whereas the actual interface of OA and soft marine clay might vary. It is thus possible that the MASW test and MAM are returning an average depth of the OA layer under the array of geophones. Site investigation results reported by Bo et al. (2012) [7] in the same region revealed severe undulations of the OA layer, indi cating that local variations in the OA could be present between our three boreholes. Lateral variations in a medium could lead to a false-depth related dispersion if a horizontally layered medium is assumed for the dispersion analysis, as reported by Lin & Lin (2007) [36]. The MASW profile is now qualitatively compared to the SPT-N pro file of borehole #2. It is observed in Fig. 2 (a) that the SPT-N value is equal to 100 at a depth of 75 m and beyond. By definition, the SPT-N value refers to the number of blows required to reach a penetration of 300 mm. When a blow count of 100 is achieved at a penetration less than 300 mm (which is often the case in very stiff soils like OA), it is a common practice to report a limiting value of 100 alongside the
5.3. Joint inversion of dispersion curve and HVSR The apparent dispersion curve obtained from the combined MASW and MAM dispersion image together with the HVSR, was inverted to generate a Vs profile. The joint inversion was performed in the win MASW [11]. The multi-objective evolutionary algorithm code uses the Pareto dominance criterion to perform the joint inversion [11]. In order to minimize the computational time, the HVSR curve was limited to the bell-shaped portion around the fundamental frequency. In the present study, 100 numbers of individual models and 100 numbers of genera tions were considered in the GA. However, it should be noted that the GA parameters need to be adjusted during the next run based on the misfit between the experimental dispersion curve and the dispersion curve after inversion. The Vs profile corresponding to the best GA model (corresponds to the lowest misfit) is plotted in Fig. 13. The Vs profile is selected based on the misfit calculated at each generation in the chosen population in the genetic algorithm. This involves considerable degree of uncertainty in the generation of final Vs profile. At each run, it may be difficult to obtain repeatable results. 5.4. Validation of MASW and MAM tests Borehole #2 was thus selected for validation purposes since it is the nearest borehole to the centre of the geophone array. Similarly, a 1D section Y–Y’ of the cross-hole test velocity model (shown in Fig. 11) was extracted due to its close proximity. The cross-hole test velocity profile is used herein to evaluate the accuracy of the MASW test in terms of the Vs values; the intrusive technique, would offer a more accurate Vs 9
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corresponding penetration depth (i.e., SPT refusal). For consistency, the values of SPT-N ¼ 100 in this study were extrapolated to a penetration depth of 300 mm. It must, however, be highlighted that while this approach is not ideal in itself, it does provide an indication of the rela tive penetration resistance. The final extrapolated profile (shown in Fig. 13) reveals the heterogeneous nature of the OA, which seems to be well captured by all the inversion methods. In general, the Vs profile seems to be quite consistent with the overall trend in the SPT-N. How ever, while the standard penetration test can identify the soft marine clay layers (as shown by the very low values of SPT-N), it is observed that the surface wave measurements are not so effective in detecting this change in soil type. This is probably due to the low impedance contrast between the fluvial sand and the marine clay layer, to which the active MASW measurements are not very sensitive. This is consistent with the flat dispersion curve at high frequencies, as shown in Fig. 8. Lastly, the importance of identifying and inverting the higher modes of the dispersion curve is highlighted: the experimental dispersion curve in Fig. 12(d) is inverted solely as the fundamental mode M0 for the sake of discussion and plotted in Fig. 13. While the overall trend in Vs closely resembles that of the M0-M3 joint inversion but with a lower resolution, it is noted in Fig. 13(b) that the M0 inversion underestimates the ve locity of the reclaimed sand by about 20% at the top 20 m. The joint inversion of an effective dispersion with HVSR method can therefore be used as a complementary method to confirm the mode identification.
the Land Transport Authority of Singapore and from Ryobi Geo technique Singapore for their logistical support in planning for this field test as well as during the testing phase. We are also grateful to Dr. Moon Sung Woo and Mr. Vinoth Ganapathiraman for their help during the field test. This project is supported by the Ministry of National Devel opment (MND) under its Land and Liveability National Innovation Challenge (L2 NIC) Awards No. (L2NICCFP2-2015-2). References [1] Aki K. Space and time spectra of stationary stochastic waves, with special reference to microtremors. Bull Earthq Res Inst 1957;35:415–56. [2] Arai H, Tokimatsu K. S-wave velocity profiling by joint inversion of microtremor dispersion curve and horizontal-to-vertical (H/V) spectrum. Bull Seismol Soc Am 2005;95(5):1766–78. https://doi.org/10.1785/0120040243. [3] Asten MW, Henstridge JD. Array estimators and the use of microseisms for reconnaissance of sedimentary basins. Geophysics 1984;49:1828–37. https://doi. org/10.1190/1.1441596. [4] Bernauer M. Reducing non-uniqueness in seismic inverse problems: new observables in seismology. Universitat Munchen; 2014. [5] Bettig B, Bard PY, Scherbaum F, Riepl J, Cotton F, Cornou C, et al. Analysis of dense array noise measurements using the modified spatial auto-correlation method (SPAC): application to the Grenoble area. Boll Di Geofis Teor Ed Appl 2001;42: 281–304. [6] Bo MW, Chu J, Choa V. Chapter 9 the Changi East reclamation project in Singapore. In: Indraratna B, Chu JBT-EG-EBS, editors. Gr. Improv. — case hist, vol. 3. Elsevier; 2005. p. 247–76. [7] Bo MW, Chang M-F, Arulrajah A, Choa V. Ground investigations for Changi East reclamation projects. Geotech Geol Eng 2012;30:45–62. https://doi.org/10.1007/ s10706-011-9448-3. [8] Boiero D, Socco LV. Joint inversion of Rayleigh-wave dispersion and P-wave refraction data for laterally varying layered models. 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[14] Dal Moro G, Moura R, Moustafa S. Multi-component joint analysis of surface waves. J Appl Geophys 2015;119:128–38. https://doi.org/10.1016/j. jappgeo.2015.05.014. [15] Dal Moro G, Moustafa SSR, Al-Arifi NS. Improved holistic analysis of Rayleigh waves for single- and multi-offset data: joint inversion of Rayleigh-wave particle motion and vertical- and radial-component velocity spectra. Pure Appl Geophys 2018;175:67–88. https://doi.org/10.1007/s00024-017-1694-8. [16] Dal Moro G, Pipan M, Gabrielli P. Rayleigh wave dispersion curve inversion via genetic algorithms and Marginal Posterior Probability Density estimation. J Appl Geophys 2007;61:39–55. https://doi.org/10.1016/j.jappgeo.2006.04.002. [17] Delgado J, L� opez Casado C, Giner J, Est�evez A, Cuenca A, Molina S. Microtremors as a geophysical exploration tool: applications and limitations. Pure Appl Geophys 2000;157:1445–62. https://doi.org/10.1007/PL00001128. [18] Diaz-Segura EG. Effect of MASW field configuration on estimation of shear wave propagation velocity in sloped terrain. G�eotech Lett 2015;5:21–7. https://doi.org/ 10.1680/geolett.14.00070. [19] Diebold JB, Stoffa PL. The traveltime equation, tau-p mapping, and inversion of common midpoint data. Geophysics 1981;46:238–54. https://doi.org/10.1190/ 1.1441196. [20] Don Z, Li V. Comparison of FK and SPAC methods in determining dispersion curves from passive surface waves. In: Proceedings of symposium on the application of geophysics to engineering and environmental problems, vol. 1; 2010. https://doi. org/10.4133/1.3446095. [21] Don Z. Analysis of surface wave benchmarking data. GeoRisk 2011;2019:853–8. https://doi.org/10.1061/41183(418)90. [22] Duffy B, Campbell J, Finnemore M, Gomez C. Defining fault avoidance zones and associated geotechnical properties using MASW: a case study on the Springfield Fault, New Zealand. Eng Geol 2014;183:216–29. https://doi.org/10.1016/j. enggeo.2014.10.017. [23] Duval A. 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6. Summary and conclusion This paper presented the results of a geophysical site investigation that was carried out on reclaimed land in the Eastern part of Singapore. The case study was centred on the combined use of MASW test, MAM and HVSR technique; with the joint inversion of the dispersion curves and HVSR profile to produce the final 1D Vs profile. Meaningful dispersion images were successfully constructed using the phase shift method where ESAC and ReMi methods fail due to the remote location and unidirectional wave field. Simple work flow was proposed to identify the relevant modes of energy from the combined dispersion image. From the dispersion image, it was observed that the maximum spectral energy is better defined at high frequencies than at the lower frequencies. Two modes with high-energy content could be distin guished in the low frequency region, but, it was difficult to ascertain their modal identity due to the presence of a high velocity contrast layer; i.e., Old Alluvium that underlies the test site. Based on a synthetic elastic model of the site stratigraphy, theoretical dispersion curves were generated to give an indication of the different modes. Then, the fundamental mode M0 and 3rd higher mode M3 were identified suc cessfully from the dispersion image and were jointly inverted into a 1D Vs profile. The latter agreed well with the bore-log information and the results of a seismic cross-hole tomography test conducted at the same site. The experimental dispersion curves were also inverted as the fundamental mode to highlight the importance of higher mode picking. Joint inversion of effective dispersion curve and HVSR provides a similar Vs profile as obtained from the combined M0-M3 inversion, but with the additional information on low velocity layers. Despite the simple geol ogy of the site, it was shown that the sole inversion of the fundamental mode leads to slight inaccuracies and low resolution in the 1D Vs profile. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements We sincerely thank our collaborators from the Geotechnical and Tunnels Division of the Infrastructure Design and Engineering Group at 10
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