by khiem tat tran - university of...
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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
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© 2008 Khiem Tat Tran
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To my father, whose lifetime of hard work has made mine easier
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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.
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TABLE OF CONTENTS page
ACKNOWLEDGMENTS ...............................................................................................................4
LIST OF FIGURES .........................................................................................................................7
ABSTRACT .....................................................................................................................................9
CHAPTER
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 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 Analysis .............................................................................................23 2.4 Multi-Channel Analysis of Passive Surface Waves (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
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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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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 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 Dispersion 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 Newberry testing 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
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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 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 combined MASW ..............................................65
4-13 Soil profile obtained from Crosshole Test .........................................................................66
4-14 Soil profile comparison of Newberry ................................................................................67
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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.
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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=ρVs2. 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?
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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=1/p from f-p domain or v=2πf/k from f-k domain. The details of the signal
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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.
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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
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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 (φ(f)) between two
signals for each frequency. The travel time (Δt(f)) between receivers can then be obtained for
each frequency by:
ftft⋅
=Δπφ
2)()( (2.1)
The distance between geophones is known, thus wave velocity is calculated by:
)()(
ftXfVR Δ
= (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. 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
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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:
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
⋅=
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
00
00
wu
BPS
(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 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.
04241
3231 =BBBB
(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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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 q of external interface loadings 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 displacements 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 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
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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 k0(f), k1(f),
k2(f)…for different modes of propagation. In other words, the phase velocities cn=ω/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
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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):
⎟⎠⎞
⎜⎝⎛ ⋅
⋅⋅−−
=
−
=
⎟⎠⎞
⎜⎝⎛ ⋅
⋅⋅−
⋅⎥⎥⎦
⎤
⎢⎢⎣
⎡⋅= ∑ ∑
lN
uiM
l
N
m
mN
vi
mlvu eepPππ 21
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 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=π/dxmin), the spread length (X) controls the solution
(Δk=2π /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
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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:
)(2)(
fkffV ⋅
=π (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 field in the phase slowness – time intercept (p-τ) plane in which phase velocities are separated.
2) A 1D Fourier transform of the wave field in the p-τ plane along the time intercept τ 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 τ (figure 2-5), calculate the travel time t at offset x as pxt += τ 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:
∑=x
txPpS ),(),( τ (2.9)
),( τpS will present a spectral amplitude in the p-τ domain.
3) Steps 1 and 2 are repeated over a specified range of p and τ to map out the spectral amplitudes in the p-τ domain.
Secondly, a 1D Fourier transform of S(p, τ) along the τ direction separates the wave field
into different frequencies, which produces data set of spectral amplitudes in the slowness (p) –
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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 1D 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).
2) Normalize U(x,f) to unit amplitude: U(x,f)→ ),(),(
fxUfxU
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:
∑ ⋅=x
ikx
fxUfxUefkV
),(),(),( (2.10)
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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)=2πf/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:
tiekxAHtxs ω−= )(),( 0 (2.11)
Where s(x,t) = displacement measured at spatial position x at time t, A= initial amplitude
of the wave field, H0 = 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)
[ ] ⎥⎦
⎤⎢⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛+−⋅−⎟
⎠⎞
⎜⎝⎛= 2
2/1
0 )(1
81)4/(exp2)(
kxO
kxikxi
kxkxH π
π (2.12)
22
Neglecting waves that decay more rapidly than x/1 , the equation 2.12 becomes:
[ ])4/(exp2)(2/1
0 ππ
−⎟⎠⎞
⎜⎝⎛≈ kxi
kxkxH (2.13)
This equation clearly shows the x/1 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 1D 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:
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
=
)()()(
)()()()()()(
)(
21
22221
11211
fRfRfR
fRfRfRfRfRfR
fR
nnnn
n
n
L
MOMM
L
L
(2.14)
)()()( * fSfSfR jiij ⋅= (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:
( )( ) ( )( ) ( )( )[ ]TnxkHxkHxkHikh ⋅⋅⋅⋅−= φφφ ,,,exp{)( 21 L (2.16)
Where φ 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:
23
)()()(),( khfRkhfkP T ⋅⋅= (2.17)
The spectrum of P (k, ω) 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
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 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:
)cos(/ θvVa = (2.18)
Where: v = real inline phase velocity, and θ = 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).
25
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.
Figure 2-1. Schematic of SASW setup
26
a)
0
200
400
600
800
1000
1200
1400
0 10 20 30 40 50 60
Frequency (Hz)
Pha
se V
eloc
ity (f
t/s)
b)
0
200
400
600
800
1000
1200
1400
0 10 20 30 40 50 60
Frequency (Hz)
Pha
se V
eloc
ity (f
t/s)
a)
0
200
400
600
800
1000
1200
1400
1600
0 10 20 30 40 50 60 70
Frequency (Hz)
Phas
e Ve
loci
ty (f
t/s)
experimentalTheoretical
b)
-60
-50
-40
-30
-20
-10
00 500 1000 1500 2000 2500 3000 3500 4000
Shear wave velocity (ft/s)
Dep
th (f
t)
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) Dispersion curve matching, b) Soil profile
27
frequency, Hz
wav
enum
ber,
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-Wavenumber Spectrum (f-k domain)
Figure 2-5. Example of data in the x-t domain
28
frequency, Hz
Slo
wne
ss, s
/ft
10 20 30 40 50 60 70 80 90 1000
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5x 10-3
Figure 2-6. Slowness-Frequency Spectrum (f-p domain)
Figure 2-7. Signal spectrum and extracted dispersion curve from Park et al. method
29
frequency, Hz
Wav
e nu
mbe
r, ra
d/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 Beamformer Spectrum (f-k domain)
Figure 2-9. Signal image and extracted dispersion curve from ReMi
30
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 1D 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.
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 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 (2^14) 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 (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 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,
32
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-
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 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
34
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 1D 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).
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 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
36
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
(λmax=V/2π.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
37
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.
Figure 3-1. Schematic of SASW setup for TAMU-0_122 and TAMU-98_220
38
0
200
400
600
800
1000
1200
1400
0 10 20 30 40 50 60 70
Frequency (Hz)
Phas
e Ve
loci
ty (f
t/s)
4f4r8f8r16r16f32f32r64f64r122f122r
Figure 3-2. Example of SASW data (4ft receiver spacing)
Figure 3-3. Experimental combined dispersion curve for SASW of TAMU-61
39
0
200
400
600
800
1000
1200
1400
0 10 20 30 40 50 60 70
Frequency (Hz)
Phas
e Ve
loci
ty (f
t/s)
Combined dispersion curve
Final dispersion curve by smoothing
Figure 3-4. Final experimental dispersion curve for SASW of TAMU-61
Figure 3-5. TAMU-0_122 recorded data in the time-trace (t-x) domain
40
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
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
41
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
42
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)
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)
43
200
300
400
500
600
700
800
900
1000
1100
1200
0 10 20 30 40 50 60 70
Frequency (Hz)
Phas
e Ve
loci
ty (f
t/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
0 10 20 30 40 50 60 70Frequency (Hz)
Phas
e Ve
loci
ty (f
t/s)
f-k transform f-p transform Park et al.transform Cylindrical Beamfomer
44
200
300
400
500
600
700
800
900
1000
1100
1200
0 10 20 30 40 50 60 70
Frequency (Hz)
Phas
e Ve
loci
ty (f
t/s)
TAMU_0-122 TAMU_98-220
Figure 3-11. Combined dispersion curve 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
0 10 20 30 40 50 60 70
Frequency (Hz)
Phas
e Ve
loci
ty (f
t/s)
45
b)
200
300
400
500
600
700
800
900
1000
0 5 10 15 20 25 30 35 40
Frequency (Hz)
Pha
se V
eloc
ity (f
t/s)
Figure 3-13. The REMI analysis: a) Combined spectrum of Passive MASW at TAMU, b) Extracted dispersion curve by manual picking
46
Figure 3-14. Dispersion curves obtained by three techniques
0
200
400
600
800
1000
1200
0 10 20 30 40 50 60 70
Frequency (Hz)
Phas
e Ve
loci
ty (f
t/s)
SASWActive MASWPassive MASW
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
0 10 20 30 40 50 60 70
Frequency (Hz)
Phas
e Ve
loci
ty (f
t/s)
Experimental dispersion curve
Theorectical dispersion curve
b)
-80
-70
-60
-50
-40
-30
-20
-10
00 500 1000 1500 2000
Shear Velocity (ft/s)
Dep
th (f
t)
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
0 10 20 30 40 50 60 70
Frequency (Hz)
Phas
e Ve
loci
ty (f
t/s)
Experimental dispersion CurveTheoretical dispersion curve
b)
-80
-70
-60
-50
-40
-30
-20
-10
00 500 1000 1500 2000
Shear Velocity (ft/s)
Dep
th (f
t)
49
a)
200
300
400
500
600
700
800
900
1000
0 10 20 30 40 50
Frequency (Hz)
Phas
e Ve
loci
ty (f
t/s)
Experimental dispersion curveTheoretical dispersion curve
b)
-80
-70
-60
-50
-40
-30
-20
-10
00 500 1000 1500 2000
Shear Velocity (ft/s)
Dep
th (f
t)
Figure 3-17. Inversion result of of TAMU obtained by Pasive MASW: a) Dispersion curve matching and b) soil profile
50
Figure 3-18. Soil profile comparison
51
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
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 produced 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 with 16348 (2^14) 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.
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), 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 1D 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.
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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
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 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 (λmax=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 (λmax=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
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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.
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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.
Figure 4-1. Newberry testing site (from Hudyma, Hiltunen, Samakur 2007)
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Figure 4-2. Dispersion curve for SASW of Newberry
Figure 4-3 Newberry active MASW recorded data in the time-trace (t-x) domain
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0 10 20 30 40 50 60 70
Frequency (Hz)
Phas
e Ve
loci
ty (f
t/s)
Combined dispersion curve
Final dispersion curve
59
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
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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)
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Figure 4-6. Extracted dispersion curves of Active MASW obtained by applying 4 signal- processing methods
Figure 4-7. Combined spectrum of Passive MASW
0
500
1000
1500
2000
2500
0 10 20 30 40 50 60 70
Frequency (Hz)
Phas
e Ve
loci
ty (f
t/s)
f-k transform f_p transform Park et al. transform Cylindrical Beamformer
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0
500
1000
1500
2000
2500
3000
3500
0 10 20 30 40 50 60 70
Frequency (Hz)
Phas
e Ve
loci
ty (f
t/s)
Figure 4-8. Combined dispersion curve of passive and active MASW
Figure 4-9. Final dispersion curve of combined MASW
0
500
1000
1500
2000
2500
3000
3500
0 10 20 30 40 50 60 70
Frequency (Hz)
Phas
e Ve
loci
ty (f
t/s)
Passive MASW Active MASW
63
Figure 4-10. Dispersion curve comparison
0
500
1000
1500
2000
2500
3000
3500
0 10 20 30 40 50 60 70
Frequency (Hz)
Phas
e Ve
loci
ty (f
t/s)
Combined MASW SASW
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Figure 4-11. Inversion result of Neberry obtained by SASW: a) Dispersion curve matching and b) soil profile
a)
200
400
600
800
1000
1200
0 10 20 30 40 50 60 70
Frequency (Hz)
Phas
e Ve
loci
ty (f
t/s)
Experimental dispersion curveTheoretical dispersion curve
b)
-45.0
-40.0
-35.0
-30.0
-25.0
-20.0
-15.0
-10.0
-5.0
0.00 500 1000 1500 2000 2500
Shear wave velocity (ft/s)
Dep
th (f
t)
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a)
0
500
1000
1500
2000
2500
3000
3500
0 10 20 30 40 50 60 70
Frequency (Hz)
Phas
e Ve
loci
ty (f
t/s)
Experimental dispersion curve
Theoretical dispersion curve
Figure 4-12. Inversion result of Neberry obtained by combined MASW: a) Dispersion curve matching and b) soil profile
b)
-120
-100
-80
-60
-40
-20
00 500 1000 1500 2000 2500 3000 3500 4000
Shear wave velocity (ft/s)
Dep
th (f
t)
66
-30
-25
-20
-15
-10
-5
00 500 1000 1500 2000 2500
Shear wave velocity (ft/s)
Dep
th (f
t)
Crosshole TestLayer Boundary
Figure 4-13. Soil profile obtained from Crosshole Test
67
Figure 4-14. Soil profile comparison of Newberry
-120
-100
-80
-60
-40
-20
00 500 1000 1500 2000 2500 3000 3500 4000
Shear wave velocity (ft/s)D
epth
(ft)
Combined MASW
SASW
Crosshole Test
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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
69
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.
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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 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 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, 74th Annual Meeting of Society 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 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.
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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.