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A Quest for Deep Site Characterizations using Surface Wave Techniques

Permanent Link: http://ufdc.ufl.edu/UFE0041742/00001

Material Information

Title: A Quest for Deep Site Characterizations using Surface Wave Techniques
Physical Description: 1 online resource (102 p.)
Language: english
Creator: Jiang, Pengxiang
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: inversion, processing, signal, surface, waves
Civil and Coastal Engineering -- Dissertations, Academic -- UF
Genre: Civil Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Surface wave techniques for soil characterizations have undergone steady development since the first come-out in 1980s. How to economically obtain shear modulus at greater depth is of particular value to various engineering problems. In this study, a comprehensive surface wave technique has been presented to show its ability for deep soil characterizations. Data from conventional active MASW, array-based MASW, ReMi, and two-dimensional passive MASW were analyzed and compared in particular. First, the cylindrical beamformer was confirmed to be the best signal processing algorithm for active data sets. Second, the new testing procedure for active test was implemented at Newberry site. This array-based technique coupled with a portable shaker allows significant improvement in the field dispersion image, particularly at low frequencies. To evaluate the dispersion result at low frequencies passive tests were followed: one using conventional linear array (ReMi technique) and the other using circular array (array-based technique). The resulted dispersion curve at overlapping frequencies shows that ReMi approach tends to underestimate phase velocity, whereas array-based active and passive approaches yield comparable phase velocity estimations provided that the issue of near-field effect has been taken into account. A combined field dispersion curve was constructed thereafter and was inverted for a quite deep stiffness profile at Newberry. Compared with previous inversion result and regional geological settings, the current application of surface wave technique in deep site characterizations is considered to be successful.
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.
Statement of Responsibility: by Pengxiang Jiang.
Thesis: Thesis (M.S.)--University of Florida, 2010.
Local: Adviser: Hiltunen, Dennis R.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0041742:00001

Permanent Link: http://ufdc.ufl.edu/UFE0041742/00001

Material Information

Title: A Quest for Deep Site Characterizations using Surface Wave Techniques
Physical Description: 1 online resource (102 p.)
Language: english
Creator: Jiang, Pengxiang
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: inversion, processing, signal, surface, waves
Civil and Coastal Engineering -- Dissertations, Academic -- UF
Genre: Civil Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Surface wave techniques for soil characterizations have undergone steady development since the first come-out in 1980s. How to economically obtain shear modulus at greater depth is of particular value to various engineering problems. In this study, a comprehensive surface wave technique has been presented to show its ability for deep soil characterizations. Data from conventional active MASW, array-based MASW, ReMi, and two-dimensional passive MASW were analyzed and compared in particular. First, the cylindrical beamformer was confirmed to be the best signal processing algorithm for active data sets. Second, the new testing procedure for active test was implemented at Newberry site. This array-based technique coupled with a portable shaker allows significant improvement in the field dispersion image, particularly at low frequencies. To evaluate the dispersion result at low frequencies passive tests were followed: one using conventional linear array (ReMi technique) and the other using circular array (array-based technique). The resulted dispersion curve at overlapping frequencies shows that ReMi approach tends to underestimate phase velocity, whereas array-based active and passive approaches yield comparable phase velocity estimations provided that the issue of near-field effect has been taken into account. A combined field dispersion curve was constructed thereafter and was inverted for a quite deep stiffness profile at Newberry. Compared with previous inversion result and regional geological settings, the current application of surface wave technique in deep site characterizations is considered to be successful.
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.
Statement of Responsibility: by Pengxiang Jiang.
Thesis: Thesis (M.S.)--University of Florida, 2010.
Local: Adviser: Hiltunen, Dennis R.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0041742:00001


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1 A QUEST FOR DEEP SITE CHARACTERIZATIONS USING SURFACE WAVE TECHNIQUES By P ENGXIANG JIANG A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2010

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2 2010 Pengxiang Jiang

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3 To my parents, for their unconditional love

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4 ACKNOWLEDGMENTS I sincerely thank Dr. Dennis Hiltu nen for serving as my advisor His rigorous academi sm and easy going personality impressed me throughout. His valuable support and encouragement were what made this possible. Special thank s go to Dr. Reynaldo Roque and Dr. Michael McVay for sitting on my supervisory committee. I would also like to thank other fellow graduate students for making the graduate study an enjoyable experience. A particular word of thanks goes to Khiem Tran, for unselfishly sharing with me much of his knowledge of surface waves. The debt I owe to my parents can never be expressed in words. The only thing I ca n do and will do is to keep them smile. Last but not least my girl friend, Jing is thanked for her love and patience.

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5 TABLE OF CONTENTS ACKNOWLEDGMENTS .................................................................................................. 4 page LIST OF FIGURES .......................................................................................................... 8 ABSTRACT ................................................................................................................... 10 CHAPTER 1 INTRODUCTION .................................................................................................... 12 1.1 Problem Statement ......................................................................................... 12 1.2 Research Objectives ...................................................................................... 13 1.3 Scope ............................................................................................................. 14 2 S URFACE WAVE TECHNIQUES ........................................................................... 15 2.1 Introduction .................................................................................................... 15 2.2 Field Considerations ....................................................................................... 15 2.2.1 Source Selection ................................................................................. 15 2.2.2 Sensor Selection ................................................................................. 16 2.2.3 Array Selection .................................................................................... 17 2.3 Signal Processing Tools ................................................................................. 19 2.3.1 Active Source MASW .......................................................................... 19 2.3.1.1 f k m ethod ............................................................................... 19 2.3.1.2 p m ethod .............................................................................. 21 2.3.1.3 Park et al. m ethod ................................................................... 21 2.3.1.4 Conventional and cylindrical b eamforming m ethods ............... 22 2.3.2 Passive Source MASW ....................................................................... 24 2.3.2.1 2D conventional FDBF ............................................................ 24 2.3.2.2 Capons h ig h r esolution MVDL ............................................... 25 2.3.2.3 Multiple signal classification (MUSIC) ..................................... 26 2.4 Inversion ......................................................................................................... 28 2.4.1 Introduction .......................................................................................... 28 2.4.2 Forward Modeling and Inversion Schemes ......................................... 28 2.4.3 Practical Considerations ...................................................................... 29 3 A CTIVE SOURCE SURFACE WAVE METHODS .................................................. 32 3.1 Introduction .................................................................................................... 32 3.2 TAMU Tes t Result .......................................................................................... 32 3.2.1 Experiment Descriptions ...................................................................... 32 3.2.2 Image Quality ...................................................................................... 33 3.2.3 Dispersion Curves ............................................................................... 34 3.3 PSU Test Result ............................................................................................. 36

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6 3.3.1 Experiment Descriptions ...................................................................... 36 3.3.2 Image Quality ...................................................................................... 37 3.3. 3 Dispersion Curves ............................................................................... 38 3.4 Newberry Test Result ..................................................................................... 39 3.4.1 General Descriptions ........................................................................... 39 3.4.2 Dispersion Analysis ............................................................................. 40 3.4.3 Additional Concerns ............................................................................ 41 3.5 Summary ........................................................................................................ 42 4 P ASSIVESOURCE SURFACE WAVE METHODS ............................................... 56 4.1 Introdu ction .................................................................................................... 56 4.2 Experiment Descriptions ................................................................................ 56 4.3 Dispersion Results ......................................................................................... 57 4.3.1 ReMi Results ....................................................................................... 57 4.3.1.1 4.5 Hz geophone vs. 1 Hz geophone ..................................... 57 4.3.1.2 Length of a rray ....................................................................... 58 4.3.2 2D Array Results ................................................................................. 59 4.3.2.1 FDBF vs. MVDL vs. MUSIC .................................................... 59 4.3.2.2 100ft array vs. 200ft array .................................................... 60 4.3.3 Active vs. 2D Passive .......................................................................... 61 4.3.4 Active vs. ReMi .................................................................................... 61 4. 3.5 Performance of Two PassiveSource Methods .................................... 62 4.4 Near Field Effect ............................................................................................ 64 4.4.1 Mitigated Solely by Cylindrical Beamformer ........................................ 65 4.4.2 Mitigated by a Longer Source Offset a nd Cylindrical Beamformer ...... 65 4.4.3 Quantification of Near Field Effect ....................................................... 66 4.5 Summary ........................................................................................................ 68 5 I NVERSION ............................................................................................................ 82 5.1 Introduction .................................................................................................... 82 5.2 Forward Modeling ........................................................................................... 82 5.3 Inversion Schemes ......................................................................................... 83 5.4 Inversion Results ............................................................................................ 84 5.4.1 Interactive Inversion (LI) ...................................................................... 84 5.4.2 Simulated Annealing (SA) ................................................................... 85 5.4.3 Appraisal and Discussion .................................................................... 86 5.5 Summary ........................................................................................................ 88 6 C LOSURE .............................................................................................................. 95 6.1 Summary ........................................................................................................ 95 6.2 Findings .......................................................................................................... 96 6.3 Conclusions .................................................................................................... 97 6.4 Recommendations ......................................................................................... 98

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7 LIST OF REFERENCES ............................................................................................... 99 BIOGRAPHICAL SKETCH .......................................................................................... 102

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8 LIST OF FIGURES Figure page 2 1 Active source method using shaker linear array with nonuniform sensors ...... 30 2 2 Schema tics of a ctive source and 2D p assive source surface wave testing ........ 30 2 3 Flowchart of Rayleigh w ave i nversion ................................................................ 31 2 4 Inversion as a combination of estimation and appraisal ..................................... 31 3 1 2 D f v power spectrum ....................................................................................... 43 3 2 3D f v pow er spectrum ....................................................................................... 44 3 3 Normal i zed spectrum at different frequencies .................................................... 45 3 4 Dispersion curve extracted from power spectrum images .................................. 46 3 5 Dispersion curve comparison ............................................................................. 47 3 6 2D dispersion power spectrums ......................................................................... 48 3 7 3D dispersion power spectrums ......................................................................... 49 3 8 Normalized spectrum at different frequencies .................................................... 50 3 9 Dispersion curves extracted from power spectrum images ................................ 51 3 10 Dispersion curve comparison ............................................................................. 52 3 11 Location of Newberry test site ............................................................................ 53 3 12 Array based a ctive test configurations ................................................................ 53 3 13 Conventional active MASW ................................................................................ 54 3 14 Array based active MASW ................................................................................. 55 4 1 4.5 Hz ReMi results ............................................................................................ 69 4 2 1 Hz ReMi results ............................................................................................... 70 4 3 Combined dispersion curve from ReMi tests ...................................................... 71 4 4 Detailed placement of the 1Hz geophone ......................................................... 71

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9 4 5 Dispersion curves for 1 00ft diameter array with different signal processing methods .............................................................................................................. 72 4 6 Dispersion curves for 2 00ft diameter array with different signal processing methods .............................................................................................................. 73 4 7 Combined dispersion curve obtained from 2D passi ve method .......................... 74 4 8 Typical passive records in timedomain and their frequency contents ................ 75 4 9 Dispersion curve comparison between active and 2D Passive methods ............ 75 4 10 Dispersion curve comparison between active and ReMi methods ...................... 76 4 11 Dispersion curve comparison between activesource and all passivesource methods .............................................................................................................. 76 4 12 Contour plot of power spectrum at various frequencies for 2D passive tests ..... 77 4 13 Active dispersion curves obtained from cylindrical and plane beamformers ....... 78 4 14 Original and modified active dispersion curves ................................................... 78 4 15 Dispersion curve comparison between modified activesource and 2D passive source methods ..................................................................................... 79 4 16 Evaluation of near field effects ........................................................................... 80 4 17 Combined active and passive dispersion curve .................................................. 81 4 18 Combined dispersion curve after smoothing ...................................................... 81 5 1 Objective function termino logies and illustration ................................................. 89 5 2 Dispersion curve fit after interactive inversion .................................................... 90 5 3 D ispersion curve fit with models of various layering SA inversion ................... 91 5 4 Inversion results using an 8 layer model for illustration ...................................... 92 5 5 Inversion result of Newberry obtained by combined MASW ............................... 93 5 6 Multi modal dispersion images obtained from various combinations of source offset and receiver inter spacing ......................................................................... 94 5 7 Dispersion image for Lovewaves ....................................................................... 94

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10 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 Science A QUEST FOR DEEP SITE CHARACTERIZATIONS USING SURFACE WAVE TECHNIQUES By Pengxiang Jiang May 2010 Chair: Dennis R. Hiltunen Major: Civil Engineering Surface wave techniques for so il characterizations have undergone steady development since the first comeout in 1980s How to economically obtain shear modulus at greater depth is of particular value to various engineering problems. In this study, a comprehensive surface wave technique has been presented to show its ability for deep soil characterizations. Data from conventional active MASW, array based MASW, ReMi, and twodimensional passive MASW were analyzed and compared in particular First, the cylindrical beamformer was confirmed to be the best signa l processing algorithm for active data sets Second, the new testing procedure for active test was implemented at Newberry site. This array based technique coupled with a portable shaker allows significant improvement in the field dispersion image, particularly at low frequencies. To evaluate the disper sion result at low frequencies passive tests were followed: one using conventional linear array (ReMi technique) and the other using circular array (array based technique). The resulted dispersion curve at ov erla pping frequencies shows that ReMi approach tends to underestimate phase velocity, whereas array based act ive and passive approaches yield comparable phase velocity estimations provided that the issue of near field effect has been taken into

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11 account A combined field dispersion curve was constructed thereafter and was inverted for a quite deep stiffness profile at Newberry. Compared with previous inversion result and regional geological settings, the current application of surface wave technique in deep site characterizations is considered to be successful.

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12 CHAPTER 1 INTRODUCTION 1.1 Problem Statement S urface wave method, a nondestructive testing method, has been widely used in geotechnical engineering to evaluate the stiffness of near surface m aterials f or various purposes, such as foundation vibrations under dynamic loadings, evaluation of liquefaction potential, anomaly detection, etc. The feasibility of surface wave method is based on the notion that the surface wave velocity is mainly governed by the shear wave velocity (Vs) of the material, which is a direct indicator of stiffness (G). The conventional active multi channel analysis of surface waves ( MASW ) with limited depth of investigation fails to meet the growing need in deeper soil characterizations. To overcome this, a very large and heavy active energy source with special design is required, which is not easily available thus significantly sacrifices the advantage of surface wave testing over other methods. So how to g o deeper as cheap as possibl e becomes the question of concern. Recently a newly developed testing procedure employing a nonuniform linear array coupled with a mini shaker (Heb e ler 2001) is claimed to be more efficient and effective in obtaining reliable experimental dispersion curve at lower frequencies It is known that the lower the frequency the deeper the depth of investigation. It is also known that the near field effect comes along with whatever active testing method is utilized Although this new experimental configuration yi elds low frequency information, their accuracy remains a question. Despite the poor performance of plane wave algorithm s applied to a nonplanar wavefield, how effective the cylindrical algorithm removes the near field effect remains another unknown. On the other hand, passive surface wave method, making use of

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13 ambient noise as its source, is probably a means to clear the aforementioned doubts. It eliminates the demand of a cumbersome active source in the first place, which makes an easier testing procedure, and above all, it obeys the planewave assumption, and thus planewave algorithm s should work out fine. However, due to the uncontrolled testing environment the wave fields could be highly complex in terms of number of source and source distribution, which in turn would deteriorate the performance of signal processing. Typically two types of passive methods are available nowadays, i.e., ReMi and 2D passive test, with ReMi the routine testing procedure. Each has its own assumptions and limitations and t heir compatibility and reliability remains unclear also In fact, the dispersion curve derived from passive data is limited in frequency range as a result of both source characteristics and array dimension. Therefore, a combined use of active and passive m ethods appears to be a good choice. On one hand, it double checks the data at an overlapping range of frequencies confirming the validity of signal processing. On the other hand, it extends resolvable frequencies to both ends, substantially increasing the depth of investigation (provided with low frequency data) without sacrificing the shallow depth resolution (provided with highfrequency data). 1.2 Research Objectives The proposed study incorporates the most recent active and passive surface wave methods in the hope of providing additional confidence in applying surface wave methods in near surface characterizations. The research objectives are listed below: 1) To confirm the best signal processing algorithm to be used in activesource surface wave methods 2) To appraise the accuracy of field dispersion curves obtained from different passive source methods

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14 3) To study quantitatively the near field effect associated with activesource methods 4) To obtain a deep soil shear wave velocity profile via the com bined use of active and passive techniques 1.3 Scope The surface wave data used for research objective 1 comes from test sites at the Texas A&M University the Pennsylvania State University and Newberry Florida The rest comes from the Newberry test site, a Florida Department of Transportation storm water runoff retention basin. For research objective 1, five signal processing algorithms, namely frequency wavenumber (f k), frequency slowness (f p), Park transform, conventional beamformer and cylindrical beamformer were compared and the best one was thus selected. For research objective 2, several passivesource surface wave test s were done, and the results obtained from ReMi and twodimensional passive tests were compared and discussed, and specifically f or two dimensional testing three signal processing algorithms (conventional 2D beamformer, Capon s high resolution beamformer, and MUSIC) were adopted for extraction of dispersion curve from complex wavefield. For objective 3, two ways of mitigating the near field effect were examined in comparison with the results from reference passivesource method. And for the last objective, a combined field dispersion curve was obtained by a close look at the active and passive dispersion curves, and was subsequently inverted via simulated annealing and an interactive inversion scheme, both of which are available in the SeisOpt ReMi software.

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15 CHAPTER 2 SURFACE WAVE TECHNIQ UES 2.1 Introduction Surface wave methods offer a nondestructive and economical means for deter mining shear wave velocity profiles. Surface waves, propagating along a free surface boundary, can be easily generated by different sources. Acco rding to the energy sources, surface wave m ethods can be divided into active source and passivesource methods. Active source methods measure surface waves generated by dynamic sources such as sledge hammers, weight drop and v ibroseis equipment, while passivesource methods utilize ambient vibrations caused by nat ural phenomena (ocean waves, wind) and manmade ( tr affic, construction ) activities. Surface wave methods consist of three main steps: 1) data acquisition of seismic surface wave in the field, 2) estimation of dispersion curve as a result of subsurface structure, 3) estimation of subsurface structure causing this dispersion by means of inversion. This chapter will provide a brief summary of these techniques, including field procedures, signal processing for experimental dispersion curve extraction, and inversion for interpretable shear wave velocity profiles with emphasis on the latest ideas and development of each step. 2.2 Field Considerations In order to collect highquality field data, several factors should be considered in the design of an experiment, because obtaining highquality data is the first s tep and a critical step for subsequent dispersion estimation and inversion. 2.2.1 Source Selection As described earlier, t here are three common source types: active impulsive, active harmonic, and passive. One major advantage of active surface wave

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16 measure ments is a control over the source, providing means for directing the measurement and analysis of the generated Rayleigh waves. While passive surface waves with low frequencies present the opportunity to sample to greater depths, their propagation characteristics are not known a priori, increasing the complexity of the post measurement analyses. Impulsive sources (sledge hammer and weight drop) allow a relatively quick test because an entire range of frequencies is generated and measured simultaneously H ow ever, the frequency content is limited and poorly controlled th us limit ing the ability to remov e external noise. Continuous harmonic sources ( vibratory shakers) on the other hand, allow each frequency to be tested individually by generating steady state harmonic waveforms, permitting the analysis to be concentrated around a narrow frequency band which dr astically decreases the effects of external noise. Besides it generates measurable energ y at lower frequencies than most i mpulsive sources do. The current procedures s eek to limit the effects of external noise wherever possible in an effort to increase the accuracy of subsequent dispersion estimates. Consequently, a harmonic oscillator was chosen as the source for the active testing described herein. The so urce chosen was an electromagnetic shaker manufactured by APS Dynamics, Inc. Typical measurements span from 4 Hz to 100 Hz, while the shaker can be operated with frequencies ranging from about 2 Hz to 200 Hz. There are often minor variations in the lowest frequency obtainable due to sitespecific conditions. 2.2.2 Sensor Selection The number of sensors u sed in the array is governed by the capabilities of the data acquisition equipmen t. In this study, a 32 channel digital signal analyzer (manufactured by Dat a Physics) was chosen based on sampling and operational

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17 criterion described below. Seismic sensors must be chosen to fit the needs of the specific testing. The most important criterion when choosing seismic sensors is the frequency range over which they pr ovide linear response. High sensitivity and resolution are also important characteristics, and sensors must also be durable and easily coupled to be implemented under field conditions. As such the conventional 4.5 Hz geophones which were used in previous active and passive tests, are replaced by ultrasensitive, high resolution, 1Hz geophones. This study utilized 16 Geospace GS 1 geophones and a sourcemounted, h igh sensitivity, l ow n oise ac celerometer in the active tests and the same geophones in the passive tests. 2.2.3 Array Selection A larger number of channels (N) can result in a hig her resolution dispersion image o nly if it is associated with a long er receiver spread length (X). There is no benefit in a mere increase of N not ac companied by the incr ease in X. The longer receiver spacing (dx) is always preferred as long as it does not cause the spatial aliasing problem (Park, 2001) In fact, there are two important parameters in array pattern to evaluate its performance: 1) mainlobe width controllin g resolution, 2) sidelobe height controlling aliasing. Therefore, f or a given testing configuration including the number of receivers, cable length, and source capability, it is very important to select an array with an appropriate combination of wavenum ber resolution, spatial aliasing, and sidelobe leakage for accurate measurement of propagating Rayleigh waves. Conventionally in an a ctive MASW test a linear array with uniformly spaced receivers are employed due to its simplicity in field operation. How ever, to get the best coverage of signal in terms of detectable frequency band and resolution of the dispersion image, a trial and error process is typically required, namely several uniform

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18 arrays with various inter spacing have to be tested before the optimal one is chosen for the specific purpose of the experiment. Therefore, it is not economical in terms of field effort. Similarly in a conventional passive source test, linear uniform array s are used, known as Refraction Microtremor (ReMi) lines. However, due to the unknown wavefield in the passive environment and the array s linear nature, ReMi procedures may present some problems. This will be discussed in detail when the test result s are presented in Chapter 4. The latest development of surface wave m ethods makes use of spatial array sampling techniques, namely to optimally sample the signal both temporally and spatially In the case of an active test (Hebeler, 2001), a linear array with nonuniformly spaced sensors is laid out. Shown in Figure 2 1 is the schematic diagram in which the shaker imparts energy into the ground and the sensors record the associated vertical motion. They are then connected to the signal analyzer, and finally the relevant results are displayed in real time. This idea is applie d to the activesource test presented herein, with 16 1 Hz geophones spaced at 8, 10, 12, 15, 18, 22, 28, 34, 42, 50, 60, 70, 80, 95, 110, 128 f t away from the shaker. The electromagnetic shaker generates a steady state wavefront one at a time. For the pas sive source test, the idea of spatial array sampling technique extends naturally to a twodimensional array on the surface. Both velocity and direction of propagation are unknown. Theoretically, any type of 2D array of fairly symmetric shape can be used. C ommon choices include circles, crosses, nested triangles, squares, etc. It is the convenience of field operation that determines a specific type of array to be used. Nonetheless, Zywicki (1999) studied passive waves with several different array

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19 geometries. From the comparison of the several array geometries, their coarrays a nd associated array patterns the circular array with equally spaced receivers along the circumference was preferred for the following reasons : (1) the array appears to be nearly identic al for a plane wave coming from any direction yielding almost constant azimuthal r esolution, (2) the symmetry of its array pattern allows one to identify a maximum wavenumber before encountering large sidelobes, and (3) the array shows good resolution char acteristics. Therefore, this recommendation was followed in our implementation of 2D passivesource testing described herein. A circular array with passive energy coming from various sources is shown in Figure 22 b), and the 1D spatial array with well controlled active energy is illustrated in a). 2.3 Signal Processing Tools Once we have goodquality experimental data, the next step is to get a credible field dispersion curve via signal processing methods. Numerous signal processing tools are available to discriminate signal against noise, leading to the dispersion curve. Discussed below are the fundamentals of these signal processing tools for both activesource records and passivesource records. 2.3.1 Active Source MASW 2.3.1.1 f k m ethod This algorithm utilizes a 2D Fourier t ransform to convert signal collected in the space time (x t) domain to frequency wavenumber ( f k) domain, for ease of indentifying and isolating different modes of Rayleigh wave propagation. 2D Fourier Transform can be written in gen eral as (Santamarina and Fratta, 2005):

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20 11 ,, 0022 [exp(())]exp((())MN uv lm lmml Ppjv ju NN w here N denotes the number of sampling points, M denotes the number of sensors, lm p denotes raw data at mth sample of lth sensor, and uvP denotes spectral value at wavenumber index u and frequency index v. This is essentially a successive application of a Fourier t ransform i n time domain, and then space domain, i.e. first from (t,x) to (f,x) then from (f,x) to (f,k) In real application of the f k transform, wavenumber resolution is of importance, since lacking resolution in wavenumber domain can easily result in spurious peaks in the power spectrum Wavenumber resolution is controlled by the largest spatial lag between sensor s, i.e. 2 k X where X is the length of the array. However, due to the limited number of sensors, a large X re sults in a large sensor spacing to achieve the desired resolution. In return, this produces another problem of spatial aliasing, where la rge values of wavenumber would alias into small values. The maximum wavenumber (or the Nyquist wavenumber) associated with an array is governed by min nyqk d As one may note, there is a tradeoff between resolution and aliasing with a given number of sensors. Therefore, the common trick is to put zero padding to the field records (Foti 2000), which would create artificial sensors at the end of array that contain zero amplitude.

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21 2.3.1.2 p m ethod This algorithm was first described by McMechan and Yedlin ( 1981) It contains two linear transformations: 1) A slan t stack procedure of the wavefield in x t domain produces result in slown essp) domain, in which phase velociti es are separated. Effectively, I t can be considered as a time domain beamform ing method: 1(,)(, )n ii iApAxtkdtpx where n is the total number of sensors, ixdenotes the offset of the ith sensor from one end of the linear array, t denotes time, which is discretized as kdt p denotes slowness, the reciprocal of velocity 2) field to slownessfrequency (pf) domain: 1 0(,)(,)exp((2))n A kFpfApkdtifkdt The power spectrum is then calculated as, *(,)(,)(,)AAASpfFpfFpf where denotes the complex conjugate. Note that energy comi ng from both directions along the linear array is summed into one slowness axis, as p. Finally, the p f power spectrum can be transformed into vf spectrum for dispersion image comparisons 2.3.1.3 Park et al. m ethod Park transform (Park, 1999) was developed at Kansas Geological Survey in the late 1990s, and has been widely used in the field of geotechnical engineering for multi channel analysis of surface waves ( a package known as Surf S eis). The procedures can be basically divided into 4 steps: 1) Apply 1D Fast Fourier Transform (fft) to each recording channel, converting signal from time domain to frequency domain, i.e., (,)(,) UxtUxf

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22 2) Normalize (,) Uxf to unity gain, i.e. (,) (,) (,) Uxf Uxf Uxf 3) Apply Discrete Fourier Transform converting the unity signal into wavenumber domain, i.e. (,) (,) (,)ikx xUxf Pkfe Uxf where x is the sensor location vector, and k are the trial wavenumbers. 4) Transform the power spectrum in f k space to f v space, i.e. (,)(,) PkfPvf via the relation of 2 () () f vf kf 2.3.1.4 Conventional and c ylindrical b eamforming m ethods A ll previous techniques are pla newave transforms, based upon the assumption that surface wave energy is coming from the far field. For the active testing, however, the source is always placed near the geophone array at a finite distance, hence creating a cylindrically propagating wavefield. Zywicki (1999) found that this cylindrical wavefield could be described by Hankel type solution. Main steps are as follows: 1) Apply fft converting signals from time domain to frequency domain. 2) Form the s patiospectral correlation m atrix, R : 11 12 1 12()()() () ()()()n n n nnRfRfRf Rf RfRfRf and *()()()ij ijRfSfSf where () i Sf is th e Fourier Transform of trace i, and denotes the com plex conjugat e Note, i n this matrix, that the main diagonals are the autopower spectrum for each sensor in the array, and the off diagonals are the cross power spectrum between each

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23 sensor pair Althou gh R is a function of frequency, it actually contains information about the spatial properties of the propagating wave field. 3) Form the steering vector, e In order to seek the maximum power associated with a particular f k pair in frequency wavenumber domain the array must be steered towards many different directions with the steering vector containing phase shift information. In active testing, the propagati on direction is known, a nd is in line with the sensor array. Therefore, t he f k analysis is reduc ed t o a onedimensional problem of seeking just the wave speed. a) For conventional beamform er 12()[exp(),exp(),...,exp()]T nekjkxjkxjkx where () ek is the steering vector associated with a trial wavenumber k, and ix is th e distance of the ith receiver from the source; b) For cylindrical beamformer 01020()exp{[(()),(()),...,(())]}T nhkjHkxHkxHkx where () hk is the cylindrical steering vector as a function of trial wavenumbers, denotes the ph ase angle of the argument in parentheses, and 0H denotes the Hankel function. 4) Calculate the steered response power. The steering vector tries to scan the wave field for possible sources of energy, and if it is successful a peak w ill occur in the power spectrum estimates for that particular f k pair. a) For conventional beamform er (,)()()()HPkfekRfek ; b) For cylin drical beamform er ,(,)()()()HPkfhkRfhk where H denotes Hermitian transpose.

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24 2.3.2 PassiveSource MASW 2. 3.2.1 2D c onventional FDBF The conventional frequency domain beamformer method (FDBF) was proposed by Lacoss ( 1969 ) when dealing with some large aperture seismic arrays. A 2D array (circular, square or cross, etc) is laid out on an open space to sample the wave field both temporally and spatially. The 2D FDBF is in fact an extension to 1D FDBF previously defined. Data is recorded in the time domain during passive measurement. Each sensor records the signal as a time history, x(n), with N sampling points. Th e spatiospectral correlation m atrix R(f), is estimated using the Bart lett window for reducing signal variance, represented as: ,, 11 ()()()B H ij injn nRfSfSf B where B is the number of blocks with block length = N/B, and H denotes Hermitian conjugation. The steering v ector is formed in the same way as 1D FDBF, except that the single wavenumber k in 1D case is replaced by a wavenumber pair ( kx, ky). The array is steered in various directions with exponential phase shift vector e( k ) written as: 12()[exp(),exp(),...,exp()]T sekjkxjkxjkx w here ix is the sensor vector coordinate for a total number of s sensors, ik are the trial wavenumber vectors in x y directions. Beamforming is used to describe an arrays ability to focus on a certain directio n in signal processing terms (Pillai 1989). Steered power response is calculated as:

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25 (,)()()()H FDBFPfkekRfek Peaks in the power spectrum for a given frequency correspond to the wavenumbers of dominant modes of Rayleigh waves. In addition to choosing the dominant mode, multiple modes may be indentified by picking the secondary peaks in the spectrum. However, those secondary peaks may sometimes be related to energy leakage due to poor sidelobe control The conventional FDBF applies uni form weight to all sensors; hence the array has a fixed mainlobe and sidel obe structure (Zywicki 1999). However, it should be noted that the wavenumber resolution in 2D passive testing plays a much more significant role than that in 1D active case Rayleigh waves may propagate from arbitrary directions with multiple modes, which significantly complicates the 2D signal processing in separat ing different energy. Meanwhile, the sidelobe control gets even worse if multiple waves exist at a particular frequency Therefore, the us e of conventional FDBF with limited wavenumber resolution and energy leakage control may result in a spurious peak in the f k contour plot This is oftentimes the case when conventional FDBF tends to overestimate phase velocit y in a mult iple wave situation (Yoon, 2005) 2.3.2.2 Capons h ighr esolution MVDL The array output power contains contributions from the desired signal along the look direction as well as the undesired ones along other directions of arrival. To minimize those undesir ed ones, Capon (1969) introduced this highresolut ion beamforming method, called m inimu m v ariance d istortionless l ook (MVDL), with power response as : 1 1 (,) ()()()MVDL HPfk ekRfek

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26 It is essentially an optim i zation method, aimed at passing a plane wave with g iven frequency and wavenumber undistorted (with unity gain) while minimiz ing power output of other waves. The optimum Capons weight ing vector is 1 1()() (,) ()()()MVDL HRfek wfk ekRfek The weigh ting vector is optimized for each trial f k pair, changing the mainlobe and sidelobe structure to minimize energy leakage from remot e portions of the spectrum. Capons method only requires an additional matrix inversion compared to FDBF and the optimum weight ing vector need not be computed prior to the power spectrum estimat ion. It should be noted that a signal, which is the desired one in the event when the steering direction coincides with its direction of arrival, becomes undesired while the array is steered along some other direction. In this case, Capon s MVDL yields bet ter resolution due to its adaptive nature of the wavenumber filter (Capon 1969). I n other cases, however, its performance has been reported as poorer than conventional FDBF (Zywicki 1999, Li, 2008 ) It may be explained by its inherent filtering power (or degree of suppression ), which depends on source distribution and power levels, which are unknowns during the time of recording (Pillai, 1993) 2.3.2.3 Multiple s ignal c lassification (MUSIC) MUSIC is another high resolution beamformin g method proposed by S chmidt ( 1979) based upon a truncated decomposition of the inverse spatiospectral correlation matrix. 1() Rf can be decomposed in terms of eigenvectors and eigenvalues as: 11 1()()()()N H iii iRffvfvf

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27 where () if and ()ivf are the ith eigenvalue and eigenvector of R(f). Dividing the eigenvectors into signal and noise subspace, it can be expressed as: 11 1 11()()()()()()()s sN N HH iii iii i iNRffvfvffvfvf in which Ns is the number of eigenvectors related to the signal spac e. The largest Ns eigenvalues defines a signal subspace. MUSIC is an approach using only the noise subspace truncated eigenexpansion, with all eigenvectors equally weighted instead of by their eigenvalues, i.e., 1 1()()()sN H MUSIC ii iNRfvfvf And the output power is estimated as: 11 (,) ()()()MUSIC H MUSICPfk ekRfek As shown in the above equation MUSIC is similar to Capons MVDL power estimate, except the entire inverse spatiospectral correlation matrix is replaced by a truncated noise subspace eigenexpansion of 1 () MUSIC Rf Some of the most effective signal prediction algorithms result from looking only into the noise characteristics of the recording channels, li ke MUSIC does. However, it is worth noting that in a real signal plus noise environment there is no easy way to know the number of signals present and these methods assume whitenoise behavior, which may not be valid in some circumstances (Pillai, 1993)

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28 2.4 Inversion 2.4.1 Introduction Inversion of a Rayleigh wave dispersion curve is a proc ess for determining the shear wave velocity profile from the dispersion relationship. Two a ssumptions are made for estimating subsurfa ce structure of a layered earth. First, it is typically assumed that t he phase velocity obtained from observation is that of the fundamental mode of Rayleigh waves. Second, it is assumed that the subsurface structure is horizontally layered, each layer being homogeneous and isotropic with constant shear wave velocity. It is known that P wave velocity and mass density are not very sensitive to the dispersion relation, whereas shear wave velocity and layer thickness are. A typical flowchart for Rayleigh wave inversion is presented in Figure 23 : 1) Calculate the theoretical dispersion curve from an assumed S wave velocity profil e (so called forward modeling). 2) Refine the model parameters (S wave velocity and layer thickness) to better match the experimental dispersion curve. 3) Continue iteration until the difference between the calculated and the experi mental fall within a specified tolerance. 4) Use the final S wave model as of the subsurface structure interpretation. 2.4.2 Forward Modeling and Inversion Schemes Forward modeling used in step 1) to calculate theoretical dispersion curves is often based on the propagator matrix method, which can be further divided into transfer matrix method, stiffness matrix method and reflectiontransmission coefficient method. They are in fact analytically exact and equivalent (Buchen and BenHador, 1996). The iterations taking place in step 3) are based on some optimization process, local or

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29 global, such as damped least square, Occam s method, simulated annealing, and genetic algorithm. 2.4.3 Practical Considerations As a matter of fact, s olutions of geophysical inversion problems are not uni que in the sens e that there can be many models that explain the data equally well dispersion curve in this case There are a number of reasons Firstly, error occurs as a result of inexact theory used in the prediction of theoretical data. For example, t he use of 1D earth model could cause errors since in most cases the earth is truly 3D. Secondly, the observational errors are ubiquitous. They could be measurement errors, instrumental errors, and numerical truncations The third reason is the most fundamental one In many inverse problems the model that one aims to determine is a continuous function of the space variables. This means that the model has an infinite number of degrees of freedom. However, in a realistic experiment the amount of data that can be used for determining the model is usually finit e. A simple count of variables shows that the data fail to carry sufficient information to uniquely retrieve the model Therefore, t he model obtained from inversion is some estimat ion of the true model with error attached to it. In this sense, inversion is a process of estimation followed by appraisal, illustrated in Figure 24.

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30 Figure 21. Active source method using shaker linear array with nonuniform sensors ( f rom Yoon, 2005) Figure 22. S chemati c s of a ctive source and 2D p assive source surface wave testing ( f rom Yoon, 2005)

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31 Figure 23. F lowchart of Rayleigh w ave i nversion ( f rom Pei 2007) Figure 24. I nversion as a combination of estimation and appraisal ( f rom Pei 2007)

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32 CHAPTER 3 A CTIVE SO URCE SURFACE WAVE METHODS 3.1 Introduction Two aspects will be considered in this chapter. First, different active signal processing algorithms described earlier will be appraised in terms of the quality of dispersion image and thereafter the optimal one w ill be chosen for dispersion curve extraction. Secondly, the advantage of array based active MASW using vibratory shaker over the conventional one with uniform linear array using sledge hammer will be explored, followed by some additional concerns. For ill ustration, the data sets are selected from the Texas A&M University (TAMU), the Pennsylvania State University ( PSU) and Newberry. 3.2 TAMU Test Result 3.2.1 Experiment Descriptions The active MASW tests were conducted with 62 receivers at inter spacing of 2 feet with a total spread of 122 feet. Two receiver layouts were laid at positions TAMU 0_122 and TAMU 98_220. For each receiver layout, five sets o f data were recorded according 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 samples per trace time interval of 0.7 8125 ms (0.00078125 s), and total recorded period of 12.8 seconds.

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33 3.2.2 Image Quality Five different active signal processing algorithms described in Chapter 2 were explored for their effectiveness in producing dispersion images, i.e., f k, p Park et al. conventional beamformer (bf) and cylindrical beamformer (cbf). Take TAMU 0_122 with source at 132 as example, represented as Line1SR10RR2, where SR represents the distance between source and t he first receiver and RR represents the receiver s inter spacing. Note, for comparison, all power spectra were imaged in the same domain (f v). Also, the frequency range and its interval, velocity range and its interval were kept identical for all cases. T he spectral values in each plot were normalized to unity for better illustration of algorithms resolution (contrast in color). It is observed in Figure 31 that the best dispersion spectra are obtained from the conventional and cylindrical beamformers, fo r vast majority of energy of the propagating Rayleigh waves being concentrated in the narrow, dark red band. Also observed is that Park s algorithm shows better quality over f k and p at low frequencies (below 15 Hz). However, it suffers higher mode cont amination at middle frequency range, which would later on cause inaccurate autopicking of local strongest energy over the frequency range of interest in obtaining the dispersion curve. Indeed, since all algorithms perform 1D Fourier transform in the time domain, the resolution in frequency axis should be ideally the same. Therefore, the different resolution in velocity axis is evidenced by the ability to separate signals from noise associated with different signal processing algorithms themselves In addi tion the 3D power spectra are plotted to give a better look at the resolution of each algorithm where the dominant mode of Rayleigh waves manifest itself as sharp

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34 mountain ridge, as shown in Figure 32 It appears that the mountains in 3D spectra produced by conventional and cylindrical beamformers are the sharpest and most distinguishable, especially compared with f k and p s. Therefore it can be argued that the effectiveness of various algorithms in discriminating signals from noise is much more clearly demonstrated in this 3D power spectral comparison, where the beamformer algorithms apparently demonstrate superiority. To further illustrate the resolution capabilities, the normalized power spectral values at several individual frequencies are displayed in Figure 33 Again for each frequency (10, 20, 30, 40 Hz), the spectral values are normalized to unity. While it may not be surprising that different algorithms result in quite similar velocity values at each freq, it is apparent that the beamform er algorithms provide the narrowest mainlobe width and the lowest sidel obe height. This is significant because that narrow mai nlobe width along with small sidelobe height would ensure best energy concentration (or least energy leakage), thus leading to a more confident interpretation of the wavenumber response (i.e., phase velocity in our case). It can be understood that the high resolution in phase velocity axis contributes to the overall high resolution of the dispersion images brought by the beamformer algorithms. To this end, it appears to be desirable that dispersion curves be extracted from the beamformer algorithms. 3.2.3 D ispersion Curves Rayleigh wave dispersion curve was obtained by the automatic picking of the velocity frequency pair of the local strongest energy from the power spectrum image. While the highest dispersion imaging quality brought by beamformer algorithms are convincing, it is fair that, for comparison, this should be done for other algorithms as

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35 well Dispersion curves are presented in Figure 34 for individual algorithm and in Figure 3 5 for comparison. It is clear that all algorithms show only one domina nt mode of Rayleigh wave propagation, assumed to be the fundamental mode, except for that of Park. All dispersion curves are similar in a sense that the phase velocity increases with deceasing frequency. It is a sign of a normally dispersive site at TAMU, that is, the shear wave velocity increases with respect to depth. Also noted is that f k and cylindrical beamformer yield nearly identical dispersion curves despite their image resolutions which is a little surprising. For Park s algorithm, the spectrum i mage shows that the fundamental mode extends all the way to frequency of 60 Hz. However, as a result of automatic picking (seeking only the local maximum at each frequency), the fundamental mode dispersion curve is cut off at frequency about 35 Hz, as show n in Figure 34c Anyway, the fundamental mode dispersion curve can be modified by manual picking at suspicious frequencies, which is not easy if without the help of spectrum image and other algorithms. As a result it appears that P ark s algorithm suffers the most from higher mode contamination in this case Put it in another way, however, Parks algorithm seems to be potentially more capable in imaging multi modal dispersion curves, as already shown in Figure 3 1 c) that some high modes were developed rel atively well. In addition, it is noticed in Figure 35 that p algorithm gives the lowest phase velocity estimates and the difference becomes more appreciable with lower frequencies. Thus i t can be hypothesized that p algorithm suffer the most from the near field effect.

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36 It must be pointed out that the highest dispersion imaging quality at low frequencies does not necessarily imply the most unbiased results. The near field effect may easily exist for an active test, and the underestimation of phase velocity at low frequency is an explicit indicator. As such, the cylindrical beamformer model, which describes the correct physical model of propagating wavefield, should theoretically produce more unbiased results than other plane wave models do. Taking account of the resolving power and the near field effect, the cyli ndrical beamformer is therefore considered to be the optimum candidate in obtaining dispersion curves for any activesource surface wave testing For simplicity, the comparison results of other data collected at TAMU when processed using different algorit hms were not shown herein, because of equal if not better quality. 3.3 PSU Test Result 3.3.1 Experiment Descriptions The active M ASW tests were conducted with 31 receivers at inter spacing of 2 ft with a total spread of 60 f t. Three receiver l ayouts were made at positions PSU 60 _12 0, PSU 120 18 0 and PSU 90_150. For the first two layout s, three sets o f data were recorded according to three positions of the active source at 10 ft, 20 ft and 3 0 ft away from the first receiver. For the third layout, four sets of data were recorded according to four positions of the active source at 10 ft, 20 ft 30 ft and 4 0 ft away from the first receiver. Each set of data was obtained with 4096 samples per trace, time interval of 0.7 8125 ms (0.00078125 s), and total recorded period of 3.2 seconds.

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37 3.3.2 Image Quality By way of example, Figure 3 6 presents the 2D power spectrum images for data collected along PSU 120_180 with source at 100, represented as Line2SR20RR2. As in the previous sections, the range and interval of fr equency and phase velocity were kept identical and the spectral power was normalized to unity. It is observed that beamformer algorithms produced the most distinguishable dispersion pattern, characterized by the narrow, dark red energy band. Also observed is that in this case Parks algorithm did a good job in separating energy from noise and no higher mode contamination occurred. On the other hand, f ks performance was fair whereas ps turned out to be the worst in terms of image resolution and continui ty. In addition, 3D power spectr al plots are presented in Figure 3 7 to further demonstrate the better resolution achieved by the beamforming algorithms. While the beamformer algorithms produced the sharpest profile contrast (mountain and valley), the Park s and f k displayed a nice pattern as well. On the contrary is p s poor performance in this 3D power plot. Very poor dispersion pattern was developed with limited information on both ends of frequency of interest. This can be expected from its 2D power spectrum image, after all. Similarly, the n ormalized spectral pl ot s are presented in Figure 3 8 to show the detailed algorithm performance at individual frequency at 15, 20, 30, and 40 Hz, respectively. Even though the different algorithms pinpointed similar phase velocity at each frequency, it is apparent that the conventional and cylindrical beamformers exhibited the least energy leakage as demonstrated by the narrow mainlobe width and shallow sidelobe height. As previously discovered, it is interesting to note in Figure 3 8 a ) that at low frequency p tends to underestimate phase velocity. Also, at high

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38 frequencies p algorithm lacks the ability of energy concentration, seen as those large side ripples. Parks algorithm and f k appeared to be fair in those characteristics, based upon this comparison. 3.3. 3 Dispersion Curves In the same manner dispersion curves were automatically picked from the power spectrum and displayed in Figure 39 A compa rison plot is presented in Figure 310. In general, those extracted dispersion curves are in good agreement. As expected, the poor image resolution provided by p algorithm result ed in a dispersion curve extended only to 15 Hz at the lower end, where others generally extended to 10 Hz. A close look at Figure 310 shows five algorithms produce d almost identical dispersion curves at frequencies larger than 25 Hz. However below 25 Hz, P ark and cylindrical beamformer produced higher phase velocities compared to others. In addition, p algorithm gave the lowest estimates and the deviations become much more appreciable with decreasing frequencies. Once again, p appears to be the most sensitive to near field effect and should be applied with caution. On the other hand, because cylindrical beamformer offers the best image resolution and t he sharp narrow energy band allows the best separation of phase velocities for a g iven frequency, it is believed to be the best candidate in extracting field dispersion curves from any active source surface wave testing. Also note that the image from Park s algorithm in this case does not reflect higher mode interference with the fundamental mode, but the second mode (could be other high mode) develops a clear trend starting from about 20 Hz up to about 55 Hz. This actually can be made good use of when considering multi modal inversion, because higher modes are more sensitive to earth layering and velocity reversal and therefore

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39 helps constrain the model during inversion. In practice, however, multi modal field dispersion curves are difficult to obtain with quality high enough to be considered in simultaneous inversion. For one thing, i t may require a lot of field effort to obtain highquality multimodal dispersion curves, typically a trail and error process in terms of various combinations of SR and RR. For another it is often difficult to discern which mode is represented by a partic ular set of secondary peaks, as the energy transfer between modes is not theoretically limited to direct transfer between adjacent modes. It could be second mode, other higher mode or a superposition of multiple modes, which in turn brings extra uncertaint ies to inversion. 3.4 Newberry Test Result 3.4.1 General Descriptions The testing site is a single Florida Department of Transportation (FDOT) storm water runoff retention basin in Alachua County off of S tate R oad 26, Newberry, Florida ( F igure 3 11). The t est site was approximately 1.6 hectares and was divided into 25 strips by 26 northsouth 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 crosshole tests. The conventional active MASW tests were conducted along Z line by 31 4.5 Hz geophones at inter spacing of 2 f t with the total spread of 60 f t. A sledge hammer was used as t he active source and it was located 2 0 ft away from the first receiver. Each set of data was obtained with 2048 samples per trace, the time interval of 0.78125 ms, and the total recorded period of 1.6 seconds. Along K line the array based active M ASW tests were performed. The standard array (Hebeler, 2001) with 16 1 Hz geophones and

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40 a total spread of 120 ft was deployed with a vibratory shaker 8 ft away from the first receiver. ( Figure 312) Four sets of data were recorded in frequency domain, star ting from 100 Hz and ends at 3 or 4 Hz, with tapered frequency intervals. It should be noted that K line and Z line are not very far from each other. 3.4.2 Dispersion Analysis In the previous sections t he best active signal processing algorithm has been co nfirmed to be the cylindrical beamformer, where the following analysis is based upon. For the conventional active MASW test on Z line, the 2D and 3D dispersion images are shown in Figure 313 a) and b) It is observed that the f undamental mode is partially contaminated by higher modes and thus the automatically extracted dispersion curve is discontinuous, shown in Figure 313 c) Even though the secondary peaks appear to be associated with second, third or even forth mode, the general trend of the fundament al mode dispersion curve is not overshadowed and can be easily retrieved. Thus it can be argued that the fundamental mode dispersion curve is obtainable from about 10 Hz at the lower end to about 85 Hz at the higher end. Similarly the active data from K l ine was processed using cylindrical beamformer. For comparison, the 2D and 3D power spectral images are displayed in Figure 314 a) and b) respectively. Beyond expectation, the performance of the array based active MASW using shaker is significantly upgraded in terms of overall power spectrum resolution and frequency range of interest. Figure 314 c) shows a clear fundamental mode dispersion curve ranging from 4 Hz to 100 Hz, which is ensured by the narrow band in 2D spectrum (Figure 314 a) and the sharp ridge in 3D spectrum ( Figure 314 b ). It is believed that this great improvement has to do with the source characteristics, the spatial array sampling techniques, as well as the sophisticated recording equipment.

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41 First, the harmonic shaker operating in a s teppedsine fashion via frequency averaging technique significantly removes the effect of external noise and hence the quality of recorded data is assured to begin with. Secondly, the array based MASW takes advantage of spatial sampling technique, and gets over the traditional tradeoff between wavenumber resolution and frequency aliasing. Thirdly, the ultrasensitive, high resolution 1Hz geophones are more capable in recording the excited wavefields. They are much more reliable in producing linear response for low frequency signals than do the conventional 4.5Hz geophones. 3.4.3 Additional Concerns First, the use of sophisticated low frequency geophones, digital signal analy zer as well as source equipment makes the capital investment neces sary to conduct t he testing (nonuniform array coupled with shaker; analyzed using beamformer algorithms) substantially higher than that of the conventional methods. However, the advantages of obtaining more accurate and inclusive dispersion estimates may justify the increased cost of the testing equ ipment. Overall, the improved capabilities of the current testing procedure seen in the above example serve to validate the use of the method as not only a viable active surface wave technique, but also a reliable in situ seismi c testing method. Secondly, it should be made clear that the comparison between the conventional MASW conducted on Z line and the array based MASW on K line indeed makes sense since these two lines are not very far apart. However, a close look at the two d ispersion curves reveals the phase velocity difference especially below 15Hz. This is in part caused by the shallower bedrock at Z line over K line, seen as lateral variability. Besides, it should be noted that in the array based test the shaker was only 8 ft away

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42 from the first receiver, and this could potentially cause near field effect, a surface wave and body wave mixture, resulting in lower phase velocity estimates at low frequencies or long wavelengths This will be further investigated in Chapter 4. 3.5 Summary 1) Conventional and cylindrical beamformers provide dispersion images with the best resolution compared to other signal processing algorithms. 2) p algorithm is found to consistently underestimate phase velocities, and the underestimation increases with decreasing frequency. This demonstrates that p algorithm potentially suffers the most from near field effect. 3) Near field effect is found to be frequency dependent. At this point it appears that the cylindrical beamformer results contain t he least contamination. 4) Active test with shakers instead of sledge hammers is considered to be more effective in obtaining experimental data with overall high signal noise ratio and low frequencies. 5) Current application of array based testing procedur e proves to be successful in obtaining inclusive dispersion estimates, but may be infected with near field effect which needs further inspection.

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43 a) b) c) d) e) Figure 31 2 D f v power spectrum a) f k, b) p c) P ark et al d) conventional beamformer and e) cylindrical beamformer

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44 a) b) c) d) e) Figure 3 2. 3D f v power spectrum (same notation used)

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45 a) b) c) d) Figure 3 3 Normalized spectrum at different frequencies a) 10 Hz, b) 20 Hz, c) 30Hz, and d) 40 Hz ( G reen for f k, cyan for p yellow for P ark et al black for conventional beamformer and r ed for cylindrical beamformer)

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46 a) b) c) d) e) Fig ure 3 4. Dispersion curve extracted from power spectrum images a) f k, b) p c) P ark et al d) conventional beamformer and e) cylindrical beamformer

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47 0 200 400 600 800 1000 1200 1400 1600 0 10 20 30 40 50 60 70 Freq, Hz V, ft/s cylindrical fdbf fk taup park Figure 3 5. Dispersion curve comparison

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48 a) b) c) d) e) Fig ure 3 6. 2D dispersion power spectrums (same notation used)

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49 a) b) c) d) e) Figure 37. 3D dispersion power spectrums (same notation used)

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50 a) b) c) d) Figure 38. Normalize d spectrum at different frequencies (same notation used)

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51 a) b) c) d) e) Figure 39. Dispersion curves extracted from power spectrum images (same notation used)

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52 0 500 1000 1500 2000 2500 0 10 20 30 40 50 60 Freq, Hz V, ft/s cylindrical fdbf fk taup park Figure 310. Dispersion curve comparison

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53 Figure 311. Location of Newberry test site ( f rom Tran, 2008) a) b) Figure 312. Array based active test configurations a) APS shaker b) n onuniform array with 16 1Hz geophones

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54 a) b) c) Figure 313. Conventional ac ti ve MASW a) 2D dispersion image, b) 3D dispersion image and c) extracted dispersion curve.

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55 a) b) c) Figur e 314. Array based active MASW a) 2D dispersion image, b) 3D dispersion image and c) extracted dispersion curve.

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56 CHAPTER 4 P ASSIVESOURCE SURFACE WAVE METHODS 4.1 Introduction Suspecting the existence of near field effect associated with the previous activesource testing using shaker, passivesource surface wave measurements wer e made in an effort to quantify it. Besides, passivesource methods have additional advantages over activesource methods ( Tokimatsu et al., 1992a): (1) greater depths of investigation can be achieved because ambient energy usually propagates with longer w avelengths at low frequencies and (2) the assumption of dominance of Rayleigh waves is more likely to be true because the Rayleigh waves generated by a distant source are well preserved while the body wave s are almost damped out Generally speaking, there are two ways of doing passivesource measurement. The ReMi technique (Louie, 2001) has been considered to be the most convenient and inexpensive way due to its 1D nature of linear array and is currently in widespread use for geotechnical applications. Al ternatively a 2D array (Zywicki, 1999) is designed to record the ambient vibrations, with its ability to detect both the direction and velocity of the passive energy. In this chapter, both passivesource methods will be evaluated in terms of compatibility and reliability. 4.2 Experiment Descriptions At Newberry test site, t hree ReMi measurements were made along K line, one with 32 4.5Hz geophones spaced at 10 ft with a total spread of 310 ft, the other two with 16 1Hz geophones spaced at 10 ft and 20 ft, respectively, with a total spread of 150 ft and 300 ft. In the mean time, t wo 2D Passive tests of circular array were conducted with center resting on the midpoint of K line. One array of 100 ft diameter

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57 was designed, with 31 4.5Hz geophones equally spac ed on the circumference. The other made use of a 200 ft diameter array using 16 1Hz geophones uniformly placed on the circumference. It should be noted that they are concentric circular arrays with varying radii, aiming at obtaining dispersion curves with a wide range of frequencies. For the experiments using 4.5Hz geophones, 20 data sets per experiment were recorded with 16384 samples per trace, sampling frequency of 512 Hz, and recording period of 32 sec for each set. For the experiments using 1Hz geophones, 20 data sets per experiment were recorded with sampling frequency of 256 Hz and recording period of 32 sec for each set. 4.3 Dispersion Results Dispersion results obtained from ReMi and 2D Passive MASW are first displayed individually and then comp ared with Active MASW results with the purpose of 1) quantifying the near field effect associated with a ctive source method; 2) analyzing the reliability of different p assive source methods. The discrepancies will be explained in greater detail in the nex t section, considering the inherent limitations and assumptions associated with each type of method. 4.3.1 ReMi Results All passive data with linear array were analyzed using commercial software SeisOpt ReMi version 4.0 Data sets with various qualities need to be combined to produce a more inclusive and clearer pf image, for ease of recognizing the fundamental mode of propagating Rayleigh waves. 4.3.1.1 4.5 Hz geophone vs. 1 Hz geophone According to ReMi s data reduction procedures, each individual data set was simultaneously processed to yield individual pf image, and those of poor spectral

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58 images were discarded and retained only those clear ones, and then they were stacked in p f domain to produce the combined pf image showing the constructive interference effect. Finally, based upon the combined pf image, the fundamental mode dispersion curve was manually picked followed by Louie s (2001) recommendations. By way of example, in Figure 4 1 it is observed that the 4.5Hz ReMi test produced a typical c ombined pf image, with dispersion curve obtained from manual picking spanning from 5 and 27 Hz. In addition, a normally dispersive property is noted such that the slowness (inverse of frequency) increases as frequency increases. On the other hand, the 1H z ReMi tests with both short and long spreads yielded some pf images surprisingly limited in frequency range, with the manually picked dispersion curves ranging from 3.5 Hz to 8 Hz, shown in Figure 4 2 Since the 4.5 Hz ReMi array and 1Hz array with 20 f t inter spacing are of about the same receiver spread (about 300 ft), it is expected that 1Hz geophones be more reliable in recording signals with low frequency. Nonetheless it is never expected that the gaining in low frequency signals came with such a significant cost of losing high frequency signals. Theoretically the ultra sensitive, highresolution 1Hz geophones should perform much better than the conventional 4.5 Hz under the same working environment. The very limited high frequency ambient energy present during the time of recording is probably the reason. Fortunately it appeared that the 1Hz geophones did show improve ment at the lower end of the frequency responses of concern. 4.3.1.2 Length of a rray In general l onger array provides better wave number resolution. Thus increasing the receiver spread from 150 ft to 300 ft is expected to result in a dispersion curve with lower frequencies. Unfortunately this is not significant as illustrated in the pf images in

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59 Figure 42. In fact, they look prett y much the same in terms of the overall spectral pattern and frequency range of interest. If anything the aliasing effect at high frequency for the longer spread is more noticeable, which is not even a concern when interpreting the dispersion curve. There fore for simplicity and consistency, the result from the longer array was used herein for interpretation of the combined ReMi dispersion curve, shown in Figure 4 3 It is observed that the interpreted ReMi dispersion curves appeared to be in good agreement between 5 and 8 Hz where they overlap, and the combined dispersion curve ranged from 3.5 Hz to about 28 Hz. 4.3.2 2D Array Results Since 2D passivesource methods make use of the spatial sampling technique, more post processing is required for the interpr etation of dispersion results. Additionally, compared to 1D ReMi array, this involves more field effort in laying out the array. Survey was done for exact geophone positioning, and all the 1Hz geophones were buried and leveled in surface soil for good ground coupling, illustrated in Figure 4 4 Various 2D passive signal processing algorithms, described in Chapter 2, were implemented and compared. 4.3.2.1 FDBF v s MVDL v s MUSIC Frequency domain beamformer is by far the most frequently used signal processin g algorithm for 2D passive data. In most cases, the conventional beamformer performs well and gives a reasonable estimate of phase velocities (Yoon, 2005). However, to take advantage of the adaptive nature of highresolution beamformers, Capon s MVDL and M USIC were applied as well, in the analysis. It is observed in Figure 4 5 and 4 6 that, for both 2D arrays FDBF and MUSIC yield ed nearly the same look, whereas MVDL did not work at all. For the smaller array,

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60 MVDL produced significant scattering in the dis persion curve which made its trend indiscernible. And for the larger array, MVDL resulted in much poorer dispersion property at high frequencies (715 Hz) and nearly nothing below 7Hz. T h e exact reason for the poor performances of Capon s MVDL is not clear but some similar results were also reported by Zywicki (1999) and Li (2008). The combined dispersion curve from two concentric circular arrays is shown in Figure 4 7 It is noted that the two dispersion curves were more or less in agreement from 10 to 15Hz where they overlap, with a slightly higher phase velocity estimates from the smaller array. It has been reported that all beamformer algorithms with poor wavenumber resolution tend to overestimate the phase velocity in a multi energy environment, especi ally true when the angular separation of two incoming waves are very close. 4.3.2.2 100 ft array v s 200 ft array Array with smaller radius is more capable in detecting passive energy with relatively high frequencies or smaller wavelengths, whereas array w ith larger radius is more capable in detecting signals with low frequencies or larger wavelengths. All these have to do with the array s wavenumber resolution and aliasing limit. That is why two different trials were made, to validate the active result at high frequencies and to extend the dispersion curve to lower frequencies for deeper explorations. Specifically in this case, the 100 ft diameter array yielded a dispersion curve spanning from about 10 Hz to 30 Hz, which was further extended to about 3 Hz by the 200 ft diameter array. Plotted in Figure 48 are the typical time records and associated frequency contents for the passive measurement. It is observed that, while for the 100 ft diameter array majority of passive energy was concentrated in frequency range of 10 to 25 Hz, the frequency distribution of passive energy was much random in the 200 ft

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61 diameter case. It should be noted that, for the latter case, the corresponding amplitudes were several order higher, which resulted from the highresolution 1 Hz geophones. Of interest is that the frequency content can be served as a first indicator of a good passive environment or not. 4.3.3 Active vs. 2D Passive B ring ing together the active dispersion curve obtained in Chapter 3 with the 2D passive one discus sed above may lead to a better look of the results. As shown in Figure 4 9 the dispersion curves generally agreed from 15 Hz outwards. Below 15 Hz however, appreciable difference in phase velocity is observed, an underestimation of nearly more than 30% fr om the active test result, which is suspected to be caused by the near field effect. To be conservative, the credible lowest frequency limit for the active test was taken around 6 Hz despite the shaker was actually shaking at as low as 4 Hz. 4.3.4 Active v s. ReMi H ow about ReMi s performance? As in the previous section, active result and ReMi result were combined for the purpose of comparison. Starting from the higher end of dispersion curve, shown in Figure 4 10, it is observed that at first ReMi agreed wi th Active MASW from 27 to 17 Hz, and then ReMi significantly went higher from 17 to 7 Hz, and eventually ReMi lagged below 7 Hz. Once again, the near field effect is highly suspected for the active result even with such an unpredictable comparison with ReM i. Also presented in Figure 4 11 is the combined dispersion curve obtained from activesource and all passivesource measurements. It is self evident that the near field effect of active test gave rise to a significantly lower estimate of phase velocities compared to

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62 the passive results. As such what s left undone is to examine thoroughly the near field effect. 4.3.5 Performance of Two PassiveSource Methods Before addressing the near field effect, something else needs to be cleared up. As being noted in Figure 4 11 that, let alone the disagreement between active and passive results, the dispersion results from two passivesource methods did not match well at low frequencies, with ReMi being significantly lower below 8 Hz. So what causes this discrepancy ? First the picking procedures involved in ReMi are inherently ambiguous and subjective. Secondly is has to do with the fundamental assumptions made in ReMi. Recommended by Louie (2001) that three possible dispersion picks be made: (1) a low phase velocity where the spectral ratio just rises above the low values of incoherent noise, (2) a highvelocity value at a spectral ratio peak near the dropoff in spectral ratio, and (3) a best guess value where the ratio is at the steepest gradient. Numerical simul ations done by Zywicki (2007) showed that these three picks in most cases bracket the true velocity but the associated velocity range can be broad such that a high level of uncertainty accompanies the interpreted dispersion curve. Additionally he pointed out that the low velocity pick s depend on the noisefloor of the recording equipment and the array mainlobe properties and thus is not justifiable in the recommendations As such in the current analysis, every effort was made to pick the best guess spect ral values, with uncertainty inevitably involved, though. ReMi comes with the assumption that equal energy propagating from all directions of arrival and this is not expected to be valid throughout in our case. Therefore, t he 2D power contour plot was attempted to question this fundamental assumption in the beginning It should be noted that since MUSIC algorithm was reported to be most

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63 capable in dealing with angular resolution of incoming waves (Li, 2008) it was herein adopted in all the contour plots. Figure 412 presents the 2D power contour plots at several individual frequencies ranging from low to high, respectively. Plotted in each graph are the power spectral contours versus the trial wavenumbers in x and y directions ( kx and ky) at a given frequency, with star indicating the peak spectral value associated with the direction of arrival of the passive energy at that particular frequency. It is observed in Figure 4 12 that single source was in dominance at low frequencies (below 7 Hz) with its locat ion relatively fixed, indicated by the wavenumber pairs (stars). Also observed is that at high frequenc ies multiple energy sources were present with scattered positions, which is consistent with ReMi s assumption. Although these sources were not ideally di stributed in all directions with equal strength, the presence of multiple energy sources increased the chance that the array al igned with some energy source and this explains the go od performance of ReMi for velocity estimates at high frequencies (above 8 Hz) compared to the active result By this means the poor performance of ReMi at low frequencies is confirmed to be attributed to the source characteristics at the site during recoding. Moreover in spatial array signal processing, a limit on the estimati on capabilities is presented by a version of the uncertainty principle it s tates that for a linear array, the direction of arrival cannot be estimated without the knowledge of the velocity of wave propagation, and vice versa (Zywicki, 2007). In seismic s urface wave environment wave velocity is a function of frequency and media in which it is traveling. Since ReMi does not determine the direction of arrival (with the nature of linear array), the velocity estimates can never be accurate. On the other hand, 2D passive survey is based on

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64 spatial sampling technique and thus is no doubt to be more capable in determining the coupled wave velocity and direction of arrival. 4.4 Near Field Effect Near field effect ha s been a long issue since SASW was developed in 1984. It has been made clear that MASW suffers less than SASW (Foti, 2000) and cylindrical beamformer also helps mitigating to some extent (Zywic ki, 2005). Meanwhile, Yoon (2005 ) did comprehensive numerical studies regarding the near field effect and sugges ted a few dimensionless parameters in judging it. Li (2008) compares the effectiveness of using cylindrical beamformer and setting farther source offsets in mitigating the near field effect with the conclusion that farther source offsets being more effecti ve whereas cylindrical beamformer being of limited value. T wo main causes of near field effects are: (1) model incompatibility between plane and cylindrical Rayleigh waves and (2) body wave interference. Both are functions of the distance between the sour ce and the receiver line As distance increases, the wave front from a point source will more closely approximate a plane wave. Also since the amplitude of body waves decreases more rapidly with distance than Rayleigh waves (geometric spreading) the inte rference from body waves will decrease with increasing distance. On the other hand, t he frequency of seismic waves should influence the amount of near field effects because highfrequency body waves attenuate more rapidly with distance ( material damping ) Based on theses findings, the near field effect on Newberry test site will be examined in greater detail and some judging criteria will be suggested accordingly.

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65 4.4.1 Mitigated Solely by Cylindrical Beamformer First, a comparison between applying plainwave beamformer and cylindrical beamformer with respect to the same set of active data is shown in Figure 4 13. It is noticed that cylindrical beamformer consistently produced higher phase velocity estimates than did planewave beamformer. This is because in cylindrical beamformer, t he Hankel function allows sensors to be aligned with the Bessel function phase rather than the equally spaced complex exponential phase used in planewave beamformer. Also, A close look may indicate that near field effect is fr equency dependent, i.e., t he difference is almost a monotonically decreasing function of frequency, and the difference converges to zero as frequency inc reases, showing the planewave beamformer is asymptotically unbiased with increasing frequency ( Zywicki 1999) In fact because the cylindrical beamformer was already adopted in the previous processing of active data in chapter 3, it can be argued that the difference between active and passive dispersion curves would be even greater had the planewave beam former been used. In this sense one may recognize how bad the body wave interference can be when the active source is only 8 ft away from the closest receiver in this case. 4.4.2 Mitigated by a Longer Source Offset a nd Cylindrical Beamformer Recognizing that the propagating wavefields from the 8 ft offset point source are unlikely to be plane waves and the unavailability of another remedy test with longer source offset, an alternative idea is tried. According to Li s experience (Li, 2008), discarding the data recorded by the first six receivers and leaving only the last 10 in play seemed to bring the correct dispersion curve comparable to the passive results and by doing that the source offset to the nearest receiver increased to 28 ft. Figure 4 14

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66 illustr ates the difference before and after the change. It is apparent that starting from about 16 Hz a huge rise in phase velocity took place and whatever cylindrical or planewave beamformer produced nearly the same response, with slightly higher estimate broug ht by the cylindrical beamformer at low frequencies. The modified active dispersion curve was thereby obtained using cylindrical beamformer for consistency. Again bringing together the modified active dispersion and the 2D passive results, displayed in Fi gure 4 15 a very good agreement was reached, starting from 6 Hz up to 20 Hz. It appears that Li s recommendation turns out to work in our case. Further, it is believed that the near field effect is by and large removed from the active data once properly t aking into account the issue pertaining source offset. 4.4.3 Quantification of Near Field Effect Most filtering criteria for near field effects on the traditional SAS W method have been expressed as functions of the ratio between the wavelength of a Rayleig h wave and the source to first receiver distance. To this end, Yoon s proposal of two dimensionless parameters was applied herein to quantitatively evaluate the near field effect associated with MASW. The two dimensionless parameters are defined as: 0 RRACf AC NormalizedArryCenter V R RplaneV NormalizedPhaseVelocity V

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67 where AC is the array center defined as the average distance of all receivers in an array relative to the source, VR is the measured Rayleig h wave velocity at frequency f0 and VR ,plane is the plane Rayleigh wave velocity at the same f requency. One of the biggest challenges using field test results is to determin e a true value (i.e., one with no near field effects) that may be used as reference. Passive waves coming from a far distance may be reasonably considered to be plane Rayleigh waves. If it is assumed that the passive surface wave tests provide unbiased results, the results can then be used as reference. As seen in the previous demonstration, since the modified active dispersion curve showed very good agreement with the 2D passive result, it was herein used as reference, to evaluate the near field effect associated with nonuniform arra y with all sensors analyzed in C hapter 3. While Figure 4 16 a) presents the near field effect in a qualitative manner (dispersion curve comparison), it is quantitatively evaluated in Figure 416 b) in the normalized plot, with normalized array center versus the normalized Rayleigh wave velocity. It is observed that for normalized AC over 2.5 there is essentially no near field effect; at normalized AC of 2 it is about 10% underestimation of phase velocity; and about 15% underestimation at normalized AC of 1; and the underestimation gets worse and worse as normalized AC drops below 0.7. Note the reversals at Normalized AC of about 1.5 and 0.9 are due to the rapid change in slopes in the dispersion curves under comparison. For clarity, the combined dispersion curve at Newberry was constructed using the modified active result and the 2D passive result, plotted in Figure 417. By applying

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68 some built in smoothing algorithm in MathCAD, the dispersion curve ready for inversion was obtained starting from 4 Hz up to 80 Hz, shown in Figure 418. 4.5 Summary 1) Dispersion curve derived from ReMi appears to be reliable only to 8 or 7 Hz, below which it shows considerable underestimation in phase velocities compared to other independent results. Doubling the array length does not help improve the dispersion data at low frequencies. Finally, the process of manual picking for dispersion curve makes ReMi analysis relatively subjective. 2) The poor performance of ReMi at low frequencies is shown to be primarily due to wavefield characteristics that violate the fundamental assumption made in ReMi analysis namely an omni direction, multi so urce wavefield. 3) For 2D passive testing, the larger size of the array the lower the frequency obtainable, and vice versa. In the overlapping frequency range, the passive dispersion curve and the modified active one agree particularly well. 2D array appears to be more reliable in obtaining low frequency dispersion data than ReMi. 4) Conventional 2D FDBF algorithm and highresolution MUSIC algorithm yield similar dispersion curves. However, Capon s algorithm shows appreciable amount of scattering and hence fails to produce reliable dispersion curve. 5) Increasing the source offset is confirmed to be more effective in mitigating near field effect than applying cylindrical beamformer alone. The normalized plot is an effective tool to quantitatively evaluate th e near field effect.

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69 a) b) Fig ure 4 1 4.5 Hz ReMi results a) Combined p f spectrum b) Manual picks

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70 a) b) Fig ure 4 2. 1 Hz ReMi results a) 1 Hz ReMi 16@10 ft b) 1 Hz ReMi 16@20 ft

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71 ReMi Dispersion Curve 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 0 5 10 15 20 25 30 Freq, Hz Phase Vel, ft/s 1Hz 20 ft 4.5Hz 10ft Figure 4 3. Combined dispersion curve from ReMi t ests Fig ure 4 4. Detailed placement of the 1 Hz geophone

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72 a) b) c) Figure 4 5 Dispersion curves for 100ft diameter array with different s ignal processing methods. a) 2D beamformer b) MUSIC and c) Capon s MVDL

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73 a) b) c) Figure 4 6 Dispersion curves for 200ft diameter array with different signal processing methods. a) 2D beamformer b) MUSIC and c) Capon s MVDL

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74 2D Passive Dispersion Curve 0 1000 2000 3000 4000 5000 6000 7000 8000 0 5 10 15 20 25 30 35 Freq, Hz V, ft/s 2D_100ft 2D_200ft Figure 4 7 Combined dispersion curve obtained from 2D passive method a ) b) Figure 4 8 Typical passive records in t ime domain and their frequency content s. a) t ime record for 2D Passive MASW of 100 ft b) its f requency content c) t ime record for 2D Passive MASW of 200 ft and d) its f requency content

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75 c) d) Figure 4 8 Continued Active Vs 2D Passive 0 1000 2000 3000 4000 5000 6000 7000 8000 0 10 20 30 40 50 60 Freq, Hz V, ft/s Active 2D_100ft 2D_200ft F igure 4 9. Dispersion curve comparison between active and 2D Passive methods

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76 Active Vs ReMi 0 1000 2000 3000 4000 5000 6000 7000 8000 0 10 20 30 40 50 60 Freq, Hz V, ft/s Active 4.5Hz ReMi 1Hz ReMi Figure 4 10. Dispersion curv e comparison between active and ReMi methods Active Vs Passive 0 1000 2000 3000 4000 5000 6000 7000 8000 0 10 20 30 40 50 60 Freq, Hz V, ft/s Active 4.5Hz_ReMi 1Hz_ReMi 2D_100ft 2D_200ft Figure 4 11. Dispersion curve comparison between activesource and all passivesource methods

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77 a) b) c) d) e) f) g) h) Figure 4 12. Contour plot of power spectrum at various frequencies for 2D passive tes ts a) 5 Hz, b) 6 Hz, c) 6.5 Hz, d) 7.5 Hz, e) 10.75 Hz, f) 15.5 Hz, g) 18.75 Hz and h) 28 Hz

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78 Dispersion Curve 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5 10 15 20 Freq, Hz V, ft/s hfdbf fdbf Figure 4 13. Active dispersion curves obtained from applying cylindrical and planewave beamformers Active Dispersion Curves 0 2000 4000 6000 0 10 20 30 40 50 Freq, Hz V, ft/s cbf_last10 bf_last10 bf_all cbf_all Figure 4 14. Original and modified active dispersion curves using cylindrical and planewave beamformers

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79 2D_Passive 500 1500 2500 3500 4500 5500 6500 7500 0 5 10 15 20 25 30 Freq, Hz V, ft/s 100ft 200ft last10 Figure 4 15. Dispersion curve comparison between the modified activesource and the 2D passivesource methods

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80 a) An Overview of Near-field Effect 0 500 1000 1500 2000 2500 3000 3500 4000 4500 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 Freq, Hz V, ft/s plane wave interpreted b) Near-field Effect Evaluation 0.4 0.5 0.6 0.7 0.8 0.9 1 0 1 2 3 4 5 6 7 8 Normalized Array Center Normalized Ratleigh Wave Velocity reference standard array Figure 4 16. Evaluation of near field effects in terms of a ) d ispersion curves and b) n ormalized parameters

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81 Combined Dispersion Curve 0 1000 2000 3000 4000 5000 6000 7000 8000 0 5 10 15 20 25 30 35 40 45 50 Freq, Hz Phase Velocity, ft/s Active Passive Figur e 4 17. Combined active and passive dispersion curve combined curve 0 1000 2000 3000 4000 5000 6000 7000 8000 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 Freq, Hz V, ft/s Figure 4 18. C ombined dispersion curve after smoothing

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82 CHAPTER 5 I NVERSION 5.1 Introduction T h e ultimate goal of any geophysical/geotechnic al characterization is to obtain the desired physical properties out of the measurements while the surface wave method is not an exception. With the development of the combined field dispersion curve in chapter 4, i nversion is the l ast and most challenging part of utilizing surface wave methods for the estimation of shear wave velocity profile. Inversion has been the focus of many recent s tudies (Song 2008, Wathelet 200 5 Pei 2007, and Zarrabi 2005) and it generally involves three steps: 1) theoretical dispersion curve calculation from any arbitrary earth model, 2) model updating to match the experimental dispersion curve, and 3) uncertainty analysis of the interpreted model. In this chapter, the inversion module embedded in SeisOpt ReMi version 4.0 was utilized for characterizing the shear wave velocity profile at the Newberry testing site. 5.2 Forward Modeling To get started (step 1) an efficient forward modeling is required to compute the theoretical dispersion curve based on an assumed earth model. The theory of Rayleigh wave dispersion has undergone development since the initial work of Thomson and Haskell ( Thomson, 1950; Haskell, 1953) Later enhancements, known as fast SchwabKnopoff method (Schwab and Knopoff, 1972), were achieved to solve the problem of numerical overflow and loss of precision at high frequencies in the original ThomsonHaskell formalism. To achieve better numerical efficiency, several distinct approaches have been further proposed, such as fast delta matrix method, Abozena method (Ab o zena, 1979) and Kennett s r eflectiont ransmission m atrix method (Kennett, 1983). All in

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83 all, these various methods are used in the computation of surface wave dispersion for perfectly elastic, isotropic, planelayered models and in fact they have been pr oved to be analytically exact and equivalent (Buchen and BenHador, 1996). It should be noted that the r eflection t ransmission m atrix method is the forward engine used in SeisOpt ReMi inversion module. 5.3 Inversion S chemes Inversion schemes can generally be categorized into linearized inversions and global optimizations. The former is a gradient based approach while the latter performs the global search. Examples of linearized inversions include Newton or quasi Newton method, Occam s method, Levenberg Marq uardt (LM) method, and some general least square method. Examples of global optimizations may include simulated a nnealing (SA), g enetic a lgorithm (GA), n eighborhood a lgorithm (NA) and neural n etworks, etc. Note that in SeisOpt ReMi, the Occam s method and simulated a nnealing (SA) are available for use. They are referred to as interactive inversion and automatic inversion, respectively. It has been widely accepted that the initial model plays a significant role i n the linearized inversion. As a result the f inal inverted model is highly dependent on the initial choice. When an appropriate initial model can be generated using some priori information about subsurface structure, li nearized inversions may find the desired global minimum solution. In case of prior i information is either scant or unavailable, the inversion may only find a local minimum solution. Figure 51 a) is presented to illustrate the concept of local and global extremes. Also, it has been reported that the critical parameters influencing inver sion are the shear wave velocity and thickness of each layer whereas mass density and Poissons ratio do not play significant role s This

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84 effectively means that mass density and Poissons ratio can be held constant to some reasonable values and only thickness and S wave velocity of each layer need to be updated during inversion. In other words for an earth model of N number of layers, the parameters of concern are reduced to 2N 1 (with an infinitely thick half space). To overcome the limitation of lineari zed inversion, essentially the initial model dependence, a much wider search space has to be explored to insure the detection of the global minimum, in case of trapped in the local minimums or met the gradient plateau, as illustrated in Figure 51 b) It h as been reported that the global optimizations, such as SA or GA, are not sensitive to the initial model and often converge to the global minimum value, where the extra computational effort is the only price to pay. Nonetheless, the fast advanced computati onal power nowadays makes it trivial. 5.4 Inversion Results In the currently analysis, the interactive inversion was first attempted to come up with earth models with reasonably fit dispersion curves, and then the Simulated Annealing was utilized for comparison. 5.4.1 Interactive Inversion (LI) In this procedure, the mass density and the Poisson s ratio were set to default as 2000 kg/m3 and such that P wave velocity is 1.73 times S wave velocity, for each layer. As recommended, the interaction followed a t opdown sequence. First the high frequency dispersion data were fit, since they sample the very top layer. Next were the intermediate frequency data, and finally the low frequency data. Based on the rule of thumb that the simplest model that fits the data well is potentially the best estimated average shear wave velocity profile no velocity reversal was introduced during the interactiveinversion process. However, it is observed that a tradeoff did exist between

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85 layer thickness and shear wave velocity whi le fitting a particular set of dispersion data. Indeed, this is particularly true for the low frequency data points which sample deeper layers. By finding the two endmember combinations of large thickness with high velocity and small thickness with low velocity, the uncertainty of the model is assumed to be bounded within. The interactive process was not stopped until the RMS error (misfit function) reached a value as small as possible. Figure 5 2 presents the theoretical fit (solid line) to the experiment al dispersion curve (dotted points). Plotted in the graph is phase velocity versus period (inverse of frequency). It is apparent that the fit was pretty good throughout the period range, with the RMS error being 12.68 m/s and the interpreted earth model i s presented in Figure 54 a) designated as LI. Thus a sevenlayer model with increasing velocity appears to be a reasonable approximation. 5.4.2 Simulated Annealing (SA) For consistency mass density and Poisson s ratio were defined as previously. Since SA does not require an initial model to start with, several earth models with varying number of layers (4, 6, 8, 10 and 20) were tried, with a reasonabl y specified range of shear wave velocity based on the experimental dispersion curve. Shown in Figure 53 are the results of dispersion curve fit from using various layer models. In each case, the model was appraised according to the dispersion curve fit, indicated by the RMS error. By way of example, Figure 53 a) presents the fit using a 4layer model. It is observed that the fit was extremely poor at both low and high periods, which is not surprising when noting the RMS error being as large as 87 m/s. In the same manner, it is observed that the RMS errors for the 6layer model, 8layer model, 10layer model and 20layer model were 32 m/s, 22 m/s, 20 m/s, and 15 m/s, respectively. As one may notice that starting from 8 layer model the fit became reasonably good and RMS errors

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86 were not changing dramatically. As such the 8layer model appeared to work in this case and the 20layer model turned out to be unrealistic, for this is only an approximation after all. Also note that the calculation time increases significantly as the number of layers increases. To test the initial model independenc e of global optimizati ons, the earth model obtained from linearized inversion was used as the initial model in SA procedures. Not surprisingly, the inverted model did not deviate a lot from the one that started from none. On the other hand, can the dispersion curve fit be improved by finetuning the model obtained from SA in the interactive inversion? Unfortunately no. This effectively indicates that SA is sufficient for a reasonable estimation of shear wave velocity profile. It should be pointed out that the model obtained after SA inversion is the one with minimum misfit to the field dispersion curve, not the averaged one by its stochastic nature. 5.4.3 Appraisal and Discussion For comparison, the interpreted models using LI and SA are presented together in Figure 54 a) Plott ed in the graph is shear wave velocity versus Depth, in SI unit. It is observed that below 10 m the shear wave velocity profiles obtained from both models agreed pretty well with each other. Some variation is noticed from 10 m to 55 m, in which SA produced a thicker layer with higher velocity from 10 m to 40m whereas LI produced a thicker layer with higher velocity from 30 m to 55 m. What is in common is that both models depicted a huge rise in shear wave velocity at the interface of about 55 m, where the v elocity reached a value readily over 2000 m/s. Also noted in common is that another jump in shear wave velocity occurred at about 150 m, with velocity value exceeded 3500 m/s, which is considered to be associated with the half space. It should

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87 be noted tha t crosshole results are available but are limited to only the first 30 ft, so a direct comparison of shear wave velocity profile appears impossible. Some scant P wave refraction data suggested that the high velocities are associated with stiff, intact lim estones. Empirically, the maximum depth of investigation is approximately 1/4 to 1/2 of the maximum wavelength resolved in the experimental dispersion curve. As shown in the combined dispersion curve in chapter 4, the maximum wavelength is around 1800 ft ( 600 m) at the lowest frequency (4 Hz), indicating a depth of investigation readily exceeds 100 m. Compared with the previous finding (Tran, 2008) with depth of investigation being about 70 ft shown in Figure 5 5 this is considered to be a great leap in terms of depth of exploration, which is impossible without ever employing the more advanced testing procedures (1D/2D) and signal processing algorithms (2D). The fit to the dispersion curve is presented in Figure 54 b) in the conventional frequency veloc ity domain. It is observed that the overall fit is nearly perfect. Thus current inversion appears to be a successful one. However, it has to be pointed out that given a nearly perfect fit the interpreted model can still be far away from the ground truth. T his is because geophysical inversions are ill posed and nonunique such that a simple oneto one relationship does not hold in most cases. It is especially true when high velocity reversal exists at shallow depth (Luke, 2009). Therefore, it is always recom mended that other independent priori information, such as layering from borehole or/and P wave velocity from seismic refraction, be used to further constrain the model during inversion.

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88 As far as surface wave inversion is concerned, Beaty (2002) and Xia (2003) both suggested that multi modal inversion be implemented whenever identifiable higher mode dispersion curves are available, despite one adopted SA inversion and the other used LM approach. Zhang (2004) showed that a carefully designed experiment c ould help improve the resolution of the multimodal dispersion image (Figure 5 6 ) and the essential acquisition parameters were number of receivers (N), inter spacing of receiver (RR), and source offset (SR). It was reported that an optimized set of measurement parameters exists for a particular site. Alternatively, Pei (2007) made use of fundamental mode Love (Figure 5 7) wave to constrain the fundamental mode Rayleigh wave inversion and showed positive applicability. In fact, Rayleigh waves and Love waves can be simultaneously recorded using threecomponent geophones (seismometers) during a passivesource measurement, requiring no additional field effort. Otherwise, SH waves have to be actively excited on the ground surface in order to generate significant amou nt of Love waves, which are subsequently measured by a series of horizontal geophones. However it should be noted that in the case of significant anisotropy, the joint inversion may not work because Rayleigh waves are essentially associated with the SV wa ve velocity profile whereas Lovewaves the SH wave velocity profile. 5.5 Summary 1) Fundamental mode Rayleigh wave inversion via simulated annealing converges without a starting model A good starting model is required for using linearized inversion such a s Occam s method. With similar layering, both inversion schemes appear to produce similar shear wave velo city profiles

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89 2) The empirical criteria that the maximum depth of characterization being about one third of the maximum wavelength appears justifiable in this case. a) b) Figure 5 1. Objective function terminologies and illustration. a) g loba l maxima and minima v s. local maxima and minima b) p itfall with gradient based linearized inversion.

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90 Figure 52. Dispersion curve fit after interactive inversion a) b) Figure 5 3. Dispersion curve fit with models of various layering SA inversion. a) 4 layer model with RMS 87 m/s b) 6 layer model with RMS 32 m/s c) 8 layer model with EMS 22 m/s d) 10layer model with RMS 20 m/s and e) 20layer model with RMS 15 m/s

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91 c) d) e) Figure 5 3 Continued

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92 a) S-wave velocity, m/s -180 -160 -140 -120 -100 -80 -60 -40 -20 0 0 500 1000 1500 2000 2500 3000 3500 4000 Z, m SA LI b) Dispersion curve 0 1000 2000 3000 4000 5000 6000 7000 8000 0 20 40 60 80 100 Freq, Hz Phase Velocity, ft/s experimental theoretical Figure 54. Inversion results using an 8 layer model for illustration a) i nterpret ed shear wave velocity profile, b) d ispersion curve fit

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9 3 a) b) Figure 5 5. Inversion result of New berry obtained by combined MASW a) d ispersion curve fit and b) soil profile. ( from Tran, 2008)

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94 Figu re 5 6. Multi modal dispersion images obtained from various combinations of source o ffset and receiver inter spacing ( from Zhang, 2004) Figure 57. Dispersion image for Lovewaves (from Pei, 2007)

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95 CHAPTER 6 C LOSURE 6 .1 Summary In this study, a comprehensive surface wave technique has been presented to show its ability for deep soil ch aracterizations. Data from conventional active MASW, array based MASW, ReMi, and twodimensional passive MASW were analyzed and compared in particular. At TAMU and PSU testing sites, the conventional active MASW tests were recorded by 62 or 32 receivers at inter spacing of 2 ft, with source (sledge hammer) offset ranging from 10 ft to 50 ft from the nearest receiver. Following analy sis by several signal processing algorithms, the cylindrical beamformer algorithm was confirmed to be the best approach, and wa s selected for application for the rest of active MASW records. At Newberry testing site, the array based active MASW tests were recorded by a standard array with 16 1Hz geophones, and with a portable vibratory shaker at 8 ft away from the first geophone. Also, ReMi tests were conducted using 16 1Hz geophones at inter spacing of 10 ft and 20 ft, and along the same line as with the array based active MASW. Lastly two 2D passive test s were recorded by circular arrays with center at approximately the center of K line. One deployed a 100 ftdiameter circular array with 31 4.5Hz geophones equally spaced on its circumference, and the other made use of a 200 ft diameter array with 16 1 Hz geophones equally distributed on its circumference From these independent testing methods, the near field effect and reliability of different passive methods were discussed in detail. Then a combined dispersion curve was formed by the results from the modified array based active MASW

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96 and 2D passive MASW. Finally this combined dispersion curve was successfully inverted as the average shear wave velocity profile for Newberry site. Comparison was made with the previous inverted profile, and followed by some discussions on potential improvement. 6.2 Findings F or active MASW: 1) Conventional and cylindrical beamformers provide the dispersion imaging with best resolution compared to other signal processing algorithms. 2) p algorithm is found to consistently underestimate phase velocities, and the underestimation increases with decreasing frequency. This demonstrates that p algorithm potentially suffers the most from near field effect. 3) Near field effect is found to be frequency dependent, and can be mitigated by either cylindrical beamformer or with a longer source offset or a combination of both. 4) Active testing with shaker instead of sledge hammer is considered to be more effective in obtaining experimental data with overall high signal noise ratio and with low frequencies. 5) Array based testing procedure has the advantage of both wavenumber resolution and spatial anti aliasing over conventional procedure, provided with the same number of receivers. F or pass ive MASW: 6) Dispersion curve derived from ReMi appears to be reliable only to 8 Hz, below which it shows considerable underestimation in phase velocities. Doubling the array length for a higher wavenumber resolution does not help improve the dispersion data at

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97 low frequencies. Finally the process of manual picking for dispersion curve makes ReMi analysis somewhat subj ective. 7) For 2D passive testing, the larger the size of the array the lower the frequency obtainable, and vice versa. With 200 ft diameter array along with 1Hz geophones the lowest frequency obtained is about 4 Hz. With 100diameter array along with 4.5Hz geophones the highest frequency obtained is about 30 Hz. 8) Conventional 2D FDBF algorithm and highresolution MUSIC algorithm yield similar dispersion curves. However, Capon s algorithm shows appreciable amount of scattering and hence fails to produc e a reliable dispersion curve. 9) In the overlapping frequency range, the 2D passive dispersion curve agrees very well with the modified active dispersion curve. For inversion: 10) Fundamental mode surface wave inversion via simulated a nnealing converges to a final earth model without the need of specifying a starting model. 11) The empirical criteria that the maximum depth of characterization being about one third of the maximum wavelength appears justifiable in this case. 6.3 Conclusions Based on th e fi ndings outlined above, conclusions are presented as follows: 1) Cylindrical beamformer is the best signal processing algorithm for active MASW dispersion imaging. 2) Array based active MASW with portable shaker proves to be the best field testing procedure in achieving a wide frequency range of dispersion data. 3) Near field effect associated with active MASW can be practically mitigated by increasing the offset between the energy source and the array of receivers. However,

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98 simply using cylindrical beamform er has limited effect if the source offset is not far enough. 4) Two dimensional p assive surface wave method proves to be an effective means to obtain low frequency dispersion curve provided no specially designed shaker is readily available. 5) ReMi approach fails in obtaining reliable dispersion curve at low frequencies, which makes it inappropriate for the purpose of deep soil characterizations. 6) A combined use of array based active MASW and twodimensional passive MASW proves to be an effective and eco nomical means of deep soil characterizations. 6.4 Recommendations Based on all the results of this study and some careful thoughts through effective communications, the following recommendations are suggested: 1) For a better spatial sampling in MASW, i ncr ease the size of array and the number of receivers to the extent possible. 2) For a better interpretation of dispersion data, more powerful inversion techniques should be developed such as global optimization based multi modal surface wave inversion, to f urther constrain the nonuniqueness of inversion. 3) For a generally better soil characterization purpose, 1D earth model derived from dispersion curves alone is insufficient to describe some specific features of a site, such as lateral discontinuity. As a result full waveform inversion in time domain shoul d be studied to directly obtain reliable 2D or even 3D earth models.

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99 LIST OF REFERENCES Beaty, K. S., Schmitt, D. R., and Sacchi, M. (2002) Simulated annealing inversion of multimode Rayleigh wave dispersion curves for geological structure. Geophysica l Journal International 151 (2), 622 631. Buchen and BenHardor (1996) Free mode surfacewave computations Geophysical Journal International 124 (3), 869 887. Capon, J. (1969) High resolution frequency wavenumber spectrum analysis Proc. of the I EEE 57(8), 14081418. Foti, S. (2000) Multistation M ethods for G eotechnical C haracterization using S urface W aves. Ph.D. dissertation, Politecnico di Torino, Italy Haskell, N. A. ( 1953) The dispersion of surfa ce waves on multilayered media. Bullet in of the Seismological Society of America, 43(1) 17 34. Hebeler, G. L. (2001) Site characterization in Shelby County, Tennessee using advanced surface wave methods M.S. Thesis, the G eorgia Institute of Technology. Li, J. (2008). Study of surface wave methods for deep shear wave velocity profiling applied to the deep sediments of the Mississippi embayment. Ph.D. dissertation, the University of Missouri. Louie, J. N. (2001) Faster, Better, Shear Wave Velocity to 100 Meters Depth from Refraction Mi crotremor Arrays Bulletin of Seismological Society of America, 91(2), 347364. Luke Barbara (2009) Role of Forward Model in SurfaceWave Studies to Delineate a Buried High Velocity Layer Journal of Engineering and Environmental Geophysics, 14(1), 1 14. McMechan, G. A. and Yedlin, M. J. (1981) Analysis of Dispersive Wav e s by Wave Field Transformation. Geophysics, 46 ( 6 ) 869 871. Park, C. B., Miller, R. D., and Xia, J. (1999) Multi Channel Analysis of Surface Wave (MASW). Geophysics, 64( 3 ) 800808. Park, C. B., Miller, R. D., Miu ra H. (2002) Optimum fie ld parameters of an MASW survey. SEG J, Tokyo, May. Park, C. B., Miller R. D. N. Ryden, J. Xia, and J. Ivanov ( 2005) Combined use of active and passive surface waves Journal of Engineering and Environmental Geophysics, 10 (3), 323 334.

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100 Pei D. (2007) Modeling and Inversion of Dispersion Curves of Surface Waves in Shallow Site Investigations Ph.D. dissertation, the University of Nevada. Pillai, S. U. (1989) Array Signal Processing, Springer Verlag, New York Santamarina, J. C. and Fratta D. ( 2005) Discrete S ignals and I nverse P roblems : An I n troduction for E ngineer s and Scientists, John Wiley & Sons, Chichester. Song X., Gu H. (2008) Pattern search algorithms for nonlinear inversion of high frequency Rayleighwave dispersion curves Computers & Geosciences 34(6), 611624. Tokimatsu, K., Tamura, S., and Kojima, H. (1992a) Effects of multiple modes on Rayleigh wave dispersion characteristics Journal of Geotechnical Engineer ing 1 18(10) 15291543. Tokimatsu, K., Shinzawa, K., and Kuwayama, S. (1992b) Use of short period microtremors for Vs profiling Journal of Geotechnical Engineering, 118(10) 15441558. Tokimatsu, K. (1995). Geotechnical site characterization using surface waves. Proceedings of 1st International Conference on Earthquake Geotechnical Engineering, IS Tokyo '95, Balkema, Rotterdam 13331368. Thomson, W. T. ( 1950 ) Transmission of elastic waves thr ough a stratified solid medium Journal of applied Physics, 21 (2), 89 93. Tran K. T. (2008) An Appraisal of Surface Wave Methods for Soil Characterization. M.S. Thesis, the University of Florida. Wathelet, M. (2005) Array recordings of ambient vibrations: surfacewave inversion. Ph.D. dissertation Universite de Liege. Xia, J., Miller, R. D., and Park, C. B. (1999) Estimation of near surface shear wave velocity by inversion of Rayleigh waves Geophysics, 64 (3), 691 700. Xia, J. Miller, R. D., and Park, C. B. ( 2003 ) Inversion of high frequency surface waves wit h fundamental and higher modes Journal of Applied Geophysics 52(1), 4557. Yoon, S. (2005) Array based measurements of surface wave dispersion and attenuation using frequency wavenumber analysis Ph.D. dissertation, the Georgia I nstitute of Technology Zarrab i, M. (2005) A new approach for estimation of shear wave velocity profiles using multistation spectral analysis of surface waves, regression line slope, and genetic algorithm methods Ph.D. dissertation, the University of Memphis.

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101 Zhang S., Chan L., an d Xia J. (2004) The Selection of Field Acquisition Parameters for Dispersion Images from Multichannel Surface Wave Data. Pure and Applied Geophysics, 161 (1), 185 201. Zywicki, D. J. (1999) Advanced Signal Processing M ethods Applied to Engineering An alysis of Seismic Surface Waves Ph.D. dissertation the Georgia Institute of Technology Zywic ki, D. J. and Rix G. J. (2005) Mitigation of Near Field Effects for Seismic Surface WaveVelocity Estimation with Cylindrical Beamformers Journal of Geotechnical and Geoenvironmental Engineering 131 (8), 970 977. Zywicki, D. J. (2007) The impact of seismic wavefield and sour ce properties on ReMi estimates Proceedings of GeoDenver 2007, Denver, Colorado, USA.

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102 BIOGRAPHIC AL SKETCH P engxiang Jiang was born i n 1985 in Zhenjiang, Jiangsu, China. He is the only child in the family. He stayed in Zhenjiang until he finished his high school education. Then he enrolled in the program of civil and e nvironmental e ngineering in University of Macau in 2004, and received his Bachelor of Science degree in June, 2008. In fall of 2008, he was admitted to the program of g eotechnical e ngineering as a graduate student with Engineering Achievement Award, in the D epartment of Civil and Coastal Engineering, University of Florida. He completed his master s program under the supervisi on of Dr. Dennis Hiltunen in May 20 10, and decided to pursue his Ph D degree afterwards.