Citation
An Appraisal of Surface Wave Methods for Soil Characterization

Material Information

Title:
An Appraisal of Surface Wave Methods for Soil Characterization
Creator:
Tran, Khiem Tat
Place of Publication:
[Gainesville, Fla.]
Publisher:
University of Florida
Publication Date:
Language:
english
Physical Description:
1 online resource (71 p.)

Thesis/Dissertation Information

Degree:
Master's ( M.E.)
Degree Grantor:
University of Florida
Degree Disciplines:
Civil Engineering
Civil and Coastal Engineering
Committee Chair:
Hiltunen, Dennis R.
Committee Members:
Roque, Reynaldo
Hudyma, Nick
Graduation Date:
5/1/2008

Subjects

Subjects / Keywords:
Fourier transformations ( jstor )
Frequency ranges ( jstor )
Phase velocity ( jstor )
Recordings ( jstor )
S waves ( jstor )
Signals ( jstor )
Soil profiles ( jstor )
Surface waves ( jstor )
Velocity ( jstor )
Wave dispersion ( jstor )
Civil and Coastal Engineering -- Dissertations, Academic -- UF
method, processing, signal, surface, wave
City of Newberry ( local )
Genre:
Electronic Thesis or Dissertation
bibliography ( marcgt )
theses ( marcgt )
Civil Engineering thesis, M.E.

Notes

Abstract:
Three popular techniques, Spectral Analysis of Surface Waves (SASW), Multi-Channel Analysis of Active Surface Waves (Active MASW) and Multi-Channel Analysis of Passive Surface Waves (Passive MASW), were conducted at two well-characterized test sites: Texas A & M University (TAMU) and Newberry. Crosshole shear wave velocity, SPT N-value, and geotechnical boring logs were also available for the test sites. For active multi-channel records, the cylindrical beamformer is the best method of signal processing as compared to frequency-wavenumber, frequency-slowness, and Park, et al. transforms. The beamformer provides the highest resolution of imaged dispersion curves, and its dominance of resolution at low frequencies over other methods allows achieving a reliable dispersion curve over a broad range of frequencies. Dispersion data obtained from all three surface wave techniques was generally in good agreement, and the inverted shear wave profiles were consistent with the crosshole, SPT N-value, and material log results. This shows credibility of non-destructive in situ tests using surface waves for soil characterization. ( en )
General Note:
In the series University of Florida Digital Collections.
General Note:
Includes vita.
Bibliography:
Includes bibliographical references.
Source of Description:
Description based on online resource; title from PDF title page.
Source of Description:
This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Thesis:
Thesis (M.E.)--University of Florida, 2008.
Local:
Adviser: Hiltunen, Dennis R.
Statement of Responsibility:
by Khiem Tat Tran

Record Information

Source Institution:
UFRGP
Rights Management:
Copyright by Khiem Tat Tran. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Embargo Date:
7/11/2008
Classification:
LD1780 2008 ( lcc )

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* Combined dispersion curve
* Final dispersion curve


1800

1600

1400

1200

1000

800

600

400

200


0 10 20 30 40 50 60 70
Frequency (Hz)



Figure 4-2. Dispersion curve for SASW of Newberry


Figure 4-3 Newberry active MASW recorded data in the time-trace (t-x) domain


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maximum attainable depths are 53 ft and 45 ft respectively. The maximum depth of investigation

at TAMU is not very deep even though the lowest frequency is as low as 3 Hz (SASW) because

of low phase velocity of soil profile that leads to a moderate maximum wavelength

(Xmax=V/27x.fmin). The bigger the maximum wavelength, the deeper depth of investigation is

obtained.

3.5 Soil Profile Comparison

The Vs profiles of TAMU derived from SASW, Active MASW, Passive MASW and

cross-hole test are all shown together in the figure 3.18. Also shown in the figure 3.18 are

crosshole Vs measurements, SPT N-values, material logs from a nearby geotechnical boring

conducted at the site.

First, regarding the shear wave velocity profiles from the three surface wave techniques, it

is observed that they are generally in good agreement. Consistent with the dispersion curves, the

SASW and passive MASW are in particularly good agreement. However, the active MASW is

slightly stiffer (higher velocity) at some depths, which is also consistent with the dispersion data.

Second, it is observed that the surface wave based shear wave velocity profiles compare

well with the crosshole results, especially at depths from 30 to 50 ft. Above 30 ft, a reversal

occurs in the profile attained from the crosshole tests that is not detected by the surface wave

tests. The surface wave tests are conducted over a relatively long array length that samples and

averages over a large volume of material, whereas the crosshole results are based upon wave

propagation between two boreholes that are only 10 ft apart, and thus these data represent a more

local condition at the site.

Lastly, there appears to be reasonable consistently between the shear wave velocity results

and the SPT N-values and material log. In the sand layer above a depth of about 30 ft, the shear



























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SV-Wave Velocity (ftIs)
0 500 1000 1500 2000







ctive MAS



I








SA--S
I






Crossholetest .
Active MASW I
-- -Passive MASW ,
SASW I
I I I


Standard Penetration
Resistance
(SPT N-Value)
10 20 30 40 50 60 70 80 90



.15

+ 14
3
+17



21


Figure 3-18. Soil profile comparison


Soil Profile


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. .. .......... ... .. . .. ... .... ...... .. .

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. . . . .


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-Experimental dispersion curve
- Theoretical dispersion curve


0 10 20 30 40

Frequency (Hz)


50 60


b)


0 500
0.0


-5.0 -


-10.0 --


-15.0 --


E -20.0 --


i -25.0 --


-30.0 --


-35.0 --


-40.0 --


-45.0


Shear wave velocity (ft/s)


Figure 4-11. Inversion result of Neberry obtained by SASW: a) Dispersion curve matching and
b) soil profile


1200


1000 +-


600



400


2000


2500









1200

1100

1000

900

800

700

600

500

400


0 10 20 30 40
Frequency (Hz)


50 60


Figure 3-11. Combined dispersion curve of TAMU from 2 shot gathers




TAMU_0-122 TAMU_98-220


1200

1100

1000

900

800

700

600

500

400

300

200


0 10 20 30 40
Frequency (Hz)


50 60 70


Figure 3-12. Final dispersion curve of TAMU obtained by active MASW


-----------------


--------- ----------









frequency (f) domain such as shown in figure 2-6. Here we observe that the most energy (largest

spectral amplitudes) is concentrated along a narrow band of p-f pairs. As with f-k, this narrow

band represents the fundamental Rayleigh wave mode of propagation. At a given frequency, the

phase velocity is calculated as the inverse of the slowness determined from the maximum

spectral amplitude. In practice, this process has been observed to produce better identification of

Rayleigh waves than does f-k.

2.3.2.3 Park et al. transform

In the mid to late 1990s, Park, Miller, Zia and others at the Kansas Geological Survey

began to develop the now popular SurfSeis software for the processing of multi-channel surface

wave data from geotechnical applications. During their development, it was discovered that the

two conventional transformation methods, f-k and p-f, did not provide adequate resolution of the

wavefield in the cases where a small number of recording channels is available (Park, et al.

1998). Because it is desirable for geotechnical applications to use small arrays, they developed

an alternative wavefield transform referred to herein as the Park, et al. transform.

This method consists of 4 steps:

1) Apply ID Fourier transform (FFT) to the wavefield along the time axis, this separates the
wavefield into components with different frequencies. The recorded data is changed from
(x-t) domain to (x-f) domain: U(x,t)-> U(x,f).

U(x,f)
2) Normalize U(x,f) to unit amplitude: U(x,f)-> U(- f)
U(x, f)

3) Transform the unit amplitude in (x-f) domain to (k-f) domain as follows: For a specified
frequency (f) and a wavenumber (k), the normalized amplitude at x is multiplied by eikx and
then summed all over the offset axis. This is repeated over a range of wavenumber for each
f, and then over all f to produce a 2D spectrum of normalized amplitudes in f-k domain.
This can be presented by:

V(k, f)= e U(x, (2.10)
V U \U(x,f)











x 103
5

4.5

4

3.5

3

D2 2.5

o 2
U)
1.5

1

0.5

0
10 20 30 40 50 60 70 80 90 100
frequency, Hz

Figure 2-6. Slowness-Frequency Spectrum (f-p domain)


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Sved Cirve CAOptim\trmi\TAMltiurtfBigsWiw_122_G22_0_l132(2),OC


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Figure 2-7. Signal spectrum and extracted dispersion curve from Park et al. method


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B


'A









f-k pairs. This narrow band represents of fundamental Rayleigh wave mode of propagation. At a

given frequency, wavenumber k is determined by picking the local strongest signal and the

dispersion curve is then built by calculating the velocities at different frequencies as:


V(f) = (2.8)
k(f)

2.3.2.2 Slowness-frequency transform (p-f).

This procedure developed by McMechan and J.Yedlin (1981) consists of two linear

transformations:

1) A slant stack of the data produces a wave field in the phase slowness time intercept (p-z)
plane in which phase velocities are separated.

2) A ID Fourier transform of the wave field in the p-T plane along the time intercept T gives
the frequency associated with each velocity. The wave field is then in slowness-frequency
(p-f) domain.

Firstly, the slant stack is a process to separate a wave field into different slowness (inverse

of velocity) and sum up all signals having the same slowness over the offset axis. The calculation

procedures as follows:

1) For a given slowness p and a time-intercept T (figure 2-5), calculate the travel time t at
offset x as t = r + px and retrieve P(x,t), the amplitude of the recorded signal for that x and
t. In practice, the recorded value of P(x,t) will often fall in between sampled data in time,
and then will be calculated via linear interpolation.

2) This process is repeated for all x in the recorded data and the results are summed to
produce:

S(p, r) = P(x,t) (2.9)
x

S(p, r) will present a spectral amplitude in the p-T domain.

3) Steps 1 and 2 are repeated over a specified range ofp and T to map out the spectral
amplitudes in the p-T domain.

Secondly, a ID Fourier transform of S(p, z) along the T direction separates the wave field

into different frequencies, which produces data set of spectral amplitudes in the slowness (p) -









LIST OF FIGURES


Figure page

2-1 Schem atic of SA SW setup ........................................................................... .............25

2-2 Dispersion curves from SASW test .............................................................................26

2-3 Inversion result ........................................................................................................ ...... 26

2-4 Frequency-Wavenumber Spectrum (f-k domain).................................................27

2-5 Exam ple of data in the x-t dom ain.......... ................. ......... ............... ............... 27

2-7 Signal spectrum and extracted dispersion curve from Park et al. method.........................28

2-9 Signal image and extracted dispersion curve from ReMi...............................................29

3-2 Example of SASW data (4ft receiver spacing) ................... ........... 38

3-3 Experimental combined dispersion curve for SASW of TAMU-61..............................38

3-4 Final experimental dispersion curve for SASW of TAMU-61 ............... .......... ....39

3-5 TAMU-0_122 recorded data in the time-trace (t-x) domain ..........................................39

3-6 Spectra of TAMU-0_122 obtained by applying methods .......................................40

3-8 Normalized spectrum at different frequencies...........................................................42

3-9 Extracted dispersion curves of TAMU-0_122 obtained by applying 4 methods...............43

3-10 Extracted dispersion curves of TAMU-88_220 obtained by applying 4 methods.............43

3-12 Final dispersion curve of TAMU obtained by active MASW .......................................44

3-14 D ispersion curves obtained by three techniques ...............................................................46

3-15 Inversion result of of TAMU obtained by SASW .................................. .................47

3-16 Inversion result of of TAMU obtained by Active MASW .............................................48

3-17 Inversion result of of TAMU obtained by Pasive MASW ..........................................49

4 -1 N ew b erry testing g site ............................................................................... ................ .. 57

4-2 Dispersion curve for SASW of Newberry ......................... ............... 58

4-3 Newberry active MASW recorded data in the time-trace (t-x) domain............................. 58









layer is constant and does not vary with depth. The theoretical dispersion curve calculation is

based on the matrix formulation of wave propagation in layered media given by Thomson

(1950). The details of the process are described as follows.

a) To determine the theoretical dispersion from an assumed profile: We can use either

transfer matrix or stiffness matrix for calculation of the theoretical dispersion. The transfer

matrix relates the displacement-stress vector at the top of the layer and at the bottom of the layer.

Using the compatibility of the displacement-stress vectors at the interface of two adjacent layers,

the displacement-stress vector at the surface can be related to that of the surface of the half-

space. Applying the radiation condition in the half-space, no incoming wave, and the condition

of no tractions at the surface, the relationship of the amplitudes of the outgoing wave in the half-

space and the displacements at the surface can be derived:

S u
P w
= B (2.3)
0 0


Where the 4x4 matrix B is the product of transfer matrices of all layers and the half-space, u and

w are the vertical and horizontal displacements at the surface. A nontrivial solution can be

obtained if the determinant of a 2x2 matrix composed by the last two rows and the first two

columns of matrix B is equal to zero. The characteristic equation 2.4 gives the theoretical

dispersion.

B31 B2 =0 (2.4)
B41 B42

Another method to obtain the theoretical dispersion is to use the stiffness matrix that

relates displacements and forces at the top and at the bottom of a layer or displacements and




















f=15Hz


09

S8

E 07

CID
a 06

0.5
N
u 04

0.3

0.2

01


0 500 1000 15M
Phase Velocity, ft/s


20O 2500 0
20]0 2mo0


N









p41


f=25Hz


50 1000 15a
Phase Velocity, ft/s


K


09 09 -
f--35Hz f f-45Hz
08- / 08-

E 07 E- 07 -

0 \ M 06 / -,
06-


Sos \ osI I
0\ 04


02 02 -

01- J 01- ----

S 500 1000 1 5E 20]0 2500 0 50 1000 1 50 2000 250
Phase Velocity, ft/s Phase Velcity, ft/s


Figure 4-5. Normalized spectrum at different frequencies (Solid line for cylindrical beamformer,
Dashpot line for Park et al. transformDashed line for f-k transform, Dotted line for f-p
transform)


4)









the phase velocity is determined. The coherence function allows checking wave energy

distribution and the ranges of frequency where the signal to noise ratio is high (according to the

coherence function close to 1). This information helps to determine the credible range of

frequency in which dispersion relationship is obtained.

One more criterion should be applied to eliminate the influence of body waves. Only the

range of frequency in which the according wavelength is not less than one third and not more

than twice of the distance from the source to the first receiver is effectively counted. In this

range, the wave field can be considered as relatively pure plane waves.

For SASW data recorded at TAMU-61, all twelve sets of data with 6 inter-receiver

distances for both forward and backward records are used for dispersion analysis. Each set gives

the dispersion relationship in a certain range of frequency. Assembling the information from the

12 sets of data, the combined dispersion curve is derived (Figure 3-3). Many points in the

combined dispersion curve are cumbersome in the inversion process, so an averaged curve is

desired. In this case, a smoothing algorithm is used to obtain the final dispersion curve (Figure 3-

4).

3.3.2 Dispersion Analysis for Active MASW

The main purpose of this part is to use the real recorded data to check and compare all of

the signal processing methods described in the chapter 2: f-k transform, f-p transform, Park, et al.

transform, and cylindrical beamformer. Then the spectrum having the best resolution will be

selected for extracting the dispersion curve.

3.3.2.1 Spectrum comparison

For each geophone layout, the data recorded with five active source locations give similar

results of spectra, so only data recorded at the closest source (10 feet away from the first

geophone) are presented here. Figure 3-5 shows the TAMU-0_122 recorded data in the time-









trace (t-x) domain. In this untransformed domain, we can only see the waves coming at different

slowness (slope), but are not able to distinguish between signals and noise. The signal processing

methods are necessarily applied to map the field wave for dispersion analysis.

For active MASW, the recorded data were used to check and compare the signal

processing methods, f-k, f-p, Park, et al. transform, and cylindrical beamformer. For

comparison, the spectra were all imaged in the same domain (figure 3.6 and figure 3.7). The

frequency interval, velocity interval, number of frequency steps, and number of velocity steps on

these spectra are identical. Also, the spectral values in all images were unity normalized, i.e., the

highest value in each spectrum is equal to 1.0, and all other values are relatively compared to

one. From these data it is apparent that the Park, et al. transform and the cylindrical beamformer

have better imaged dispersion curves at low frequencies (<15Hz) than that of the f-k and f-p

transforms. Overall, the spectrum obtained from the cylindrical beamformer has the highest

resolution. Resolution of spectra in the frequency-phase velocity (f-v) domain can be separated

into 2 components: resolution along the frequency axis and resolution along the phase velocity

axis. All four methods apply a 1-D Fourier transform along the time direction to discriminate

among frequencies for a given phase velocity, thus the resolutions along the frequency axis for

each method are not much different. However, for the resolution along the phase velocity axis,

the cylindrical beamformer appears best able to separate phase velocities for a given frequency.

To provide further illustration of resolution capabilities, figure 3.8 shows the normalized

spectral values of TAMU-0_122 at 4 frequencies: 10, 20, 30, and 40 Hz. For each frequency, the

spectral values are normalized to unity, i.e. the maximum value along the phase velocity axis is

equal to 1. Even though the strongest peak for each method occurs at similar phase velocities for

each frequency, the highest peak of the cylindrical beamformer is most dominant to other local


















a) b)




1400 1400

1200 1230

100 0 1030


69 g O
o803 00




2W 2W
I ir



203 200


10 20 30 40 90 60 70 80 10 20 3D 40 90 60 70
frequency, Hz frequency, Hz



c) d)



1400 14)0

120 1200














020 0 40 5 60 70 80 10 20 0 40 5 60 70
0 0










10 20 3) 40 so 60 70 80 10 20 3) 40 5) 60 70
frequency, Hz freq uency, Hz


Figure 3-7. Spectra of TAMU-88 220 obtained by applying methods: a) f-k transform b) f-p
transform c) Park, et al. transform d) Cylindrical beamformer









The spectrum shown in figure 4-7 is derived by combining that of 15 data sets. Manual picking

points at the lowest edge of area in which the signals are relatively strong gives the dispersion

curve of passive MASW for Newberry.

4.3.4 Combined Dispersion Curve of Active and Passive MASW

The principal goal of passive MASW is to obtain the dispersion relationship at low

frequencies (<15 Hz) but we also need the dispersion property at higher frequencies (>15Hz) for

characterization of soil at shallow depths. Combining dispersion curves achieved from both

active and passive is a good solution to broaden the range of frequency.

For Newberry, the active MASW and passive MASW give the dispersion property at

ranges of frequency of 5 to 15 Hz and 10 to 60 Hz, respectively. The combined dispersion curve

at the frequencies of 5 to 60 Hz allows attaining the detailed soil profile from ground surface to a

great depth. The overlapping of the dispersion curves between frequencies of 10 to 15 Hz shows

the agreement of the two methods and brings the credibility of the combined dispersion curve.

Some points on the combined dispersion curve cannot be handled in the inversion, so the curve

should be simplified by using smoothing algorithm to derive the final dispersion curve shown in

the figure 4-10.

4.3.5 Dispersion Curve Comparison

It is observed that the dispersion data from combined MASW and SASW is generally in

good agreement, particularly at the high frequency range (figure 4-10). However, combined

MASW dispersion data appear to be higher, especially at the low frequency range.

4.4 Inversion Results

After finishing the dispersion analysis, the inversion algorithm (part 2.2.3) is now applied

to characterize soil profiles from the dispersion curves. Two dispersion curves of SASW and

combined MASW are used for inversion and the derived soil profiles are shown in figure 4-11









to a need of large testing spaces especially for a 2-D geophone layout. The length of a 1D

geophone spread must not be less than the maximum expected wavelength. For a 2-D circular

geophone layout, the diameter should be equal to the maximum expected wavelength.

It is typical that many sets of data are recorded for each geophone layout and these data

will be combined to improve spectra for dispersion analysis.

2.4.2 Dispersion Curve Analysis

The methods of dispersion curve analysis depend on the geophone layouts applied to

record data. Two methods have been suggested as follows:

2.4.2.1 The 1-D geophone array.

This method was first developed by Louie (2001) and named Refraction Microtremor

(ReMi). Two-dimensional slowness-frequency (p-f) transform (part 2.3.2.2) is applied to

separate Rayleigh waves from other seismic arrivals, and to recognize the true phase velocity

against apparent velocities. Different from active waves that have a specific propagation

direction inline with the geophone array, passive waves arrives from any direction. The apparent

velocity Va in the direction of geophone line is calculated by:

V =v / cos(O) (2.18)

Where: v = real inline phase velocity, and 0 = propagation angle off the geophone line.

It is clear that any wave comes obliquely will have an apparent velocity higher than the

true velocity of inline waves, i.e., off-line wave signals in the slowness-frequency images will

display as peaks at apparent velocities higher than the real inline phase velocity. Dispersion

curves are extracted by manual picking of the relatively strong signals at lowest velocities (figure

2-8).









CHAPTER 2
SURFACE WAVE METHODS

2.1 Introduction

The motivation for using surface waves for soil characterization originates from the

inherent nature of this kind of wave. Surface waves propagate along a free surface, so it is

relatively easy to measure the associated motions, and carry the important information about the

mechanical properties of the medium. So far, three popular techniques: SASW, Active MASW,

Passive MASW have been developed to use surface waves for soil characterization. This chapter

will provide a brief summary of these techniques, including the advantages, disadvantages of

each.

2.2 Spectral Analysis of Surface Waves Tests (SASW)

SASW was first introduced by Nazarian (1984) to the engineering community. Advantages

of SASW are a simple field test operation and a straightforward theory, but it also has some

disadvantages. This method assumes that the most energetic arrivals are Rayleigh waves. When

noise overwhelms the power of artificial sources such as in urban areas or where body waves are

more energetic than Rayleigh waves, SASW will not yield reliable results. Also during the

processing of data, SASW requires some subjective judgments that sometimes influence the final

results. SASW is described as follows.

2.2.1 Field Testing Elements and Procedures

This method uses an active source of seismic energy, recorded repeatedly by a pair of

geophones at different distances. The Figure 2.1 shows a schematic of SASW testing

configuration. To fully characterize the frequency response of surface waves, these two-

transducer tests are repeated for several receiver spacings. The maximum depths of investigation

will depend on the lowest frequency (longest wavelength) that is measured. The sources are









CHAPTER 4
TESTING AND EXPERIMENTAL RESULTS AT NEWBERRY

4.1 Site Description

The testing site is a single Florida Department of Transportation (FDOT) storm water

runoff retention basin in Alachua County off of state road 26, Newberry, Florida (figure 4-1).

The test site was approximately 1.6 hectares and was divided into 25 strips by 26 north-south

gridlines marked from A to Z with the gridline spacing of 10 ft. Each gridline was about 280 ft in

length with the station 0 ft at the southern end of the gridline. Five PVC-cased boreholes

extending to the depth of 60 ft were installed for cross-hole tests.

4.2 Tests Conducted

SASW, Active MASW, and Passive MASW were conducted in Newberry for comparison

of the obtained soil profiles. The details of field testing procedures of each kind of test are

described as follows.

4.2.1 The SASW Tests

The SASW tests were conducted on gridline Z with configurations having the source-first

receiver distance equal to inter-receiver distance. All configurations were employed with the

common midpoint (CMP) at position Z-80 for inter-receiver distances of: 4 ft, 6 ft, 8 ft, 12 ft, 16

ft, 24 ft, 32 ft, 40 ft and 50 ft. For each receiver layout, the source was placed front and behind

for recording forward and backward wave propagations. Hammers were used to produce active

wave fields.

4.2.2 Active MASW Tests

The active MASW tests were conducted by 31 receivers at spacing of 2 feet with the total

receiver spread of 60 feet. The active source was located 30 ft away from the first receiver. Many

sets of data were collected by moving both the source and receiver layout 4 ft each. Each set of









LIST OF REFERENCES


Aki, K. and Richards, P. G. (1980), Quantitative Seismology: Theory and Methods, W. H.
Freeman and Company, San Francisco, 932 pp.

Hudyma, N., Hiltunen, D.R., and Samakur, C. (2007), "Variability of Karstic Limestone
Quantified Through Compressional Wave Velocity Measurements," Proceedings of
GeoDenver 2007, New Peaks in Geotechnics, American Society of Civil Engineers,
Denver, CO, February 18-21.

Louie, J. N. (2001), "Faster, Better, Shear-Wave Velocity to 100 Meters Depth from Refraction
Microtremor Arrays," Bulletin of Seismological Society ofAmerica, Vol. 91, No. 2, pp.
347-364.

Marosi, K.T. and Hiltunen, D.R. (2001), "Systematic Protocol for SASW Inversion",
Proceedings of the Fourth International Conference on Recent Advances in, Geotechnical
Earthquake Engineering and Soil Dynamics, San Diego, March 26-31.

McMechan, G. A. and Yedlin, M. J. (1981), "Analysis of Dispersive Waves by Wave Field
Transformation," Geophysics, Vol. 46, No. 6, pp. 869-871.

Nazarian, S. (1984), "In Situ Determination of Elastic Moduli of Soil Deposits and Pavement
Systems by Spectral-Analysis-Of-Surface-Waves Method," Ph.D. Dissertation, The
University of Texas at Austin, 453 pp.

Park, C. B., Miller, R. D., and Xia, J. (1999), "Multi-Channel Analysis of Surface Wave
(MASW)," Geophysics, Vol. 64, No. 3, pp. 800-808.

Park, C. B., Miller, R. D., Xia, J., and Ivanov J. (2004), "Imaging Dispersion Curves of Passive
Surface Waves," Expanded Abstracts, 74 Annual Meeting of Society ofExploration
Geophysicists, Proceedings on CD ROM.

Park, C. B., Xia, J., and Miller, R. D. (1998), "Imaging Dispersion Curves of Surface Waves on
Multi-Channel Record," Expanded Abstracts, 68th Annual Meeting of Society of
Exploration Geophysicists, pp. 1377-1380.

Santamarina J.C., Fratta D. (1998) "Discrete signals and inverse problems in civil engineering",
ASCE Press, New York.

Thomson W.T. (1950) "Transmission of elastic waves through a stratified solid medium", J.
Applied Physics, vol. 21 (1), pp. 89-93

Zywicki, D. J. (1999), "Advanced Signal Processing Methods Applied to Engineering Analysis
of Seismic Surface Waves," Ph.D. Thesis, Georgia Institute of Technology, 357 pp.









Neglecting waves that decay more rapidly than 1 / x the equation 2.12 becomes:


H,(kx) 2 exp[i(kx / 4)] (2.13)


This equation clearly shows the 1 / x decay and plane wave nature of the cylindrical wave

equation in the far-field. In other words, at a relatively large distance x, the cylindrical wave field

approaches the plane wave field.

b) Cylindrical wavefield transform: Based upon the cylindrical wavefield model, a

cylindrical wavefield transform can be described as follows (Zywicki 1999):

1) Apply ID Fourier transform to wavefield along the time direction

2) Build a spatiospectral correlation matrix R(f): The spatiospectral correlation matrix R(f) at
frequency f for a wave field recorded by n receivers is given by:



R (f) R1 (f) ... R,,(f)
R Rf) (f) R22 (f) ... R2, (f)
R(f)= (2.14)

R,, (f) R2 (f) -.. R,(f)

R (f)= S, (f) S* (f) (2.15)

Where Rij (f)= the cross power spectrum between the ith and jth receivers, Si (f) = Fourier
spectrum of the ith receiver at frequency f, denotes complex conjugation.

3) Build a cylindrical steering vector: the cylindrical steering vector for a wavenumber k is
built by applying the Hankel function as follows:

h(k)= exp{-i- [qH(H(k x, ))(H(k ,2 )), .., I(H(k. x, ))]T (2.16)

Where q denotes taking the phase angle of the argument in parentheses. T denotes
changing a vector from a column to a row or adversely.

4) Calculate the power spectrum estimate of the fieldwave: For a given wavenumber k and
frequency f, the power spectrum estimate is determined by:




























0



0~
.c '**~(
Q_


0 10 20 30 40
Frequency (Hz)


50 60


0 10 20 30 40

Frequency (Hz)


Figure 2-2. Dispersion curves from SASW test: a) Combined raw dispersion curve and b) Final

dispersion curve after averaging




a) experimental b)
-. -.. Theoretical Shear wave velocity (ft/s)


1600


1400


1200


1000-

0
800


S600
I-


0 10 20 30 40

Frequency(Hz)


50 60 70


Figure 2-3. Inversion result: a) Dispersion curve matching, b) Soil profile


50 60


0 500 1000 1500 2000 2500 3000 3500 4000


0



-10



-20



. -30
a.



-40



-50











-Experimental dispersion curve
- Theorectical dispersion curve


a)


1200

1100

1000

900
M-
>, 800
o
S700

S600

c 500

400
300

200
0





b)


Shear Velocity (ft/s)
500 1000


50 60 70


1500


2000


Figure 3-15. Inversion result of of TAMU obtained by SASW: a) Dispersion curve matching and
b) soil profile


10 20 30 40
Frequency (Hz)


-40
Q.

-50

-60

-70

-80









The soil profile derived from the third step is not necessarily unique. It is credible only

when we have a good dispersion curve from the second step. Thus, this research will focus on

the second step to get the best dispersion curves from among different methods of signal

processing. The data recorded during a field test includes both signal and ambient noise. It is

necessary to use signal-processing methods to discriminate against noise and enhance signal. The

first question can be answered if we can successfully separate the desired signals of surface

waves from background noise. The second question can be answered if we can obtain dispersion

curves at low frequency. The lower frequency at which we have dispersive relation, the deeper

depth of investigation we obtain.

1.2 Research Objectives

The research objectives are as follows:

1. To find the best method of signal processing to obtain the most credible dispersion curve
for a large range of frequency.

2. To check the accuracy of three surface wave techniques by comparison with results from
cross-hole tests.

1.3 Scope

For the first research objective, the author has developed programming codes to map the

signal spectra of the recorded data by four different methods named as frequency wavenumber

transform (f-k), frequency slowness transform (f-p), Park et al. transform, and cylindrical

beamformer transform. The dispersion curves are then obtained by picking points that have

relatively strong power spectral values on the spectra. These points carry information of

frequency wavenumber (f-k), frequency slowness (f-p) or frequency velocity (f-v)

relationships. Straightforward dispersion curves in frequency velocity (f-v) domain can be built

by calculation of v=l/p from f-p domain or v=2tf/k from f-k domain. The details of the signal









CHAPTER 1
INTRODUCTION

1.1 Problem Statement

Near surface soil conditions control the responses of foundations and structures to

earthquake and dynamic motions. To get the optimum engineering design, the shear modulus (G)

of underlying layers must be determined correctly. The most popular method used to obtain the

shear modulus is non-destructive in situ testing via surface waves. An important attribute of this

testing method is ability to determine shear wave (Vs) velocity profile from ground surface

measurements. Then shear modulus is calculated from G=pVs2. Three popular techniques,

Spectral Analysis of Surface Waves (SASW), Multi-Channel Analysis of Active Surface Waves

(Active MASW) and Multi-Channel Analysis of Passive Surface Waves (Passive MASW) have

been developed for non-destructive in situ testing, but their accuracy remains a question. This

research will apply these three techniques to characterize the soil profiles at two testing sites. The

accuracy will be appraised by comparing the soil profiles derived from these techniques with soil

profiles derived from cross-hole tests, a highly accurate but invasive testing technique.

Non-destructive in situ surface wave testing technique can be divided into three separate

steps: field testing to measure characteristics of particle motions associated with wave

propagation, signal processing to extract dispersion curves from experimental records, and using

an inversion algorithm to obtain the mechanical properties of soil profiles. For SASW, the testing

and data analysis steps are well established. However, for the multi-channel techniques, a

number of wave field transformation methods are available, but the best method has not been

confirmed. Two of the most important criteria for establishing the best method are:

1) From which method can we derive the most credible soil profile?
2) From which method can we maximize the depth of investigation?









ACKNOWLEDGMENTS

First of all, I thank Dr. Dennis R. Hiltunen for serving as my advisor. His valuable

support, encouragement during my research and studies were what made this possible. I thank

the other members of my thesis committee, Dr. Reynaldo Roque and Dr. Nick Hudyma.

I would like to thank my parents for encouraging my studies. I thank the remaining

members of my family for their support. I thank all of my friends who treated me like family.

Lastly, I extend thanks to my wife, who has supported my decisions and the results of those

decisions for the past 2 years.


































ODn

b)
1000
9000-----------------------------------
900

S800---- -----------

700

600

S500

400

300
300 --------------- -------- -----------------

200
0 5 10 15 20 25 30 35 40

Frequency (Hz)



Figure 3-13. The REMI analysis: a) Combined spectrum of Passive MASW at TAMU, b)
Extracted dispersion curve by manual picking










CHAPTER 5
CLOSURE

5.1 Summary

Three surface wave techniques, SASW, active MASW, and passive MASW, were

conducted at two test sites:

* A National Geotechnical Experiment site (NGES) at Texas A & M University (TAMU).

* A Florida Department of Transportation (FDOT) storm water runoff retention basin in
Alachua County off of state road 26, Newberry, Florida.

The SASW tests were recorded for many receiver layouts with inter-receiver distances ranging

from 4 ft to 128 ft and active sources ranging from light hammers to heavy shakers. The active

MASW tests were recorded by 32 or 62 receivers at inter-spacing of 2 ft and the passive MASW

tests were recorded by 32 receivers at inter-spacing of 10 ft. Crosshole tests were also conducted

at the two test sites.

For active multi-channel records, the signal processing methods, f-k, f-p, Park, et al.

transform, and cylindrical beamformer were used to map the dispersion curve images. After

comparing all of these images together, the best method of signal processing has been confirmed.

The shear wave velocity profiles from three surface wave techniques were obtained and

their accuracy has been appraised by comparing to that obtained from crosshole tests.

5.2 Findings

Based upon the work described herein, the findings are derived as follows:

* For active multi-channel records, Park et al. transform and the cylindrical beamformer have
better imaged dispersion curves at low frequencies (<15Hz) than that of two traditional
transforms, f-k and f-p.

* For active multi-channel records, the cylindrical beamformer is the best method of signal
processing as compared to f-k, f-p, and Park, et al. transforms. The cylindrical beamformer
provides the highest resolution of imaged dispersion curves, and its dominance of













1.2




-0 0.8
E

(D 0.6


0.4


0.2


10 20 30 40 50 60 70 80 90 100
frequency, Hz

Figure 2-8. Cylindrical Beamformer Spectrum (f-k domain)


Slowneis


Figure 2-9. Signal image and extracted dispersion curve from ReMi








a) b)






1200 I2:,6














10 1000 30 0 60 70 B 10 30 40 0 60 70 50
frequency, Hz frequency Hz
o C

200 200


10 23 30 40 s0 60 70 s 10 2 30 40 O 60 70 80
frequency, Hz frequency, Hz





























Figure 3-6. Spectra of TAMU-0_122 obtained by applying methods: a) f-k transform b) f-p
transform c) Park, et al. transform d) Cylindrical beamformer
12GO 1".T.

1000 ,0,.,:

800 1,.L









10 20 30 to so 60 10 80 10 20 30 t 0 6 60 10 SO
frequency, Hz frequency, Hz

Figure 3-6. Spectra of TAMU-0_122 obtained by applying methods: a) f-k transform b) f-p
transform c) Park, et al. transform d) Cylindrical beamformer


















a) b)



2000 2000

1800 1800

1600 1600

14)0 14)0

1200 120
o c
o100 100



0- 6 a- 6



200 2

10 20 0 40 s 60 TO 60 10 20 0 40 s 60 70 00

tequency,Hz tequency, Hz







2000 2000

1800 1800

1@)0 100

14)0 14)0


1200 100
r-i



6 0 [1 6 0 0

400 40

200 2


10 20 30 40 0o 60 70 80 10 20 30 40 so 60 70 80
tequency~, Hz tequency, Hz



Figure 4-4. Spectra of Newberry obtained by applying methods: a) f-k transform b) f-p
transform c) Park, et al. transform d) Cylindrical beamformer









peaks on its spectrum, i.e., the cylindrical beamformer reduces side ripples, and most of the

energy concentrates at the strongest peak. The sharpest peak of the cylindrical beamformer

allows the best separation of phase velocities for any given frequency. Thus, the high resolution

along the phase velocity axis contributes to the highest overall resolution of the cylindrical

beamformer. This can be understood that the cylindrical wavefield equations present the

motions of waves created by an active source more properly than do plane wavefield equations.

3.3.2.2 Dispersion curve extraction

The dispersion curves from all mentioned signal-processing methods are extracted by

selecting the strongest signals at every frequency and shown in figure 3.9 and figure 3.10. For

the recorded data, even though the extracted dispersion curves of the methods are similar, the

curves (figure 3.11) obtained by the cylindrical beamformer were selected to present for the test

site because of their highest credibility. Because they are also very similar, the two dispersion

curves of TAMU-0_122 and TAMU-98_220 were combined, averaged and smoothened to derive

the final one for Active MASW testing of TAMU (figure 3.12). This is also rational since it is

desirable to compare these results with those from passive MASW, and this data was collected

over the full 310 feet length of the array.

3.3.3 Dispersion Analysis for Passive MASW

The data of ID receiver array at TAMU were analyzed by commercial software Seisopt

ReMi that uses the Louie (2001) method of data analysis. This method applies two-dimensional

slowness-frequency (p-f) transform to separate Rayleigh waves from other seismic arrivals and

to recognize true phase velocity against apparent velocities (see Part 2.3.2.2). The combined

spectrum from several passive records allows obtaining the dispersion curve over a larger range

of frequencies (figure 3.13).
































Phasee eloiti Ve


0 2 0 80 00 1230 14B0 16I 1800 3o00
Phase eloidty


0 210 4011 8 E 1 0i 1200 140 16nO
Ptase elo&iti e


SFrequency=40 Hz









I I



0 2 I 40 M 800 1000 1i 130 16 1800 00
Ptase Veloid t


Figure 3-8. Normalized spectrum at different frequencies (Solid line for cylindrical beamformer,
Dashpot line for Park, et al. transform, Dashed line for f-k transform, Dotted line for
f-p transform)


j/ \\ Frequency










I/


18n am


=20 Hz









AN APPRAISAL OF SURFACE WAVE METHODS FOR SOIL CHARACTERIZATION


By

KHIEM TAT TRAN




















A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF ENGINEERING

UNIVERSITY OF FLORIDA

2008









P(k, f) = h(k)T R(f) h(k)


The spectrum of P (k, co) allows separating fundamental mode Rayleigh waves from other waves

(figure 2.8). Similar to previous methods, here we observe that the most energy (largest spectral

amplitudes) is concentrated along a narrow band of f-k pairs. This narrow band represents the

fundamental Rayleigh wave mode of propagation. At a given frequency, wavenumber k is

determined by picking the local strongest signal and the dispersion curve is then built by

calculating the velocities at different frequencies by equation 2.8.

2.3.3 Inversion Analysis

The inversion algorithm of this method is the same as that of SASW (part. 2.2.3). The only

difference would be that the iterative inversion calculation of MASW is quicker than that of

SASW because MASW usually brings smoother dispersion curves that allow quickly achieving

the stopping criteria in the inversion process.

2.4 Multi-Channel Analysis of Passive Surface Waves (Passive MASW)

Passive wave utilization has been intensively studied recently. It derives from useful

inherent characteristics of the passive surface waves. The most important advantage of testing

methods using passive waves is the ability to obtain deep depths of investigation with very little

field effort. Desired Rayleigh waves from passive seismic arrivals are relatively pure plane

waves at low frequencies allow determining Vs profiles up to hundreds meter depth. The

shortcoming is that this method is only able to apply for noisy testing sites (urban areas close to

roads...) but not for quiet test sites (rural areas).

2.4.1 Field Testing Elements and Procedures

Passive wave fields (background noise) are recorded simultaneously by many geophones

located in 1-D or 2-D arrays. With a requirement of recording waves at long wavelengths,

geophone spacing of passive MASW is often larger than that used in active MASW. This leads


(2.17)















* Combined dispersion curve

* Final dispersion curve by smoothing


1400


1200


1000


800


600


400


200


n


v


0 10 20 30 40

Frequency(Hz)


50 60


Figure 3-4. Final experimental dispersion curve for SASW of TAMU-61


Tracef 5 10 15 20 25 30 35 40 45 50 55 60



o i




0 4o
-8---- --8
.---- --- -- -- ---- - -- -- -- - ---- - -- ------- ---- --


1- o




o 0\

o -- ---- --- -- -- ------- ------- -- ----------- -- -- --o-- ------ ----
CO 0

t ----- --_ -----




A
- -


gg ^ ____ _ ____ I I I I 1 I I I __-------_ _------- ----- -


Figure 3-5. TAMU-0_122 recorded data in the time-trace (t-x) domain


i t '-'
i s









4) Transform V(k,f) to the phase velocity frequency domain: V(k,f) V(v,f) by changing
the variables such that c(f)=27tf/k.

The spectrum of V(v,f) is shown as an example in figure 2-7. Here we observe that the

most energy (largest spectral amplitudes) is concentrated along a narrow band of f-v pairs. This

narrow band represents the fundamental Rayleigh wave mode of propagation. At a given

frequency, phase velocity is determined by picking the local strongest signal in the narrow band.

2.3.2.4 Cylindrical beamformer transform

a) Cylindrical wavefield: The previous three transforms, f-k, p-f, Park, are based on a

plane wavefield model for the surface wave propagation. A plane wavefield is a description of

the motion created by a source located an infinite distance from the receivers. Surface wave

testing methods, however, employ a source at a finite distance, and thus the wavefield is

cylindrical and not planar. Zywicki (1999) has noted that a cylindrical wavefield can be

described by a Hankel-type solution as given by:

s(x, t)= AH (kx)e "' (2.11)

Where s(x,t) = displacement measured at spatial position x at time t, A= initial amplitude

of the wave field, HO = the Hankel function of first kind of order zero which has the real part and

imaginary part are respectively Bessel functions of the first kind and the second kind of order

zero. The cylindrical wave equation allows accurate modeling of wave motions at points close to

the active source, and this brings advantages in determining dispersion relationship at low

frequencies (long wavelengths).

At a relatively large distance x, the Hankel function can be expanded as: (Aki and G.Richards

1980)


H,(kx)=2 exp[i(kx-7r/4)]- 1- k+ ( (2.12)
=iKx 8x 8 (kx)]



































2008 Khiem Tat Tran









CHAPTER 3
TESTING AND EXPERIMENTAL RESULTS AT TAMU

3.1 Site Description

The data were collected at the National Geotechnical Experiment site (NGES) on the

campus of Texas A & M University (TAMU). The TAMU site is well documented, and consists

of an upper layer of approximately 10 m of medium dense, fine, silty sand followed by hard clay.

The water table is approximately 5 m below the ground surface. Because of space limitations, all

the tests including two-sensor and multi-sensor tests were only ID receiver layout and conducted

on a straight line of nearly 400 feet. The positions are marked with one-foot increment from 0 to

400 as TAMU-0 400.

3.2 Tests Conducted

On the mentioned line, three kinds of tests, SASW, Active MASW and Passive MASW

were conducted for comparison. The details of field-testing elements and procedures of each

kind of tests are described as follows.

3.2.1 The SASW Tests

The conducted SASW tests are divided into two categories that were recorded at two

positions, TAMU-61 and TAMU-128. The SASW tests were conducted with configurations

having the source-first receiver distance equal to inter-receiver distance. At each position, many

configurations were used in common midpoint (CMP) style with the inter-receiver distance at 4

ft, 8 ft, 16 ft, 32 ft, 64 ft, and 122 ft. For each receiver layout, the active source was placed both

front and behind for recording forward and backward (reverse) wave propagations. The active

sources were hammers for the inter-receiver distances up to 16 ft, and shakers for larger

distances.

















--- Combined MASW -*- SASW


3500


3000


2500 ----


2000


1500 ----


1000 -- -


500 ----


0
0 1----------------
0 10 20 30 40

Frequency(Hz)


50 60 70


Figure 4-10. Dispersion curve comparison


























0.2


10 20 30 40 50 60 70 80 90 100
frequency, Hz

Figure 2-4. Frequency-Wavenumber Spectrum (f-k domain)



x









EP x






t i



Figure 2-5. Example of data in the x-t domain









data was obtained with 2048 (2A11) samples, the time interval of 0.78125 ms (0.00078125 s),

and the total recorded period of 1.6 seconds.

For comparison with SASW tests, only one set of data collected by a receiver array having

the centerline at position Z-80 (same as CMP of SASW) is analyzed in this thesis. For this

record, the wave field was produced by an active source at position Z-20, and the receiver spread

wasatZ-50 110.

4.2.3 Passive MASW Tests

The passive MASW tests were conducted by 32 receivers deployed at inter-spacing of 10

feet spanning a distance of 310 feet at Z-0_310. In order to obtain a good combined spectrum, 15

sets of data were recorded with 16348 (2A14) samples, the time interval of 1.9531 ms (0.0019531

s), and the total recorded period of 32 seconds.

4.3 Dispersion Results

This section will express the dispersion results of three surface wave methods. The

dispersion curves of active MASW and passive MASW will be combined to broaden the range

of frequency for inversion.

4.3.1 Dispersion Analysis for SASW Tests

The fundamental concepts of SASW analysis are the same as that expressed in part 3.3.1.

For SASW data recorded at Newberry, all 16 sets of data with 8 inter-receiver distances for both

forward and backward records are used for dispersion analysis. The combined dispersion curve

from 16 data sets and the averaged dispersion curve are shown in the figure 4.2. With very well

recorded data, the obtained final dispersion curve is smoother than that of TAMU, and this

allows a quicker process of inversion.









TABLE OF CONTENTS

page

A CK N O W LED G M EN T S ................................................................. ........... ............. .....

LIST OF FIGURES .................................. .. ..... ..... ................. .7

ABSTRAC T ...........................................................................................

CHAPTER

1 IN TR OD U CTION .......................................................................... .. ... .... 10

1.1 Problem Statem ent .................. ................................ ........ .. ............ 10
1.2 Research Objectives .................. ............................. ......................... 11
1 .3 S c o p e ................... .......................................................... ................ 1 1

2 SU RFA CE W A V E M ETH O D S ................................................................ ........ ...............13

2.1 Introduction ........................................................................ .... .... ............ 13
2.2 Spectral Analysis of Surface Waves Tests (SASW)................. ............................13
2.2.1 Field Testing Elements and Procedures............. ............................................13
2.2.2 D ispersion Curve A nalysis........................................... .......... ............... 14
2.2.3 Inversion Analysis .......................... .............................. .. .............. 14
2.3 Multi-Channel Analysis of Active Surface Waves (Active SASW).............................16
2.3.1 Field Testing Elements and Procedures............. ............................................17
2.3.2 Dispersion Curve Analysis.............................................. 17
2.3.2.1 Frequency-wavenumber transform (f-k)............ ........ ............. 17
2.3.2.2 Slowness-frequency transform (p-f). ............................................... 19
2.3.2.3 Park et al. transform ......... ......... .. .. ......... .....................20
2.3.2.4 Cylindrical beamformer transform ............................................. 21
2 .3.3 Inversion A naly sis ..................... .. .......... .. ...... ................... ...... ......... .. 23
2.4 Multi-Channel Analysis of Passive Surface Waves (Passive MASW)........................23
2.4.1 Field Testing Elem ents and Procedures ......... ................. .....................23
2.4.2 D ispersion Curve A nalysis.......................................... ........... ............... 24
2.4.2.1 The 1-D geophone array. .............. .................... ....................... 24
2.4.2.2 The 2-D geophone array. .............. .................... ....................... 25
2 .4 .3 Inversion A naly sis............ ... ...................................................... .... .... .... ... 25

3 TESTING AND EXPERIMENTAL RESULTS AT TAMU..............................................30

3 .1 S ite D e scrip tio n ....................................................................................................... 3 0
3.2 T ests C conducted ......... .... .... ........ .... .. ................. ...... .... ... .30
3.2.1 The SA SW Tests ......... ...... ........................ ........ .......... ................. 30
3.2.2 A active M A SW T ests ......... ................. ................................... ......................3 1
3.2.3 Passive M A SW Tests ........... .................................................. ............... 31
3.3 D ispersion R results ........... ... .................. .................. .... .......... .. .31









--Experimental dispersion curve
- Theoretical dispersion curve


3500


3000

2500


2000


1500

1000

500


0 10 20 30 40
Frequency(Hz)


50 60 70


Shear wave velocity (ft/s)

0 500 1000 1500 2000 2500 3000 3500 4000


0


-20


-40


-60


-80


-100


-120


Figure 4-12. Inversion result of Neberry obtained by combined MASW: a) Dispersion curve
matching and b) soil profile








--- f-k transform f_p transform


2500


2000 -


1500 -1


1000 -


500 --


0 10 20 30 40
Frequency(Hz)


50 60 70


Figure 4-6. Extracted dispersion curves of Active MASW obtained by applying 4 signal-
processing methods


sec0lmete












0 00333


Frequency. Hz


a


0 uo
0


AverFq d R i Sp
o.ol^ ZZ


Figure 4-7. Combined spectrum of Passive MASW


24097


U

S


Park et al. transform


Cylindrical Beamformer


- ---------------"-








---- -- -- -- -- -- -
- - -












* f-k transform f-p transform Park et al.transform Cylindrical Beamfomer


1200

1100

1000

900

800

700

600

500

400

300

200


0 10 20 30 40
Frequency (Hz)


50 60 70


Figure 3-9. Extracted dispersion curves of TAMU-0_122 obtained by applying 4 methods


* f-k transform f-p transform


1200

1100


1000

900

800

700


600

500

400


300

200


Park et al.transform


Cylindrical Beamfomer


0 10 20 30 40 50 60 70
Frequency (Hz)


Figure 3-10. Extracted dispersion curves of TAMU-88_220 obtained by applying 4 methods


------------
- --

eqs. -


- - - - - -


J

- - -- -- -









and figure 4-12. Also dispersion curve matching between theoretical curve and experimental

curve is shown for reference.

All dispersion curves of Newberry are typical curves whose phase velocities continuously

increase with decreasing frequency. Thus the typical soil profiles with shear velocity increasing

with depth increase are obtained. That the slope of dispersion curves changes suddenly from a

low value at frequencies more than 20 Hz to a very high value at frequencies less than 20 Hz can

be explained by a big increasing step of shear velocity.

For SASW, the dispersion property is obtained at the lowest frequency of 12 Hz only and

the maximum velocity of about 1800ft/s. This does not allow achieving a great depth of

investigation because of the short maximum obtained wavelength (Xmax=24ft). The reliable

depth of investigation is only about 25 ft.

For combined MASW tests, the dispersion property at low frequencies can be derived from

passive wave fields. The combined dispersion curve is attained in a broad range of frequency

from 5 Hz to 60 Hz and the maximum phase velocity of about 3000 ft/s (Xmax=95ft). This

allows increasing the credible depth of investigation up to about 70 ft. It is clear that the

classified depth is considerately increased by using passive wave fields in soil characterization.

4.5 Crosshole Tests

Five PVC-cased boreholes extending to the depth of 60 ft were installed at position J-20,

K-10, K-20, K-30 and M-20. The crosshole test was conducted along gridline K with the

hammer at K-30, and two receivers at K-20 and K-10. The system including the hammer and two

receivers were lowered from the surface by steps of 2 ft. Manual hammer blows created active

waves, and the time of wave travel were recorded by the two receivers at different depths. From









measurement process due to multi-channel recording. Its quick and easy field operation allows

doing many tests for both vertical and horizontal soil characterization.

2.3.1 Field Testing Elements and Procedures

In Active MASW, wave field from an active source is recorded simultaneously by many

geophones (usually >12) placed in a linear array and typically at equidistant spacings. The active

source can be either a harmonic source like a vibrator or an impulsive source like a

sledgehammer. Depending on the desired depth of investigation, the strength of source will be

properly selected to create surface wave field at the required range of frequencies.

If the wave field is treated as plane waves in data analysis, the distance from source to the

nearest receiver (near offset) cannot be smaller than half the maximum wavelength, which is also

approximately the maximum depth of investigation (Park et al. 1999). However, with cylindrical

wave field analysis, this near offset can be selected smaller to reduce the rapid geometric

attenuation of wave propagation.

2.3.2 Dispersion Curve Analysis

To determine accurate dispersion information, multi-channel data processing methods are

required to discriminate against noise and enhance Rayleigh wave signals. The following will

discuss on four methods used for separating signals from background noise.

2.3.2.1 Frequency-wavenumber transform (f-k).

For a given frequency, surface waves have uniquely defined wavenumbers ko(f), ki(f),

k2(f)... for different modes of propagation. In other words, the phase velocities Cn=co/kn are fixed

for a given frequency. The f-k transform allows separation of the modes of surface waves by

checking signals at different pairs of f-k.

The Fourier transform is a fundamental ingredient of seismic data processing. For

example, it is used to map data from time domain to frequency domain. The same concept is









related to the geophone distances, and range from sledgehammers at short receiver spacings (1-

2m) to heavy dropped weights, bulldozers, and large vibration shakers at large receiver spacings

(50-100m).

2.2.2 Dispersion Curve Analysis

Each recorded time signal is transformed into frequency domain using FFT algorithm. A

cross power spectrum analysis calculates the difference in phase angles (4(f)) between two

signals for each frequency. The travel time (At(f)) between receivers can then be obtained for

each frequency by:

At(f) = (2.1)
27r f

The distance between geophones is known, thus wave velocity is calculated by:

X
VR(f) = (2.2)
At(f)

Considering each pair of signals, an estimate of the relationship between wave velocity and

frequency over a certain range of frequency is obtained. Gathering the information from different

pairs of geophones the combined dispersion curve is derived (Figure 2.2a). Then the combined

one is averaged to get the final dispersion curve for inversion (Figure 2.2b).

2.2.3 Inversion Analysis

Inversion of Rayleigh wave dispersion curve is a process for determining the shear wave

velocity profile from frequency-phase velocity dispersion relationship. This process consists of

evaluation of theoretical dispersion curves for an assumed profile and comparison with the

experimental dispersion curve. When the theoretical dispersion curve and the experimental

dispersion relatively match, the assumed profile is the desired solution. The assumed medium is

composed of horizontal layers that are homogeneous, isotropic and the shear velocity in each

























0 20 40 60 80 100 120 140 160 180 200

Frequency (Hz)


I I I I I I I


a
S 0.5
3
u


I I I I I I I I I


0 20 40 60 80 100 120 140 160 180

Frequency (Hz)

Figure 3-2. Example of SASW data (4ft receiver spacing)


200


1400


1200-


1000


800 ------


600-


400--------


200


0
0 10 20 30 40

Frequency (Hz)


---4f
- 4r
8f
8r
- 16r
--- 16f
- 32f
---32r
64f
64r
122f
122r


50 60 70


Figure 3-3. Experimental combined dispersion curve for SASW of TAMU-61









Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Engineering

AN APPRAISAL OF SURFACE WAVE METHODS FOR SOIL CHARACTERIZATION

By

Khiem Tat Tran

May 2008

Chair: Dennis R. Hiltunen
Major: Civil Engineering

Three popular techniques, Spectral Analysis of Surface Waves (SASW), Multi-Channel

Analysis of Active Surface Waves (Active MASW) and Multi-Channel Analysis of Passive

Surface Waves (Passive MASW), were conducted at two well-characterized test sites: Texas A

& M University (TAMU) and Newberry. Crosshole shear wave velocity, SPT N-value, and

geotechnical boring logs were also available for the test sites. For active multi-channel records,

the cylindrical beamformer is the best method of signal processing as compared to frequency-

wavenumber, frequency-slowness, and Park, et al. transforms. The beamformer provides the

highest resolution of imaged dispersion curves, and its dominance of resolution at low

frequencies over other methods allows achieving a reliable dispersion curve over a broad range

of frequencies. Dispersion data obtained from all three surface wave techniques was generally in

good agreement, and the inverted shear wave profiles were consistent with the crosshole, SPT N-

value, and material log results. This shows credibility of non-destructive in situ tests using

surface waves for soil characterization.









extended to any sequential series other than time. The f-k analysis uses 2D Fourier transform that

can be written as (Santamaria and Fratta 1998):



P, = p, e 2 e L (2.7)
1=0 [m=0

Where:

N = number of time samples, M = number of receivers in space

Pu,v = spectral value at wavenumber index u and frequency index v

pl,m = recorded data at mth sample of Ith receiver

This transform is essentially two consecutive applications of a ID Fourier transform as

shown in the following:

Input data in (t,x) domain 1D Fourier Transform in the time direction

(Data in (f,x) domain)

1D Fourier Transform in the spatial direction

(Data in (f,k) domain)

One main problem of the 2D transform is the requirement of a large number of receivers

to obtain a good resolution in wavenumber direction. Because the geophone spacing dx controls

the highest obtainable wavenumber (kmax=2/dxmin), the spread length (X) controls the solution

(Ak=27 /X). To obtain a good solution the spread length must be large but it is often difficult due

to site size restrictions. The usual trick to improve the solution is to add a substantial number of

zero traces at the end of field record (zero padding), which essentially creates artificial receiver

locations with no energy.

Figure 2.4 shows a spectrum in f-k domain where the signals are successfully separated from the

background noise. Here we observe that the most energy is concentrated along a narrow band of









the known distance between two receivers and the difference between times of wave travel

recorded by two receivers, the shear wave velocity is calculated (figure 4-13).

For the Newberry testing site, the soil profile below the depth of 25 ft is very stiff. By

using the manual hammer that only created waves at relatively low frequencies, the time of wave

travel in rock were not definitely determined. In this case, a hammer that can produce wave

fields at high frequencies is necessary. Unfortunately, such a hammer was not available at the

time of testing, so the maximum depth at which we could obtain the shear wave velocity was

only 25 ft.

4.6 Soil Profile Comparison

Soil profiles of Newberry derived from SASW, combined MASW, and cross-hole test are

all shown together in figure 4-14. First, regarding Vs profiles from combined MASW and

SASW, it is observed that they are generally in good agreement. Consistent with the dispersion

curves, the SASW and combined MASW are in particularly good agreement for shallow depths

up to 18ft that is presented in the dispersion curves at high frequencies. However, the combined

MASW is slightly stiffer (higher velocity) at some deeper depths. Second, it is observed that the

surface wave based Vs profiles compare well with the crosshole results. However, the Vs

profiles at the depth from 10 to 15ft are different. It can be explained that: 1) Crosshole tests

were conducted at gridline K that is 180 ft away from the testing line of the nondestructive tests

and the Vs profile changes over the test size. 2) The surface wave tests are conducted over a

relatively long array length that sample and average over a large volume of material, whereas the

crosshole results are based upon wave propagation between two boreholes that are only 10 ft

apart, and thus these data represent a more local condition at the site.









4-4 Spectra of Newberry obtained by applying methods............... ..... ...............59

4-5 Normalized spectrum at different frequencies....................... .............60

4-6 Extracted dispersion curves of Active MASW obtained by applying 4 signal-
processing methods .................. .............................................. .........61

4-7 Com bined spectrum of Passive M A SW ............................................................................61

4-8 Combined dispersion curve of passive and active MASW ............................................62

4-9 Final dispersion curve of com bined M A SW ........................................ .....................62

4-10 D ispersion curve com parison.......................................................................... 63

4-11 Inversion result of N eberry obtained by SA SW ........................................ .....................64

4-12 Inversion result of Neberry obtained by combined MASW..............................................65

4-13 Soil profile obtained from Crosshole Test .............................. .....................66

4-14 Soil profile comparison of Newberry .................................. .......................... 67































8









4.3.2 Dispersion Analysis for Active MASW Tests

Similar to what was described in chapter 3, the active multi-channel records of Newberry

are also analyzed by four signal processing methods. Then the spectrum having the best

resolution will be selected for extracting the dispersion curve.

Figure 4-3 and figure 4-4 show the data recorded of the active wave field in untransformed

domain (x-t) and transformed domain (f-v), respectively. We can easily recognize the desired

fundamental mode Rayleigh waves that is successfully separated from other noisy waves in the

transformed domain. Here we observe that the most energy (largest spectral amplitudes) is

concentrated along a narrow band. This narrow band represents the fundamental Rayleigh wave

mode of propagation. As before, the cylindrical beamformer transform shows its dominance by

the best resolution spectrum. The best resolution of the cylindrical beamformer transform can be

seen more clearly in the figure 4-5 of normalized spectra in which the spectral values are

checked for particular frequencies to evaluate the separation of phase velocities. Here we observe

that the cylindrical beamformer transform reduces side ripples or most of energy concentrates at

the strongest peak. The sharpest peak of the cylindrical beamformer transform allows the best

separation of phase velocities for any given frequency.

The dispersion curves obtained from the four signal processing methods are shown

together in figure 4-6, and the one from the cylindrical beamformer is selected to represent the

active MASW tests of Newberry.

4.3.3 Dispersion Analysis for Passive MASW Tests

The passive wave data recorded by ID receiver array at Newberry are analyzed by

commercial software Seisopt ReMi 4.0. The signals of passive waves are not usually very strong

so many spectra of data sets should be considered. Each spectrum is only good for a small range

of frequency. The combined spectrum allows obtaining dispersive relationship in a larger range.









forces at the top of a half-space. The global stiffness matrix S is diagonally assembled by

overlapping all the stiffness matrices of layers and half-space. The vector u of interface

displacements and the vector gof external interface loadings can be related: S u = q. The

Rayleigh waves can exist without interface loadings so:

Su = 0 (2.5)

The nontrivial solution of the interface displacements can be derived with the determinant of S

being zero. The theoretical dispersion can be achieved from the equation 2.6

SS = 0 (2.6)

b) To determine a reasonable assumed profile: An initial model needs to be specified as

a start point for the iterative inversion process. This model consists of S-wave velocity, Poisson's

ratio, density, and thickness parameters. It is necessary to start from the most simple and

progressively add complexity (Marosi and Hiltunen 2001). The assumed profile will be updated

after each iteration and a least-squares approach allows automation of the process.

2.3 Multi-Channel Analysis of Active Surface Waves (Active SASW)

This method was first developed by Park, et al.(1999) to overcome the shortcomings of

SASW in presence of noise. The most vital advantage of MASW is that transformed data allow

identification and rejection of non-fundamental mode Rayleigh waves such as body waves, non-

source generated surface waves, higher-mode surface waves, and other coherent noise from the

analysis. As a consequence, the dispersion curve of fundamental Rayleigh waves can be picked

directly from the mode-separated signal image. The obtained dispersion curve is expected to be

more credible than that of SASW, and this method can be automated so that it does not require

an experienced operator. An additional advantage of MASW is the speed and redundancy of the









3.3.1 Dispersion Analysis for SASW Tests ...................................31
3.3.2 Dispersion Analysis for Active MASW.........................................................32
3.3.2.1 Spectrum com prison ........................................ ...... ............... 32
3.3.2.2 D ispersion curve extraction ..................................... ............... 34
3.3.3 Dispersion Analysis for Passive M ASW .................................. ............... 34
3.4 Inversion R results .......... .... ............. ...... .................. ....... 35
3.5 Soil Profile Com prison ................................................................. ............... 36

4 TESTING AND EXPERIMENTAL RESULTS AT NEWBERRY .............. ...............51

4 .1 S ite D e scrip tio n ............. .. ............. .................................................................... 5 1
4.2 Tests Conducted .......... ... ................................... .. .... ...... .. .. ........ .... 51
4.2.1 The SA SW Tests .......... ........ ........................... .. ...... 51
4.2.2 A active M A SW Tests .................................... .................. ............... 51
4.2.3 Passive M A SW Tests ................... ........ .................................. ............... 52
4.3 D ispersion R esults................... .......... ................................ .............. .. .............. 52
4.3.1 Dispersion Analysis for SASW Tests .................................... ............... 52
4.3.2 Dispersion Analysis for Active MASW Tests .............. ............... 53
4.3.3 Dispersion Analysis for Passive MASW Tests .............. ..........................53
4.3.4 Combined Dispersion Curve of Active and Passive MASW ............................54
4.4 Inversion R results ........... ... ........................................... .................. 54
4 .5 C rosshole T ests ....................................................... 55
4.6 Soil Profile Com prison ......................................... ........................ ............... 56

5 C L O S U R E ............. ..... ............ ................. ...........................................6 8

5 .1 S u m m a ry ................................................................................................................. 6 8
5.2 F findings ......... ..................................... ............................68
5.3 C onclu sion s ............. ................. ..................... .............................................69
5.4 Recommendations for Further Work ................................ ...............69

LIST OF REFERENCES .........................................................................70

BIOGRAPHICAL SKETCH .................. ............... ......... 71


















6












4.7 Summary of Newberry Tests

All of the signal processing methods and non-destructive testing techniques described in

chapter 2 are applied to analyze the real recorded data of Newberry. Also, the crosshole test is

briefly described. The conclusion has been derived as follows:

1) One more time, the cylindrical beamformer transform gives the best resolution of signal
imaging for active wave fields.

2) The soil profiles of Newberry derived from SASW, combined MASW are relatively well
matched each other.

3) The matching in soil profiles of Newberry derived from non-destructive tests and from
cross-hole tests is good but not excellent because the crosshole test was taken far away
from the testing line of nondestructive tests.

4) Combining of active MASW and passive MASW shows an excellent solution to increase
the depth of investigation.






ALACHUA .
STATE OF COUNTY a
FLORIDA
Newbeny GAINESVILLE



-I -I-
AppM nate "c100w





--_ ,,,__ _ __. -; -

(a) (b)



Figure 4-1. Newberry testing site (from Hudyma, Hiltunen, Samakur 2007)









The disadvantage of ReMi is to require the manual picking, as this depends on subjective

judgment, and sometimes influence the final results.

2.4.2.2 The 2-D geophone array.

Park, et al. (2004) introduced a data processing scheme for a 2D cross layout and then

developed for 2D circular layout. This method is extended from the method applied for active

MASW tests (part 2.3.2.3).

2.4.3 Inversion Analysis

The inversion algorithm of this method is the same that of SASW (part. 2.2.3). Usually, the

dispersion curves from passive MASW are in a small range of low frequencies (<20Hz), so the

soil profiles at shallow depths are not very precise. Passive data are sometimes combined with

that of active MASW to broaden the range to higher frequencies. The combination of dispersion

curves brings better results of soil characterization.




Computer

111W ~ L~~Spfeedimi Anal-, zer





Source Vertical Vertical
Receiver i Receiver




X/2

S X (Variable)



Figure 2-1. Schematic of SASW setup









BIOGRAPHICAL SKETCH

Khiem Tat Tran was born in1978 in Thanh Hoa, Vietnam, and remained in Thanh Hoa

until he graduated from Lam Son High School in 1996. He enrolled in Hanoi University of Civil

Engineering, and graduated with a Bachelor of Science in civil engineering in spring 2001. He

decided that it would be most beneficial to gain a few years of work experience before

continuing on with graduate studies so he worked for five years in Vietnam until he moved to US

for studying. He enrolled at the University of Florida in Gainesville, FL in August of 2006 where

he worked as a graduate research assistant under Dr. Dennis Hiltunen. He completed his studies

in May of 2008, graduating with a Master of Engineering degree, and continued to pursue a PhD

program in University of Florida.









3.3.4 Dispersion Curve Comparison

It is observed from figure 3.14 that the dispersion data from all three techniques is

generally in good agreement, particularly at the high and low frequency ranges. However, active

MASW dispersion data appear to be higher in a middle frequency range. It is also observed that

the active and passive MASW data is smoother than the SASW data. The ripples in the SASW

data are mostly produced by slight mismatches in the combined dispersion data from multiple

receiver spacings. Each spacing samples a slightly different zone of soil, and lateral variability

of soil properties will produce a mismatch in dispersion data.

3.4 Inversion Results

After finishing the dispersion analysis, the inversion algorithm (part 2.2.3) is applied to

characterize soil profiles from the dispersion curves. The inversion module of commercial

software Seisopt and inversion algorithm developed by D.R.Hiltunen & Gardner (2003) are

applied to derive the soil profile. Both give similar results which are shown in figure 3-15,

figure 3-16, and figure 3-17 for tests: SASW, Active MASW and Passive MASW respectively.

Also dispersion curve matching between theoretical curve and experimental curve is shown for

reference.

In all three cases, the inversion routine was able to match the experimental data very well.

However, it is noted for all three cases that the theoretical models are not able to exactly match

the experimental data in some localized areas. These fluctuations are due to localized variability

in the soil profile that the surface wave inversion algorithm is not able to detect.

The maximum depth of investigation depends on the lowest frequency in which the

dispersive relationship is achieved and on shear velocity. By using heavy shakers to create the

active field wave, the lowest frequency of SASW is 3 Hz and the maximum attainable depth is

65 feet. For active MASW and passive MASW, the lowest frequencies are 6 Hz and 5 Hz; the









resolution at low frequencies over other methods allows achieving a reliable dispersion
curve over a broad range of frequencies.

* There is generally good agreement between dispersion results from SASW, active MASW,
and passive MASW surface wave tests.

* The surface wave-based shear wave velocities are in good agreement with the crosshole
results, and the shear wave velocities appear consistent with SPT N-values and material
logs.

* Combining dispersion curves from active and passive MASW is an economical solution to
achieve reliable soil profiles to relatively large depths because it does not require heavy
weights or expensive vibration shakers for attaining the dispersion properties at low
frequencies

5.3 Conclusions

Based on the findings outlined above, the conclusions are as follows:

1) Cylindrical beamformer is the best method of signal processing for active field waves
because it gives the highest resolution of imaged dispersion curves.

2) The good matching of soil profiles obtained from SASW, active MASW, passive MASW,
and crosshole tests shows credibility of non-destructive in situ tests using surface waves for
soil characterization.

3) Combining dispersion curves from active and passive MASW to broaden the range of
frequency considerately increases the depth of investigation.

5.4 Recommendations for Further Work

The following recommendations are suggested after reviewing all of the findings and

conclusions previously discussed:

* Cylindrical beamformer should be applied in commercial software.

* Signal processing methods for passive wave fields need to be developed further to use for
testing areas without very strong passive signals.

* Lateral discontinuous effects significantly influence the results of soil characterization.
Currently, the Vs profiles from MASW are averaged over the length of receiver spread and
the results are not very credible in the cases of drastically changed Vs profiles over the test
size. Numerical methods (e.g., finite difference) need to be developed to handle the lateral
discontinuous effects.

* Full-waveform methods that directly give soil profiles from recorded data should be
developed to further limit the non-uniqueness of the inversion process.












1200



1000



4 800

8 0 0- SASW
600 --Active MASW
> Passive MASW

400 -- ------------ -- --
a-


200



0
0 10 20 30 40 50 60 70

Frequency (Hz)



Figure 3-14. Dispersion curves obtained by three techniques









processing methods will be described in the chapter 2 and the results will be shown in the

chapters 3 and 4.

For the second research objective, SASW, Active MASW, and Passive MASW have been

conducted in two test sites:

1. A National Geotechnical Experiment site (NGES) at Texas A & M University (TAMU).

2. A Florida Department of Transportation (FDOT) storm water runoff retention basin in
Alachua County off of state road 26, Newberry, Florida.

Also cross-hole tests were completed at these two sites for comparison. All the test results and

comparisons are available in chapters 3 and 4.










- Experimental dispersion curve
- Theoretical dispersion curve


10 20 30 40


Frequency (Hz)


Shear Velocity (ft/s)
1000


1500


2000


Figure 3-17. Inversion result of of TAMU obtained by Pasive MASW: a) Dispersion curve
matching and b) soil profile


1000


900

800

700

600

500

400

300


S-40

-50

-60

-70

-80









3.2.2 Active MASW Tests

The active MASW tests were conducted with 62 receivers at spacing of 2 feet with the

total receiver spread of 122 feet. Two receiver layouts were laid at positions TAMU-0_122 and

TAMU-98_220. For each receiver layout, five sets of data were recorded accordingly to five

positions of the active source at 10 ft, 20 ft, 30 ft, 40 ft, and 50 ft away from the first receiver.

For the record TAMU-0_122, the active source was located at TAMU 132, 142, 152, 162, 172,

and for the record TAMU-98 220, the active source was located at TAMU 88, 79, 68, 58, 48

(see Figure 3.1). Each set of data was obtained with 16,348 (2A14) samples, the time interval of

0.78125 ms (0.00078125 s), and the total recorded period of 12.8 seconds.

3.2.3 Passive MASW Tests

The passive MASW tests were conducted by 32 receivers deployed at inter-spacing of 10

feet spanning a distance of 310 feet at site position TAMU-0_310. For the passive tests, several

sets of data were obtained for combining spectra in the dispersion analysis. In this case, 26 sets

of data were recorded with 16,348 (2A14) samples, the time interval of 1.9531 ms (0.0019531 s),

and the total recorded period of 32 seconds.

3.3 Dispersion Results

In this section, the dispersion curves from SASW, Active MASW and Passive MASW are

extracted for inversion. Also, several signal processing methods are applied for Active MASW

data to evaluate these methods and obtain the best dispersion curve.

3.3.1 Dispersion Analysis for SASW Tests

The dispersion results of tests at TAMU-61 and TAMU-128 are similar so only tests at

TAMU-61 are presented here in detail. The Figure 3-2 shows an example of data obtained with

inter-receiver distance of 4 ft and reverse recording (4r). The cross power spectrum (CPS) phase

is used to calculate the frequency-dependent time delay. Then with the known receiver distance,










a)

1200
1100
1000
900
S800
2 700
600
2 500
400
300
200


- Experimental dispersion Curve
- Theoretical dispersion curve


0 10 20 30 40 50 60


Frequency (Hz)


Shear Velocity (ft/s)


1000


. -40
CL
-50

-60

-70

-80


1500


2000


Figure 3-16. Inversion result of of TAMU obtained by Active MASW: a) Dispersion curve
matching and b) soil profile















Shear wave velocity (ft/s)

0 500 1000 1500 2000


2500 3000 3500 4000


Figure 4-14. Soil profile comparison of Newberry


0







-20







-40







S-60
a.






-80







-100







-120










wave velocities and the N-values are approximately uniform. Below 30 ft, the shear wave

velocities and the N-values increase in the hard clay material

3.6 Summary of TAMU Tests

Base upon the results presented herein, the following conclusions appear to be appropriate:

1. For active multi-channel records, the cylindrical beamformer is the best method of signal
processing as compared to f-k, f-p, and Park, et al. transforms. The beamformer provides
the highest resolution of imaged dispersion curves, and its dominance of resolution at low
frequencies over other methods allows achieving a reliable dispersion curve over a broad
range of frequencies.

2. There is generally good agreement between dispersion results from SASW, active MASW,
and passive MASW surface wave tests.

3. The surface wave-based shear wave velocities are in good agreement with the crosshole
results, and the shear wave velocities appear consistent with SPT N-values and material
logs.


TAMU-0_122


cj!tive scour!ce


61 spacings @ 2ft = 122ft 10 10 10 10 10


0 122 132 142 152 162 172
receiver
active source TAMU-98_220
S10 10 10 10 10 61 apacings B 2ft = 122ft

46 56 68 76 68 98 \ 220
receiver

Figure 3-1. Schematic of SASW setup for TAMU-0_122 and TAMU-98_220








-*- Passive MASW Active MASW


3500


3000


2500 ------------


2000 -------------
o
0






500 ----- -- --------------
0



0 -- I i i I
0 10 20 30 40 50 60 70
Frequency (Hz)


Figure 4-8. Combined dispersion curve of passive and active MASW



3500


3000 -


2500

4-
> 2000



w 1500


1000


500 -


0 10 20 30 40
Frequency(Hz)


Figure 4-9. Final dispersion curve of combined MASW


50 60 70













Shear wave velocity (ft/s)
500 1000 1500


-5-


-10-


-15-


-20


-25 -


* Crosshole Test
- Layer Boundary


Figure 4-13. Soil profile obtained from Crosshole Test


2000


2500




Full Text

PAGE 1

1 AN APPRAISAL OF SURFACE WAVE ME THODS FOR SOIL CHARACTERIZATION By KHIEM TAT TRAN A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ENGINEERING UNIVERSITY OF FLORIDA 2008

PAGE 2

2 2008 Khiem Tat Tran

PAGE 3

3 To my father, whose lifetime of hard work has made mine easier

PAGE 4

4 ACKNOWLEDGMENTS First of all, I thank Dr. Dennis R. Hiltunen for serving as m y advisor. His valuable support, encouragement during my research and studi es were what made this possible. I thank the other members of my thesis committee, Dr. Reynaldo Roque and Dr. Nick Hudyma. I would like to thank my parents for encour aging my studies. I thank the remaining members of my family for their support. I thank all of my friends who treated me like family. Lastly, I extend thanks to my wife, who has supported my decisi ons and the results of those decisions for the past 2 years.

PAGE 5

5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ............................................................................................................... 4 LIST OF FIGURES .........................................................................................................................7 ABSTRACT ...................................................................................................................... ...............9 CHAP TER 1 INTRODUCTION .................................................................................................................. 10 1.1 Problem Statement ........................................................................................................ 10 1.2 Research Objectives ...................................................................................................... 11 1.3 Scope ..................................................................................................................... ........11 2 SURFACE WAVE METHODS ............................................................................................. 13 2.1 Introduction ...................................................................................................................13 2.2 Spectral Analysis of Surface Waves Tests (SASW) ..................................................... 13 2.2.1 Field Testing Elements and Procedures ............................................................ 13 2.2.2 Dispersion Curve Analysis ................................................................................ 14 2.2.3 Inversion Analysis .............................................................................................14 2.3 Multi-Channel Analysis of Ac tive Surface W aves (Active SASW) ............................. 16 2.3.1 Field Testing Elements and Procedures ............................................................ 17 2.3.2 Dispersion Curve Analysis ................................................................................ 17 2.3.2.1 Frequency-wavenumber transform (f-k). ............................................ 17 2.3.2.2 Slowness-frequency transform (p-f). ..................................................19 2.3.2.3 Park et al. transform ............................................................................ 20 2.3.2.4 Cylindrical beamformer transform ..................................................... 21 2.3.3 Inversion Analysis .............................................................................................23 2.4 Multi-Channel Analysis of Passi ve Surface W aves (Passive MASW) ........................ 23 2.4.1 Field Testing Elements and Procedures ............................................................ 23 2.4.2 Dispersion Curve Analysis ................................................................................ 24 2.4.2.1 The 1-D geophone array. ....................................................................24 2.4.2.2 The 2-D geophone array. ....................................................................25 2.4.3 Inversion Analysis .............................................................................................25 3 TESTING AND EXPERIMENTAL RESULTS AT TAMU ................................................. 30 3.1 Site Description .............................................................................................................30 3.2 Tests Conducted ............................................................................................................30 3.2.1 The SASW Tests ............................................................................................... 30 3.2.2 Active MASW Tests .........................................................................................31 3.2.3 Passive MASW Tests ........................................................................................ 31 3.3 Dispersion Results ....................................................................................................... ..31

PAGE 6

6 3.3.1 Dispersion Analysis for SASW Tests ............................................................... 31 3.3.2 Dispersion Analysis for Active MASW ............................................................ 32 3.3.2.1 Spectrum comparison ......................................................................... 32 3.3.2.2 Dispersion curve extraction ................................................................ 34 3.3.3 Dispersion Analysis for Passive MASW .......................................................... 34 3.4 Inversion Results ...........................................................................................................35 3.5 Soil Profile Comparison ................................................................................................ 36 4 TESTING AND EXPERIMENTAL RESULTS AT NEWBERRY ...................................... 51 4.1 Site Description .............................................................................................................51 4.2 Tests Conducted ............................................................................................................51 4.2.1 The SASW Tests ............................................................................................... 51 4.2.2 Active MASW Tests .........................................................................................51 4.2.3 Passive MASW Tests ........................................................................................ 52 4.3 Dispersion Results ....................................................................................................... ..52 4.3.1 Dispersion Analysis for SASW Tests ............................................................... 52 4.3.2 Dispersion Analysis for Active MASW Tests .................................................. 53 4.3.3 Dispersion Analysis for Passive MASW Tests ................................................. 53 4.3.4 Combined Dispersion Curve of Active and Passive MASW ............................ 54 4.4 Inversion Results ...........................................................................................................54 4.5 Crosshole Tests .............................................................................................................55 4.6 Soil Profile Comparison ................................................................................................ 56 5 CLOSURE ....................................................................................................................... .......68 5.1 Summary .................................................................................................................. .....68 5.2 Findings .........................................................................................................................68 5.3 Conclusions ...................................................................................................................69 5.4 Recommendations for Further Work ............................................................................ 69 LIST OF REFERENCES ...............................................................................................................70 BIOGRAPHICAL SKETCH .........................................................................................................71

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7 LIST OF FIGURES Figure page 2-1 Schematic of SASW setup ................................................................................................. 25 2-2 Dispersion curves from SASW test ................................................................................... 26 2-3 Inversion result........................................................................................................... ........26 2-4 Frequency-Wavenumber Spectrum (f-k domain) .............................................................. 27 2-5 Example of data in the x-t domain ..................................................................................... 27 2-7 Signal spectrum and extracted disp ersion curve from Park et al. method ......................... 28 2-9 Signal image and extracted dispersion curve from ReMi .................................................. 29 3-2 Example of SASW data (4ft receiver spacing) .................................................................. 38 3-3 Experimental combined dispersion curve for SASW of TAMU-61 .................................. 38 3-4 Final experimental dispersi on curve for SASW of TAMU-61 .......................................... 39 3-5 TAMU-0_122 recorded data in the time-trace (t-x) domain ............................................. 39 3-6 Spectra of TAMU-0_122 obtai ned by applying m ethods .................................................. 40 3-8 Normalized spectrum at different frequencies ................................................................... 42 3-9 Extracted dispersion curves of TAM U-0_122 obtained by applying 4 methods............... 43 3-10 Extracted dispersion curves of TA M U-88_220 obtained by applying 4 methods ............. 43 3-12 Final dispersion curve of TA MU obt ained by active MASW ...........................................44 3-14 Dispersion curves obtai ned by three techniques ................................................................ 46 3-15 Inversion result of of TAMU obtained by SASW .............................................................47 3-16 Inversion result of of TA MU obtained by Active MASW ................................................48 3-17 Inversion result of of TA MU obtained by Pasive MASW ................................................49 4-1 Newberry testing site .........................................................................................................57 4-2 Dispersion curve for SASW of Newberry ......................................................................... 58 4-3 Newberry active MASW recorded data in the tim e-trace (t-x) domain ............................. 58

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8 4-4 Spectra of Newberry obtained by applying methods .........................................................59 4-5 Normalized spectrum at different frequencies ................................................................... 60 4-6 Extracted dispersion curves of Activ e MASW obtained by applying 4 signalprocessing methods ............................................................................................................ 61 4-7 Combined spectrum of Passive MASW ............................................................................ 61 4-8 Combined dispersion curve of passive and active MASW ................................................62 4-9 Final dispersion curve of combined MASW ..................................................................... 62 4-10 Dispersion curve comparison ............................................................................................. 63 4-11 Inversion result of Neberry obtained by SASW ................................................................64 4-12 Inversion result of Neberry obtained by com bined MASW .............................................. 65 4-13 Soil profile obtained from Crosshole Test .........................................................................66 4-14 Soil profile comparison of Newberry ................................................................................ 67

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9 Abstract of Thesis Presen ted to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Engineering AN APPRAISAL OF SURFACE WAVE ME THODS FOR SOIL CHARACTERIZATION By Khiem Tat Tran May 2008 Chair: Dennis R. Hiltunen Major: Civil Engineering Three popular techniques, Sp ectral Analysis of Surface Waves (SASW), Multi-Channel Analysis of Active Surface Waves (Active MA SW) and Multi-Channel Analysis of Passive Surface Waves (Passive MASW), we re conducted at two well-characterized test sites: Texas A & M University (TAMU) and Newberry. Crosshole shear wave velocity, SPT N-value, and geotechnical boring logs were also available for the test sites. For active multi-channel records, the cylindrical beamformer is the best method of signal processing as compared to frequencywavenumber, frequency-slowness, and Park, et al. transforms. The beamformer provides the highest resolution of imaged dispersion curves, and its dominance of resolution at low frequencies over other methods allows achieving a reliable dispersion curve over a broad range of frequencies. Dispersion data obtained from a ll three surface wave tec hniques was generally in good agreement, and the inverted shear wave profiles were consistent with the crosshole, SPT Nvalue, and material log results. This shows cr edibility of non-destructiv e in situ tests using surface waves for soil characterization.

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10 CHAPTER 1 INTRODUCTION 1.1 Problem Statement Near surface soil conditions control the responses of f oundations and structures to earthquake and dynam ic motions. To get the optimu m engineering design, the shear modulus (G) of underlying layers must be determined corr ectly. The most popular method used to obtain the shear modulus is non-destructive in situ testing via surface waves. An important attribute of this testing method is ability to determine shear wa ve (Vs) velocity profile from ground surface measurements. Then shear modulus is calculated from G= Vs 2. Three popular techniques, Spectral Analysis of Surface Waves (SASW), Mu lti-Channel Analysis of Active Surface Waves (Active MASW) and Multi-Channel Analysis of Passive Surface Waves (Passive MASW) have been developed for non-destructive in situ testin g, but their accuracy remains a question. This research will apply these three t echniques to characterize the soil profiles at two testing sites. The accuracy will be appraised by comparing the soil pr ofiles derived from thes e techniques with soil profiles derived from cross-hole tests, a highl y accurate but invasive testing technique. Non-destructive in situ surface wave testing technique can be divided into three separate steps: field testing to measure characteristic s of particle motions associated with wave propagation, signal processing to extract dispersion curves from e xperimental records, and using an inversion algorithm to obtain the mechanical pr operties of soil profiles For SASW, the testing and data analysis steps are well established. However, for the multi-channel techniques, a number of wave field transfor mation methods are available, bu t the best method has not been confirmed. Two of the most important criteria for establ ishing the best method are: 1) From which method can we derive th e most credible soil profile? 2) From which method can we maximi ze the depth of investigation?

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11 The soil profile derived from the third step is not necessarily unique. It is credible only when we have a good dispersion curve from the second step. Thus, this research will focus on the second step to get the best dispersion cu rves from among different methods of signal processing. The data recorded during a field test includes both signal and ambient noise. It is necessary to use signal-processing methods to discriminate against noise and enhance signal. The first question can be answered if we can successf ully separate the desired signals of surface waves from background noise. The second question can be answered if we can obtain dispersion curves at low frequency. The lower frequency at which we have dispersive relation, the deeper depth of investigation we obtain. 1.2 Research Objectives The research objectives are as follo ws: 1. To find the best method of signal processing to obtain the most credible dispersion curve for a large range of frequency. 2. To check the accuracy of three surface wave techniques by comparison with results from cross-hole tests. 1.3 Scope For the firs t research objective, the author has developed programming codes to map the signal spectra of the recorded da ta by four different methods named as frequency wavenumber transform (f-k), frequency slowness transform (f -p), Park et al. transform, and cylindrical beamformer transform. The dispersion curves are then obtained by pick ing points that have relatively strong power spectral values on the spectra. These points carry information of frequency wavenumber (f-k), frequency slowness (f-p) or frequency velocity (f-v) relationships. Straightforward disp ersion curves in frequency velocity (f-v) domain can be built by calculation of v=1/p from f-p domain or v=2 f/k from f-k domain. The details of the signal

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12 processing methods will be described in the chap ter 2 and the results will be shown in the chapters 3 and 4. For the second research objective, SASW, Ac tive MASW, and Passive MASW have been conducted in two test sites: 1. A National Geotechnical Experime nt site (NGES) at Texas A & M University (TAMU). 2. A Florida Department of Transportation (F DOT) storm water runoff retention basin in Alachua County off of state ro ad 26, Newberry, Florida. Also cross-hole tests were completed at these two sites for comparison. A ll the test results and comparisons are available in chapters 3 and 4.

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13 CHAPTER 2 SURFACE WAVE METHODS 2.1 Introduction The m otivation for using surface waves for soil characterization originates from the inherent nature of this kind of wave. Surface waves propagate along a free surface, so it is relatively easy to measure the associated motions, and carry the important information about the mechanical properties of the medium. So far, three popular techniques: SASW, Active MASW, Passive MASW have been developed to use surf ace waves for soil characterization. This chapter will provide a brief summary of these techniques, including the advantages, disadvantages of each. 2.2 Spectral Analysis of Surface Waves Tests (SASW) SASW was first introduced by N azarian (1984) to the engine ering community. Advantages of SASW ar e a simple field test operation and a straightforward theory, but it also has some disadvantages. This method assumes that the most energetic arrivals ar e Rayleigh waves. When noise overwhelms the power of artificial sources such as in urban areas or where body waves are more energetic than Rayleigh waves, SASW will not yield reliable results. Also during the processing of data, SASW requires some subjective judgments that sometimes influence the final results. SASW is described as follows. 2.2.1 Field Testing Elemen ts and Procedures This m ethod uses an active source of seismic energy, recorded repeatedly by a pair of geophones at different distances. The Figure 2.1 shows a schematic of SASW testing configuration. To fully characterize the fre quency response of surface waves, these twotransducer tests are repeated fo r several receiver spacings. The ma ximum depths of investigation will depend on the lowest frequency (longest wave length) that is measured. The sources are

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14 related to the geophone distances, and range from sledgehammers at short receiver spacings (12m) to heavy dropped weights, bulld ozers, and large vibr ation shakers at larg e receiver spacings (50-100m). 2.2.2 Dispersion Curve Analysis Each reco rded time signal is transformed in to frequency domain using FFT algorithm. A cross power spectrum analysis calculate s the difference in phase angles ( (f)) between two signals for each frequency. The travel time ( t(f)) between receivers can then be obtained for each frequency by: f t ft 2 )( )( (2.1) The distance between geophones is known, thus wave velocity is calculated by: )( )( ft X fVR (2.2) Considering each pair of signals, an estimate of the relationship between wave velocity and frequency over a certain range of frequency is obtained. Gatheri ng the information from different pairs of geophones the combined dispersion curve is derived (Fi gure 2.2a). Then the combined one is averaged to get the final disp ersion curve for inversion (Figure 2.2b). 2.2.3 Inversion Analysis Inversion of Rayleigh wave dispersion curve is a process for determ ining the shear wave velocity profile from frequency-phase velocity dispersion relationship. This process consists of evaluation of theoretical dispersion curves fo r an assumed profile and comparison with the experimental dispersion curve. When the theore tical dispersion curve and the experimental dispersion relatively match, the assumed profile is the desired solution. The assumed medium is composed of horizontal layers that are homogene ous, isotropic and the shear velocity in each

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15 layer is constant and does not vary with depth. The theoretical dispersion curve calculation is based on the matrix formulation of wave pr opagation in layered media given by Thomson (1950). The details of the pro cess are described as follows. a) To determine the theoretical di spersion from an assumed profile: We can use either transfer matrix or stiffness matrix for calcula tion of the theoretical dispersion. The transfer matrix relates the displacement-stress vector at th e top of the layer and at the bottom of the layer. Using the compatibility of the di splacement-stress vectors at the interface of two adjacent layers, the displacement-stress vector at the surface can be related to that of the surface of the halfspace. Applying the radiation condition in the half-space, no incoming wave, and the condition of no tractions at the surface, the relationship of the amplitudes of the outgoing wave in the halfspace and the displacements at the surface can be derived: 0 0 0 0 w u B P S (2.3) Where the 4x4 matrix B is the product of transfer matrices of all layers and the half-space, u and w are the vertical and horizontal displacements at the surface. A nontri vial solution can be obtained if the determinant of a 2x2 matrix comp osed by the last two rows and the first two columns of matrix B is equal to zero. The ch aracteristic equation 2.4 gives the theoretical dispersion. 04241 3231 BB BB (2.4) Another method to obtain the theoretical dispersion is to use the stiffness matrix that relates displacements and forces at the top and at the bottom of a layer or displacements and

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16 forces at the top of a half-sp ace. The global stiffness matrix S is diagonally assembled by overlapping all the stiffness matrices of layers and half-space. The vector u of interface displacements and the vector q of external interface loadi ngs can be related: S u = q The Rayleigh waves can exist without interface loadings so: S u = 0 (2.5) The nontrivial solution of the interface displacemen ts can be derived with the determinant of S being zero. The theoretical dispersion can be achieved from the equation 2.6 0 S (2.6) b) To determine a reasonable assumed profile: An initial model needs to be specified as a start point for the iterative inve rsion process. This model consists of S-wave velocity, Poissons ratio, density, and thickness parameters. It is necessary to start from the most simple and progressively add complexity (Marosi and Hilt unen 2001). The assumed profile will be updated after each iteration and a least-squares a pproach allows automation of the process. 2.3 Multi-Channel Analysis of Ac tive Surface Waves (Active SASW) This m ethod was first developed by Park, et al.(1999) to overcome the shortcomings of SASW in presence of noise. The most vital advantage of MASW is that transformed data allow identification and rejection of non-fundamental mode Rayleigh waves such as body waves, nonsource generated surface waves, higher-mode surf ace waves, and other coherent noise from the analysis. As a consequence, the dispersion curv e of fundamental Rayleigh waves can be picked directly from the mode-separated signal image. The obtained dispersion curve is expected to be more credible than that of SA SW, and this method can be automa ted so that it does not require an experienced operator. An additional advantag e of MASW is the speed and redundancy of the

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17 measurement process due to multi-channel recording. Its quick and easy field operation allows doing many tests for both vertical an d horizontal soil characterization. 2.3.1 Field Testing Elemen ts and Procedures In Active MASW wave field from an activ e source is recorded simultaneously by many geophones (usually >12) placed in a linear array a nd typically at equidistant spacings. The active source can be either a harmonic source like a vibrator or an impul sive source like a sledgehammer. Depending on the desired depth of investigation, the strength of source will be properly selected to create surface wave fiel d at the required range of frequencies. If the wave field is treated as plane waves in data analysis, the distan ce from source to the nearest receiver (near offset) cannot be smaller th an half the maximum wavelength, which is also approximately the maximum depth of investigati on (Park et al. 1999). Howe ver, with cylindrical wave field analysis, this near offset can be selected smalle r to reduce the rapid geometric attenuation of wave propagation. 2.3.2 Dispersion Curve Analysis To determ ine accurate dispersion informati on, multi-channel data processing methods are required to discriminate against noise and e nhance Rayleigh wave signals. The following will discuss on four methods used for separating signals from background noise. 2.3.2.1 Frequency-wavenumber transform (f-k). For a given frequency, s urface waves ha ve uniquely defined wavenumbers k0(f), k1(f), k2(f)for different modes of propagation. In other words, the phase velocities cn= /kn are fixed for a given frequency. The f-k transform allows separation of the modes of surface waves by checking signals at different pairs of f-k. The Fourier transform is a fundamental in gredient of seismic data processing. For example, it is used to map data from time doma in to frequency domain. The same concept is

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18 extended to any sequential series other than time. The f-k analysis uses 2D Fourier transform that can be written as (Santamaria and Fratta 1998): l N ui M l N m m N vi ml vue ep P 2 1 0 1 0 2 (2.7) Where: N = number of time samples, M = number of receivers in space Pu,v = spectral value at wavenumber index u and frequency index v pl,m = recorded data at mth sample of lth receiver This transform is essentially two consecutive applications of a 1D Fourier transform as shown in the following: Input data in (t,x) domain 1D Fourier Transform in the time direction (Data in (f,x) domain) 1D Fourier Transform in the spatial direction (Data in (f,k) domain) One main problem of the 2D transf orm is the requirement of a large number of receivers to obtain a good resolution in wavenumber dire ction. Because the geophone spacing dx controls the highest obtainable wavenumber (kmax= /dxmin), the spread length (X ) controls the solution ( k=2 /X). To obtain a good solution the spread lengt h must be large but it is often difficult due to site size restrictions. The usual trick to improve the solution is to add a substantial number of zero traces at the end of field reco rd (zero padding), which essentia lly creates artificial receiver locations with no energy. Figure 2.4 shows a spectrum in f-k domain where the signals are successfully separated from the background noise. Here we observe that the most energy is concentrated along a narrow band of

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19 f-k pairs. This narrow band represents of funda mental Rayleigh wave mo de of propagation. At a given frequency, wavenumber k is determined by picking the local strongest signal and the dispersion curve is then built by calculating th e velocities at different frequencies as: )( 2 )( fk f fV (2.8) 2.3.2.2 Slowness-frequency transform (p-f). This procedure developed by McMechan and J.Yedlin (1981) consists of two linear transformations: 1) A slant stack of the data produces a wave fiel d in the phase slowness time intercept (p) plane in which phase velocities are separated. 2) A 1D Fourier transform of the wave field in the pplane along the time intercept gives the frequency associated with each velocity. Th e wave field is then in slowness-frequency (p-f) domain. Firstly, the slant stack is a process to separate a wave field into different slowness (inverse of velocity) and sum up all signals having the same slowness over th e offset axis. The calculation procedures as follows: 1) For a given slowness p and a time-intercept (figure 2-5), calculate the travel time t at offset x as p xt and retrieve P(x,t), the amplitude of the recorded signal for that x and t. In practice, the recorded value of P(x,t) wi ll often fall in between sampled data in time, and then will be calculated via linear interpolation. 2) This process is repeated for all x in the r ecorded data and the results are summed to produce: xtxPpS ),(),( (2.9) ),( pS will present a spectral amplitude in the pdomain. 3) Steps 1 and 2 are repeated ove r a specified range of p and to map out the spectral amplitudes in the pdomain. Secondly, a 1D Fourier transform of S(p, ) along the direction separates the wave field into different frequencies, which produces data set of spectral amplitudes in the slowness (p)

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20 frequency (f) domain such as shown in figure 2-6. Here we observe that the most energy (largest spectral amplitudes) is concentrated along a narrow band of p-f pairs. As with f-k, this narrow band represents the fundamental Rayleigh wave mode of propagation. At a given frequency, the phase velocity is calculated as the inverse of the slowness determined from the maximum spectral amplitude. In practice, this process has been observed to produce better identification of Rayleigh waves than does f-k. 2.3.2.3 Park et al. transform In the mid to late 1990s, Park, Miller, Zia and others at the Kansas Geological Survey began to develop the now popular SurfSeis softwa re for the processing of multi-channel surface wave data from geotechnical applications. During their developm ent, it was discovered that the two conventional transformation me thods, f-k and p-f, did not provi de adequate resolution of the wavefield in the cases where a small number of r ecording channels is available (Park, et al. 1998). Because it is desirable for geotechnical applications to us e small arrays, they developed an alternative wavefield transform referred to herein as the Park, et al. transform. This method consists of 4 steps: 1) Apply 1D Fourier transform (FFT) to the wave field along the time axis, this separates the wavefield into components with different freque ncies. The recorded data is changed from (x-t) domain to (x-f) domain: U(x,t) U(x,f). 2) Normalize U(x,f) to unit amplitude: U(x,f) ),( ),( fxU fxU 3) Transform the unit amplitude in (x-f) domain to (k-f) domain as follows: For a specified frequency (f) and a wavenumber (k), the nor malized amplitude at x is multiplied by eikx and then summed all over the offset axis. This is repeated over a range of wavenumber for each f, and then over all f to produce a 2D spectrum of normalized amplitudes in f-k domain. This can be presented by: x ikxfxU fxU efkV ),( ),( ),( (2.10)

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21 4) Transform V(k,f) to the phase velo city frequency domain: V(k,f) V(v,f) by changing the variables such that c(f)=2f/k. The spectrum of V(v,f) is shown as an exampl e in figure 2-7. Here we observe that the most energy (largest spectral amplitudes) is c oncentrated along a narrow band of f-v pairs. This narrow band represents the fundamental Raylei gh wave mode of propagation. At a given frequency, phase velocity is determined by picki ng the local strongest sign al in the narrow band. 2.3.2.4 Cylindrical beamformer transform a) Cylindrical wavefield: The previous three transforms, f-k, p-f, Park, are based on a plane wavefield model for the surface wave propag ation. A plane wavefield is a description of the motion created by a source located an infini te distance from the receivers. Surface wave testing methods, however, employ a source at a finite distance, and t hus the wavefield is cylindrical and not planar. Zy wicki (1999) has noted that a cylindrical wavefield can be described by a Hankel-type solution as given by: tiekxAHtxs )(),(0 (2.11) Where s(x,t) = displacement measured at spat ial position x at time t, A= initial amplitude of the wave field, H0 = the Hankel function of firs t kind of order zero which has the real part and imaginary part are respectively Bessel functions of the first kind and the second kind of order zero. The cylindrical wave equati on allows accurate modeling of wa ve motions at points close to the active source, and this brings advantages in determining dispersi on relationship at low frequencies (long wavelengths). At a relatively large distance x, the Hankel function can be expa nded as: (Aki and G.Richards 1980) 2 2/1 0)( 1 8 1)4/(exp 2 )( kx O kx i kxi kx kxH (2.12)

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22 Neglecting waves that decay more rapidly than x / 1, the equation 2.12 becomes: )4/(exp 2 )(2/1 0 kxi kx kxH (2.13) This equation clearly shows the x / 1decay and plane wave nature of the cylindrical wave equation in the far-field. In other words, at a rela tively large distance x, the cylindrical wave field approaches the plane wave field. b) Cylindrical wavefield transform: Based upon the cylindrical wavefield model, a cylindrical wavefield transform can be described as follows (Zywicki 1999): 1) Apply 1D Fourier transform to wavefield along the time direction 2) Build a spatiospectral correlation matrix R(f): Th e spatiospectral correlation matrix R(f) at frequency f for a wave field reco rded by n receivers is given by: )()()( )()()( )()()( )(2 1 2 22 21 1 12 11fRfRfR fRfRfR fRfRfR fRnn n n n n (2.14) )()()(*fSfSfRj i ij (2.15) Where Rij (f) = the cross power spectrum between the ith and jth receivers, Si (f) = Fourier spectrum of the ith receiver at frequency f, denotes complex conjugation. 3) Build a cylindrical steering vector: the cylindr ical steering vector for a wavenumber k is built by applying the Hankel function as follows: T nxkHxkHxkHikh ,, exp{)(2 1 (2.16) Where denotes taking the phase angle of the argument in parentheses. T denotes changing a vector from a column to a row or adversely. 4) Calculate the power spectrum estimate of th e fieldwave: For a given wavenumber k and frequency f, the power spectrum estimate is determined by:

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23 ) ()()(),( khfRkhfkPT (2.17) The spectrum of P (k, ) allows separating fundamental mode Rayleigh waves from other waves (figure 2.8). Similar to previous methods, here we observe that the most energy (largest spectral amplitudes) is concentrated along a narrow band of f-k pairs. This narrow band represents the fundamental Rayleigh wave mode of propagation At a given frequency, wavenumber k is determined by picking the local strongest signal and the disp ersion curve is then built by calculating the velocities at different frequencies by equation 2.8. 2.3.3 Inversion Analysis The inversion algorithm of this method is the same as that of SASW (part. 2.2.3). The only difference would be that the iter ative inversion calcul ation of MASW is qu icker than that of SASW because MASW usually brings smoother di spersion curves that allow quickly achieving the stopping criteria in the inversion process. 2.4 Multi-Channel Analysis of Pass ive Surface Waves (Passive MASW) Passive wave utilization has been intensivel y studied recently. It derives from useful inherent characteristics of the passive surface wa ves. The most important advantage of testing methods using passive waves is the ability to obtain deep depths of investig ation with very little field effort. Desired Rayleigh wa ves from passive seismic arrivals are relatively pure plane waves at low frequencies allow determining Vs profiles up to hundreds meter depth. The shortcoming is that this method is only able to apply for noisy test ing sites (urban areas close to roads) but not for quiet te st sites (rural areas). 2.4.1 Field Testing Elemen ts and Procedures Passive wave fields (background noise) are recorded simultaneously by many geophones located in 1-D or 2-D arrays. With a requireme nt of recording waves at long wavelengths, geophone spacing of passive MASW is often larger than that used in active MASW. This leads

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24 to a need of large testing spaces especially for a 2-D geophone layout. The length of a 1D geophone spread must not be less than the maximum expected wavelength. For a 2-D circular geophone layout, the diameter should be equal to the maximum expected wavelength. It is typical that many sets of data are r ecorded for each geophone layout and these data will be combined to improve spec tra for dispersion analysis. 2.4.2 Dispersion Curve Analysis The methods of dispersion curve analysis depend on the geophone layouts applied to record data. Two methods have been suggested as follows: 2.4.2.1 The 1-D geophone array. This method was first develope d by Louie (2001) and named Refraction Microtremor (ReMi). Two-dimensional slowness-frequency (p-f ) transform (part 2.3.2.2) is applied to separate Rayleigh waves from other seismic arri vals, and to recognize th e true phase velocity against apparent velocities. Different from active waves that have a specific propagation direction inline with the geophone array, passive waves arrives from any direction. The apparent velocity Va in the direction of geophone line is calculated by: )cos(/ vVa (2.18) Where: v = real inline phase velocity, and = propagation angle off the geophone line. It is clear that any wave come s obliquely will have an appa rent velocity higher than the true velocity of inline waves, i.e., off-line wa ve signals in the slowness-frequency images will display as peaks at apparent ve locities higher than the real inline phase velocity. Dispersion curves are extracted by manual picking of the relati vely strong signals at lo west velocities (figure 2-8).

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25 The disadvantage of ReMi is to require the ma nual picking, as this depends on subjective judgment, and sometimes influence the final results. 2.4.2.2 The 2-D geophone array. Park, et al. (2004) introduced a data proces sing scheme for a 2D cross layout and then developed for 2D circular layout. This method is extended from the method applied for active MASW tests (part 2.3.2.3). 2.4.3 Inversion Analysis The inversion algorithm of this method is the same that of SASW (part. 2.2.3). Usually, the dispersion curves from passive MASW are in a small range of low frequencies (<20Hz), so the soil profiles at shallow depths are not very prec ise. Passive data are sometimes combined with that of active MASW to broaden the range to higher frequencies. The combination of dispersion curves brings better result s of soil characterization. Figure 2-1. Schematic of SASW setup

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26 a)0 200 400 600 800 1000 1200 1400 0102030405060Frequency (Hz)Phase Velocity (ft/s) b)0 200 400 600 800 1000 1200 1400 0102030405060Frequency (Hz)Phase Velocity (ft/s) a) 0 200 400 600 800 1000 1200 1400 1600 010203040506070Frequency (Hz)Phase Velocity (ft/s) experimental Theoretical b)-60 -50 -40 -30 -20 -10 0 05001000150020002500300035004000Shear wave velocity (ft/s)Depth (ft) Figure 2-2. Dispersion curves from SASW test: a) Combined raw dispersion curve and b) Final dispersion curve after averaging Figure 2-3. Inversion result: a) Disp ersion curve matching, b) Soil profile

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27 frequency, Hzwavenumber, rad/ft 10 20 30 40 50 60 70 80 90 100 0.2 0.4 0.6 0.8 1 1.2 1.4 Figure 2-4. Frequency-Wavenu mber Spectrum (f-k domain) Figure 2-5. Example of data in the x-t domain

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28 frequency, HzSlowness, s/ft 10 20 30 40 50 60 70 80 90 100 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 x 10-3 Figure 2-6. Slowness-Freque ncy Spectrum (f-p domain) Figure 2-7. Signal spectrum and extracted dispersion curve from Park et al. method

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29 frequency, HzWave number, rad/ft 10 20 30 40 50 60 70 80 90 100 0.2 0.4 0.6 0.8 1 1.2 1.4 Figure 2-8. Cylindrical Bea mformer Spectrum (f-k domain) Figure 2-9. Signal image and extract ed dispersion curve from ReMi

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30 CHAPTER 3 TESTING AND EXPERIMENTAL RESULTS AT TAMU 3.1 Site Description The data were collected at the National Ge otechnical Experiment site (NGES) on the campus of Texas A & M University (TAMU). The TA MU site is well documented, and consists of an upper layer of approximately 10 m of medium dense, fine, silty sand followed by hard clay. The water table is approximately 5 m below th e ground surface. Because of space limitations, all the tests including two-sensor a nd multi-sensor tests were only 1D receiver la yout and conducted on a straight line of nearly 400 feet. The positions are marked with one-foot increment from 0 to 400 as TAMU-0_400. 3.2 Tests Conducted On the mentioned line, three kinds of te sts, SASW, Active MASW and Passive MASW were conducted for comparison. The details of fi eld-testing elements and procedures of each kind of tests are described as follows. 3.2.1 The SASW Tests The conducted SASW tests are divided into tw o categories that were recorded at two positions, TAMU-61 and TAMU-128. The SASW tests were conducted with configurations having the source-first receiver di stance equal to inter-receiver di stance. At each position, many configurations were used in common midpoint (CMP) style with the in ter-receiver distance at 4 ft, 8 ft, 16 ft, 32 ft, 64 ft, and 122 ft. For each r eceiver layout, the active source was placed both front and behind for recording forward and back ward (reverse) wave propagations. The active sources were hammers for the inter-receiver dist ances up to 16 ft, and shakers for larger distances.

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31 3.2.2 Active MASW Tests The active MASW tests were conducted with 62 receivers at spacing of 2 feet with the total receiver spread of 122 f eet. Two receiver layouts were laid at positions TAMU-0_122 and TAMU-98_220. For each receiv er layout, five sets of data we re recorded accordingly to five positions of the active source at 10 ft, 20 ft, 30 ft, 40 ft, and 50 ft away from the first receiver. For the record TAMU-0_122, th e active source was located at TAMU 132, 142, 152, 162, 172, and for the record TAMU-98_220, the active sour ce was located at TAMU 88, 79, 68, 58, 48 (see Figure 3.1). Each set of data was obtained with 16,348 (2^14) samples, the time interval of 0.78125 ms (0.00078125 s), and the total r ecorded period of 12.8 seconds. 3.2.3 Passive MASW Tests The passive MASW tests were conducted by 32 receivers deployed at inter-spacing of 10 feet spanning a distance of 310 feet at site pos ition TAMU-0_310. For the passive tests, several sets of data were obtained for combining spectra in the dispersion analysis. In this case, 26 sets of data were recorded with 16,348 (2^14) samples, the time interval of 1.9531 ms (0.0019531 s), and the total recorded period of 32 seconds. 3.3 Dispersion Results In this section, the disp ersion curves from SASW, Active MASW and Passive MASW are extracted for inversion. Also, several signal processing methods are applied for Active MASW data to evaluate these methods and obtain the best dispersion curve. 3.3.1 Dispersion Analysis for SASW Tests The dispersion results of tests at TAMU-61 and TAMU-128 are similar so only tests at TAMU-61 are presented here in detail. The Figur e 3-2 shows an example of data obtained with inter-receiver distance of 4 ft and reverse record ing (4r). The cross power spectrum (CPS) phase is used to calculate the frequency-dependent time delay. Then with the known receiver distance,

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32 the phase velocity is determined. The cohe rence function allows checking wave energy distribution and the ranges of fr equency where the signal to noise ratio is high (according to the coherence function close to 1). This informati on helps to determine the credible range of frequency in which dispersi on relationship is obtained. One more criterion should be applied to elim inate the influence of body waves. Only the range of frequency in which the according wavele ngth is not less than one third and not more than twice of the distance from the source to the first receiver is effectively counted. In this range, the wave field can be considered as relatively pure plane waves. For SASW data recorded at TAMU-61, all twelve sets of data with 6 inter-receiver distances for both forward and backward records ar e used for dispersion analysis. Each set gives the dispersion relationship in a certain range of frequency. Assembling the information from the 12 sets of data, the combined dispersion curve is derived (F igure 3-3). Many points in the combined dispersion curve are cumbersome in the inversion process, so an averaged curve is desired. In this case, a smoothing algorithm is us ed to obtain the final dispersion curve (Figure 34). 3.3.2 Dispersion Analysis for Active MASW The main purpose of this part is to use the r eal recorded data to ch eck and compare all of the signal processing methods descri bed in the chapter 2: f-k transfor m, f-p transform, Park, et al. transform, and cylindrical beamformer. Then the spectrum having the best resolution will be selected for extracting the dispersion curve. 3.3.2.1 Spectrum comparison For each geophone layout, the data recorded with five active source locations give similar results of spectra, so only data recorded at th e closest source (10 feet away from the first geophone) are presented here. Figure 3-5 shows the TAMU-0_122 recorded data in the time-

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33 trace (t-x) domain. In this untransformed domain we can only see the waves coming at different slowness (slope), but are not able to distinguish between signals a nd noise. The signal processing methods are necessarily applied to map th e field wave for dispersion analysis. For active MASW, the recorded data were used to check and compare the signal processing methods, f-k, f-p, Park, et al. tr ansform, and cylindrical beamformer. For comparison, the spectra were all imaged in th e same domain (figure 3.6 and figure 3.7). The frequency interval, velocity interval, number of frequency steps, and number of velocity steps on these spectra are identical. Also, the spectral valu es in all images were unity normalized, i.e., the highest value in each spectrum is equal to 1.0, a nd all other values are relatively compared to one. From these data it is apparent that the Park et al. transform and th e cylindrical beamformer have better imaged dispersion curves at low frequencies (<15Hz) than that of the f-k and f-p transforms. Overall, the spectrum obtained from the cylindrical beamformer has the highest resolution. Resolution of spectra in the frequency-phase velocity (f-v) do main can be separated into 2 components: resolution along the frequency axis and resolution alo ng the phase velocity axis. All four methods apply a 1-D Fourier tran sform along the time direction to discriminate among frequencies for a given phase velocity, thus the resolutions along th e frequency axis for each method are not much different. However, fo r the resolution along the phase velocity axis, the cylindrical beamformer appears best able to separate phase velocities for a given frequency. To provide further illustrati on of resolution capabilities, fi gure 3.8 shows the normalized spectral values of TAMU-0_122 at 4 frequencies: 10, 20, 30, and 40 Hz. For each frequency, the spectral values are normalized to unity, i.e. the maximum valu e along the phase velocity axis is equal to 1. Even though the strongest peak for ea ch method occurs at similar phase velocities for each frequency, the highest peak of the cylindrical beamformer is most dominant to other local

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34 peaks on its spectrum, i.e., the cylindrical beamfo rmer reduces side ripples, and most of the energy concentrates at the strongest peak. The sharpest peak of the cylindrical beamformer allows the best separation of phase velocities fo r any given frequency. Thus, the high resolution along the phase velocity axis co ntributes to the highest overa ll resolution of the cylindrical beamformer. This can be understood that th e cylindrical wavefield equations present the motions of waves created by an active source more properly than do plane wavefield equations. 3.3.2.2 Dispersion curve extraction The dispersion curves from all mentioned si gnal-processing methods are extracted by selecting the strongest signals at every frequency and shown in figure 3.9 and figure 3.10. For the recorded data, even though th e extracted dispersion curves of the methods are similar, the curves (figure 3.11) obtained by the cylindrical bea mformer were selected to present for the test site because of their highest credibility. Because they are also very similar, the two dispersion curves of TAMU-0_122 and TAMU-98_220 were comb ined, averaged and smoothened to derive the final one for Active MASW testing of TAMU (f igure 3.12). This is also rational since it is desirable to compare these results with those fr om passive MASW, and this data was collected over the full 310 feet length of the array. 3.3.3 Dispersion Analysis for Passive MASW The data of 1D receiver arra y at TAMU were analyzed by commercial software Seisopt ReMi that uses the Louie (2001) method of data analysis. This method applies two-dimensional slowness-frequency (p-f) transform to separate Rayleigh waves from othe r seismic arrivals and to recognize true phase velocity against appare nt velocities (see Part 2.3.2.2). The combined spectrum from several passive records allows obt aining the dispersion curve over a larger range of frequencies (figure 3.13).

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35 3.3.4 Dispersion Curve Comparison It is observed from figure 3.14 that the dispersion data from all three techniques is generally in good agreement, particularly at th e high and low frequency ranges. However, active MASW dispersion data appear to be higher in a middle frequency range It is also observed that the active and passive MASW data is smoother th an the SASW data. The ripples in the SASW data are mostly produced by slight mismatches in the combined dispersion data from multiple receiver spacings. Each spacing samples a slightly different zone of soil, and lateral variability of soil properties will produce a mismatch in dispersion data. 3.4 Inversion Results After finishing the dispersion analysis, the in version algorithm (part 2.2.3) is applied to characterize soil profiles from the dispersion curves. The inversion module of commercial software Seisopt and inversion algorithm de veloped by D.R.Hiltunen & Gardner (2003) are applied to derive the soil profile. Both give similar results which are shown in figure 3-15, figure 3-16, and figure 3-17 for tests: SASW, Active MASW and Passive MASW respectively. Also dispersion curve matching between theoretical curve and experimental curve is shown for reference. In all three cases, the inversion routine was ab le to match the experimental data very well. However, it is noted for all three cases that the theoretical models are not able to exactly match the experimental data in some localized areas. Th ese fluctuations are due to localized variability in the soil profile that the surface wave i nversion algorithm is not able to detect. The maximum depth of investigation depends on the lowest frequency in which the dispersive relationship is achie ved and on shear velocity. By using heavy shakers to create the active field wave, the lowest fre quency of SASW is 3 Hz and th e maximum attainable depth is 65 feet. For active MASW and passive MASW, th e lowest frequencies are 6 Hz and 5 Hz; the

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36 maximum attainable depths are 53 ft and 45 ft re spectively. The maximum depth of investigation at TAMU is not very deep even though the lowest frequency is as low as 3 Hz (SASW) because of low phase velocity of soil profile that leads to a moderate maximum wavelength ( max=V/2 .fmin). The bigger the maximum wavelength, the deeper depth of investigation is obtained. 3.5 Soil Profile Comparison The Vs profiles of TAMU derived from SASW, Active MASW, Passive MASW and cross-hole test are all shown together in the figure 3.18. Also shown in the figure 3.18 are crosshole Vs measurements, SPT N-values, mate rial logs from a n earby geotechnical boring conducted at the site. First, regarding the shear wave velocity prof iles from the three surface wave techniques, it is observed that they are genera lly in good agreement. Consistent with the disper sion curves, the SASW and passive MASW are in particularly g ood agreement. However, the active MASW is slightly stiffer (higher velocity) at some depths, which is also consistent with the dispersion data. Second, it is observed that th e surface wave based shear wave velocity profiles compare well with the crosshole results, especially at de pths from 30 to 50 ft. Above 30 ft, a reversal occurs in the profile attained fr om the crosshole tests that is not detected by the surface wave tests. The surface wave tests are conducted ove r a relatively long array length that samples and averages over a large volume of material, wh ereas the crosshole resu lts are based upon wave propagation between two bore holes that are only 10 ft apart, and thus these data represent a more local condition at the site. Lastly, there appears to be reasonable consiste ntly between the shear wave velocity results and the SPT N-values and material log. In the sand layer above a depth of about 30 ft, the shear

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37 wave velocities and the N-va lues are approximately uniform. Below 30 ft, the shear wave velocities and the N-values increas e in the hard clay material 3.6 Summary of TAMU Tests Base upon the results presented herein, the following conclusions app ear to be appropriate: 1. For active multi-channel records, the cylindrical beamformer is the best method of signal processing as compared to f-k, f-p, and Park, et al. transforms. The beamformer provides the highest resolution of imaged dispersion cu rves, and its dominance of resolution at low frequencies over other methods allows achievi ng a reliable dispersion curve over a broad range of frequencies. 2. There is generally good agreement between di spersion results from SASW, active MASW, and passive MASW surface wave tests. 3. The surface wave-based shear wave velocitie s are in good agreement with the crosshole results, and the shear wave velocities appear consistent with SPT N-values and material logs. Figure 3-1. Schematic of SASW setup for TAMU-0_122 and TAMU-98_220

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38 0 200 400 600 800 1000 1200 1400 010203040506070Frequency (Hz)Phase Velocity (ft/s) 4f 4r 8f 8r 16r 16f 32f 32r 64f 64r 122f 122r Figure 3-2. Example of SASW data (4ft receiver spacing) Figure 3-3. Experimental combined di spersion curve for SASW of TAMU-61

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39 0 200 400 600 800 1000 1200 1400 010203040506070 Frequency (Hz)Phase Velocity (ft/s) Combined dispersion curve Final dispersion curve by smoothing Figure 3-4. Final experimental disp ersion curve for SASW of TAMU-61 Figure 3-5. TAMU-0_122 recorded da ta in the time-trace (t-x) domain

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40 Figure 3-6. Spectra of TAMU0_122 obtained by applying methods: a) f-k transform b) f-p transform c) Park, et al. transf orm d) Cylindrical beamformer Figure 3-6. Spectra of TAMU0_122 obtained by applying methods: a) f-k transform b) f-p transform c) Park, et al. transf orm d) Cylindrical beamformer

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41 Figure 3-7. Spectra of TAMU88_220 obtained by applying methods: a) f-k transform b) f-p transform c) Park, et al. transf orm d) Cylindrical beamformer

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42 Figure 3-8. Normalized spectru m at different frequencies (Solid line for cylindrical beamformer, Dashpot line for Park, et al. transform Dashed line for f-k transform, Dotted line for f-p transform) Figure 3-8. Normalized spectrum at different frequencies (Solid li ne for cylindrical beamformer, Dashpot line for Park, et al. transform, Da shed line for f-k transform, Dotted line for f-p transform)

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43 200 300 400 500 600 700 800 900 1000 1100 1200 010203040506070 Frequency (Hz)Phase Velocity (ft/s) f-k transform f-p transform Park et al.transform Cylindrical Beamfomer Figure 3-9. Extracted dispersion curves of TAMU-0_122 obtained by applying 4 methods Figure 3-10. Extracted dispersion curves of TAMU-88_220 obtained by applying 4 methods 200 300 400 500 600 700 800 900 1000 1100 1200 010203040506070 Frequency (Hz)Phase Velocity (ft/s) f-k transform f-p transform Park et al.transform Cylindrical Beamfomer

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44 200 300 400 500 600 700 800 900 1000 1100 1200 010203040506070 Frequency (Hz)Phase Velocity (ft/s) TAMU_0-122 TAMU_98-220 Figure 3-11. Combined dispersion curv e of TAMU from 2 shot gathers Figure 3-12. Final dispersion curve of TAMU obtained by active MASW 200 300 400 500 600 700 800 900 1000 1100 1200 010203040506070 Frequency (Hz)Phase Velocity (ft/s)

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45 b) 200 300 400 500 600 700 800 900 1000 0510152025303540 Frequency (Hz)Phase Velocity (ft/s) Figure 3-13. The REMI analysis: a) Combined spectrum of Passive MASW at TAMU, b) Extracted dispersion curve by manual picking

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46 Figure 3-14. Dispersion curves obtained by three techniques 0 200 400 600 800 1000 1200 010203040506070Frequency (Hz)Phase Velocity (ft/s) SASW Active MASW Passive MASW

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47 Figure 3-15. Inversion result of of TAMU obtained by SASW: a) Dispersion curve matching and b) soil profile a)200 300 400 500 600 700 800 900 1000 1100 1200 010203040506070 Frequency (Hz)Phase Velocity (ft/s) Experimental dispersion curve Theorectical dispersion curve b)-80 -70 -60 -50 -40 -30 -20 -10 0 0 500100015002000 Shear Velocity (ft/s)Depth (ft)

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48 Figure 3-16. Inversion result of of TAMU obtained by Active MASW: a) Dispersion curve matching and b) soil profile a) 200 300 400 500 600 700 800 900 1000 1100 1200 010203040506070 Frequency (Hz)Phase Velocity (ft/s) Experimental dispersion Curve Theoretical dispersion curve b) -80 -70 -60 -50 -40 -30 -20 -10 0 0 500100015002000 Shear Velocity (ft/s)Depth (ft)

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49 a) 200 300 400 500 600 700 800 900 1000 01020304050 Frequency (Hz)Phase Velocity (ft/s) Experimental dispersion curve Theoretical dispersion curve b) -80 -70 -60 -50 -40 -30 -20 -10 0 0 500100015002000 Shear Velocity (ft/s)Depth (ft) Figure 3-17. Inversion result of of TAMU obtained by Pasive MASW: a) Dispersion curve matching and b) soil profile

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50 Figure 3-18. Soil profile comparison

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51 CHAPTER 4 TESTING AND EXPERIMENTAL RESULTS AT NEWBERRY 4.1 Site Description The testing site is a single Florida Depart ment of Transportation (FDOT) storm water runoff retention basin in Alachua County off of state road 26, Newberry, Florida (figure 4-1). The test site was approximately 1.6 hectares and was divided into 25 strips by 26 north-south gridlines marked from A to Z w ith the gridline spacing of 10 ft. Each gridline was about 280 ft in length with the station 0 ft at the southern end of the gridline. Five PVC-cased boreholes extending to the depth of 60 ft were installed for cross-hole tests. 4.2 Tests Conducted SASW, Active MASW, and Passi ve MASW were conducted in Newberry for comparison of the obtained soil profiles. The details of fiel d testing procedures of each kind of test are described as follows. 4.2.1 The SASW Tests The SASW tests were conducted on gridline Z with configurations having the source-first receiver distance equal to inte r-receiver distance. All configurat ions were employed with the common midpoint (CMP) at position Z-80 for inter-receiver distances of: 4 ft, 6 ft, 8 ft, 12 ft, 16 ft, 24 ft, 32 ft, 40 ft and 50 ft. For each receiv er layout, the source was placed front and behind for recording forward and backward wave propa gations. Hammers were used to produce active wave fields. 4.2.2 Active MASW Tests The active MASW tests were c onducted by 31 receivers at spaci ng of 2 feet with the total receiver spread of 60 feet. The active source was located 30 ft away from the first receiver. Many sets of data were collected by moving both the source and receiver layout 4 ft each. Each set of

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52 data was obtained with 2048 (2^11) samples, the time interval of 0.78125 ms (0.00078125 s), and the total recorded period of 1.6 seconds. For comparison with SASW tests, only one set of data collected by a receiver array having the centerline at position Z-80 (same as CMP of SASW) is analyzed in this thesis. For this record, the wave field was produc ed by an active source at position Z-20, and the receiver spread was at Z-50_110. 4.2.3 Passive MASW Tests The passive MASW tests were conducted by 32 receivers deployed at inter-spacing of 10 feet spanning a distance of 310 feet at Z-0_310. In order to obtain a good combined spectrum, 15 sets of data were recorded w ith 16348 (2^14) samples, the tim e interval of 1.9531 ms (0.0019531 s), and the total recorded period of 32 seconds. 4.3 Dispersion Results This section will express the dispersion re sults of three surface wave methods. The dispersion curves of active MASW and passive MA SW will be combined to broaden the range of frequency for inversion. 4.3.1 Dispersion Analysis for SASW Tests The fundamental concepts of SASW analysis are the same as that expressed in part 3.3.1. For SASW data recorded at Newberry, all 16 sets of data with 8 inter-receiver distances for both forward and backward records are used for dispersion analysis. The combined dispersion curve from 16 data sets and the averaged dispersion curv e are shown in the figure 4.2. With very well recorded data, the obtained final dispersion curv e is smoother than that of TAMU, and this allows a quicker process of inversion.

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53 4.3.2 Dispersion Analysis for Active MASW Tests Similar to what was described in chapter 3, the active multi-channel records of Newberry are also analyzed by four signal processing methods. Then the spectrum having the best resolution will be selected for extracting the dispersion curve. Figure 4-3 and figure 4-4 show the data recorded of the active wave field in untransformed domain (x-t) and transformed domain (f-v), re spectively. We can easily recognize the desired fundamental mode Rayleigh waves that is successf ully separated from other noisy waves in the transformed domain. Here we observe that the most energy (largest spectral amplitudes) is concentrated along a narrow band. This narrow band represents the fundamental Rayleigh wave mode of propagation. As before, the cylindric al beamformer transform shows its dominance by the best resolution spectrum. The best resolution of the cylindrical beamformer transform can be seen more clearly in the figure 4-5 of normali zed spectra in which the spectral values are checked for particular frequencies to evaluate the separation of phase velocities. Here we observe that the cylindrical beamformer transform reduces side ripples or most of energy concentrates at the strongest peak. The sharpest peak of the cy lindrical beamformer transform allows the best separation of phase velocities for any given frequency. The dispersion curves obtained from the four signal processing methods are shown together in figure 4-6, and the one from the cylin drical beamformer is selected to represent the active MASW tests of Newberry. 4.3.3 Dispersion Analysis for Passive MASW Tests The passive wave data recorded by 1D r eceiver array at Newberry are analyzed by commercial software Seisopt ReMi 4.0. The sign als of passive waves are not usually very strong so many spectra of data sets should be consid ered. Each spectrum is only good for a small range of frequency. The combined spectrum allows obtaining dispersive relations hip in a larger range.

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54 The spectrum shown in figure 4-7 is derived by co mbining that of 15 data sets. Manual picking points at the lowest edge of area in which the signals are relatively st rong gives the dispersion curve of passive MASW for Newberry. 4.3.4 Combined Dispersion Curve of Active and Passive MASW The principal goal of passive MASW is to obtain the dispersion relationship at low frequencies (<15 Hz) but we also need the disp ersion property at higher frequencies (>15Hz) for characterization of soil at shallow depths. Co mbining dispersion curv es achieved from both active and passive is a g ood solution to broaden th e range of frequency. For Newberry, the active MASW and passive MASW give the dispersion property at ranges of frequency of 5 to 15 Hz and 10 to 60 Hz, respectively. The combined dispersion curve at the frequencies of 5 to 60 Hz allows attaini ng the detailed soil profile from ground surface to a great depth. The overlapping of the dispersion curves between frequencies of 10 to 15 Hz shows the agreement of the two methods and brings the credib ility of the combined dispersion curve. Some points on the combined dispersion curve cannot be handled in the inversion, so the curve should be simplified by using smoothing algorithm to derive the final dispersion curve shown in the figure 4-10. 4.3.5 Dispersion Curve Comparison It is observed that the dispersion data from combined MASW and SASW is generally in good agreement, particularly at the high freque ncy range (figure 4-10). However, combined MASW dispersion data appear to be higher, especially at the low frequency range. 4.4 Inversion Results After finishing the dispersion analysis, the in version algorithm (part 2.2.3) is now applied to characterize soil profiles from the disper sion curves. Two dispersion curves of SASW and combined MASW are used for inversion and th e derived soil profiles ar e shown in figure 4-11

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55 and figure 4-12. Also dispersion curve matching between theoretical curve and experimental curve is shown for reference. All dispersion curves of Newberry are typical curves whose phase ve locities continuously increase with decreasing frequency. Thus the ty pical soil profiles with shear velocity increasing with depth increase are obtained. That the slope of dispersion curves changes suddenly from a low value at frequencies more than 20 Hz to a very high value at frequencies less than 20 Hz can be explained by a big increasi ng step of shear velocity. For SASW, the dispersion property is obtained at the lowest frequency of 12 Hz only and the maximum velocity of about 1800ft/s. This does not allow achievi ng a great depth of investigation because of the short maximum obtained wavelength ( max=24ft). The reliable depth of investigation is only about 25 ft. For combined MASW tests, the dispersion prope rty at low frequencies can be derived from passive wave fields. The combined dispersion curv e is attained in a broad range of frequency from 5 Hz to 60 Hz and the maximum phase velocity of about 3000 ft/s ( max=95ft). This allows increasing the credible depth of investig ation up to about 70 ft. It is clear that the classified depth is considerately increased by using passive wave fields in soil characterization. 4.5 Crosshole Tests Five PVC-cased boreholes extending to the de pth of 60 ft were inst alled at position J-20, K-10, K-20, K-30 and M-20. The crosshole test was conducted along gridline K with the hammer at K-30, and two receivers at K-20 and K-10. The system including the hammer and two receivers were lowered from the surface by step s of 2 ft. Manual hammer blows created active waves, and the time of wave travel were recorded by the two receivers at different depths. From

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56 the known distance between two receivers and th e difference between times of wave travel recorded by two receivers, th e shear wave velocity is calculated (figure 4-13). For the Newberry testing site, the soil profile below the depth of 25 ft is very stiff. By using the manual hammer that only created waves at relatively low frequencies, the time of wave travel in rock were not definitely determined In this case, a hammer that can produce wave fields at high frequencies is necessary. Unfort unately, such a hammer was not available at the time of testing, so the maximum depth at whic h we could obtain the shear wave velocity was only 25 ft. 4.6 Soil Profile Comparison Soil profiles of Newberry derived from SASW combined MASW, and cross-hole test are all shown together in figure 4-14. First, re garding Vs profiles from combined MASW and SASW, it is observed that they ar e generally in good agreement. Consistent with the dispersion curves, the SASW and combined MASW are in particularly good agreement for shallow depths up to 18ft that is presented in the dispersion curves at high frequencies. However, the combined MASW is slightly stiffer (higher velocity) at some deeper depths. Second, it is observed that the surface wave based Vs profiles compare well with the crosshole results. However, the Vs profiles at the depth from 10 to 15ft are different It can be explained that: 1) Crosshole tests were conducted at gridline K that is 180 ft away from the testing line of the nonde structive tests and the Vs profile changes over the test size. 2) The surface wave tests are conducted over a relatively long array length that sample and aver age over a large volume of material, whereas the crosshole results are based upon wave propagation between two boreholes that are only 10 ft apart, and thus these data represent a more local condition at the site.

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57 4.7 Summary of Newberry Tests All of the signal processing methods and non-de structive testing techniques described in chapter 2 are applied to analyze th e real recorded data of Newberry. Also, the crosshole test is briefly described. The conclusi on has been derived as follows: 1) One more time, the cylindrical beamformer tr ansform gives the best resolution of signal imaging for active wave fields. 2) The soil profiles of Newberry derived from SASW, combined MASW are relatively well matched each other. 3) The matching in soil profiles of Newberry de rived from non-destructive tests and from cross-hole tests is good but not excellent becau se the crosshole test was taken far away from the testing line of nondestructive tests. 4) Combining of active MASW and passive MASW shows an excellent solution to increase the depth of investigation. Figure 4-1. Newberry testing site (from Hudyma, Hiltunen, Samakur 2007)

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58 Figure 4-2. Dispersion curv e for SASW of Newberry Figure 4-3 Newberry active MASW record ed data in the time-trace (t-x) domain 0 200 400 600 800 1000 1200 1400 1600 1800 2000 010203040506070Frequency (Hz)Phase Velocity (ft/s) Combined dispersion curve Final dispersion curve

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59 Figure 4-4. Spectra of Newberry obtained by ap plying methods: a) f-k transform b) f-p transform c) Park, et al. transf orm d) Cylindrical beamformer

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60 Figure 4-5. Normalized spectrum at different frequencies (Solid li ne for cylindrical beamformer, Dashpot line for Park et al. transformDashe d line for f-k transform, Dotted line for f-p transform)

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61 Figure 4-6. Extracted dispersion curves of Active MASW obtained by applying 4 signalprocessing methods Figure 4-7. Combined spectrum of Passive MASW 0 500 1000 1500 2000 2500 010203040506070 Frequency (Hz)Phase Velocity (ft/s) f-k transform f_p transform Park et al. transform Cylindrical Beamformer

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62 0 500 1000 1500 2000 2500 3000 3500 010203040506070 Frequency (Hz)Phase Velocity (ft/s) Figure 4-8. Combined dispersion cu rve of passive and active MASW Figure 4-9. Final dispersion curve of combined MASW 0 500 1000 1500 2000 2500 3000 3500 010203040506070 Frequency (Hz)Phase Velocity (ft/s) Passive MASW Active MASW

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63 Figure 4-10. Dispersion curve comparison 0 500 1000 1500 2000 2500 3000 3500 010203040506070 Frequency (Hz)Phase Velocity (ft/s) Combined MASW SASW

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64 Figure 4-11. Inversion result of Neberry obtaine d by SASW: a) Dispersion curve matching and b) soil profile a)200 400 600 800 1000 1200 010203040506070Frequency (Hz)Phase Velocity (ft/s) Experimental dispersion curve Theoretical dispersion curve b)-45.0 -40.0 -35.0 -30.0 -25.0 -20.0 -15.0 -10.0 -5.0 0.0 05001000150020002500Shear wave velocity (ft/s)Depth (ft)

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65 a) 0 500 1000 1500 2000 2500 3000 3500 010203040506070 Frequency (Hz)Phase Velocity (ft/s) Experimental dispersion curve Theoretical dispersion curve Figure 4-12. Inversion result of Neberry obtaine d by combined MASW: a) Dispersion curve matching and b) soil profile b)-120 -100 -80 -60 -40 -20 0 05001000150020002500300035004000 Shear wave velocity (ft/s)Depth (ft)

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66 -30 -25 -20 -15 -10 -5 0 0 500 1000 1500 2000 2500 Shear wave velocity (ft/s)Depth (ft) Crosshole Test Layer Boundary Figure 4-13. Soil profile obtai ned from Crosshole Test

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67 Figure 4-14. Soil profile comparison of Newberry -120 -100 -80 -60 -40 -20 0 05001000150020002500300035004000 Shear wave velocity (ft/s)Depth (ft) Combined MASW SASW Crosshole Test

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68 CHAPTER 5 CLOSURE 5.1 Summary Three surface wave techniques, SASW, active MASW, and passive MASW, were conducted at two test sites: A National Geotechnical Experime nt site (NGES) at Texas A & M University (TAMU). A Florida Department of Transportation (F DOT) storm water runoff retention basin in Alachua County off of state ro ad 26, Newberry, Florida. The SASW tests were recorded for many receiver layouts with inter-receiver distances ranging from 4 ft to 128 ft and active sources ranging fr om light hammers to heavy shakers. The active MASW tests were recorded by 32 or 62 receivers at inter-spacing of 2 ft and the passive MASW tests were recorded by 32 receiv ers at inter-spacing of 10 ft. Cro sshole tests were also conducted at the two test sites. For active multi-channel records, the signal processing methods f-k, f-p, Park, et al. transform, and cylindrical beamformer were used to map the dispersion curve images. After comparing all of these images together, the best method of signal processing has been confirmed. The shear wave velocity profiles from thr ee surface wave techniques were obtained and their accuracy has been appraised by comparing to that obtained from crosshole tests. 5.2 Findings Based upon the work described herein, the findings are derived as follows: For active multi-channel records, Park et al. transform and the cylindrical beamformer have better imaged dispersion curves at low freque ncies (<15Hz) than that of two traditional transforms, f-k and f-p. For active multi-channel records, the cylindrical beamformer is the best method of signal processing as compared to f-k, f-p, and Park, et al. transforms. The cylindrical beamformer provides the highest resolution of imaged dispersion curves, and its dominance of

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69 resolution at low frequencies over other me thods allows achieving a reliable dispersion curve over a broad range of frequencies. There is generally good agreement between di spersion results from SASW, active MASW, and passive MASW surface wave tests. The surface wave-based shear wave velocitie s are in good agreement with the crosshole results, and the shear wave velocities appear consistent with SPT N-values and material logs. Combining dispersion curves from active and passive MASW is an economical solution to achieve reliable soil profiles to relatively large depths because it does not require heavy weights or expensive vibration shakers for attaining the dispersi on properties at low frequencies 5.3 Conclusions Based on the findings outlined above, the conclusions are as follows: 1) Cylindrical beamformer is th e best method of signal proc essing for active field waves because it gives the highest resolutio n of imaged dispersion curves. 2) The good matching of soil profiles obtained from SASW, active MASW, passive MASW, and crosshole tests shows credibility of non-destructive in situ tests using surface waves for soil characterization. 3) Combining dispersion curves from active a nd passive MASW to br oaden the range of frequency considerately increase s the depth of investigation. 5.4 Recommendations for Further Work The following recommendations are suggested after reviewing all of the findings and conclusions previously discussed: Cylindrical beamformer should be applied in commercial software. Signal processing methods for passi ve wave fields need to be developed further to use for testing areas without very strong passive signals. Lateral discontinuous effects si gnificantly influence the resu lts of soil characterization. Currently, the Vs profiles from MASW are aver aged over the length of receiver spread and the results are not very credible in the cases of drastically changed Vs profiles over the test size. Numerical methods (e.g., finite difference) need to be develope d to handle the lateral discontinuous effects. Full-waveform methods that directly give so il profiles from recorded data should be developed to further limit the non-un iqueness of the inversion process.

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70 LIST OF REFERENCES Aki, K. and Richards, P. G. (1980), Quantita tive Seismology: Theory and Methods, W. H. Freeman and Company, San Francisco, 932 pp. Hudyma, N., Hiltunen, D.R., and Samakur, C. (2007), Variability of Karstic Limestone Quantified Through Compressional Wa ve Velocity Measurements, Proceedings of GeoDenver 2007, New Peaks in Geotechnics American Society of Civil Engineers, Denver, CO, February 18-21. Louie, J. N. (2001), Faster, Better, Shear-Wav e Velocity to 100 Meters Depth from Refraction Microtremor Arrays, Bulletin of Seismological Society of America Vol. 91, No. 2, pp. 347-364. Marosi, K.T. and Hiltunen, D.R. (2001), "Systematic Protocol for SASW Inversion", Proceedings of the Fourth International C onference on Recent Advances in, Geotechnical Earthquake Engineering and Soil D ynamics, San Diego, March 26-31. McMechan, G. A. and Yedlin, M. J. (1981), A nalysis of Dispersive Waves by Wave Field Transformation, Geophysics Vol. 46, No. 6, pp. 869-871. Nazarian, S. (1984), In Situ Determination of Elastic Moduli of Soil Deposits and Pavement Systems by Spectral-Analysis-Of-Surface-Wa ves Method, Ph.D. Dissertation, The University of Texas at Austin, 453 pp. Park, C. B., Miller, R. D., and Xia, J. (1999), Multi-Channel Analysis of Surface Wave (MASW), Geophysics Vol. 64, No. 3, pp. 800-808. Park, C. B., Miller, R. D., Xia, J., and Ivanov J. (2004), Imaging Dispersion Curves of Passive Surface Waves, Expanded Abstracts, 74th Annual Meeting of Soc iety of Exploration Geophysicists Proceedings on CD ROM. Park, C. B., Xia, J., and Miller, R. D. (1998) Imaging Dispersion Curves of Surface Waves on Multi-Channel Record, Expanded Abstracts, 68th Annual Meeting of Society of Exploration Geophysicists pp. 1377-1380. Santamarina J.C., Fratta D. (1998) Discrete signals and inverse problems in civil engineering, ASCE Press, New York. Thomson W.T. (1950) Transmission of elastic wa ves through a stratifie d solid medium, J. Applied Physics, vol. 21 (1), pp. 89-93 Zywicki, D. J. (1999), Advanced Signal Proces sing Methods Applied to Engineering Analysis of Seismic Surface Waves, Ph.D. Thesis, Georgia Institute of Technology, 357 pp.

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71 BIOGRAPHICAL SKETCH Khiem Tat Tran was born in1978 in Thanh Hoa, Vietnam, and remained in Thanh Hoa until he graduated from Lam Son High School in 1996. He enrolled in Hanoi University of Civil Engineering, and graduated with a Bachelor of Science in civil engineer ing in spring 2001. He decided that it would be most beneficial to gain a few year s of work experience before continuing on with graduate studies so he worked for five years in Vietnam until he moved to US for studying. He enrolled at the University of Florida in Gainesville, FL in August of 2006 where he worked as a graduate research assistant under Dr. Dennis Hiltunen. He completed his studies in May of 2008, graduating with a Master of Engineering degree, and c ontinued to pursue a PhD program in University of Florida.