Norfarah Nadia Ismail
*1
, Sung-Ho Joh
†1
, and Raja Hassanul Musa Raja Ahmad
1
1
Department of Civil and Environmental Engineering, Chung-Ang University, Korea
ABSTRACT
Surface-wave methods are beneficial due to their intrusive features and have been successful in determining subsurface profiles of normally dispersive geotechnical sites. However, when a soft layer is entrapped between stiffer layers, surface-wave data are complicated by multiple modes of surface waves and multiple reflections of body waves. Therefore, surface-wave velocities are poorly evaluated due to the predicament in interpreting surface-wave data. In this paper, a refined version of the conventional beamforming technique was proposed to make a reliable stiffness profiling even for the geotechnical sites with a soft entrapped layer. The refined version is capable of a more practical determination of surface-wave velocities and also a more rational inversion analysis of surface-wave dispersion relations. Practicality in determination of surface-wave velocities was implemented by an automated determination of surface-wave velocities and a seamless recovery of spatially-aliased wave numbers. Also rationality in inversion analysis was attained using apparent surface-wave velocities based on the locations of source and receivers. Validity of the proposed scheme was verified using synthetic seismograms generated from a layered system with a soft entrapped layer. And feasibility and reliability of the proposed method was proved by field applications at a highway compaction site. Lastly, the results were compared with the ones from downhole tests, which show a good agreement between two shear-wave velocity profiles.
Keywords: velocity inversion, apparent velocities, inversion, beamforming technique.
1.
INTRODUCTION
Accurate stiffness profiling of geotechnical sites with a soft layer entrapped has been a challenge to researchers in recent years. Recently, some of surface-wave inversion analyses have been focused on higher-mode velocities to evaluate an improved shear-wave velocity profile. However, sometimes mode velocities are complicated in case of inversely dispersive sites and soft-entrapped-layer sites. Resulting velocities are not necessarily following either a fundamental or a specific normal mode. This paper attempts to elaborate the determination of surface-wave velocities at complicated sites with a soft entrapped layer. As an optimal surface-wave method for the complicated sites, a refined version of the conventional beamforming technique was proposed to
* Corresponding author: Email: shjoh@cau.ac.kr
†
Presenter: Email: norfarahnadia@gmail.com
ITC2012 (Oct 30- Nov 21, 2012, Kuala Lumpur, Malaysia)
1

| International Technical Conference 2012 | N. N. ISMAIL∙S. H. JOH∙R. H. M. RAJA AHMAD make a reliable stiffness profiling for the geotechnical sites with a soft entrapped layer. In this paper, background theory pertinent to the proposed technique is discussed in detail. Later, validity and reliability of the proposed method was verified using a field application.
2.
LIMITATIONS OF STIFFNESS IMAGING FOR A GEOTECHNICAL SITE WITH
VELOCITY INVERSION
2.1.
Mode Misidentification
Fundamental and higher modes in surface-wave propagation are essential features in a multi-layered system. When surface waves propagate through a multi-layered system, the stiffness of each layer affects the propagation of the surface waves. Dynamic stiffness matrix method (Kausel and Roesset,
1981; Kausel and Peek, 1982) can determine apparent surface-wave velocities corresponding to the locations of source and receivers. In Figure 1, the apparent velocities determined by dynamic stiffness matrix method are compared with fundamental- and higher-mode velocities for three layered systems: normally dispersive site, shallow bedrock site and a soft layer entrapped site.
For a typical site with increasing stiffness or so called a normally dispersive layer, the governing mode is usually the same as the fundamental mode. But this is not true for a shallow bedrock site or a soft layer entrapped site. Typically for a high-frequency range, phase velocities of normal modes are close to each other, and, therefore, it is not easy to separate fundamental and
S R S R S R
5.0 m
10.0 m
Vs=150 m/sec
Vs=300 m/sec
5.0 m
Half-space
Vs=150 m/sec
2.8 m
6.1 m
2.6 m
3.9 m
Vs=253 m/sec
Vs=388 m/sec
Vs=556 m/sec
Vs=142 m/sec
7.8 m
Half-space
Vs=450 m/sec
Vs=516 m/sec
Vs=450 m/sec
(a) *R = 1m *S = 3,6,12,24m
600
500
400
Source Offset
3m
6m
12m
24m
300
200
(b) *R = 1m *S = 3,6,12,24m
600
500
400
Source Offset
3m
6m
12m
24m
300
200
Half-space
(c)
Vs=930 m/sec
*R = 1m *S = 3,6,12,24m
600
500
400
Source Offset
3m
6m
12m
24m
300
200
100
0
6
1
Fundamental Mode
Higher Modes
2 4 6 2
10
Wavelength, m
4 6
100
2
100
0
6
1
Fundamental Mode
Higher Modes
2 4 6 2
10
Wavelength, m
4 6
100
2
100
0
6
1
Fundamental Mode
Higher Modes
2 2 4 6 2
10
Wavelength, m
4 6
100
Figure 1: Phase velocity dispersion curves for typical geological sites: (a) normally dispersive site, (b) shallow bedrock site and (c) complicated site with a soft layer entrapped
2 ITC2012 (October 30-November 01, 2012, Kuala Lumpur)

Profiling of Geotechnical Site with Velocity Inversion by Beamforming Technique | Civil Engineering | higher modes up to a high frequency range. It is well known that this instability in inversion analysis generally results in large fluctuations in resulting shear-wave velocities (Xia et al. 2000). In surface-wave propagation, the superposed mode is also an important feature, because it is the actual mode generated during testing (Joh et al., 2006). For a shallow bedrock site and a complicated site, as shown in Figure 1(b) and 1(c), the superposed mode does not fall into specific normal modes, but it is somewhere between the normal modes. Superposed mode is also called apparent velocity or an effective velocity, which is dependent on the actual locations of source and receivers. Currently,
SASW and CSW are using apparent velocities in their analysis to obtain shear-wave velocity profile.
In addition to these methods, the recently evolved beamforming technique is also utilizing apparent velocities in its approach to obtain a shear-wave velocity profile.
2.2.
Interpretation of Surface-Wave Propagation at a Site with Strong Stiffness Contrast
In surface-wave measurement, one critical step in determination of the dispersion curves is to interpret a phase spectrum (Joh 1996). The region with low-quality phase angles where the phase angles do not follow a general trend is eliminated or masked. In case of shallow bedrock site or a geotechnical site with a soft entrapped layer, strong stiffness contrasts can be observed, thus leading to interference between different wave groups propagating with different phase velocities. This interference is the indication of mode collision and may cause misleading in the resulting values of
(a)
0
-20
-40
(b)
-60
180
90
0
-90
-180
0
(c)
600
#1
50 100
Frequency,Hz
R
1
= 24m
R
2
= 48m
150 200
S-Wave Velocity, m/sec
500 1000
0
0
500
10
400 20
30
300
200
100
Phase not Corrected
Phase Corrected
Fundamental mode
Normal modes
0
3 4 5 6 7 8 9
10
2 3 4 5 6 7 8 9
Frequency, Hz
100
2
Figure 2. Mode related problems experienced by SASW method: (a) time traces, (b) phase spectrum and (c) phase velocity dispersion curves.
ITC2012 (October 30-November 01, 2012, Kuala Lumpur)
3

| International Technical Conference 2012 | N. N. ISMAIL∙S. H. JOH∙R. H. M. RAJA AHMAD a phase velocity dispersion curve. In Figure 2, numerical simulation for a complicated model of a geotechnical site was performed for SASW analysis using the dynamic stiffness matrix method.
Synthetic seismograms in Figure 2(a) were determined using a 24-m long measurement array with two receivers deployed at the locations of 24 m and 48 m from the source, and used to generate impulse response. The resulting phase spectrum in Figure 2(b) is mixed up with phase-difference spectra corresponding to two different wave groups. Phase difference spectrum of the second wave group at frequencies around 15~20 Hz should be interpreted differently from the way it appears, because it is covered up by the first wave group and not shown. The need of experienced interpretation is crucial in this case. Without experienced interpretation, one can simply make a mistake in counting the number of cycles and resulted in an incorrect shear-wave velocity profile.
Resulting phase velocities based on the corrected and the non-corrected phase spectra are compared in Figure 2(c).
3.
BEAMFORMING TECHNIQUE FOR THE IMPROVED DETERMINATION OF
DISPERSION RELATION
Beamforming technique was developed for transmitting and receiving signals in a prescribed direction. Once source and receiver locations are known, together with information on signal delays between receivers, wave velocities propagating through receivers can be directly determined.
Beamforming technique has been successfully employed for surface-wave measurements at geotechnical sites by researchers (Zywicki, 1999; Zywicki and Rix, 2005). Their beamforming technique, however, is a long measurement array based on 15 receivers with uneven receiver spacings ranging 0.94 m to 10 m, as shown in Figure 3(a). The measurement array is 60-m long and the source offset is 0.94 m. In this paper, a new measurement configuration was suggested to
Figure 3: Measurement array for beamforming technique: (a) Zywicki’s long measurement array and (b) short measurement array. alleviate the difficulties involved in using a long measurement array and also to identify localized
4 ITC2012 (October 30-November 01, 2012, Kuala Lumpur)

Profiling of Geotechnical Site with Velocity Inversion by Beamforming Technique | Civil Engineering | lateral variability. This configuration includes scheme for array length, number of receivers and source offset. As shown in Figure 3(b), the length of measurement array is shortened to 3 to 9 m long, number of receivers is reduced from 15 to 4, and multiple locations of source are employed to generate surface waves with a wide range of wavelength. Typical source offsets are R, 2R, 4R, 8R and 16R from the first receiver, where R is the array length. The beamforming technique based on the measurement configuration of Figure 3(b) is referred to the short-array beamforming technique.
Wavelengths of surface waves measured by the beamforming technique are limited to the minimum wavelength, which is governed by receiver spacing of the array, d . The limitation of measured wavelength is related with spatial aliasing. Spatial aliasing is the phenomenon in which a wave number is decreased by 2

/ d when the wave number exceeds maximum wave number k max
(

2

/ d ) (Joh 2012). Therefore, the wave number that can be identified is limited to k max
, which gives rise to the problem of aliasing. However, the aliased wave number can be recovered by the formulation in Eq. (1). Thanks to the recovery of aliased wave numbers by Eq. (1), the short-array beamforming technique can characterize stiffness of shallow to deep material for the measurement array used for the tests, so that an abrupt change of stiffness in layered system can be identified in details.
k
= D d j
= D j +
2 n p d
= D d j
+
2 n p d
= k
+
2 p d n , ( n

0 , 1 , 2 ,  ) (1)
The short-array beamforming technique has a capability of alleviating the difficulties induced at complicated geotechnical sites with strong stiffness contrasts between layers, including the site with a soft layer entrapped. To demonstrate this capability of the short-array beamforming technique in dealing with complicated sites, numerical simulations were performed for the geotechnical site with a soft entrapped layer in Figure 2(c) by the proposed beamforming technique.
Four receivers were employed at the locations of 24 m, 25 m, 26 m, and 27 m from the source and the synthetics seismograms are shown in Figure 4(a). Beamforming technique directed in generating of f-k spectrum, as shown in Figure 4(b) and provides an automated interpretation.
Therefore, it does not have the complication as experienced by SASW test. In this case, beamforming technique has the advantage of automated interpretation and resulted in a more sensible phase-velocity dispersion curve, which is equivalent to fundamental- and higher-mode velocities as well as SASW velocities with phase correction, as shown in Figure 4(c). In Figure 4(c), the fundamental-mode velocity has a trend of a rising and falling pattern at the frequency range of
15 to 30 Hz, and then the velocity approaches to the surface-wave velocity of the first layer.
Therefore, this can be an evidence that the short-array beamforming technique can produce a successful interpretation of surface-wave data even for the complicated sites.
ITC2012 (October 30-November 01, 2012, Kuala Lumpur)
5

| International Technical Conference 2012 | N. N. ISMAIL∙S. H. JOH∙R. H. M. RAJA AHMAD
(a)
0
-20
-40
-60
R
1
= 24m
R
4
= 27m
(b)
(c)
200
100
0
0 2 4 wavenumber, k
6
600
500
400
300
200
100
0
3
Evidence of velocity inversion
Beamforming technique
Fundamental mode
Higher modes
4 5 6 7 8 9
10
2 3 4 5 6 7 8 9
100
Frequency, Hz
2
8
Figure 4: Improved definition of dispersion relations by beamforming technique: (a) time traces (b) f-k maps and (c) dispersion curves
4.
VALIDATION OF BEAMFORMING TECHNIQUE USING REAL FIELD DATA
Field measurements were made to verify the validity of beamforming technique at a geotechnical site with a complicated layering. The measurements were done at a highway compaction site of
Nonsan, Korea. For reference of shear-wave velocity, downhole tests were done at the same location where beamforming tests were made. Also the boring made for the downhole tests revealed bedrock located at the depth of 16 m. Beamforming tests were performed using four 2-Hz geophones with 1-m receiver spacings. The source was applied at three different source offsets, 3, 6,
12 m from the first geophone.
Resulting dispersion curves from beamforming test is presented in Figure 5(b) for all source offsets. For the experimental dispersion curves, array inversion analysis (Joh 1996) was performed to determine the shear-wave velocity profiles. The array inversion analysis utilizes the actual locations of source and receivers for computing theoretical velocities by forward modeling analysis.
Therefore, the array inversion analysis can match each individual experimental dispersion curve with the corresponding theoretical dispersion curve for different source offsets. As shown in Figure
5(b), experimental and theoretical dispersion curves are well compared, which indicates that the inversion analysis was reliably performed. The shear-wave velocity profile is shown in Figure 5(c) and being compared to downhole test and CAP-SASW test. Two different modes corresponding to two different layers with varying stiffness can be seen clearly at frequency rage of 25 to 40 Hz. This
6 ITC2012 (October 30-November 01, 2012, Kuala Lumpur)

Profiling of Geotechnical Site with Velocity Inversion by Beamforming Technique | Civil Engineering |
(a)
500
400
300
200
500
400
300
200
500
400
300
200
100
S = 3m
100
S = 6m
100
S = 12m
0
0 2 4 6 8 wavenumber, k
10 12
0
0 2 4 6 8 wavenumber, k
10 12
0
0 2 4 6 8 wavenumber, k
10 12
(b)
600
500
400
Source Offset
3m 6m 12m
: Exp.
: Theo.
600
500
400
Source Offset
3m 6m 12m
: Exp.
: Theo.
(c)
Shear-Wave Velocity, m/sec
300 600 900 1200
0
0
5
300 300
10
Downhole
CapSASW
Beamforming
200 200
15
100
0
10
Fundamental mode
Higher modes
2 4 6 8
100
Frequency, Hz
2 4
100 Fundamental mode
Higher modes
0
4 6 8
1
2 4 6 8
10
Wavelength, m
2
20
25
30
Figure 5: Field application: (a) f-k plots for three different source offsets, (b) dispersion relations in frequency and wavelength domain and (c) comparison of shear-wave velocity profiles from beamforming technique, downhole test and CAP-SASW test indicates that beamforming technique can reliably investigate shear-wave velocities of complicated geotechnical sites with velocity inversion. The comparison of the beamforming profile and the
CAP-SASW profile indicates that the beamforming technique has equivalent reliability to the
CAP-SASW technique. Also, judged from the fact that the compacted embankment is about 10-m thick and the bottom-most layer is about 2-m thick rock debris fill, beamforming technique is a more successful technique to identify the soft-entrapped layer between stiff layers.
5.
SUMMARY AND CONCLUSIONS
In this paper, the short-array version of the beamforming technique was proposed to determine a better and reliable shear-wave velocity profile for complicated sites like the one with a soft entrapped layer. The short-array beamforming technique has unique features different from the conventional one. First of all, the short-array beamforming technique is based on a short (i.e. 6- to
9-m long) measurement array with four receivers deployed. Secondly, the technique can evaluate surface-wave velocities for short wavelengths by recovery of spatially-aliased wave numbers.
Lastly, the technique utilizes apparent velocities for the actual locations of source and receivers for inversion analysis. The short-array beamforming technique was proved to have validity and reliability by two different approaches: 1. numerical simulations of surface-wave measurements at a geotechnical site with a soft entrapped layer, 2. field application made at a highway compaction site
ITC2012 (October 30-November 01, 2012, Kuala Lumpur)
7

| International Technical Conference 2012 | N. N. ISMAIL∙S. H. JOH∙R. H. M. RAJA AHMAD over a soft original ground. The comparison using downhole test results and boring information confirmed that the beamforming technique has equivalent accuracy to the CAP-SASW technique.
6.
ACKNOWLEDGMENTS
This research was part of the project, “Development of Surface-Wave Technique for Geotechnical
Structures with Large Aggregate Fills”, supported by Korea MLTM and the 2010 Chung-Ang
University ASEAN Young Scientist Scholarship (CAYSS). Their financial support is gratefully acknowledged.
REFERENCES
Joh SH (1996). Advances in the data interpretation technique for spectral-analysis-of-surface-waves (SASW) measurements. Ph. D. thesis, Department of Civil Engineering, University of Texas.
Joh SH (2012). Refined beamformer for directional surface-wave measurements at geotechnical structures. Presented at
91th Annual Meeting of the Transportation Research Board.
Kausel E and Roesset JM (1981). Stiffness matrices for layered soils. Bulletin of the Seismological Society of America,
71(6), pp 1743-1761.
Stokoe KH, Joh SH, and Woods RD (2004). Some contributions of in situ geophysical measurements to solving geotechnical engineering problems. 2 nd International conference on site characterization, Porto, Portugal, pp.
97-133.
Xia J, Miller RD, and Park CB (2000). Advantages of calculating shear-wave velocity from surface waves with higher modes. Society of Exploration Geophysicists 90 th Annual Meeting, Calgary, Canada, pp. 1295-1298.
Zywicki DJ (1999). Advanced signal processing methods applied to engineering analysis of seismic surface waves. Ph.
D. thesis, Department of Civil Engineering, Georgia Institute of Technology..
Zywicki DJ and Rix GJ (2005). Mitigation of near-field effects for seismic wave velocity estimation with cylindrical beamformers. Journal of Geotechnical and Geoenvironmental Engineering. 131(8), pp. 970-977.
8 ITC2012 (October 30-November 01, 2012, Kuala Lumpur)