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Geotechnical site investigation for tunneling and underground works by advanced passive surface wave survey
Tunnelling and Underground Space Technology 90 (2019) 319–329
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Tunnelling and Underground Space Technology journal homepage: www.elsevier.com/locate/tust
Geotechnical site investigation for tunneling and underground works by advanced passive surface wave survey
T
Yunhuo Zhanga,b, Yunyue Elita Lia, Taeseo Kua,
⁎
a b
Department of Civil and Environmental Engineering, National University of Singapore, 1 Engineering Drive 2, Singapore 117576, Singapore Geotechnical & Tunnel Division, Land Transport Authority Singapore, 1 Hampshire Road, Singapore 219428, Singapore
ARTICLE INFO
ABSTRACT
Keywords: Crosscorrelation Site investigation Rayleigh/Love wave Passive surface wave Bedrock depth Shear wave velocity
This study introduces crosscorrelation seismic interferometry, a new and feasible complimentary surface wave survey for geotechnical site investigation for tunneling and underground works. Crosscorrelation seismic interferometry uses ambient noise as source to estimate the green’s functions received by geophones. The proposed methodology is presented and demonstrated by three case studies in Singapore. The 1st case study demonstrates the workflow of the proposed method. Conventional active multichannel analysis of surface waves (MASW) and passive microtremor array measurement (MAM) have also been carried out on the same site. The comparison with classic active MASW shows that the dispersion curves and shear wave velocity profiles derived by crosscorrelation are more comparable and reasonable. With multiple signal classification (MUSIC) beamforming, the direction of arrival (DOA) of ambient noise field can be characterized. As the prerequisite of crosscorrelation method, with the known DOA, it also affords the opportunity to measure both Rayleigh and Love waves. The 2nd case study demonstrates that the polarization of shear wave velocities can be distinguished by the proposed method. The 3rd case study shows a feasible way to construct a 2D shear wave velocity profile. In short, with a simple linear array, fewer geophones, crosscorrelation is considered to be an attractive complement to the conventional MAM and MASW survey.
1. Introduction
Sharma et al., 1999, Hulme and Burchell, 1999). Each discrete borehole requires considerable cost and time to be completed. A typical borehole may take a few days to over a week to be drilled. Therefore, there has been a strong demand for a complement that is faster, productive, accurate, and also convenient to implement. The pioneers of exploration geophysicists introduced the geophysical survey. In the 1960s the research and development of geophysical survey techniques was subsequently deployed into the industry of site investigation of geotechnical, geo-environmental and earthquake engineering (Sham et al., 2019, Sakai and Takatsuka, 1999, Nord et al., 1992). Among several types of geophysical surveys, seismic survey is more popular for geotechnical site investigation, as the depth of interest is in the order of a few meters to tens of meters. With multiple types of elastic waves, a seismic survey measures the ground motion. There are two major types of elastic waves in seismic surveys: one is seismic reflection and/or refraction surveys, which utilize the body wave. As a classic and popular method, the seismic reflection/refraction is well documented in numerous textbooks. It has been researched and applied widely to detect an interface with large impedance contrast. However, the seismic reflection/refraction requires intense active sources to
Geotechnical site investigation of subsurface ground condition is the starting step for tunneling and underground works and is crucial for every single construction project. One of essential objectives of site investigation is to map out the subsurface profile, especially the interface of underlying soft soil and stiff stratum (e.g., bedrock or very stiff soil). Mixed face condition of soil/rock material is undesirable and needs to be comprehensively investigated prior to tunneling. To achieve this objective, conventional site investigation has been conducted mainly by drilling boreholes and/or measuring penetration resistance in situ (e.g., standard penetration test and cone penetration test). The distance of boreholes varies case by case according to the needs of the specific project. It may not be feasible to drill boreholes in some locations. In Singapore, tunneling may often encounter noticeable changes in soil/rock layers and mixed ground as reported by Zhao et al. (2007) and Krishnan et al. (1999). In Singapore, a typical spacing between two boreholes is between 50 m and 200 m along the proposed underground developments, with a typical depth of about 60 m or shallower, depending on the specific objective of the project (Zhou and Zhao, 2016,
⁎
Corresponding author. E-mail addresses: [email protected], [email protected] (Y. Zhang), [email protected] (Y.E. Li), [email protected] (T. Ku).
https://doi.org/10.1016/j.tust.2019.05.003 Received 22 January 2019; Received in revised form 20 April 2019; Accepted 11 May 2019 Available online 23 May 2019 0886-7798/ © 2019 Elsevier Ltd. All rights reserved.
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(a)
Impulsive Source
Geophone B
Geophone A
(b)
Impulsive Source
Geophone B
Geophone A Virtual Source A’
Fig. 1. Conceptual sketch of (a) an impuslive source and two geophones receiving the source wavelet at different timing; (b) crosscorrelation to turn a geophone to a virtual source and the estimated green’s function received at geophone B.
2 1 3 Fig. 2. Site location layout on the geological map of Singapore.
generate the elastic waves for field acquisition. The active source can be a sledgehammer, weight drop, and even explosives, depending on the actual site condition, nearby activities, and the subsurface ground condition. It may not be environmentally friendly and convenient to carry out, especially in an urban environment. Another aspect of the limitation of the seismic reflection/ refraction is attributed to the large open space required for geophone installation and source shooting. Another major type of elastic waves is the surface wave, mainly known as Rayleigh and Love waves. The dispersion of Rayleigh and Love waves can be used to estimate the shear wave velocity profile. Both active and passive acquisition have been studied and applied to surface waves, especially for Rayleigh waves. Stokoe et al. (1994) introduced the spectral analysis of surface waves (SASW) which was an early type of surface wave-based application for one-dimensional (1D) shear wave velocity profile estimation. The inversion is based on the dispersion curve of Rayleigh and Love waves. It has been studied and developed over the past decade. Park et al. (1999) introduced the multichannel analysis of surface waves (MASW) method, as another type of active surface wave survey. MASW has since been widely applied and continuously developed to construct shear wave velocity
profiles in both one- (1D) and two-dimensional (2D) space. Both SASW and MASW require an active source. Hence, similar limitations of seismic reflection/refraction may still exist. However, the active source is not necessarily to be very intensive, if the objective is only to derive a 1D shear wave velocity profile. Therefore, the possibility of utilizing the surface wave passively has drawn attention. The microtremor array measurement (MAM), which is a passive surface wave survey, was introduced by Okada and Suto (2003). For the application, generally geophones need to be installed in a 2D array rather than a straight line (Hayashi, 2008). In Singapore, Moon et al. (2017) and Subramaniam et al. (2019) investigated the feasibility of using the MAM to detect the bedrock of different geological formations. MAM is more attractive than active MASW since it does not require any active source. However, MAM requires several geophones in a 2D array, such as an ‘L’ shape, triangle, circle, etc. Therefore, its deployability is still highly dependent on the site’s conditions. For instance, if the targeted investigation depth is 100 m, a 100 × 100 m empty site would be required for MAM field acquisition. There is a need to make the array smaller with fewer geophones, which can make a passive surface wave survey less constrained by site conditions and more implementable. 320
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(a)
(b)
N 8
7
6
5
4 3
9
2
10
1
11 Reference Borehole
Testing site
Borehole No. 50126 Multichannel Analysis Of Surface Waves (MASW) Microtremor Array Measurement (MAM)
Bishan-Ang Mo Kio Park, Singapore
Crosscorrelation
Fig.3. Detailed location and array configuration at Site #1: (a) Detailed location of Site #1, (b) Geophone array configuration (passive testing: 11 geophones at 6 m interval each in ‘L’ shape; active testing: 24 geophones at 1.5 m interval each along a straight line).
2. Methodology Crosscorrelation is crosscorrelating the noise signals received from each of two geophones. As long as the signals are recorded long enough, the green’s function can be approximated by crosscorrelation. Fig. 1 sketches out the concept of crosscorrelation. As shown in Fig. 1(a), two geophones (A and B) are installed at a certain distance away from each other. An impulsive source is excited away to geophone A. The impulsive source wavelet propagates towards the two geophones while arriving earlier at geophone A at ta and later at geophone B at tb . Assuming the wavelet amplitude is constant as 1, the wave equations for this simplified case are:
da = e iw (t
(1)
t a)
da for the waveform received at geophone A, and db = eiw (t
(2)
t b)
db for the waveform received at geophone B,where i is the imaginary number, and w is the angular frequency, t is the travel time. Fig. 1(b) explicitly illustrates the concept of crosscorrelation, i.e., to cross-correlate (‘*’ denotes crosscorrelation, which is convolution of one signal with another signal flipped.) the two waveforms received at geophone A and B using the Eq. (3):
Fig. 4. Beamforming results of 4.5–20 Hz ambiont noise at Site #1: colormap denotes the normalized energy level, radius denotes the phase velocity, azimuth denotes the direction of arrival (DOA).
Crosscorrelation seismic interferometry (crosscorrelation for short in subsequent sections) is a different way of using ambient noise, as well as another type of passive surface wave survey. The green’s function between two geophones can be approximated by crosscorrelation of the recorded passive signals from ambient noise, provided ambient noise is uncorrelated, and the principal noise needs to be identified. The green’s function between two geophones by crosscorrelation is equivalent to the waveform received at one geophone from the virtual source excited at another geophone location (Claerbout, 1968, Wapenaar, 2004, Chang et al., 2016, Zhang et al., 2019). This paper introduces the methodology and geotechnical application of crosscorrelation in urban site investigation. The performance of crosscorrelation is appraised and discussed by comparing across conventional surface wave surveys (e.g. MASW and MAM). Both Rayleigh and Love wave crosscorrelation are investigated. It is also demonstrated that 1D and 2D shear wave velocity profiles can be reasonably generated by this method, with fewer geophones (6–8 geophones in our cases) and a small site area (30–40 m linear site in our cases) to construct the geophone array.
da
db = eiw (t
ta ) e iw (t tb)
= eiw (tb
t a)
(3)
The waveform obtained by Eq. (3) is approximated green’s function, which is equivalent to the waveform received at geophone B when a virtual source is excited at the location of geophone A (Claerbout, 1968, Wapenaar, 2004, Chang et al., 2016, Dou et al., 2017). By doing so, it is possible to turn one of the geophones in an array as a virtual source, thereafter the signal processing of active testing can be replicated based on the green’s functions established by crosscorrelation. There are ways to estimate the green’s functions by crosscorrelation. We discuss two common approaches. One is the cross coherence method, while another is cross correlation proposed by Claerbout (1968) and discussed by Bakulin and Calvert (2004) and Wapenaar (2004). The computation of cross coherence and cross correlation in the frequency domain can be written as Eqs. (4) and (5), respectively:
chAB =
u (rA, s ) u' (rB,s ) u (rA, s ) u' (rB,s )
chAB for cross coherence and 321
(4)
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Fig. 5. Waveforms from (a) active MASW, (b) passive MAM testing and (c) estimated green’s function by crosscorrelation.
ccAB = u (rA, s ) u' (rB,s )
(5) Fig. 6. Dispersion spectrum from (a) active MASW testing, (b) passive MAM testing (‘L’ shape array, processed by SPAC) and (c) passive testing (linear array, processed by crosscorrelation). Colormap denotes the energy level.
ccAB for cross correlation. where u (rA, s ) is the waveform excited at s and received at geophone A, while u' (rB,s ) is the transpose of the complex conjugate of the waveform excited at s and received at geophone B. We need to pay attention on the direction of arrival (DOA) of ambient noise prior to applying the crosscorrelation. The green’s function approximates the waveforms of surface wave, provided ambient noise is either evenly distributed around the area, or there is a principal DOA of ambient noise which coincides with the geophone array. Though we can use a small size 2D array to determine the DOA prior to the real array profile design (Halliday et al., 2008); we can also determine the DOA after we collect the noise then apply azimuthal adjustment on the
dispersion measurements (Cheng et al., 2016). The proposed crosscorrelation requires the information of DOA of ambient noise field in order to install the geophone array according to the DOA. The multiple signal classification (MUSIC) algorithm can be used to work out the beamforming to characterize the DOA of ambient noise with the frequency band of interest (Kirlin, 1992, Godara, 1997). Eqs. (6) to (9) are applied based on MUSIC to work out the beamforming of the DOA from a 2D array of geophone signals. Firstly, ambient noise signals need to be 322
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eigenvalues, the (l m ) smallest eigenvalues of the spatial correlation matrix S are referred to select the eigenvector. It is the noise space, denoted as El . l denotes the signal emitted at lth geophone from the virtual source (reference geophone) and can be composed as a function of different azimuth ( ) and phase velocity (c ) by Eq. (7): l(
, c) =
xl u ( , c ) c
(7)
where xl denotes the location vector of the lth geophone, and u ( , c ) is the DOA’s unit vector. A steering vector is then constructed for signals recorded from all geophones by Eq. (8):
t ( , c ) = [eiw
1 ( , c)
eiw
l ( ,c)
]
(8)
where w is the angular frequency. The steering vector can be projected onto the noise subspace by Eq. (9): Fig. 7. Dispersion curves by picking the maxima of the dispersion image spectrum shown in Fig. 6.
B ( , c) =
1 t ' ( , c ) Ul
2
(9)
where t ( , c ) denotes the transpose of the steering vector’s complex conjugate. The steering vector scans through the entire coverage of azimuth and phase velocity for beamforming. Ul is a l × (l m) matrix, formed by the eigenvectors, which is derived according to the spatial correlation matrix S, by searching for the smallest (l m ) eigenvalues. The azimuth of the DOA and the corresponding phase velocity of the principal ambient noise can be identified by the peaks in the MUSIC spectrum, denoted as the beamformer B ( , c ) . With the characterized DOA of ambient noise field, field acquisition and signal processing can be carried out accordingly. Several field testings have been conducted all over Singapore. We have found that the road traffic is the major attribution to ambient noise in Singapore. Hence, the principal DOA of ambient noise is generally from the nearby major road. In view of page limits and to avoid unnecessary repetition, we selected three actual field tests carried out at three different sites in Singapore. Fig. 2 shows the locations of the testing sites on the geological map of Singapore. '
0
10
20
30
3. Crosscorrelation vs. MASW and MAM
40
This section presents the application of crosscorrelation with the case study at Site #1. We also compare its performance versus the conventional surface wave survey, e.g., the active MASW and passive MAM. Site #1 is located in the center of Singapore, in the region of Bukit Timah Granite Formation (Fig. 2). The detailed location is shown by the satellite image in Fig. 3(a). The testing site is in a public park, namely Bishan – Ang Mo Kio Park, near a junction of two major roads. Both active and passive data acquisition have been carried out at a same site, but at different times. There is a reference borehole in the middle of the active geophone array and the corner of the passive geophone array as shown in Fig. 3. Fig. 3(b) presents the array configuration of the active and passive field acquisition. The active testing deployed 24 geophones in a straight-line formation with a 1.5 m spacing between each geophone. The offset of the source to the nearest geophone was 5.5 m. Though 20 shots by a 7-kg sledge hammer were engaged at both sides of the linear array, the result presented in later part is just based on one side’s shots. The sampling rate was 0.5 ms with the duration of 1 s for each shot. In addition, 11 geophones with 6 m spacing in an ‘L’ shape formation were used for passive testing; as noted, the corner coincided with the reference borehole as well as the middle of active testing. The sampling rate was 2 ms with a record duration of 30 mins. By applying the MUSIC beamforming using Eqs. (6) to (9), the beamforming of 4.5 – 20 Hz has been worked out based on the ambient noise signals of 30 mins recorded in the ‘L’ shape array. The result is shown in Fig. 4, in which the colormap represents the beamformer. It is the MUSIC spectrum B ( , c ) by Eq. (9). The radius denotes the phase velocity in m/s and the azimuth denotes the DOA. The selected frequency band of 4.5–20 Hz is the band of interest for near-surface site
50
Backfill (Very soft to soft soil) Residual Soil (Firm soil) Completely weathered granite (Firm to stiff soil) Highly weathered granite (stiff soil) Moderately weathered granite (moderate strong rock) Moderately weathered granite (strong to very strong rock) Fig. 8. 1D shear wave velocity profiles inverted by different dispersion curves. The bore log of the reference borehole is shown side by side in scale. The weathering layering is shown in legend.
transformed to the frequency domain. For instance, there are l numbers of geophones. In each geophone, n numbers of signal data are recorded. Thus, the recorded noise forms a matrix (l × n) . Spatial correlation matrix S is expressed as Eq. (6):
S = NN'
(6)
where N' is the complex conjugate transpose ofN. In MUSIC, the principal signal and noise spaces can be distinguished by eigenvalues or eigenvectors. Supposing there are m large 323
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(a)
Testing site N
(b)
(c)
#1 #2 #3 #4 #5 #6 #7 #8
11 veridical geophones @ 8m c/c in ‘L’ shape N
N
8 multi-component geophones @ 8m c/c Fig. 9. Detailed location plan and array configuration at Site #2: (a) Site #2 location, (b) detailed location and the passive testing array for characterizing the DOA, (c) linear array configuration of multi-component geophones and the directions of the two horizontal components, with trace number indicated.
after vertical stacking are shown in Fig. 5(a). Fig. 5(b) is the vertical stack of the passive signals obtained by splitting the entire 30 min of data into a 1sec-window with 50% overlapping. Using Eq. (5) and setting geophone #6 (i.e., the corner geophone of the ‘L’ shape array) as the virtual source, green’s functions are approximated by crosscorrelation and shown in Fig. 5(c). The change from Fig. 5(b) and (c) exhibits an apparent transformation of random ambient noise to clear signal, as a realization of the crosscorrelation depicted in a conceptual sketch (Fig. 1(a) and (b)). The green’s functions shown in Fig. 5(c) agree with the MUSIC beamforming results shown in Fig. 4, as there is a clear signal from geophone #6 to #1 which is in line with the principal DOA, NW towards SE in this case. For another leg of ‘L’ array, as shown in Fig. 5(c), it appears that there were signals coming from both directions of geophone #6 to #11. Therefore, the green’s functions of geophone #1 to #6 are chosen for further signal processing to construct a dispersion curve. The signal processing based on both active waveforms and the green’s functions by crosscorrelation follows the classic phase shift method suggested by Park et al. (1999) as written in Eq. (10):
Fig. 10. Beamforming results of 3–15 Hz ambiont noise at Site #2: colormap denotes the normalized energy level, radius denotes the phase velocity, azimuth denotes the DOA.
investigation, which is from about 10 to tens of meters below ground. It is shown that ambient noise within this frequency band was principally coming from the north west (NW) towards the south east (SE). This outcome is explainable since the testing site is located at the junction of two major roads. Ambient noises within 4.5 – 20 Hz are reasonably attributed to the road traffic of the near field, and the DOA from the MUSIC beamforming reaffirms it. With the understanding of the DOA after characterizing ambient noise field by MUSIC beamforming, only geophones #1 to #6 (Fig. 3(b)) are chosen to derive the estimated green’s functions by crosscorrelation, since they are almost in line with the principal DOA, which is aligned along NW - SE. A vertical stack of all the shots at one side of the active testing is carried out to increase the signal to noise ratio (S/N). The waveforms
F (c , w ) =
+
F (x , w ) iw x e c dx |F (x , w )|
(10)
where x is the location vector of geophones, c is the phase velocity and w is the angular frequency. The peak of the dispersion spectrum F (c, w ) indicates the dispersion curve. For MAM, using the passive signals acquired in the ‘L’ shape array, spatial auto correlation (SPAC) presented by Hayashi (2008) is adopted for the signal processing to obtain the dispersion curve. SPAC is expressed in Eq. (11):
SPAC (x , w ) =
324
1 2
2 0
Re (COH (x , , w )) d = J0
w ×x c (w )
(11)
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Fig. 11. 3–15 Hz bandpass filtered waveforms from (a) Vertical component and (c) Horizontal 2 component and estimated green’s function by crosscorrelation: (b) from Vertical component and (d) Horizontal 2 component.
where Re means the real number, x is the location vector of geophones, c (w ) is the phase velocity, w is the angular frequency, COH is coherence and is the azimuth of the geophone to the reference geophone. J0 is Bessel function. The dispersion spectrum SPAC (x , w ) is approximated by fitting the integration of the coherence matrix to the first order of Bessel function. Fig. 6 shows the dispersion spectrum from active testing (24 geophones in linear formation), passive testing—MAM (11 geophones in ‘L’ shape array), and passive testing—crosscorrelation (6 geophones in linear formation along the principal DOA of ambient noise). It is apparent that the shape and pattern of high energy zones in Fig. 6(a) and (c) are more closely agreed, whereas the ones in Fig. 6(b) are rather departed from them. This observation is more visible in Fig. 7, where the picks of the dispersion spectrum are extracted and plotted together. The dispersion curves from active testing and crosscorrelation are almost overlapping, nevertheless the dispersion curve of low frequency (below 6 Hz in this case) has not been retrieved from the active test due to the ambiguity from the low S/N. The dispersion curve processed by SPAC using the signal acquired from the MAM (‘L’ shape) seems to match perfectly only between about 6–7 Hz with the dispersion curve from active testing. The phase velocity even drops in the low frequency zone, which is not expected in this region based on the experience and knowledge of local geology. In fact, a similar trend/pattern was observed in other test sites although we do not present here to avoid the repetition of same results. Based on the dispersion curve, an initial model is approximated by converting the dispersion curve to a shear wave velocity profile using Eqs. (12) and (13):
h=a×
Vs =
c b
=a×c w
Bullen et al. (1985). A genetic algorithm (GA) is used for the inversion of the dispersion curve. A 1D shear wave velocity profile is produced by choosing the one with the best fit of inverted dispersion curve compared with the experimental measurement. As shown in Fig. 8, the three methods produce similar results in the upper 12 m, except crosscorrelation for the upper 4 m. From 12 m downwards, the crosscorrelation indicates VS is more than 450 m/s, whereas MAM is less and active MASW is even greater. Based on the measured dispersion curve, the VS profile may not be reliable for active testing beyond 450 m/s (e.g., at deeper depth). Nevertheless, both active MASW and crosscorrelation show a similar pattern and shape in the VS profile. More importantly, they both indicate the sudden increase of the VS at about 25 m depth which just corresponds to the bedrock depth as shown in the bore log of the reference borehole. At this site, the VS inverted from the dispersion curve by SPAC with the ‘L’ shape MAM gives relatively larger departure, especially in deeper layers in terms of VS magnitude. In short, crosscorrelation is able to produce a reasonable green’s functions. Although there are some guidelines that suggest long spatial coverage and temporal acquisition (Xia et al., 2009, Foti et al., 2018), in our investigation, we found that the investigation depth can be increased with good quality passive signals. The estimated green’s functions can be used to produce a comparable and reasonable dispersion curve as demonstrated through the comparison with active MASW result. Eventually, it is feasible to apply crosscorrelation to estimate the VS profile reasonably. It also can provide reliable outcomes for lower frequency bands which the active test may not be able to. It increases the illumination depth of site investigation from active MASW.
(12)
4. Application of crosscorrelation for Rayleigh and Love waves Most surface wave surveys are based on the Rayleigh wave. Some recent investigations on Love waves were reported based on active testing (Eslick et al., 2008, Pan et al., 2016, Pegah et al., 2017). In this section, we present the 2nd case study to demonstrate that both Rayleigh and Love waves are captured passively by crosscorrelation, using multicomponent geophones. Crosscorrelation is applied to process the
(13)
where h is the depth of each soil layer, is the wavelength, c is the phase velocity, w is the angular frequency, a is set as 1/3 in this case (typical range: 1/2 to 1/4 (Nazarian et al., 1983)), Vs is the shear wave velocity and b is a constant in the range of 0.9–0.95 as suggested by 325
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neighborhood park, namely Springleaf Garden. The nearest major road is the Seletar Expressway in the south of the site, as shown in Fig. 9(a). As discussed in the methodology, the condition to apply crosscorrelation needs to ensure the geophones along the principal DOA of ambient noise. Due to the reciprocity of the Rayleigh wave and particle motion of Love wave, to find and distinguish the Love wave becomes extremely dependent on the DOA. The Love wave can be measured, identified, and distinguished only if the horizontal component geophones installed are orthogonalized to the principal DOA of ambient noise. All the other azimuths would measure a mixture of Rayleigh and Love waves. To characterize the DOA of ambient noise field, an ‘L’ shape array of 11 single component geophones (Fig. 9(b)) was placed to acquire ambient noise for about 30 mins. Fig. 10 shows the beamforming results. It indicates that for the band of 3–15 Hz, the principal DOA of ambient noise is from south (S) and south east (SE) towards north (N) and north west (NW). We can also note that there is secondary DOA of ambient noise which is from northwest (NW) towards southeast (SE). The observation tallies with the site location in relation to adjacent roads as shown in Fig. 9. The expressway may be the main contributor of the passive source for this site. Based on the understanding of ambient noise field, eight multicomponent geophones were installed on site as shown in Fig. 9(c), at 8 m intervals and for about 30 mins recording duration. There are two horizontal components in each multi-component geophone, and the directions were kept constant throughout, as indicated in Fig. 9(c); Horizontal 1 direction was along the direction of the linear array, as well as along the principal DOA, while Horizontal 2 direction was normal to the array as well as the principal DOA. Hence, the particle motion measured by Horizontal 2 directional component should be mainly attributed to Love waves. The original Rayleigh and Love waveforms stacked over 1sec-windows are plotted in Fig. 11(a) and (c). The green’s functions are calculated by referring to geophone #1 as a virtual source. Fig. 11(b) and (d) are for Rayleigh and Love waves, respectively. With the estimated green’s functions, the dispersion spectra of Rayleigh and Love waves are shown in Fig. 12(a) and (b). The maximum of the dispersion spectrum is picked to retrieve the dispersion curves. The dispersion curves of Rayleigh and Love waves are shown in Fig. 12(c). Based on the processed dispersion curves, the vertically-polarized shear wave velocity (SV) and horizontally-polarized shear wave velocity (SH) are derived by inverting the dispersion curves of Rayleigh and Love waves, respectively. Fig. 13 shows the 1D SV and SH profiles with the bore log of the reference borehole aside. The bedrock (moderately weathered rock) is found at 32 m deep from the bore log. This is close to the indicated level on SV and SH profiles, which shows distinct increases. Considering the general relation between VS and geostatic stress states (Ku and Mayne, 2012, 2013, 2015, Pegah et al., 2017), the observed VS anisotropy is not surprising due to large in-situ horizontal stress in the Bukit Timah region (Sharma et al., 1999). This 2nd case study shows that crosscorrelation can be successfully used for the analysis of both Rayleigh and Love waves. The SV and SH profile can be utilized to infer the bedrock depth. Fig. 12. Dispersion spectrum from green’s functions by crosscorrelation from (a) Vertical component, (b) Horizontal 2 component and (c) extracted Rayleigh and Love waves’ dispersion curves by picking the maxima of Fig. 12(a) and (b).
5. Application of crosscorrelation for 2D profiling Previous sections introduced crosscorrelation to produce a 1D shear wave velocity profile. This section presents a case study to demonstrate the feasibility of producing 2D shear wave velocity profiles. 24 Geophones have been placed in a grid of 8 m spacing on site #3 (Fig. 2). The exact site location and geophone array configuration are shown in Fig. 14. The 40 m × 24 m grid array has been set up in the sport field of the National University of Singapore (NUS). An expressway is to the north east, while a campus road is located at its south and south west.
passive signals for green’s functions, which are used to derive the dispersion curves of Rayleigh and Love waves. The polarization of shear waves in vertical and horizontal directions is estimated from Rayleigh and Love waves, respectively. The second site (Fig. 2) is located in the north of Singapore, in the region of Bukit Timah Granite Formation. The exact location is shown in Fig. 9. The testing site is in a
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The field acquisition was held in the morning rush hour from 7.30am to 9.00am with a sampling rate of 2 ms. Beamforming has been carried out by MUSIC with the entire recorded signals from the 24 geophones. Fig. 15 shows the results of ambient noise at 6–20 Hz. It indicates ambient noise mainly comes from two directions, south/south west and north east. This is expected as it coincides with the nearby major roads. Together with the other two cases mentioned earlier, the traffic appears to be the main contributor of ambient noises within the frequency band of interest. Based on the principal DOA of ambient noise, it is reasonable to choose the six geophones in each of the four rows to process separately, since they are along the principal DOA. Fig. 16(a) presents the dispersion spectra of each of the four rows, using the approximated green’s functions by crosscorrelation. Fig. 16(b) shows the extracted dispersion curves, based on which to estimate shear wave velocity profiles individually. Interpolation has been carried out to produce a 2D (Fig. 17) profile over 50 m deep and 24 m wide, based on the shear wave velocity profiles from each of the four rows. This site is in sedimentary geological formation. Since this section just aims to illustrate the possibility of creating a 2D profile, we may choose an arbitrary threshold. Nevertheless, to make the result more realistic, we refer to the bedrock depth from a nearby borehole. We find the cut-off velocity can be chosen as 700 m/s. This is quite close as Moon et al. (2017) reported by using MAM (SPAC). The white dashed line in Fig. 17 indicates the inferred bedrock profile, which agrees with the reference boreholes near the testing site.
0.0 10.0 20.0 30.0 35.0 Legends
Backfill (Very soft to soft soil)
Residual soil Completely weathered granite Moderately weathered granite rock
Fig. 13. 1D shear wave velocity profiles inverted by Rayleigh and Love waves’ dispersion curves. The bore log of the reference borehole is shown side by side in scale. The weathering layering is shown in legend.
6. Discussion In this study, crosscorrelation has been demonstrated to be capable of and suitable for geotechnical site investigation; 1D and 2D shear wave velocity profiles can be reasonably estimated, so as bedrock depth can be accurately inferred. Ambient noise is mainly attributed to the road traffic in Singapore. It can be used as the source for passive surface wave survey. Both Rayleigh and Love waves can be captured and utilized by crosscorrelation. A short field acquisition (30 min in the cases investigated in this paper), and a simple, short linear array (30–40 m) with just six to eight geophones are found adequate. It makes the implementation more convenient and less subject to site constraints, as compared with the conventional MAM that requires a large open space in which to place a 2D array with more geophones. It shall be noted that there are conditions to be complied with in order to apply crosscorrelation. The DOA of ambient noise needs to be characterized to determine the orientation of the linear geophone array. Hence, although the DOA would be intuitively estimated (e.g., location of major road) based on our cases, a 2D array may be still required near the interested site to confirm the DOA of ambient noise. In the event of constructing a 2D VS profile, crosscorrelation is practically more convenient compared to active MASW, since it doesn’t require intense active sources. Moreover, passive MAM would not be an ideal option at all for constructing 2D VS profiles. Another point to be noted may be the near-field sources and activities which may be highly irregular over the period of recording compared to far-field effects, e.g., sudden footsteps or high amplitude noises. It is recommended to keep the geophones less disturbed in the field acquisition. Other than the advantages and pre-conditions of crosscorrelation, the fundamental assumption of 1D surface wave shall always apply, i.e., the soil layering model is assumed horizontally homogeneous. In other words, if the ground condition of the testing site varies significantly,
Fig. 14. Detailed location plan and geophone array configuration at Site #3.
Fig. 15. Beamforming results of 6–20 Hz ambient noise at Site #3: colormap denotes the normalized energy level, radius denotes the phase velocity, azimuth denotes the DOA.
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(a)
(b)
Fig. 16. Dispersion curves of the 4 rows at Site #3; (a) dispersion images and (b) extracted dispersion curves.
none of 1D surface wave testing is suitable, including crosscorrelation. Last but not least, the shear wave velocity profile from crosscorrelation also heavily relies on the optimization of the inversion, which is a classic non-linear, non-unique problem. To mitigate the inversion problem, the initial model is constrained by referring the dispersion curve to velocity and wavelengths. By doing so, the final shear wave velocity profile is found more reasonable compared to leaving the initial model with no constraints.
surface wave survey has been investigated and applied in Singapore. It is found easier and more practical to be implemented on site than the conventional MAM that requires a large 2D array. The DOA of ambient noises needs to be identified prior to placing the linear geophone arrays for crosscorrelation. Multi-component geophones can be used to capture both Rayleigh and Love waves, provided the principal DOA is orthonormal to a horizontal component. 2D shear wave velocity profiles can be constructed effectively by constructing several lines of the linear array, either simultaneously or one by one. The shear wave velocity profiles obtained from the proposed methodology can be successfully used to infer bedrock depth, which is valuable for geotechnical site investigation for tunneling and underground works.
7. Conclusion Crosscorrelation, a feasible and attractive complementary passive
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surface seismology. Geophysics 73 (3), G1–G6. Foti, S., Hollender, F., Garofalo, F., Albarello, D., Asten, M., Bard, P.-Y., Comina, C., Cornou, C., Cox, B., Di Giulio, G., 2018. Guidelines for the good practice of surface wave analysis: a product of the InterPACIFIC project. Bullet. Earthquake Eng. 16 (6), 2367–2420. Godara, L.C., 1997. Application of antenna arrays to mobile communications. II. Beamforming and direction-of-arrival considerations. Proc. IEEE 85 (8), 1195–1245. Halliday, D., Curtis, A., Kragh, E., 2008. Seismic surface waves in a suburban environment: active and passive interferometric methods. Leading Edge 27 (2), 210–218. Hayashi, K., 2008. Development of surface-wave methods and its application to site investigations (PhD Thesis). Kyoto University. Hulme, T., Burchell, A., 1999. Tunnelling projects in Singapore: an overview. Tunnell. Underground Space Technol. 14 (4), 409–418. Kirlin, R.L., 1992. The relationship between semblance and eigenstructure velocity estimators. Geophysics 57 (8), 1027–1033. Krishnan, R., Copsey, J., Algeo, R., Shirlaw, J., 1999. Design of the civil works for Singapore's North East line. Tunnell. Underground Space Technol. 14 (4), 433–448. Ku, T., Mayne, P.W., 2012. Evaluating the in situ lateral stress coefficient (K0) of soils via paired shear wave velocity modes. J. Geotech. Geoenviron. Eng. 139 (5), 775–787. Ku, T., Mayne, P.W., 2013. Profiling of K0 lateral stress coefficient in soils using paired directional G0 ratios. J. Appl. Geophys. 94, 15–21. Ku, T., Mayne, P.W., 2015. In situ lateral stress coefficient (K0) from shear wave velocity measurements in soils. J. Geotech. Geoenviron. Eng. 141 (12), 06015009. Moon, S.-W., Hayashi, K., Ku, T., 2017. Estimating spatial variations in bedrock depth and weathering degree in decomposed granite from surface waves. J. Geotech. Geoenviron. Eng. 143 (7), 04017020. Nazarian, S., Stokoe, I., Kenneth, H., Hudson, W., 1983. Use of spectral analysis of surface waves method for determination of moduli and thicknesses of pavement systems. Transport. Res. Rec. 930, 38–45. Nord, G., Olsson, P., By, T., 1992. Probing ahead of TBMs by geophysical means. Tunnell. Underground Space Technol. 7 (3), 237–242. Okada, H., Suto, K., 2003. The microtremor survey method. Soc. Explor. Geophys. Pan, Y., Xia, J., Xu, Y., Gao, L., 2016. Multichannel analysis of Love waves in a 3D seismic acquisition system. Geophysics 81 (5), EN67–EN74. Park, C.B., Miller, R.D., Xia, J., 1999. Multichannel analysis of surface waves. Geophysics 64 (3), 800–808. Pegah, E., Liu, H., Dastanboo, N., 2017. Evaluation of the lateral earth pressure coefficients at-rest in granular soil deposits using the anisotropic components of S-wave velocity. Eng. Geol. 230, 55–63. Sakai, S., Takatsuka, T., 1999. Development of a geophysical exploration technique for detecting shallow strata boundaries. Tunnell. Underground Space Technol. 14, 21–29. Sham, J.F., Lai, W.W., Chan, W., Koh, C.L., 2019. Imaging and condition diagnosis of underground sewer liners via active and passive infrared thermography: a case study in Singapore. Tunnell. Underground Space Technol. 84, 440–450. Sharma, J., Chu, J., Zhao, J., 1999. Geological and geotechnical features of Singapore: an overview. Tunnell. Underground Space Technol. 14 (4), 419–431. Stokoe, K.H., Wright, S., Bay, J., Roesset, J., 1994. Characterization of geotechnical sites by SASW method. Geophys. Character. Sites 15–25. Subramaniam, P., Zhang, Y., Ku, T., 2019. Underground survey to locate weathered bedrock depth using noninvasive microtremor measurements in Jurong sedimentary formation, Singapore. Tunnell. Underground Space Technol. 86, 10–21. Wapenaar, K., 2004. Retrieving the elastodynamic Green's function of an arbitrary inhomogeneous medium by cross correlation. Phys. Rev. Lett. 93 (25), 254301. Xia, J., Miller, R.D., Xu, Y., Luo, Y., Chen, C., Liu, J., Ivanov, J., Zeng, C., 2009. Highfrequency Rayleigh-wave method. J. Earth Sci. 20 (3), 563–579. Zhang, Y., Li, Y.E., Zhang, H., Ku, T., 2019. Near-surface site investigation by seismic interferometry using urban traffic noise in Singapore. Geophysics 84 (2), B169–B180. Zhao, J., Gong, Q., Eisensten, Z., 2007. Tunnelling through a frequently changing and mixed ground: a case history in Singapore. Tunnell. Underground Space Technol. 22 (4), 388–400. Zhou, Y., Zhao, J., 2016. Assessment and planning of underground space use in Singapore. Tunnell. Underground Space Technol. 55, 249–256.
0.0 10.0 20.0 30.0 40.0 50.0
Backfill (Very soft to soft soil)
Estuary Clay Residual soil Completely weathered sediments Moderately weathered sedimentary rock Slightly weathered sedimentary rock Fig. 17. 2D shear wave velocity profile cutting across the short side of testing site. Colormap denotes the velocity contour. Bore log of the reference borehole is side by side.
Acknowledgements The authors would appreciate and acknowledge the funding from Land Transport Authority Singapore (LTA, Award Number R-302-000164-490; PI- Dr. Taeseo Ku) and Petroleum Engineering Professorship (EDB) and Ministry of Education of Singapore Tier-1 Grant R-302-000165-133. References Bakulin, A., Calvert, R., 2004. Virtual source: New method for imaging and 4D below complex overburden. In: SEG Technical Program Expanded Abstracts 2004.) Society of Exploration Geophysicists, pp. 2477–2480. Bullen, K.E., Bullen, K.E., Bolt, B.A., 1985. An introduction to the theory of seismology. Cambridge University Press. Chang, J.P., De Ridder, S.A., Biondi, B.L., 2016. High-frequency Rayleigh-wave tomography using traffic noise from Long Beach, California. Geophysics 81 (2), B43–B53. Cheng, F., Xia, J., Luo, Y., Xu, Z., Wang, L., Shen, C., Liu, R., Pan, Y., Mi, B., Hu, Y., 2016. Multichannel analysis of passive surface waves based on crosscorrelations. Geophysics 81 (5), EN57–EN66. Claerbout, J.F., 1968. Synthesis of a layered medium from its acoustic transmission response. Geophysics 33 (2), 264–269. Dou, S., Lindsey, N., Wagner, A.M., Daley, T.M., Freifeld, B., Robertson, M., Peterson, J., Ulrich, C., Martin, E.R., Ajo-Franklin, J.B., 2017. Distributed acoustic sensing for seismic monitoring of the near surface: a traffic-noise interferometry case study. Sci. Rep. 7. Eslick, R., Tsoflias, G., Steeples, D., 2008. Field investigation of Love waves in near-
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Contents lists available at ScienceDirect
Tunnelling and Underground Space Technology journal homepage: www.elsevier.com/locate/tust
Geotechnical site investigation for tunneling and underground works by advanced passive surface wave survey
T
Yunhuo Zhanga,b, Yunyue Elita Lia, Taeseo Kua,
⁎
a b
Department of Civil and Environmental Engineering, National University of Singapore, 1 Engineering Drive 2, Singapore 117576, Singapore Geotechnical & Tunnel Division, Land Transport Authority Singapore, 1 Hampshire Road, Singapore 219428, Singapore
ARTICLE INFO
ABSTRACT
Keywords: Crosscorrelation Site investigation Rayleigh/Love wave Passive surface wave Bedrock depth Shear wave velocity
This study introduces crosscorrelation seismic interferometry, a new and feasible complimentary surface wave survey for geotechnical site investigation for tunneling and underground works. Crosscorrelation seismic interferometry uses ambient noise as source to estimate the green’s functions received by geophones. The proposed methodology is presented and demonstrated by three case studies in Singapore. The 1st case study demonstrates the workflow of the proposed method. Conventional active multichannel analysis of surface waves (MASW) and passive microtremor array measurement (MAM) have also been carried out on the same site. The comparison with classic active MASW shows that the dispersion curves and shear wave velocity profiles derived by crosscorrelation are more comparable and reasonable. With multiple signal classification (MUSIC) beamforming, the direction of arrival (DOA) of ambient noise field can be characterized. As the prerequisite of crosscorrelation method, with the known DOA, it also affords the opportunity to measure both Rayleigh and Love waves. The 2nd case study demonstrates that the polarization of shear wave velocities can be distinguished by the proposed method. The 3rd case study shows a feasible way to construct a 2D shear wave velocity profile. In short, with a simple linear array, fewer geophones, crosscorrelation is considered to be an attractive complement to the conventional MAM and MASW survey.
1. Introduction
Sharma et al., 1999, Hulme and Burchell, 1999). Each discrete borehole requires considerable cost and time to be completed. A typical borehole may take a few days to over a week to be drilled. Therefore, there has been a strong demand for a complement that is faster, productive, accurate, and also convenient to implement. The pioneers of exploration geophysicists introduced the geophysical survey. In the 1960s the research and development of geophysical survey techniques was subsequently deployed into the industry of site investigation of geotechnical, geo-environmental and earthquake engineering (Sham et al., 2019, Sakai and Takatsuka, 1999, Nord et al., 1992). Among several types of geophysical surveys, seismic survey is more popular for geotechnical site investigation, as the depth of interest is in the order of a few meters to tens of meters. With multiple types of elastic waves, a seismic survey measures the ground motion. There are two major types of elastic waves in seismic surveys: one is seismic reflection and/or refraction surveys, which utilize the body wave. As a classic and popular method, the seismic reflection/refraction is well documented in numerous textbooks. It has been researched and applied widely to detect an interface with large impedance contrast. However, the seismic reflection/refraction requires intense active sources to
Geotechnical site investigation of subsurface ground condition is the starting step for tunneling and underground works and is crucial for every single construction project. One of essential objectives of site investigation is to map out the subsurface profile, especially the interface of underlying soft soil and stiff stratum (e.g., bedrock or very stiff soil). Mixed face condition of soil/rock material is undesirable and needs to be comprehensively investigated prior to tunneling. To achieve this objective, conventional site investigation has been conducted mainly by drilling boreholes and/or measuring penetration resistance in situ (e.g., standard penetration test and cone penetration test). The distance of boreholes varies case by case according to the needs of the specific project. It may not be feasible to drill boreholes in some locations. In Singapore, tunneling may often encounter noticeable changes in soil/rock layers and mixed ground as reported by Zhao et al. (2007) and Krishnan et al. (1999). In Singapore, a typical spacing between two boreholes is between 50 m and 200 m along the proposed underground developments, with a typical depth of about 60 m or shallower, depending on the specific objective of the project (Zhou and Zhao, 2016,
⁎
Corresponding author. E-mail addresses: [email protected], [email protected] (Y. Zhang), [email protected] (Y.E. Li), [email protected] (T. Ku).
https://doi.org/10.1016/j.tust.2019.05.003 Received 22 January 2019; Received in revised form 20 April 2019; Accepted 11 May 2019 Available online 23 May 2019 0886-7798/ © 2019 Elsevier Ltd. All rights reserved.
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(a)
Impulsive Source
Geophone B
Geophone A
(b)
Impulsive Source
Geophone B
Geophone A Virtual Source A’
Fig. 1. Conceptual sketch of (a) an impuslive source and two geophones receiving the source wavelet at different timing; (b) crosscorrelation to turn a geophone to a virtual source and the estimated green’s function received at geophone B.
2 1 3 Fig. 2. Site location layout on the geological map of Singapore.
generate the elastic waves for field acquisition. The active source can be a sledgehammer, weight drop, and even explosives, depending on the actual site condition, nearby activities, and the subsurface ground condition. It may not be environmentally friendly and convenient to carry out, especially in an urban environment. Another aspect of the limitation of the seismic reflection/ refraction is attributed to the large open space required for geophone installation and source shooting. Another major type of elastic waves is the surface wave, mainly known as Rayleigh and Love waves. The dispersion of Rayleigh and Love waves can be used to estimate the shear wave velocity profile. Both active and passive acquisition have been studied and applied to surface waves, especially for Rayleigh waves. Stokoe et al. (1994) introduced the spectral analysis of surface waves (SASW) which was an early type of surface wave-based application for one-dimensional (1D) shear wave velocity profile estimation. The inversion is based on the dispersion curve of Rayleigh and Love waves. It has been studied and developed over the past decade. Park et al. (1999) introduced the multichannel analysis of surface waves (MASW) method, as another type of active surface wave survey. MASW has since been widely applied and continuously developed to construct shear wave velocity
profiles in both one- (1D) and two-dimensional (2D) space. Both SASW and MASW require an active source. Hence, similar limitations of seismic reflection/refraction may still exist. However, the active source is not necessarily to be very intensive, if the objective is only to derive a 1D shear wave velocity profile. Therefore, the possibility of utilizing the surface wave passively has drawn attention. The microtremor array measurement (MAM), which is a passive surface wave survey, was introduced by Okada and Suto (2003). For the application, generally geophones need to be installed in a 2D array rather than a straight line (Hayashi, 2008). In Singapore, Moon et al. (2017) and Subramaniam et al. (2019) investigated the feasibility of using the MAM to detect the bedrock of different geological formations. MAM is more attractive than active MASW since it does not require any active source. However, MAM requires several geophones in a 2D array, such as an ‘L’ shape, triangle, circle, etc. Therefore, its deployability is still highly dependent on the site’s conditions. For instance, if the targeted investigation depth is 100 m, a 100 × 100 m empty site would be required for MAM field acquisition. There is a need to make the array smaller with fewer geophones, which can make a passive surface wave survey less constrained by site conditions and more implementable. 320
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(a)
(b)
N 8
7
6
5
4 3
9
2
10
1
11 Reference Borehole
Testing site
Borehole No. 50126 Multichannel Analysis Of Surface Waves (MASW) Microtremor Array Measurement (MAM)
Bishan-Ang Mo Kio Park, Singapore
Crosscorrelation
Fig.3. Detailed location and array configuration at Site #1: (a) Detailed location of Site #1, (b) Geophone array configuration (passive testing: 11 geophones at 6 m interval each in ‘L’ shape; active testing: 24 geophones at 1.5 m interval each along a straight line).
2. Methodology Crosscorrelation is crosscorrelating the noise signals received from each of two geophones. As long as the signals are recorded long enough, the green’s function can be approximated by crosscorrelation. Fig. 1 sketches out the concept of crosscorrelation. As shown in Fig. 1(a), two geophones (A and B) are installed at a certain distance away from each other. An impulsive source is excited away to geophone A. The impulsive source wavelet propagates towards the two geophones while arriving earlier at geophone A at ta and later at geophone B at tb . Assuming the wavelet amplitude is constant as 1, the wave equations for this simplified case are:
da = e iw (t
(1)
t a)
da for the waveform received at geophone A, and db = eiw (t
(2)
t b)
db for the waveform received at geophone B,where i is the imaginary number, and w is the angular frequency, t is the travel time. Fig. 1(b) explicitly illustrates the concept of crosscorrelation, i.e., to cross-correlate (‘*’ denotes crosscorrelation, which is convolution of one signal with another signal flipped.) the two waveforms received at geophone A and B using the Eq. (3):
Fig. 4. Beamforming results of 4.5–20 Hz ambiont noise at Site #1: colormap denotes the normalized energy level, radius denotes the phase velocity, azimuth denotes the direction of arrival (DOA).
Crosscorrelation seismic interferometry (crosscorrelation for short in subsequent sections) is a different way of using ambient noise, as well as another type of passive surface wave survey. The green’s function between two geophones can be approximated by crosscorrelation of the recorded passive signals from ambient noise, provided ambient noise is uncorrelated, and the principal noise needs to be identified. The green’s function between two geophones by crosscorrelation is equivalent to the waveform received at one geophone from the virtual source excited at another geophone location (Claerbout, 1968, Wapenaar, 2004, Chang et al., 2016, Zhang et al., 2019). This paper introduces the methodology and geotechnical application of crosscorrelation in urban site investigation. The performance of crosscorrelation is appraised and discussed by comparing across conventional surface wave surveys (e.g. MASW and MAM). Both Rayleigh and Love wave crosscorrelation are investigated. It is also demonstrated that 1D and 2D shear wave velocity profiles can be reasonably generated by this method, with fewer geophones (6–8 geophones in our cases) and a small site area (30–40 m linear site in our cases) to construct the geophone array.
da
db = eiw (t
ta ) e iw (t tb)
= eiw (tb
t a)
(3)
The waveform obtained by Eq. (3) is approximated green’s function, which is equivalent to the waveform received at geophone B when a virtual source is excited at the location of geophone A (Claerbout, 1968, Wapenaar, 2004, Chang et al., 2016, Dou et al., 2017). By doing so, it is possible to turn one of the geophones in an array as a virtual source, thereafter the signal processing of active testing can be replicated based on the green’s functions established by crosscorrelation. There are ways to estimate the green’s functions by crosscorrelation. We discuss two common approaches. One is the cross coherence method, while another is cross correlation proposed by Claerbout (1968) and discussed by Bakulin and Calvert (2004) and Wapenaar (2004). The computation of cross coherence and cross correlation in the frequency domain can be written as Eqs. (4) and (5), respectively:
chAB =
u (rA, s ) u' (rB,s ) u (rA, s ) u' (rB,s )
chAB for cross coherence and 321
(4)
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Fig. 5. Waveforms from (a) active MASW, (b) passive MAM testing and (c) estimated green’s function by crosscorrelation.
ccAB = u (rA, s ) u' (rB,s )
(5) Fig. 6. Dispersion spectrum from (a) active MASW testing, (b) passive MAM testing (‘L’ shape array, processed by SPAC) and (c) passive testing (linear array, processed by crosscorrelation). Colormap denotes the energy level.
ccAB for cross correlation. where u (rA, s ) is the waveform excited at s and received at geophone A, while u' (rB,s ) is the transpose of the complex conjugate of the waveform excited at s and received at geophone B. We need to pay attention on the direction of arrival (DOA) of ambient noise prior to applying the crosscorrelation. The green’s function approximates the waveforms of surface wave, provided ambient noise is either evenly distributed around the area, or there is a principal DOA of ambient noise which coincides with the geophone array. Though we can use a small size 2D array to determine the DOA prior to the real array profile design (Halliday et al., 2008); we can also determine the DOA after we collect the noise then apply azimuthal adjustment on the
dispersion measurements (Cheng et al., 2016). The proposed crosscorrelation requires the information of DOA of ambient noise field in order to install the geophone array according to the DOA. The multiple signal classification (MUSIC) algorithm can be used to work out the beamforming to characterize the DOA of ambient noise with the frequency band of interest (Kirlin, 1992, Godara, 1997). Eqs. (6) to (9) are applied based on MUSIC to work out the beamforming of the DOA from a 2D array of geophone signals. Firstly, ambient noise signals need to be 322
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eigenvalues, the (l m ) smallest eigenvalues of the spatial correlation matrix S are referred to select the eigenvector. It is the noise space, denoted as El . l denotes the signal emitted at lth geophone from the virtual source (reference geophone) and can be composed as a function of different azimuth ( ) and phase velocity (c ) by Eq. (7): l(
, c) =
xl u ( , c ) c
(7)
where xl denotes the location vector of the lth geophone, and u ( , c ) is the DOA’s unit vector. A steering vector is then constructed for signals recorded from all geophones by Eq. (8):
t ( , c ) = [eiw
1 ( , c)
eiw
l ( ,c)
]
(8)
where w is the angular frequency. The steering vector can be projected onto the noise subspace by Eq. (9): Fig. 7. Dispersion curves by picking the maxima of the dispersion image spectrum shown in Fig. 6.
B ( , c) =
1 t ' ( , c ) Ul
2
(9)
where t ( , c ) denotes the transpose of the steering vector’s complex conjugate. The steering vector scans through the entire coverage of azimuth and phase velocity for beamforming. Ul is a l × (l m) matrix, formed by the eigenvectors, which is derived according to the spatial correlation matrix S, by searching for the smallest (l m ) eigenvalues. The azimuth of the DOA and the corresponding phase velocity of the principal ambient noise can be identified by the peaks in the MUSIC spectrum, denoted as the beamformer B ( , c ) . With the characterized DOA of ambient noise field, field acquisition and signal processing can be carried out accordingly. Several field testings have been conducted all over Singapore. We have found that the road traffic is the major attribution to ambient noise in Singapore. Hence, the principal DOA of ambient noise is generally from the nearby major road. In view of page limits and to avoid unnecessary repetition, we selected three actual field tests carried out at three different sites in Singapore. Fig. 2 shows the locations of the testing sites on the geological map of Singapore. '
0
10
20
30
3. Crosscorrelation vs. MASW and MAM
40
This section presents the application of crosscorrelation with the case study at Site #1. We also compare its performance versus the conventional surface wave survey, e.g., the active MASW and passive MAM. Site #1 is located in the center of Singapore, in the region of Bukit Timah Granite Formation (Fig. 2). The detailed location is shown by the satellite image in Fig. 3(a). The testing site is in a public park, namely Bishan – Ang Mo Kio Park, near a junction of two major roads. Both active and passive data acquisition have been carried out at a same site, but at different times. There is a reference borehole in the middle of the active geophone array and the corner of the passive geophone array as shown in Fig. 3. Fig. 3(b) presents the array configuration of the active and passive field acquisition. The active testing deployed 24 geophones in a straight-line formation with a 1.5 m spacing between each geophone. The offset of the source to the nearest geophone was 5.5 m. Though 20 shots by a 7-kg sledge hammer were engaged at both sides of the linear array, the result presented in later part is just based on one side’s shots. The sampling rate was 0.5 ms with the duration of 1 s for each shot. In addition, 11 geophones with 6 m spacing in an ‘L’ shape formation were used for passive testing; as noted, the corner coincided with the reference borehole as well as the middle of active testing. The sampling rate was 2 ms with a record duration of 30 mins. By applying the MUSIC beamforming using Eqs. (6) to (9), the beamforming of 4.5 – 20 Hz has been worked out based on the ambient noise signals of 30 mins recorded in the ‘L’ shape array. The result is shown in Fig. 4, in which the colormap represents the beamformer. It is the MUSIC spectrum B ( , c ) by Eq. (9). The radius denotes the phase velocity in m/s and the azimuth denotes the DOA. The selected frequency band of 4.5–20 Hz is the band of interest for near-surface site
50
Backfill (Very soft to soft soil) Residual Soil (Firm soil) Completely weathered granite (Firm to stiff soil) Highly weathered granite (stiff soil) Moderately weathered granite (moderate strong rock) Moderately weathered granite (strong to very strong rock) Fig. 8. 1D shear wave velocity profiles inverted by different dispersion curves. The bore log of the reference borehole is shown side by side in scale. The weathering layering is shown in legend.
transformed to the frequency domain. For instance, there are l numbers of geophones. In each geophone, n numbers of signal data are recorded. Thus, the recorded noise forms a matrix (l × n) . Spatial correlation matrix S is expressed as Eq. (6):
S = NN'
(6)
where N' is the complex conjugate transpose ofN. In MUSIC, the principal signal and noise spaces can be distinguished by eigenvalues or eigenvectors. Supposing there are m large 323
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(a)
Testing site N
(b)
(c)
#1 #2 #3 #4 #5 #6 #7 #8
11 veridical geophones @ 8m c/c in ‘L’ shape N
N
8 multi-component geophones @ 8m c/c Fig. 9. Detailed location plan and array configuration at Site #2: (a) Site #2 location, (b) detailed location and the passive testing array for characterizing the DOA, (c) linear array configuration of multi-component geophones and the directions of the two horizontal components, with trace number indicated.
after vertical stacking are shown in Fig. 5(a). Fig. 5(b) is the vertical stack of the passive signals obtained by splitting the entire 30 min of data into a 1sec-window with 50% overlapping. Using Eq. (5) and setting geophone #6 (i.e., the corner geophone of the ‘L’ shape array) as the virtual source, green’s functions are approximated by crosscorrelation and shown in Fig. 5(c). The change from Fig. 5(b) and (c) exhibits an apparent transformation of random ambient noise to clear signal, as a realization of the crosscorrelation depicted in a conceptual sketch (Fig. 1(a) and (b)). The green’s functions shown in Fig. 5(c) agree with the MUSIC beamforming results shown in Fig. 4, as there is a clear signal from geophone #6 to #1 which is in line with the principal DOA, NW towards SE in this case. For another leg of ‘L’ array, as shown in Fig. 5(c), it appears that there were signals coming from both directions of geophone #6 to #11. Therefore, the green’s functions of geophone #1 to #6 are chosen for further signal processing to construct a dispersion curve. The signal processing based on both active waveforms and the green’s functions by crosscorrelation follows the classic phase shift method suggested by Park et al. (1999) as written in Eq. (10):
Fig. 10. Beamforming results of 3–15 Hz ambiont noise at Site #2: colormap denotes the normalized energy level, radius denotes the phase velocity, azimuth denotes the DOA.
investigation, which is from about 10 to tens of meters below ground. It is shown that ambient noise within this frequency band was principally coming from the north west (NW) towards the south east (SE). This outcome is explainable since the testing site is located at the junction of two major roads. Ambient noises within 4.5 – 20 Hz are reasonably attributed to the road traffic of the near field, and the DOA from the MUSIC beamforming reaffirms it. With the understanding of the DOA after characterizing ambient noise field by MUSIC beamforming, only geophones #1 to #6 (Fig. 3(b)) are chosen to derive the estimated green’s functions by crosscorrelation, since they are almost in line with the principal DOA, which is aligned along NW - SE. A vertical stack of all the shots at one side of the active testing is carried out to increase the signal to noise ratio (S/N). The waveforms
F (c , w ) =
+
F (x , w ) iw x e c dx |F (x , w )|
(10)
where x is the location vector of geophones, c is the phase velocity and w is the angular frequency. The peak of the dispersion spectrum F (c, w ) indicates the dispersion curve. For MAM, using the passive signals acquired in the ‘L’ shape array, spatial auto correlation (SPAC) presented by Hayashi (2008) is adopted for the signal processing to obtain the dispersion curve. SPAC is expressed in Eq. (11):
SPAC (x , w ) =
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1 2
2 0
Re (COH (x , , w )) d = J0
w ×x c (w )
(11)
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Fig. 11. 3–15 Hz bandpass filtered waveforms from (a) Vertical component and (c) Horizontal 2 component and estimated green’s function by crosscorrelation: (b) from Vertical component and (d) Horizontal 2 component.
where Re means the real number, x is the location vector of geophones, c (w ) is the phase velocity, w is the angular frequency, COH is coherence and is the azimuth of the geophone to the reference geophone. J0 is Bessel function. The dispersion spectrum SPAC (x , w ) is approximated by fitting the integration of the coherence matrix to the first order of Bessel function. Fig. 6 shows the dispersion spectrum from active testing (24 geophones in linear formation), passive testing—MAM (11 geophones in ‘L’ shape array), and passive testing—crosscorrelation (6 geophones in linear formation along the principal DOA of ambient noise). It is apparent that the shape and pattern of high energy zones in Fig. 6(a) and (c) are more closely agreed, whereas the ones in Fig. 6(b) are rather departed from them. This observation is more visible in Fig. 7, where the picks of the dispersion spectrum are extracted and plotted together. The dispersion curves from active testing and crosscorrelation are almost overlapping, nevertheless the dispersion curve of low frequency (below 6 Hz in this case) has not been retrieved from the active test due to the ambiguity from the low S/N. The dispersion curve processed by SPAC using the signal acquired from the MAM (‘L’ shape) seems to match perfectly only between about 6–7 Hz with the dispersion curve from active testing. The phase velocity even drops in the low frequency zone, which is not expected in this region based on the experience and knowledge of local geology. In fact, a similar trend/pattern was observed in other test sites although we do not present here to avoid the repetition of same results. Based on the dispersion curve, an initial model is approximated by converting the dispersion curve to a shear wave velocity profile using Eqs. (12) and (13):
h=a×
Vs =
c b
=a×c w
Bullen et al. (1985). A genetic algorithm (GA) is used for the inversion of the dispersion curve. A 1D shear wave velocity profile is produced by choosing the one with the best fit of inverted dispersion curve compared with the experimental measurement. As shown in Fig. 8, the three methods produce similar results in the upper 12 m, except crosscorrelation for the upper 4 m. From 12 m downwards, the crosscorrelation indicates VS is more than 450 m/s, whereas MAM is less and active MASW is even greater. Based on the measured dispersion curve, the VS profile may not be reliable for active testing beyond 450 m/s (e.g., at deeper depth). Nevertheless, both active MASW and crosscorrelation show a similar pattern and shape in the VS profile. More importantly, they both indicate the sudden increase of the VS at about 25 m depth which just corresponds to the bedrock depth as shown in the bore log of the reference borehole. At this site, the VS inverted from the dispersion curve by SPAC with the ‘L’ shape MAM gives relatively larger departure, especially in deeper layers in terms of VS magnitude. In short, crosscorrelation is able to produce a reasonable green’s functions. Although there are some guidelines that suggest long spatial coverage and temporal acquisition (Xia et al., 2009, Foti et al., 2018), in our investigation, we found that the investigation depth can be increased with good quality passive signals. The estimated green’s functions can be used to produce a comparable and reasonable dispersion curve as demonstrated through the comparison with active MASW result. Eventually, it is feasible to apply crosscorrelation to estimate the VS profile reasonably. It also can provide reliable outcomes for lower frequency bands which the active test may not be able to. It increases the illumination depth of site investigation from active MASW.
(12)
4. Application of crosscorrelation for Rayleigh and Love waves Most surface wave surveys are based on the Rayleigh wave. Some recent investigations on Love waves were reported based on active testing (Eslick et al., 2008, Pan et al., 2016, Pegah et al., 2017). In this section, we present the 2nd case study to demonstrate that both Rayleigh and Love waves are captured passively by crosscorrelation, using multicomponent geophones. Crosscorrelation is applied to process the
(13)
where h is the depth of each soil layer, is the wavelength, c is the phase velocity, w is the angular frequency, a is set as 1/3 in this case (typical range: 1/2 to 1/4 (Nazarian et al., 1983)), Vs is the shear wave velocity and b is a constant in the range of 0.9–0.95 as suggested by 325
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neighborhood park, namely Springleaf Garden. The nearest major road is the Seletar Expressway in the south of the site, as shown in Fig. 9(a). As discussed in the methodology, the condition to apply crosscorrelation needs to ensure the geophones along the principal DOA of ambient noise. Due to the reciprocity of the Rayleigh wave and particle motion of Love wave, to find and distinguish the Love wave becomes extremely dependent on the DOA. The Love wave can be measured, identified, and distinguished only if the horizontal component geophones installed are orthogonalized to the principal DOA of ambient noise. All the other azimuths would measure a mixture of Rayleigh and Love waves. To characterize the DOA of ambient noise field, an ‘L’ shape array of 11 single component geophones (Fig. 9(b)) was placed to acquire ambient noise for about 30 mins. Fig. 10 shows the beamforming results. It indicates that for the band of 3–15 Hz, the principal DOA of ambient noise is from south (S) and south east (SE) towards north (N) and north west (NW). We can also note that there is secondary DOA of ambient noise which is from northwest (NW) towards southeast (SE). The observation tallies with the site location in relation to adjacent roads as shown in Fig. 9. The expressway may be the main contributor of the passive source for this site. Based on the understanding of ambient noise field, eight multicomponent geophones were installed on site as shown in Fig. 9(c), at 8 m intervals and for about 30 mins recording duration. There are two horizontal components in each multi-component geophone, and the directions were kept constant throughout, as indicated in Fig. 9(c); Horizontal 1 direction was along the direction of the linear array, as well as along the principal DOA, while Horizontal 2 direction was normal to the array as well as the principal DOA. Hence, the particle motion measured by Horizontal 2 directional component should be mainly attributed to Love waves. The original Rayleigh and Love waveforms stacked over 1sec-windows are plotted in Fig. 11(a) and (c). The green’s functions are calculated by referring to geophone #1 as a virtual source. Fig. 11(b) and (d) are for Rayleigh and Love waves, respectively. With the estimated green’s functions, the dispersion spectra of Rayleigh and Love waves are shown in Fig. 12(a) and (b). The maximum of the dispersion spectrum is picked to retrieve the dispersion curves. The dispersion curves of Rayleigh and Love waves are shown in Fig. 12(c). Based on the processed dispersion curves, the vertically-polarized shear wave velocity (SV) and horizontally-polarized shear wave velocity (SH) are derived by inverting the dispersion curves of Rayleigh and Love waves, respectively. Fig. 13 shows the 1D SV and SH profiles with the bore log of the reference borehole aside. The bedrock (moderately weathered rock) is found at 32 m deep from the bore log. This is close to the indicated level on SV and SH profiles, which shows distinct increases. Considering the general relation between VS and geostatic stress states (Ku and Mayne, 2012, 2013, 2015, Pegah et al., 2017), the observed VS anisotropy is not surprising due to large in-situ horizontal stress in the Bukit Timah region (Sharma et al., 1999). This 2nd case study shows that crosscorrelation can be successfully used for the analysis of both Rayleigh and Love waves. The SV and SH profile can be utilized to infer the bedrock depth. Fig. 12. Dispersion spectrum from green’s functions by crosscorrelation from (a) Vertical component, (b) Horizontal 2 component and (c) extracted Rayleigh and Love waves’ dispersion curves by picking the maxima of Fig. 12(a) and (b).
5. Application of crosscorrelation for 2D profiling Previous sections introduced crosscorrelation to produce a 1D shear wave velocity profile. This section presents a case study to demonstrate the feasibility of producing 2D shear wave velocity profiles. 24 Geophones have been placed in a grid of 8 m spacing on site #3 (Fig. 2). The exact site location and geophone array configuration are shown in Fig. 14. The 40 m × 24 m grid array has been set up in the sport field of the National University of Singapore (NUS). An expressway is to the north east, while a campus road is located at its south and south west.
passive signals for green’s functions, which are used to derive the dispersion curves of Rayleigh and Love waves. The polarization of shear waves in vertical and horizontal directions is estimated from Rayleigh and Love waves, respectively. The second site (Fig. 2) is located in the north of Singapore, in the region of Bukit Timah Granite Formation. The exact location is shown in Fig. 9. The testing site is in a
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The field acquisition was held in the morning rush hour from 7.30am to 9.00am with a sampling rate of 2 ms. Beamforming has been carried out by MUSIC with the entire recorded signals from the 24 geophones. Fig. 15 shows the results of ambient noise at 6–20 Hz. It indicates ambient noise mainly comes from two directions, south/south west and north east. This is expected as it coincides with the nearby major roads. Together with the other two cases mentioned earlier, the traffic appears to be the main contributor of ambient noises within the frequency band of interest. Based on the principal DOA of ambient noise, it is reasonable to choose the six geophones in each of the four rows to process separately, since they are along the principal DOA. Fig. 16(a) presents the dispersion spectra of each of the four rows, using the approximated green’s functions by crosscorrelation. Fig. 16(b) shows the extracted dispersion curves, based on which to estimate shear wave velocity profiles individually. Interpolation has been carried out to produce a 2D (Fig. 17) profile over 50 m deep and 24 m wide, based on the shear wave velocity profiles from each of the four rows. This site is in sedimentary geological formation. Since this section just aims to illustrate the possibility of creating a 2D profile, we may choose an arbitrary threshold. Nevertheless, to make the result more realistic, we refer to the bedrock depth from a nearby borehole. We find the cut-off velocity can be chosen as 700 m/s. This is quite close as Moon et al. (2017) reported by using MAM (SPAC). The white dashed line in Fig. 17 indicates the inferred bedrock profile, which agrees with the reference boreholes near the testing site.
0.0 10.0 20.0 30.0 35.0 Legends
Backfill (Very soft to soft soil)
Residual soil Completely weathered granite Moderately weathered granite rock
Fig. 13. 1D shear wave velocity profiles inverted by Rayleigh and Love waves’ dispersion curves. The bore log of the reference borehole is shown side by side in scale. The weathering layering is shown in legend.
6. Discussion In this study, crosscorrelation has been demonstrated to be capable of and suitable for geotechnical site investigation; 1D and 2D shear wave velocity profiles can be reasonably estimated, so as bedrock depth can be accurately inferred. Ambient noise is mainly attributed to the road traffic in Singapore. It can be used as the source for passive surface wave survey. Both Rayleigh and Love waves can be captured and utilized by crosscorrelation. A short field acquisition (30 min in the cases investigated in this paper), and a simple, short linear array (30–40 m) with just six to eight geophones are found adequate. It makes the implementation more convenient and less subject to site constraints, as compared with the conventional MAM that requires a large open space in which to place a 2D array with more geophones. It shall be noted that there are conditions to be complied with in order to apply crosscorrelation. The DOA of ambient noise needs to be characterized to determine the orientation of the linear geophone array. Hence, although the DOA would be intuitively estimated (e.g., location of major road) based on our cases, a 2D array may be still required near the interested site to confirm the DOA of ambient noise. In the event of constructing a 2D VS profile, crosscorrelation is practically more convenient compared to active MASW, since it doesn’t require intense active sources. Moreover, passive MAM would not be an ideal option at all for constructing 2D VS profiles. Another point to be noted may be the near-field sources and activities which may be highly irregular over the period of recording compared to far-field effects, e.g., sudden footsteps or high amplitude noises. It is recommended to keep the geophones less disturbed in the field acquisition. Other than the advantages and pre-conditions of crosscorrelation, the fundamental assumption of 1D surface wave shall always apply, i.e., the soil layering model is assumed horizontally homogeneous. In other words, if the ground condition of the testing site varies significantly,
Fig. 14. Detailed location plan and geophone array configuration at Site #3.
Fig. 15. Beamforming results of 6–20 Hz ambient noise at Site #3: colormap denotes the normalized energy level, radius denotes the phase velocity, azimuth denotes the DOA.
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(a)
(b)
Fig. 16. Dispersion curves of the 4 rows at Site #3; (a) dispersion images and (b) extracted dispersion curves.
none of 1D surface wave testing is suitable, including crosscorrelation. Last but not least, the shear wave velocity profile from crosscorrelation also heavily relies on the optimization of the inversion, which is a classic non-linear, non-unique problem. To mitigate the inversion problem, the initial model is constrained by referring the dispersion curve to velocity and wavelengths. By doing so, the final shear wave velocity profile is found more reasonable compared to leaving the initial model with no constraints.
surface wave survey has been investigated and applied in Singapore. It is found easier and more practical to be implemented on site than the conventional MAM that requires a large 2D array. The DOA of ambient noises needs to be identified prior to placing the linear geophone arrays for crosscorrelation. Multi-component geophones can be used to capture both Rayleigh and Love waves, provided the principal DOA is orthonormal to a horizontal component. 2D shear wave velocity profiles can be constructed effectively by constructing several lines of the linear array, either simultaneously or one by one. The shear wave velocity profiles obtained from the proposed methodology can be successfully used to infer bedrock depth, which is valuable for geotechnical site investigation for tunneling and underground works.
7. Conclusion Crosscorrelation, a feasible and attractive complementary passive
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0.0 10.0 20.0 30.0 40.0 50.0
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Estuary Clay Residual soil Completely weathered sediments Moderately weathered sedimentary rock Slightly weathered sedimentary rock Fig. 17. 2D shear wave velocity profile cutting across the short side of testing site. Colormap denotes the velocity contour. Bore log of the reference borehole is side by side.
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