The Pennsylvania State University. The Graduate School. Department of Civil and Environmental Engineering

Transcription

1 The Pennsylvania State University The Graduate School Department of Civil and Environmental Engineering DETECTION OF SUBSURFACE VOIDS IN STRATIFIED MEDIA USING SEISMIC WAVE METHODS A Thesis in Civil Engineering by Ashutosh Srivastava 2009 Ashutosh Srivastava Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science May 2009

2 The thesis of Ashutosh Srivastava was reviewed and approved* by the following: Jeffrey Laman Associate Professor of Civil and Environmental Engineering The Pennsylvania State University Thesis Advisor Andrea J. Schokker Professor and Head of Civil Engineering, University of Minnesota Duluth Angelica Palomino Assistant Professor of Civil and Environmental Engineering The Pennsylvania State University Peggy A. Johnson Head of the Department of Civil and Environmental Engineering The Pennsylvania State University *Signatures are on file in the Graduate School

3 ii ABSTRACT The primary objective of this study is to investigate the effect of sub-surface anomalies such as voids in the stratified soil media on surface wave propagation. A data processing protocol was developed for processing seismic wave data for void detection by studying the signal simultaneously in the time and frequency domain using continuous wavelet transformation (CWT). The effect of voids in the soil media was examined by qualitatively comparing the signal properties acquired from the controlled laboratory experiments on the soil media, both with and without voids. For the controlled experimental study, a wooden box of dimensions 4.5m x 1.67m x 1.37m ( 15 x5 6 x4 6 ), was constructed and filled with sand and gravel in two layers. A void of known dimension was excavated in the soil mass in the box at a known location. Micro seismic waves were produced using a 7.25kg (16-lb) sledge hammer and a rubber mallet. The vertical response of the soil mass surface was recorded using the SignalCalc 620 Dynamic Signal Analyzer and was processed using the MATLAB 7.0 wavelet toolbox. Time-frequency plots of the seismic wave signals obtained from the unvoided soil mass experiment indicate that damped, uniform undulations are due to the surface wave dispersive behavior. Also, data obtained from the voided soil mass experiment indicate that the void anomalies cause low strength ripples in the time-frequency plots, usually in the low frequency region of the time-frequency plots. This observation has been used to study the properties of voids. In addition to the experimental study, a numerical study was also conducted. The wave propagation phenomenon was simulated for voided and stratified regions using the

4 iii finite difference method in the Wave2000pro software. Thus, a refraction test was performed in the soil box to determine the shear wave velocity profile. The receiver data was processed with the same protocol that was used for analyzing the experimental test data conducted in the soil box with void. The time-frequency maps constructed using the experimental data confirm the numerical results. Finally, the time-frequency maps using different types of wavelets for the same set of experimental data were compared. From this analysis it was concluded that the wavelets that correlates with the properties of the original signal produce time-frequency plots with all the signal features distinctively so that all the signal properties can be separately studied. Thus, wavelet analysis of the seismic wave signals obtain from the micro-seismic tests can effectively investigate the sub surface void anomalies.

5 TABLE OF CONTENTS iv LIST OF FIGURES... ix LIST OF TABLES... xii ACKNOWLEDGEMENTS... xiii CHAPTER 1 INTRODUCTION Background Problem Statement Objectives Scope of Research Organization of Report...6 CHAPTER 2 LITERATURE REVIEW Introduction Elastic Wave Propagation in Homogenous, Isotropic Half-space Seismic Wave Methods Seismic Refraction Survey Seismic Reflection Survey... 13

6 2.3.3 Surface Wave Methods v 2.4 Applicability of Seismic Methods in Void and Sinhole Detection Analysis of Seismic Test Data Time-history Analysis Wavelet Analysis Continous Wavelet Transformation (CWT) Wavelet Families Daubechies Wavelets Symlet Wavelet Family Meyer Wavelet Mexican Hat Wavelet Gaussian Wavelet Family Numerical Simulation of Wave-propagation in Elastic Media Summary... 40

7 CHAPTER 3 TESTING PROGRAM vi 3.1 Introduction Data Acquisition System Signal Analyzer Geophones Energy Source Data Acquisition Software Laboratory Test Setup In-situ Soil Properties Tests: Refraction Test on Soil Box Summary CHAPTER 4 NUMERICAL SIMULATION Introduction Parameters for FDTD Simulation of Wave Propagation Phenomenon Image Size Material Properties Boundary Condition... 55

8 4.2.4 Source Confiurgation vii Receiver Confiugration Time Step Scale Maximum Frequency Numerical Simulation of Wave Propagation in Layered Media Summary CHAPTER 5 RESULTS AND DISCUSSION Introduction Data Processing Data Processing Software MATLAB 7.0 Programming Platform and Wavelet Toolbox Seisimager 2D Data Processing Protocol Data Processing Results In-situ Refraction Survey for In-site Shear Wave Velocity Profile Wavelet Analysis of the Experimental Data... 65

9 Analysis Using Different Wavelet Families viii Wavelet Analysis of Soil Box Test Data Wavelet Analysis of the Numerical Simulation Data Summary CHAPTER 6 SUMMARY AND CONCLUSIONS Summary Conclusions Recommendations for Future Research REFERENCES APPENDIX A APPENDIX B... 89

10 ix LIST OF FIGURES Figure 2.1. P, S and R-waves in Elastic Isotropic Homogenous Half-space... 9 Figure 2.2. Seismic Refraction Geometry Figure 2.3. Seismic Reflection Geometry Figure 2.4. Travel-time Curve Figure 2.5. Arrival Time Estimation of Reflected Waves from Horizontal Interface Figure 2.6. Sine Function with Different Scales Figure 2.7. db2 Wavelet Function with Different Scales Figure 2.8. Place the Scaled Wavelet at the Signal Origin and Calculate Wavelet Coefficient Figure 2.9. Shift the Scaled Wavelet to New Time Location and Calculated Wavelet Coefficient Figure 2.10(a). Three Dimensional Wavelet Coefficient Plot Figure 2.10(b). Contour Plot of Wavelet Coefficients Figure Synthetic Signal Figure Power Spectral Density Plot of the Signal given by Equation

11 Figure Wavelet Coefficient Map x Figure Daubechies Wavelet Family Figure Symlet Wavelet Family Figure Meyer Wavelet Figure Mexican Hat Wavelet Figure Gaussian Wavelet of Order Figure Surface Wave Front Figure Sample Grid and Cells Figure 3.1 General Layout of the Data Acquisition System Setup Figure 3.2. Gisco SN4 Geophones Figure 3.3 (a). Wooden Test Box Layout Figure 3.3 (b). Wooden Test Box Figure 3.4(a). Test Setup Scheme Without Void Figure 3.4 (b). Test Setup Scheme for Void Detection Figure 3.4 (c). Void Detail (Section 1-1) Figure 3.5 (a). Test Setup for Refraction Test #

12 Figure 3.5 (b). Test Setup for Refraction test # xi Figure 4.1. Numerical Model Setup Figure 5.1. Protocol for Data Processing Figure 5.2 (a) Shear Wave Velocity Profile for Refraction Test #1 Conducted on Full Length Soil Box Figure 5.2 (b) Shear Wave Velocity Profile for Refraction Test #2 Conducted on Full Length Soil Box Figure 5.3. Figure 5.3. Time-Frequency Plot for Channel 6 Generated from 7.25kg (16 lb) Sledgehammer on Soil Box with Void Using Different Types of Wavelet Figure 5.4. Time-Frequency Plot for Channels 1, 4, and 10 Generated from 7.25kg (16 lb) Sledgehammer on Soil Box without Void Figure 5.5. Time-frequency Plot for Channels 1, 4, and 10 Generated from 7.25kg (16 lb) Sledgehammer on Soil Box with Void Figure 5.6. Time-frequency Plot for Channels 1, 4, and 10 Generated from Rubber Mallet on Soil Box with Void Figure 5.7. Time-frequency Plot of Receivers 1, 4, and 10 Generated from Numerical Simulation... 76

13 xii LIST OF TABLES Table 2.1. Wavelet Families Table 3.1. Portable Computer Specifications... 44

14 xiii ACKNOWLEDGEMENTS I would like to thank my committee members Dr. Jeffrey Laman, Dr Andrea Schokker and Dr Angelica Palomino, with special thanks to Dr. Laman and Dr. Schokker for their advising roles. I would also like to thank Edwin Rueda who assisted with the construction of the wooden soil box and testing. This study was supported by the Pennsylvania Transportation Institute and the Pennsylvania Department of Transportation. I am thankful for their financial support. Finally, my sincere thanks go to my fiancée, Janani Iyer and my family. Without there motivation, support, love and encouragement, this accomplishment would not have been possible.

15 1 Chapter 1 Introduction 1.1 Background Detection of obstacles, voids, cavities, subsurface rock profiles, or underground utilities is required for the planning, design, and remediation of existing sub-structures (foundations, tunnels or basements). These sub-surface features affect the soil properties such as shear strength, shear modulus, in-situ density and bed rock profile in their vicinity. The design and planning process of any sub-structure are primarily dependent on these sub-surface soil properties. Detection of these sub surface features has received much consideration due to rapid formation of sinkholes and damage to infrastructure (Alexander and Book 1984; Canace and Dalton 1984; Stewart 1987). Most of the currently used, traditional methods of determining the soil properties are laboratory based tests and require transportation of the soil samples from the site. The collection and transportation of soil samples results in a disturbed sample and thus may not represent the soil conditions in-situ (Powrie 2004). The other drawback of laboratory testing is that the procedure requires a fixed time for transporting samples and conducting tests. To overcome the drawbacks of the laboratory testing, a large variety of in-situ tests were developed. These tests include the vane shear test, cone penetration method, sand cone replacement method, bore-hole shear test, rock pressure meter test, dilatometer test, KoStep blade test, and rock shear test (Roy 2007). These in-situ tests are very quick and can provide results in real time. However, they may require sophisticated instruments and

16 2 substantial manpower. Another drawback of in-situ tests is that the depth of exploration of these tests is limited to near the surface, and the spatial resolution of the variation of the soil properties is poor. To overcome the resolution problem, non-destructive, in-situ tests were developed. These methods include multi-channel analysis of surface waves (MASW), spectral analysis of surface waves (SASW), seismic refraction survey, seismic reflection survey, electrical imaging, ground penetrating radar, subsurface penetrating radar, and microgravity survey (Belesky and Hardy, 1986). Most of these exploration methods are based on the generation-collection methods. In these methods radio or acoustic waves, or electric current is generated in the ground and the surface vertical response or electric current is measured with the help of geophones or electrodes. Then, the data is processed and deductions are made about the sub-surface soil properties based on the data analysis. These methods vary widely in feasibility, cost to benefit ratio, applicability, and effectiveness. Dobecki and Upchurch (2006) compared the effectiveness of various geophysical methods in detecting sinkholes and other ground subsidence and concluded that seismic wave based sub-surface exploration techniques are very successful in determining the elastic moduli of the soil layers surrounding these ground features. Seismic wave based exploration techniques utilize different types of data processing tools to extract the medium property information about the medium. Seismic methods include the travel time estimation or spectral analysis of the elastic waves (surface waves, compression waves and shear waves) generated in a medium due to an impact on the ground surface (Richart, Woods, and Hall 1970). Travel time based methods include the refraction and reflection

17 3 method and spectral analysis methods include spectral analysis of surface waves (SASW) and multichannel analysis of surface waves (MASW). Most of the current commercially available software for the seismic wave data processing, such as Seisimager 2D and Surfseis, identify the surface wave component with a built-in algorithm and estimate the quality of the signal based on the power and arrival time of the surface wave component. In some cases, the software algorithm for surface wave identification fails due to ripples in the signal generated from the reflection of waves from voids and other anomalies (Park, and Heljeson 2006). Thus, there is a need for an efficient and accurate procedure for the surface wave identification during signal processing. Signal processing techniques have improved exponentially due to advancements in the available computational resources. Signals can now be analyzed more effectively and quickly using different methods simultaneously (Yilmaz 1987; Tokimatsu 1997; Ganji, Gucunski, Nazarian 1998). These methods include Fourier analysis, time domain analysis, time-series analysis, wavelet analysis and fractal analysis. Recently, wavelet transformation has gained popularity due to its wide range of applicability (Shokouhi and Gucunski 2003). Traditional spectrum analysis only provides the frequency content of the signal but contains no information on the location of the signal where these frequencies are occurring. However, wavelet transforms can be used to study the time localization of the signal (the variation of the frequency content of the signal with time) (Walker 1999). Kaiser (1994) defined the wavelet transformation as, the convolution between a function known as wavelet and the original signal. The convolution result is used to

18 4 form time-frequency maps to give a representation of the signal in both the time and frequency domain. 1.2 Problem Statement The conventional seismic wave test approach that are generally used to estimate the soil properties at the site of interest lacks the information of spectrum variation in the time domain due to the presence of cavities and layers of soil. The spectrum variation information of the reflected waves from any cavities or anomalies is lost when a Fourier transform is performed on seismic test data. Travel time based methods that are generally used in the case of reflection and refraction of seismic waves do not supply information about change in frequency content. Time-frequency maps can be used to study the change in frequency content over time and thus can be used for cavity detection in the region with distributed soil properties. This research demonstrates a new scheme for the detection of voids by analyzing the surface wave component of a signal travelling through voided stratified soil media by improving on the currently available signal processing methods used in the seismic wave tomography. The focus is on the analysis of data obtained from the seismic wave tests using different families of wavelets and development of a scheme for detecting voids in the soil media. In this study the wave propagation was considered as elastic because these seismic tests the strains produced by the impact are small and the media particles are not permanently deformed.

19 5 1.3 Objectives The primary objectives of this research are as follows: Develop a method to identify the surface wave component from the signal generated by the seismic wave test using wavelet transform in the voided soil media. Propose the most efficient and effective mother wavelet for seismic wave test applications by investigating the effect of different types of wavelets on the analysis. Develop a wavelet based protocol for processing of seismic wave data for void detection. 1.4 Scope of Research This research focuses on the development of a protocol for processing seismic wave data for void detection using wavelet transformation. Other methods of void detection, uncertainties associated with the measurement of data, participation of higher Raleigh wave modes, data scatter and systematic error (Marosi 2004; Tuomi 1999) are not examined in this study. Also the effect of porosity and saturation level of the soil was not considered. The primary method used to investigate wave propagation in stratified voided media consists of micro-seismic tests conducted under laboratory conditions. The data is analyzed using wavelets from different classes, or families, to investigate the effect of wavelet selection on wavelet analysis and the generation of time-frequency plots. The effect of voids is studied simultaneously in the time domain as well as the frequency domain using time-frequency plots generated from wavelet analysis of the signals. A numerical model is developed using finite difference methods and focuses on simulation

20 6 of wave propagation in stratified voided soil media. The numerical model is then used to study the wave propagation in the voided soil media. Results from the numerical simulation and the laboratory tests are utilized to develop a protocol for the void detection in the stratified soil media. 1.5 Organization of Report Chapter two presents a literature review of the relevant studies on the fundamentals of wave propagation phenomenon in elastic media and seismic wave test methods. The wavelet transformation is also briefly discussed. The finite difference simulation of wave propagation phenomenon in stratified soil media is reviewed. Chapter three presents details of the testing program. It includes a description of the data acquisition system and laboratory test setups. Chapter three also reviews soil property tests conducted to provide input data for the finite difference simulation model. Chapter four investigates the aspects of numerical modeling of wave propagation in stratified soil media and an overview of the parameters associated with finite difference time domain (FDTD) simulation of wave propagation in elastic media, and also the numerical model used for the simulation of the soil box test. Chapter five presents details of the analytical program related to laboratory testing and an overview of the data processing methods used for analyzing laboratory tests and numerical simulation test data. Also included are the results from all laboratory tests. Chapter five also presents a detailed discussion of numerical simulation results and comparison with experimental results. Chapter six provides a summary and conclusions from the research and recommendations for future research.

21 7 Chapter 2 Literature Review 2.1 Introduction There has been a large volume of research completed on the development of seismic wave based sub-surface exploration techniques such as the seismic refraction survey and seismic reflection survey. These techniques typically use time or frequency domain based data analysis methods. But seismic wave test data is localized in time and, therefore, the current time and frequency domain methods are not sufficient to extract all the information from the data. Time-frequency maps are a representation of the signal in both time and frequency domain and thus more information can be extracted from the signal by studying it in both domains, rather than in a single domain. Very limited research has been conducted relative to time-frequency domain analysis, particularly with regard to wavelet transformation. This literature review highlights some of the pertinent research regarding traditional seismic wave sub-surface exploration test data analysis procedures, the applicability of these traditional seismic wave methods in void detection, and an introduction to the wavelet transformation. Also included is an overview of wave propagation phenomenon in elastic media and a discussion of the different types of waves. Finally, the fundamentals of finite difference and its capability to accurately model wave propagation phenomenon is discussed. 2.2 Elastic Wave Propagation in Homogeneous, Isotropic Half Space In a three dimensional homogenous and isotropic medium, the equations of motion for an elastic wave are written as (Richart, Woods, and Hall 1970):

22 u ε 2 i 2 ρ = ( λ+ G) + G u 2 i (2.1) t x i 8 where, ρ = density of the elastic medium. u i = (u, v, w) T, is the displacement vector in the cartesian co-ordinates. x i = (x, y,z ) T, ε is the cubical dilation and is equal to the volume strain of the system. λ = Lame s first constant G = Lame s second constant or shear modulus. = Laplacian operator in the cartesian co-ordinates. For a homogenous and isotropic elastic half-space, Equation (2.1) results in three solutions, representing three types of waves: (1) dilatational wave, (2) distortional wave, and (3) surface wave: 1. Dilatational wave (Primary wave, P-wave, pressure waves, compression waves): P-waves result in the dilatation of the medium. In the region affected by P- waves, the medium particles vibrate along, or parallel to, the direction of travel of the wave energy. The P-wave velocity is highest among all the wave types discussed here (P, S and R). P-waves carry only 7 percent (approximately) of the total energy (Richart, Woods, and Hall 1970). 2. Distortional wave (Secondary wave, S-wave, shear waves): S-waves result in the distortion of the medium. In the region affected by S- waves, the medium particles vibrate perpendicular to the direction of wave

23 9 propagation. The wave velocity of S-waves is greater than R-waves but less than P-waves. Approximately 26 percent of the total energy is carried by S- waves (Richart, Woods, and Hall 1970). 3. Surface wave (Rayleigh wave, R-wave): R-waves move across the free surface and are confined to a zone near the free boundary of the half-space. As it passes, a surface particle moves in a circle or ellipse in the direction of propagation, depending on the medium properties. The amplitude of the R-waves decreases rapidly with depth. R-waves decay slowly with distance in comparison to the body waves (P- and S-waves), and their velocity is slightly less than that of S-waves. Surface waves carry approximately 67 percent of the total energy (Richart, Woods, and Hall 1970). Source Figure 2.1. P-, S- and R-waves in Elastic Isotropic Homogenous Half-space (Richart, Woods, and Hall 1970)

24 10 The above discussion includes wave propagation in a homogeneous and continuous elastic media. However, soil media is porous. Biot M.A, (1956) studied the propagation of elastic waves in a fluid-saturated porous solid and concluded that wave propagation in a fluid saturated porous solid media results in two dilation waves. He termed them: wave of the first kind and wave of the second kind. He also concluded that the wave velocity of the first kind wave was higher than the second kind wave. However, wave of second kind showed the higher attenuation than the wave of first kind. Berryman J.G., (1982) further investigated the effect of porosity on the wave velocity of the two dilation waves and the shear wave and concluded that the velocity of the wave of first kind decreases as the porosity of the media is increased. However, the velocity of the wave of second kind increases as the porosity increases and also the shear wave velocity also decrease as the porosity increases. In this research, the effect of porosity and the saturation level were not considered. The soil media was assumed to be a homogeneous solid media and elastic wave propagation was considered. 2.3 Seismic Wave Methods Conventional laboratory or on site methods of determining soil properties are: (1) triaxial shear test, (2) vane shear test, (3) direct shear test, (4) uniaxial shear test, and (5) cone penetration method. These are either performed on the samples from the site or on the site. However, with these methods it is difficult to determine in-situ soil properties below the uppermost layers. Richart, Woods, and Hall (1970) and Dobecki and Upchurch (2006) investigated seismic wave methods and concluded that seismic wave methods are advantageous in determining in-situ soil properties efficiently as they are performed on

25 the surface. With the use of wave propagation physics principles, important soil properties can be determined at lower depths. There are generally three types of seismic surveys conducted for subsurface soil profiling: (1) seismic refraction survey, (2) seismic reflection survey, and (3) seismic surface wave methods Seismic Refraction Survey Seismic refraction surveys are a commonly used, traditional, geophysical technique to determine soil properties, depth of bedrock, water table depth, or other density contrasts (Dobecki, and Romig 1985). The seismic refraction method has been used extensively to characterize sub-surface soil conditions at environmental and engineering sites. Redpath (1973) formulated a seismic refraction survey procedure for data acquisition and processing. He summarized the theory and practice of using a refraction survey for shallow and sub-surface investigations. A seismic refraction survey requires measurement of travel time of the seismic energy component generated by a seismic source selected on the basis of seismic line length resolution desired, and environmental suitability of the seismic source. The P-wave or S-wave travels down to the top of rock (or other distinct density contrast), is refracted along the top of rock, and returns to the surface as a head wave along a wave front (Figure 2.2) (Richart, Woods, and Hall 1970). Based on the typical energy sources used during a refraction test, the refraction survey is limited to the mapping of soil layers that occur at depths less than 30.5m ( 100 ). If a seismic refraction survey is required for greater depths, then the geophone array spacing is increased. However, due to site dimensions and input energy restrictions, achieving results for depths more than 30.5m ( 100 ) is practically not feasible. The major disadvantage of seismic refraction occurs where a soil layer of low wave velocity 11

26 12 underlies a soil layer of high wave velocity. In these circumstances, seismic refraction fails to detect the underlying low velocity layer. Seismic refraction survey data processing is based on a first arrival concept (Redpath, 1973). Data processing requires manual selection of the P-wave arrival times from the signal at each geophone location. During the selection process, knowledge of the seismic wave propagation is required to differentiate the refracted P-wave arrival time from other seismic waves, such as surface waves and S-waves. Thus, identification of each wave class is required within the signal for accurate arrival time determination. The traditional method assumes that the P-wave arrival coincides with the seismic wave energy arrival, i.e. the arrival time of P-waves at a geophone is the time at which the data acquisition system records the first non-zero reading at the geophone. This assumption is based on the fact that P-waves travel faster than other seismic waves, such as surface waves and S- waves. But, in a region with extreme tomography, this assumption may fail and leads to erroneous results due to reflections from the void anamolies. Advanced inversion methods are available in some commercial software such as Seisimager2D that utilize a complex ray tracing algorithm to image relatively small targets such as foundation elements. Software, such as Seisimager2D, can be utilized to perform refraction profiling in the presence of localized low velocity zones such as voids (Geometrics, Inc. 2006). However some software may require accurate picking of P-wave arrival time.

27 13 Figure 2.2. Seismic Refraction Geometry (Richart, Woods, and Hall et.al 1970) Seismic Reflection Survey Seismic reflection survey, like seismic refraction survey, is a common method of exploration geophysics that uses the principles of seismology to estimate subsurface properties from reflected seismic waves. Hunter et.al (1984) outlined the basic principles of seismic reflection surveys and formulated data acquisition and processing protocols. Seismic reflection surveys require travel time measurement of the reflected seismic energy component of P-waves from the desired subsurface density contrast such as voids, layer interfaces, and bedrock. Hunter et.al (1984) also summarized the seismic reflection surveys equipment details, test procedure and data processing and concluded that the equipment used for seismic reflection survey is similar to that used for seismic refraction surveys, but field and data processing procedures employed in seismic reflection methods are different than those used in seismic refraction surveys. The seismic reflection survey data collection and

28 14 processing procedures are intended to maximize the energy reflected along vertical ray paths by subsurface density contrast (Figure 2.3) (Steeples and Miller, 1990). In a seismic reflection survey, the first arrival data at the geophones do not represent reflected seismic energy. The reflected component of seismic energy is identified by collecting and filtering multi-fold or highly redundant data from numerous shot points per geophone placement in a complex set of overlapping seismic arrival data. The data and field processing for a seismic reflection survey is highly complicated and requires more processing time than seismic refraction survey. Seismic reflection surveys have several advantages over seismic refraction surveys. Seismic reflection surveys can be performed in the presence of low velocity zones or velocity inversions (a low velocity layer under a high velocity layer) and have better lateral resolution than seismic refraction surveys. Gruber and Rieger (2003) listed the limitations of the seismic reflection survey. The main limitation of seismic reflection surveys is the higher data processing time than seismic refraction survey. Also the cutoff depths at which the reflections from subsurface density contrasts (e.g., bedrock, horizontal soil layer interfaces, voids, etc.) and the surface waves that carry most of the energy arrives approximately at the same time, is low. Thus, the P-wave reflections from the density contrasts located below the cutoff depth arrive at geophones after the surface waves have passed, making these deeper subsurface density contrasts easier to detect and differentiate.

29 15 Figure 2.3. Seismic Reflection Geometry (Richart, Woods, and Hall 1970) Surface Wave Methods Surface waves based methods, like body wave based methods are one of the most common methods used for determining the sub-surface tomographical features. Surface wave methods utilize properties of surface waves (S-waves) that are confined to a zone near the boundary of the half-space and carry the major portion of input energy. Richart, Woods, and Hall (1970) investigated the surface wave propagation and observed that in the zone of varying soil properties, surface waves display a phenomenon known as dispersion. If the material properties of elastic media are constant and independent of depth, then the surface wave velocity in elastic media will be constant and independent of frequency content of input excitation. However, if the material properties of the elastic media are a function of depth, then surface wave velocity in elastic media is also the function of input excitation frequency content. This phenomenon is also known as

30 16 dispersive behavior. All techniques for processing surface wave data utilize this phenomenon to obtain information regarding the elastic properties of sub-surface soil mass. Park, Miller, and Xia (1999) and Stokoe II et.al (1994) discussed surface wave propagation and dispersion behavior in detail and concluded that the bulk of surface wave energy is confined to a zone of half-space about one wavelength deep and relates to the lowest excitation frequency. The depth of investigation for surface wave methods is directly proportional to the longest wavelength or lowest frequency that can be analyzed. Therefore, in surface wave methods, the depth of investigation is enhanced by increasing the wavelength of input energy or by lowering frequency. In surface wave tests, an impact is used to deliver input energy. As impact magnitude increases, longer wavelengths and increasing depths of investigation are possible. For this research, 7.25kg (16-lb) sledge hammer and a rubber mallet was used to vary the depth of investigation. The effect of source weight on the frequency input spectra was also studied. 2.4 Applicability of Seismic Methods in Void and Sinkhole Detection Detection of obstacles, voids and cavities is necessary for planning, designing, and remediation of foundations, excavations, and evaluation of abandoned mines. There are other applications where void detection is necessary, such as for determination of size and location of sinkhole voids. Dobecki and Upchurch (2006) compared the effectiveness of available geophysical techniques, such as ground penetrating radar, microgravity, electrical resistivity, seismic wave refraction, and seismic reflection survey in locating anomalies, such as voids and rocks, with an emphasis on the seismic methods. Dobecki and Upchurch concluded that geophysical techniques are an effective means to predict

31 17 approximate locations and causes of sinkholes and other anomalies, like water filled or air filled voids. Seismic methods include both body and surface wave evaluation based on spectral analysis and travel time based techniques. In spectral analysis, data from receivers is analyzed in the frequency domain, whereas in travel time based techniques, arrival time of reflected and refracted waves from the layer interface or from any anomaly is measured at receivers. Thus, travel time based techniques can be used to detect anomalies, such as sub-surface voids and strata interfaces. Richart, Woods, and Hall (1970) investigated the wave propagation phenomenon in elastic media and concluded that elastic waves carry significant information about the medium in which they travel, such as medium stiffness, elastic modulus, Poisson s ratio, presence of anomalies like voids and cracks. This information can be retrieved by wave propagation based techniques. Micro-seismic methods have been used extensively to study material properties of stratified soil media by interpreting properties of surface waves. Past research has investigated the use of micro-seismic methods to detect subsurface voids. Cooper and Ballard (1988) have shown that the presence of any cavities or anomalies near the surface tends to increase arrival time and voids can be detected using this phenomenon. Belesky and Hardy (1986) studied effects of horizontal strata on arrival time and found that the phenomenon of increase in arrival time due to shallow cavities cannot be applied in the case of stratified soil profiles, as this procedure cannot differentiate between signals arriving from anomalies and reflections from different layers of soil media.

32 18 Seismic wave methods, such as spectral analysis of surface waves (SASW) and multichannel analysis of surface waves (MASW) have received attention due to relatively simple test and data analysis procedures. Dravinski (1983) proved analytically and Curro (1983) proved experimentally that seismic surface wave methods such as MASW are sensitive to shallow cavities or other anomalies and can be more effective in detecting near surface anomalies. Belesky and Hardy (1986) investigated the micro-seismic surface wave data in the frequency domain and found that the presence of voids or any other obstacle tends to influence amplitude of surface waves more than arrival time. The research illustrated that the cavity locations can be determined by examining the attenuation of signal amplitude over time and distance. Belesky and Hardy (1986) concluded that analyzing the signal in the frequency domain would be more effective than analyzing the signal in the time domain only. Al-Shayea, Woods, and Gilmore (1994) applied the SASW method to a sand bin test case with an artificially placed void and found that the phase velocity decreased when the receivers were placed along the void axis. Gucunski, Gunji, and Maher (1996) investigated the effect of discontinuities like voids, rigid obstacles or horizontal layers of soil on the dispersion behavior and found that the presence of such anomalies produce fluctuations in the dispersion curve due to reflection of surface waves from these discontinuities. Ganji, Gucunski, and Maher (1997) numerically simulated the wave propagation phenomenon in an elastic half-space with a shallow void and observed the same fluctuations in the dispersion curves. They concluded that this phenomenon can be used to detect underground obstacles. Gukunski and Shokouhi (2005) used wavelet transformation to analyze data from finite element simulations of SASW tests in a half-

33 19 space to construct wavelet time-frequency maps and successfully detected the size, shape, and location of obstacles placed near the surface and proposed a void detection scheme based on the results. 2.5 Analysis of Seismic Test Data Data obtained from seismic tests can be analyzed within time or frequency domains. Richart, Woods, and Hall (1970) discussed both types of analysis. The spectral analysis of data obtained from SASW or MASW tests lack the information of spectrum variation in the time domain due to the presence of cavities and layers of soil media. The travel time based method, used in the case of reflection and refraction of seismic waves, does not produce information regarding changes in frequency content. Gucunski (2005) analyzed the data both in time and frequency domains using wavelet transformation and concluded that the wavelet transformation can detect the waves reflected from void anomalies. In this study, the test data is analyzed both in time and frequency domains, using time-history as well as wavelet analysis Time-history Analysis Time-history analysis includes the study of reflection and refraction of waves in the time domain. P-waves velocity is the highest among all wave types. Therefore, P-waves will be the first to arrive at a given point, along any given path, in the absence of any extreme tomography. This makes P-waves relatively easy to identify. Reflection survey data analysis consists of two main steps: 1) arrival time estimation; 2) formulation of travel time curves. Richart, Woods, and Hall (1970) discussed both the estimation of arrival time of direct and reflected waves to the geophones and also, the formulation of travel time curves (see Figure 2.4). For layers in which the wave velocity ( v ) is not a p

34 20 function of depth (H), it can be determined as the reciprocal slope of the travel time curve, and the depth can be determined by measuring the scaled intercept on the timeaxis. Travel Time (t) Reflected wave 1 v p Direct wave 2H v p Distance from the Source (d) Figure 2.4. Travel Time Curve (Richart, Woods, and Hall, 1970) By analyzing the signal obtained from a geophone array, the time signature of the horizontal strata or anomalies can be distinguished from the rest of the signal using ray theory (see Figure 2.5). d 1 3 θ 2 v 1 t 1 v v 2 t 2 v 4 φ Figure 2.5. Arrival Time Estimation of Reflected Waves from Horizontal Interface (Richart, Woods, and Hall, 1970)

35 21 The time taken by wave-123 to reach 3 = 2 d 2 v t 2 1 and the time taken by wave-143 to reach 3 = where, v 1 = wave velocity in layer 1 v 2 = wave velocity in layer 2 t 1 = thickness of layer 1 t 2 = thickness of layer 2 2 2t2 + v cosϕ 2 d t2 tanϕ 2 v t 2 1 and φ, θ is defined from the Snell s law: sinθ v = sinϕ v 1 2, There are also some disadvantages of the P-wave reflection. One major disadvantage is that reflected P-waves arrive at the geophones after they have been excited by direct waves (Gruber, and Rieger, 2003). Excitation of the geophones results in undesirable vibrations with a slow dying rate and thus contaminates signals coming from reflections from targeted anomalies, making the methods using first arrivals disadvantageous. Another problem with P-waves is that they carry just 7% of the total energy, with the remainder being lost to attenuation from traveling in soil media; thus, signals become weaker as they are collected further from the source of generation.

36 Wavelet Analysis Continuous Wavelet Transformation (CWT) Wavelet analysis is a relatively new technique that can be applied to dynamic soil response data to study signals in the time and frequency domains simultaneously. Kaiser (1994) defined the wavelet transformation as, the convolution between a function known as wavelet and the original signal. A function, defined as a mother wavelet Ψ(t), is required before performing a wavelet transformation. This function must be well defined, localized in time and frequency domains, and should have a zero mean (Kaiser, 1994). There are many types of mother wavelets developed for purposes such as time series analysis, dynamic data analysis, de-noising signals, image processing, and speech recognition (Walker, 1999) and will be discussed later in this chapter. A wavelet ψ ( τ ) at time location t, scale a and integration variable τ is given by a,t the following equation (Walnut 2002): ψ a τ ) = (,t 1 t τ ψ a a (2.2) Continuous wavelet transform (CWT) W Ψx of any signal x(t) with wavelet ψ ( t ) having range of scales a is defined as follows (Walnut 2002): W x ψ a,t + * = x( τ ) ψ a, t ( τ ) d τ (2.3) * where ψ a,t ( τ ) is the complex conjugate of ψ ( τ ), W ψ x a, t is the wavelet coefficient, and a is the scale of a wavelet that is the inverse function of frequency. To demonstrate the functionality of scale, sine waves with different scales are plotted in Figures 2.6 (a) through (c). The higher value of scale results in a more compressed wave and also a,t

37 frequency has increased. Thus from Figure 2.6 it is evident that scale is inversely related to radian frequency of sine functions Sin(t) f=sin(t) ; a=1 Sin(2t) f=sin(2t) ; a=1/ Time(t) Time(t) a) Sine Function with scale a = 1 b) Sine Function with scale a = 1/2 Sin(4t) f=sin(4t) ; a=1/ Time(t) c) Sine Function with scale a = 1/4 Figure 2.6. Sine Function with Different Scales In the case of wavelets the scale works in the same way as in the example of sine waves shown in Figure 2.6. A db2 wavelet was plotted with different scales and is shown in Figure 2.7. It is clear from the plots that a small value of scale results in a more compressed wavelet and thus has a higher frequency content than the mother wavelet.

38 f=ψ(t) ; a= f=ψ(2t) ; a=1/2 Ψ(t) Ψ(t) Time (t) a) Wavelet with scale a = 1 Ψ(4t f=ψ(4t) ; a=1/ Time (t) c) Wavelet with scale a = 1/ Time (t) b) Wavelet with scale a = 1/2 Figure 2.7. db2 Wavelet Function with Different Scales From the Figure 2.7 it can also be concluded that in the wavelet analysis, the scales can be related to the frequency of the wavelet and thus can be related to the frequency of the signal. To compute the frequency related to the scale, the center frequency, F c, of the mother wavelet is computed. The center frequency is determined from the power spectral density (PSD) plot of the mother wavelet. The frequency corresponding to the highest power peak in the PSD plot is assigned as the center frequency of the mother wavelet. For a given wavelet with scale a, its center frequency is also scaled by the factor F c /a. If the sampling period of the data is also considered, then the frequency corresponding to the wavelet of certain scale a is given as: Fc Fa = (2.4) a.

39 25 Thus, a higher scale represents low frequency and a low scale represents a high frequency. The CWT process can be regarded as an integration over the time length of the original signal x(t) multiplied by a scaled wavelet. Equation (2.3) represents the mathematical expression of this process. This process produces wavelet coefficients that are a function of scale and time location. The step by step procedure of CWT process is explained below. 1. Select a mother wavelet. 2. Select the scale range. This step identifies the frequency range of interest because scales are related to the frequencies. 3. Select the scale interval. This step determines the scale values to be used in the CWT process. 4. Take the wavelet with the initial value of scale and compare it to a section at the start of the original signal x(t) (Figure 2.8). Calculate the wavelet coefficient from Equation (2.3). 5. Shift the scaled wavelet to the new time position and calculate the wavelet coefficients (Figure 2.9). This process is continued for the full length of the signal. 6. Scale the mother wavelet according to the scale interval and the scale range. 7. Repeat steps 4 and The wavelet coefficient is then plotted either as a three dimension plot or as a contour plot.

40 26 X Sample# Wavelet of scale a Figure 2.8. Place the Scaled Wavelet at the Signal Origin and Calculate Wavelet Coefficient X Sample# Wavelet of scale a Figure 2.9. Shift the Scaled Wavelet to New Time Location and Calculate Wavelet Coefficient The analyzing wavelet that correlates with the properties of the original time varying signal, x(t), provides a larger value of the wavelet coefficient, or vice-versa. Because the seismic signal varies rapidly in the time domain, its time-frequency plot is expected to have considerable undulation as presented in Figure Figure 2.10(a) presents the three dimensional plot of wavelet coefficients and Figure 2.10(b) presents the contour plot of the same data. Due to undulations in the three dimensional plot, all features are difficult to interpret. However, the contour plot provides an effective way to study all features. Thus, in this research, contour plots were used to study the signals

41 27 rather than three dimensional plots. In Figure 2.10(a), the undulations are plotted as ripples in the contour plot. In the analysis, these ripples are referred as undulations as they are crests and troughs in the three dimensional plot as indicated in Figures 2.10(a) and 2.10(b). Undulations Sample# Scale (a) Three Dimensional Wavelet Coefficient Plot High Coefficient 80 Scale Each light contrast region represents a peak and dark contrast represent trough in three dimensional plot. This feature is referred as undulation in the data analysis Sample# (b) Contour Plot of Wavelet Coefficients Figure 2.10 Three Dimensional Wavelet and Contour Wavelet Plots Low Coefficient

42 A contour plot can be used to extract information both in global time and in the frequency domain efficiently and accurately. To demonstrate the functionality of wavelet transformations, a synthetic signal of known characteristics presented in Figure 2.11 and defined by Equation (2.5) is analyzed. The wavelet coefficient map is generated using the wavelet toolbox of MATLAB 7.0. x(t) = 0 0.0<t<0.2 (2.5) = Sin(40 t) 0.2<t<1.0 = 0 1.0<t<2.6 = Sin(10 t) 2.6<t<3.1 = 0 3.1<t< Amplitude (m) Time (seconds) Figure Synthetic Signal The signal defined by Equation (2.5) consists of two different frequencies of 40 hertz and 10 hertz respectively. Thus, the power spectral density of this signal consists of two spikes at 10 and 40 hertz (Figure 2.12).

43 Power Spectral Density Frequency (Hertz) Figure Power Spectral Density Plot of the Signal given by Equation 2.5 However, the spectrum plot fails to locate these frequencies in the time domain. A continuous wavelet transformation was performed on the Equation (2.5) signal and the wavelet coefficient map is plotted in Figure 2.13.

44 30 Sample # Peak strength region 2 Scale High contrast region represent the presence of non-zero value in signal. Peak strength region 1 Figure 2.13 Wavelet Coefficient Map Figure 2.13 presented two distinct regions of high color contrast that also corresponds to the presence of the non-zero signal in that time range. Also, in the high contrast regions, the maximum color contrast occurs at different scales. In the peak strength region 1, the highest color contrast occurs around scale 71, corresponding to high frequency presence in the corresponding portion of the signal. However, in the peak strength region 2 the highest contrast occurs around scale 120, corresponding to low frequency presence in the corresponding portion of the signal. Thus, it can be concluded from Figure 2.11 that a wavelet coefficient map is able to provide information about the frequency variation in time and can be used to detect reflected waves from any cavity or obstacle that arrives later than the signal from the incident wave directly from the source. In the field, horizontal layers of soil or any obstacles and anomalies reflect incident

45 31 waves. In addition to wavelet transformation, the signal can also be processed through low pass or high pass filters, depending on the signal and site characteristics, to identify the reflected wave data. The wavelet transformation can then be applied to obtain a map, as shown in Figure 2.13, to determine shape and size of any anomalies present in the soil media Wavelet Families In the research the affect of different type of wavelets on the continuous wavelet transformation (CWT) was investigated and was utilized in the development of a protocol for processing of seismic wave data for void detection. The CWT process depends primarily on the selection of mother wavelet. It is a very important step in wavelet analysis because an appropriate mother wavelet will produce the time-frequency plot with distinct features that could be used for analyzing the signal properties. Wavelets are broadly divided into small groups, known as wavelet families. Classification of wavelet families is based on several criteria (Daubechies, 1992). The main criteria are: The support width of the mother wavelet function ψ ( τ ) The speed of convergence to zero of the wavelet functions. The time t or frequency at which function value goes to infinity. The symmetry of the mother wavelet function that is useful in avoiding dephasing of the original signal. The number of vanishing moments for ψ ( τ ) that is useful for compression procedure of signals or images. a,t a,t

46 The regularity of the mother wavelet function ψ ( τ ) that is useful in smoothing the reconstructed signal and for the estimated function in nonlinear regression analysis. Table 2.1 lists several wavelet families that are extensively used in signal and image processing. a,t 32 Table 2.1. Wavelet Families (Daubechies, 1992) Wavelet Family Short Name db sym meyr dmey gaus mexh morl Wavelet Family Name Daubechies wavelets Symlets Meyer Discrete approximation of Meyer wavelet Gaussian Wavelet Mexican hat Morlet wavelet Daubechies Wavelets Daubechies (1992) discussed the property of Daubechies wavelets. The Daubechies wavelets (Figure 2.14) have the highest number of vanishing moments but do not result in optimum smoothness for a given support width. Daubechies wavelets are widely used in solving a broad range of problems, such as self-similarity properties of a signal or fractal problems, signal discontinuities, and so forth. The Daubechies wavelet has a large variation in the properties from order 2 to order 10. Due to large vanishing points and finite supported width the wavelets from this family are expected perform better for seismic wave data.

47 Figure Daubechies Wavelet family (Daubechies, 1992) db2 db3 db4 db5 db6 db7 db8 db9 db Symlet Wavelet Family The Symlet wavelets (Figure 2.15) have the greatest number of vanishing points for a given supported width and are highly symmetric (Daubechies, 1992). Symlet wavelet applications are the same as the Daubechies wavelet applications. Due to very high vanishing points for a supported length, these wavelets are expected to extract minor details of the signal that include noise embedded in the signal sym2 sym3 sym4 sym5 sym sym7 sym8 sym9 sym10 Figure Symlet Wavelet Family (Daubechies, 1992) Meyer Wavelet Daubechies (1992) provides the detail discussion on Meryer Wavlet. Meyer wavelet (Figure 2.16) is orthogonal, biorthogonal, symmetric, and infinitely derivable. The Meyer

48 34 wavelet is widely used for data mining processes and for interpreting electroencephalography signals. The Meyer wavelet can be used to process the seismic wave data, because the shape of this wavelet resembles surface waves traveling in media and thus correlates with the signal properties and produce high resolution time-frequency maps. However, if data is contaminated with ambient noise, correlation will result in undesired high frequency ripples in a time-frequency map Figure Meyer Wavelet (Daubechies, 1992) Mexican Hat Wavelet Mexican hat wavelets are also discussed by Daubechies, (1992). Mexican hat wavelets (Figure 2.17) are computed from the second derivative of the Gaussian probability density function. Since the Gaussian probability density function is symmetric, this wavelet is also symmetric, but not orthogonal. The Mexican hat wavelet can be used for continuous wavelet transformation, but lacks the ability to perform discrete wavelet transformation. This wavelet has small number of vanishing point. Thus, this wavelet is expected to eliminate the noise embedded in the seismic signal data but it might also eliminate some signal details.

49 Figure Mexican Hat Wavelet (Daubechies, 1992) Gaussian Wavelet Family The wavelet functions of the Gaussian wavelet family (Figure 2.18) are the derivatives of the Gaussian probability function. The Gaussian wavelets of even order are symmetric and those of odd order are asymmetric. Like the Mexican hat wavelet, these wavelets can be used for continuous wavelet transformation, but lack the ability to perform discrete wavelet transformation (Daubechies, 1992) and also expected to perform same in analyzing seismic wave data Figure Gaussian Wavelet of Order 1 (Daubechies, 1992)

50 Numerical Simulation of Wave-propagation in Elastic Media Richart, Woods, and Hall (1970) investigated the wave propagation phenomenon in elastic media and determined that wave propagation in elastic media can be approximated in two dimensions by assuming that the wave propagation occurs in one plane and there is no interference from the waves reflected in the lateral direction. This is a valid assumption due to the fact that a point source in an elastic half space creates a hemispherical wavefront with the material particles vibrating either along the zenith or the radial direction of the wave motion. This prevents any interference between the waves propagating in planes through the source and at different azimuth angles (Figure 2.19). Figure Surface Wave Front (Richart, Woods, and Hall 1970)

51 In two dimensions, the equations of motion of an elastic wave can be written as Richart, Woods, and Hall (1970): u u u ρ = ( λ+ 2G ) + G t x y v v v ρ = ( λ+ 2G ) + G t x y where, 2 u + ( λ+ 2G ) x y 2 u + ( λ+ 2G ) x y (2.6) (2.7) ρ is the density of the elastic medium, u = Displacement in x-direction. v = Displacement in the y-directions, t = time and λ,g = Lame s constants. Equation (2.6) and (2.7) is an elliptical, partial differential equation which can be solved using the finite difference method (Kreyszig, 2005). The domain is discretized into finite grids and boundary conditions are applied. Loading is simulated using a point source acting on the surface of infinite stratified elastic media. In wave propagation problems, the element dimensions are chosen by considering the highest frequency for the lowest velocity wave. Large grid dimensions filter high frequencies, whereas very small element dimensions introduce numerical instability and require considerable computational resources (Schechter, Chaskellis, Mignogna, and Delsanto 1994). The time increment is carefully chosen to maintain numerical stability and accuracy. Numerical instability may cause the solution to diverge if the time increment is too large, whereas a very short time increment can cause spurious oscillations, also known as Gibb s phenomenon. Schechter, Chaskellis, Mignogna, and Delsanto (1994) also determined conditions which ensure that finite difference simulation can accurately predict the wave

52 38 propagation in elastic half-space and ensure numerical stability. For numerical stability, the time step, t is chosen by the von-neumann stability criterion. In the case of finite difference equations, this criterion yields: ε t (2.8) 2 2 v l + v t where, ε = lattice or grid size, v l = longitudinal wave velocity, and v t = transverse wave velocity. When the boundary conditions are imposed, the finite difference equation for displacements u and v at time t+ t is given by Schechter, Chaskellis, Mignogna, and Delsanto (1994): u( t+ t,i, j ) = c ( i, j )u( t,i, j ) + c ( i, + c + c + c + c ( i, ( i, ( i, ( i, j )u( t,i j )v( t,i, j ) j )v( t,i j )v( t,i, 1, j ) + c + c ( i, j )v( t,i+ 1, j+ 1) + c ( i, , j 1) + c j+ 1) + c ( i, 14 j )u( t j )u( t,i, 11 ( i, t,i, j ) + c ( i, j )v( t,i ( i, j )v( t,i 1, j+ 1) + c ( i, j )u( t,i, j 1) , j 1) + c j ) + c 15 j )u( t,i j )v( t,i , j ) 1, j+ 1) ( i, j )v( t,i+ 1, ( i, j )v( t,i, j 1) j ) (2.9) v( t+ t,i, j ) + c ( i, j )v( t,i 1, j ) + c ( i, + c + c + c = c ( i, ( i, j )v( t,i, j ) j )u( t,i, j ) ( i, j )u( t,i 1, j 1) + c ( i, j )u( t,i, j+ 1) + c + c ( i, j )v( t t,i, j ) + c ( i, j )v( t,i, + c ( i, j )u( t,i+ 1, j+ 1) + c ( i, ( i, j )u( t,i ( i, j )u( t,i 1, j+ 1) + c ( i, j )v( t,i, j 1) , j 1) + c j ) + c 15 j )v( t,i j )u( t,i , j ) 1, j+ 1) ( i, j )u( t,i+ 1, ( i, j )u( t,i, j 1) j ) (2.10) The finite difference equations (2.9) and (2.10) utilize a central difference scheme in the spatial domain, and leapfrog time iterations in the time domain. To impose continuity of stresses and displacements across interfaces and boundaries of four cells surrounding a

53 39 cross point (i,j), a rigorous cross point formulation makes it possible to use the same finite difference equations by making changes in weights, c(i,j). The c(i,j) are the weights that help to validate solutions at each interior node, as well as boundary nodes, and depend on the material properties of the four cells surrounding the node point (i,j) as shown in Fig (i-1,j+1) (i,j+1) (i+1,j+1) I II (i-1,j) (i+1,j) III IV (i-1,j-1) (i,j-1) Figure Sample Grid and Cells (i+1,j-1) There are many finite difference software currently available that can solve wave propagation equations in two dimensional space. Wave2000 Pro Version 2.2 is one one of these software packages for computational ultrasonics (elastic wave propagation) and utilizes the above-mentioned finite difference scheme for calculating approximate solutions to wave equations in 2-Dimensional domain. Wave2000 computes the full elastic wave solution in an arbitrary two-dimensional domain subjected to specified acoustic sources. The software not only simulates the complete spatial and timedependent acoustic solution, but also simulates measurements in a variety of source and

54 40 receiver configurations. It is user friendly, has an extensive material library and incorporates a wide range of source types that includes line source, point source, and sphere source along with a wide variety of source waveforms. Other features of this software include infinite boundary condition modeling, free boundary condition modeling, and an ASCII export data facility. The software also offers a user friendly GUI and helpfile. Due to such flexibility and wide range of applicability, Wave2000 Pro Version 2.2 was used in this research. 2.7 Summary The exploration of the sub-surface tomography is an important part of planning and designing structures. The currently available techniques for quick and efficient detection of the tomographical features can vary widely in feasibility, cost-to-benefit ratio, applicability, and effectiveness (Dobecki and Upchurch, 2006). Among these techniques, the seismic wave techniques have been found to be successful in determining the subsurface soil properties (Seed, 1957). This chapter summarized fundamentals of wave propagation in elastic media and seismic wave methods currently available for profiling sub surface tomography, including void detection. Also included were the reviews of wavelet fundamentals analysis and different types of wavelets; along with the finite difference method basics that are used for numerically simulating wave propagation in stratified and voided soil media.

55 41 Chapter 3 Testing Program 3.1 Introduction Seismic wave tests require specialized electronic data acquisition and instrumentation common to seismic ground motion testing equipment. In addition, specialized data processing software is needed to process the acquired data. Each component of the equipment and each of the commercially available software packages used in this research is described in detail in this chapter. The data acquisition setup requires a portable computer, a signal analyzer, and a significant number of horizontal and vertical geophones. This chapter includes a description of the data acquisition system, software used for acquisition and data processing, and techniques used in data processing and experimental test setups. This experimental program was designed to measure the vertical response of the ground surface from the seismic tests conducted on the soil box. The seismic tests include refraction test to determine the shear wave velocity distribution of the soil media in the box and the tests conducted on the soil media with and without a void. The data from the latter tests were analyzed to develop a void detection scheme. 3.2 Data Acquisition System The data acquisition system (Figure 3.1) used for the laboratory experiments consists of: (1) Agilent Technologies TM signal analyzer, (2) portable computer, (3) SN4-4.5 Hz digital grade geophones, (4) energy source, and (5) data acquisition software to interface

56 42 the signal analyzer with the portable computer. This data acquisition system is owned by PennDOT and operated by the Penn State University Signal Analyzer A Data Physics Agilent Technologies TM VXI mainframe E8408A signal analyzer was used in the present study. This signal analyzer is a 4-slot, C-size mainframe that contains a one-slot E8491B with an IEEE-1394 PC link and one message-based VXI module. This module allows a direct connection from the portable computer to the VXI mainframe via a standard IEEE-1394 bus card. The VXI mainframe contains two Agilent E1433B, 8 channel, 196 Ksa/sec digitizers and digital signal processing (DSP) modules. The E1433B module is a single slot, C-size, register based VXI module that includes DSP, transducer signal conditioning, alias protection, digitization, and high-speed measurement computation. Figure 3.1 General Layout of the Data Acquisition System Setup

57 Geophones Geophones are highly sensitive instruments used to measure ground motions generated by ground disturbances. A geophone consists of a spring supported coil, surrounded by a permanent magnet. When the geophone case is excited, the magnet tends to remain at rest due to inertia effects. The relative motion between the coil and the magnet generates direct current into the coil due to magnetic induction as it moves through the magnetic field. The current is directly proportional to the velocity of motion. This direct current is measured and analyzed using a digital signal analyzer and is then recorded in the portable storage device. In the present study, Gisco TM SN4 digital grade geophones were used (see Figure 3.2) that are the part of the data acquisition system owned by Penn State University. These are high sensitivity, low frequency geophones that are widely used in seismic tests. The technical specifications of these geophones are presented in Table 3.1. Both vertical and horizontal geophones are used to capture the response of ground particles for vertical and shear impact. A P-wave refraction survey is performed with a vertical impact while the S- wave survey is performed with a shear impact. By combining the results from both tests the properties of the sub surface soil can be determined with more accuracy. (a) Horizontal Geophone (b)vertical Geophone Figure 3.2 Gisco SN4Geophones

58 44 Table 3.1. SN4-4.5 Hz Digital Grade Geophone Specifications Specifications Natural frequency Coil frequency Value 4.5 Hz ± 0.5 Hz With maximum tilt angle of 25 o 375 Ω Open circuit damping 0.60 Sensitivity 28.8 v/m/s Distortion <0.3% Maximum coil excursion Moving Mass Diameter Height Weight Operating Temp. Range 4.0 mm mg 26.0 mm 37.0 mm 77.0 g C to C Energy Source An energy source generates micro-seismic waves in the soil media. Methods include the following: 1. A 4.5 kg to 7 kg (10 lb to 15 lb) sledge hammer is typically used in traditional SASW tests.

59 45 2. A heavy drop weight that is able to generate lower frequency (high wavelength) surface waves is used. The impact energy sources strike either a metallic or rubber plate that serves to engage soil mass at the impact point and distribute the energy to create a body wave rather than localized distorted energy. 3. A steady-state vibrator to generate single frequency waves. In a steady state survey, seismic waves of a single frequency are generated by a vertically oscillating vibrator. The displaced shape of the ground due to steady state vibration can be approximated by a sine curve that can be captured by a vertical geophone array. The wave length of a Raleigh wave can easily be estimated as the distance between two successive troughs and peaks. Once wavelength is calculated, the velocity of surface waves, which is approximately equal to shear wave velocity, is computed using the principles of basic wave mechanics. This shear velocity represents the average property of sub surface zone of depth equivalent to the half wavelength of surface waves. By decreasing the frequency, wavelength can be increased; thus increasing the depth of survey. For a homogenous, isotropic, elastic half space, shear wave velocity is independent of depth, but, for an elastic half space whose properties vary with depth, it is an effective method to find the shear wave velocity distribution along depth Data Acquisition Software A SignalCalc 620 Dynamic Signal Analyzer was used as interface software for the signal analyzer and the portable computer during the experiments. SignalCalc 620 Dynamic Signal Analyzer is interface software for high-speed, industry standard HP VXI digital signal processing hardware. This software was developed by Data Physics

60 46 Corporation and is part of the Data Physics signal analyzer equipment. This software can interface with an unlimited number of input channels and can perform Fourier transforms, real-time order analysis, real-time octave analysis, modal testing, amplitude domain measurements (histograms), probability density plots, modal testing, disk record and playback, and waterfall and spectrogram construction. 3.3 Laboratory Test Set Up A wooden box of dimension 4.5m x 1.67m x 1.37m ( 15 x5 6 x4 6 ) was constructed to simulate a limited test sample of layered medium inside a laboratory. The dimensions of the wooden box are shown in Figure 3.3. (a) Wooden Test Box Layout

61 47 (b) Wooden Test Box Figure 3.3. Wooden Test box Initially, the box was filled in two layers: 1) 0.5m ( 1 8 ) thick bottom gravel layer (#8 Limestone) and 2) 0.76m ( 2 6 ) thick top sand layer to stratify the soil region. The particle size distribution of the sand layer is given in Appendix A. Both layers were compacted using a powered, mechanical compactor. The required material property for the study was shear wave velocity distribution in the soil media as it is required for the numerical simulation model input. Thus, the in-situ refraction test was performed on the full filled soil box to directly determine the shear wave velocity distribution. Other properties of the soil were not determined. That includes in-situ density, saturation, porosity and void ratio.

62 The soil box was initially filled till the intermediate partition (Figure 3.3(a)) and the seismic tests were performed. The tests with this setup were conducted in two sets with geophones at a spacing of 0.15m ( 6 ) and 0.203m (8 ) and a source offset of 0.254m ( 10 ) and 0.23m (9 ), respectively. The data from both test setups were processed using the MATLAB 7.0 programming platform and MATLAB 7.0 wavelet toolbox. Timehistory plots and time-frequency plots for both test setups show that the near field effects such as body wave interference and cylindrically spreading point source dominated the signal, and thus, the arrival time of the three kinds of waves are indistinguishable. The final tests were conducted on the full length of the box, filled in two different material layers to minimize contamination from the near field effects. During preliminary tests, a 7.25 kg (16 lb) sledgehammer was utilized with a steel impact plate as an energy source. This resulted in the generation of unnecessary echo in the soil box and contaminated the signal. The energy source was varied to capture the effect of weight and frequency of impact for testing in a soil box. The best results came from a 7.25 kg (16 lb) sledgehammer and variations of impact force and plate type. A soft impact produced with a small swing of the sledge hammer on a steel plate was used to generate low frequency waves, and a hard impact produced with large swing of a rubber mallet was used to generate a high frequency signal. The impact energy was not explicitly measured but data was analyzed from the final tests to study the properties of the impact. The test setup for void detection is illustrated in Figure 3.4. The data acquisition system used in the study has the limitation of sixteen channels. Thus, the test was setup with 0.305m (1 ) spacing to cover the full length of the box. But the same test setup was utilized to capture the vertical response of the top surface of the soil box with and without 48

63 a void. Thus to make room for the void, four channels were removed. The resulting test set up consisted of 11 channels with a receiver spacing of 0.305m (1 ) from channel one to nine. Channel 10 is separated by 0.91m ( 3 ) from channel 9 and 1.22m ( 4 ) from channel 11, as shown in figure 3.4. A void of 0.46m ( 1 6 ) long, 0.91m ( 3 ) wide, and 0.61m ( 2 ) deep was excavated at a distance of 1.14m ( 3 9 ) from the left edge of the soil box. Initially the void of dimension 0.152m x 0.152m x 0.152m ( 1 x1 x1 ) was targeted. But as the void was excavated, the walls of the void were not stable enough and were collapsing inside. Thus the void was excavated till the walls were stable. The final size of the void was measured and used in the analysis. The void was finally covered with 1/4 plywood and a 4 soil was placed over the plywood (Figure 3.4(c)). The energy source was placed at channel 1 so that the distance between the energy source and void was maximized and near field effect was minimized. 49 Figure 3.4(a). Test Setup Scheme in Absence of Void

64 Figure 3.4(b). Test Setup Scheme for Void Detection Figure 3.4(c). Void Detail (Section 1-1) 3.4 In-situ Shear Wave Velocity Determination: Refraction Test on Soil Box The wave propagation phenomenon was simulated for voided and stratified regions, using the finite difference method in the Wave2000Pro software. The Wave2000Pro software requires shear wave velocity as an input for the numerical model. Thus only shear wave velocity distribution was determined with a refraction test. To increase the

65 51 accuracy of the results the geophone spacing was kept at 0.152m ( 6 ). The data acquisition system used in the study has the limitation of sixteen channels, thus, with the 0.152m ( 6 ) spacing and sixteen channels, half of the box was covered. Two seismic refraction tests were conducted with sixteen channels and a geophone spacing of 0.152m ( 6 ) and an overlap of 0.152m ( 6 ). A total of eight impacts were made in each of the two test configurations with source spacing of 0.91m (3 ). The first six impacts were made within the geophone array spread and the last two impacts were made at a distance of 2 feet from one end. The refraction test was done according to the general procedure set up by Redpath (1973). The details of the test setup for the refraction tests are shown in Figure 3.5. Figure 3.5 (a). Test Setup for Refraction Test #1

66 52 Figure 3.5 (b). Test Setup for Refraction Test #2 3.5 Summary This chapter presents the details of the testing program, including details of the data acquisition and instrumentation system, laboratory test setup for void detection, and setup for the in-situ testing conducted for determining the shear wave velocity of the soil mass in the soil box.

67 53 Chapter 4 Numerical Simulation 4.1 Introduction The numerical simulation of surface wave propagation was completed with a finite difference software program, Wave2000 Pro Version 2.2. The objectives of the numerical study were to simulate the wave propagation phenomenon in stratified and voided elastic media and to investigate the affect of the voids on the vertical response of the stratified elastic media. This chapter is a review of the parameters associated with finite difference time domain (FDTD) simulation of wave propagation in elastic media, and the numerical model used for the simulation of the soil box test. 4.2 Parameters for FDTD Simulation of Wave Propagation Phenomenon The finite difference method is a powerful tool used to solve a large variety of conventional partial differential equations. Due to the simplicity and applicability of this method, finite difference is widely used for solving partial differential equations of wave propagation in the time domain. In this study, Wave2000 Pro Version 2.2 finite difference software was used for numerical simulation. Wave2000 Pro Version 2.2 is a unique software package used for solving computational ultrasonic problems. It provides solutions to a broad range of two dimensional ultrasound problems. With this software, the problem domain and objects within the domain are specified in a PCX image file format. The image data is composed of individual pixels that can have gray levels from 1 to 256 (0-255). Each pixel represents a single finite difference grid and its gray level

68 54 value represents a unique material assigned to that gray level. It is possible to construct objects of any shape and size via the graphical user interface and assign different material properties to these objects. The parameters that govern the ultrasonic simulations are: 1) image size; 2) material properties; 3) boundary conditions; 4) source configuration; 5) receiver configuration; 6) time step scale; 7) maximum frequency. These parameters are briefly discussed below: Image Size Image size determines the magnitude and size of a problem and also determines the computational resources requirement. Image size is determined by two parameters: (1) physical dimension of the problem, and (2) desired image resolution. Physical dimension is the actual size of the problem domain measured in millimeters and image resolution is the number of pixels in one millimeter. Resolution of the image is directly proportional to accuracy of the final results, but higher resolution results in high computational demands; thus, a balance should be maintained between computational resources and desired precision. For geophysics problems, the physical dimension of the problem is huge, as compared with other types of ultrasonic problems. Therefore, in order to match the computational demand of the problem with capabilities of available computational resources, resolution of the image is kept low around 0.2 pixels per millimeter Material Properties The Wave2000 Pro Version 2.2 package comes with a built-in material library that contains details of properties of many materials that are used for general ultrasonic problems. The software also allows for addition of user-defined materials to the library.

69 55 The software requires the material properties in order to calculate longitudinal wave velocity and shear wave velocity, using the relationship shown below: λ+ 2G v p = (4.1) ρ G v s = (4.2) ρ where, λ and G are the Lame s constants and ρ is the material density. For the numerical simulation the shear wave velocity was directly determined by the refraction tests conducted on the soil box Boundary Conditions The user may input boundary conditions within the object, as well as at the external four edges of the object. Three types of boundary conditions can be used: 1. Longitudinal mode fixed: This boundary condition acts as fixed condition for the particle motion in the direction of the wave propagation. 2. Shear mode fixed: This boundary condition acts as fixed condition for the particle motion in the direction perpendicular to the wave propagation direction. 3. Infinite boundary condition: This boundary condition is imposed on any of the external four edges of the problem domain to make that side boundary appear as an infinite medium matched to the material just inside the boundary of the object. Infinite boundary condition is very useful in simulating geophysical problems Source Configuration A source is used to generate ultrasonic disturbance in the problem domain. A source can be placed inside the problem domain or at any external edges. The source waveform

70 56 can be manipulated using temporal functions, including continuous and pulsed sinusoids, exponentially damped sinusoids, and sinusoids with a Gaussian time envelope. An arbitrary source waveform can also be defined that allows incorporating actual ultrasonic waveforms from an experiment into the simulation Receiver Configuration A receiver is used to capture response of the medium at any desired location. Any number of receivers can be defined inside the domain of the problem or at external edges to measure displacement or velocity. Receiver measurements can be saved to file for subsequent processing and analysis. The file contains both longitudinal and transverse displacements made at the receiver location in ASCII format that can be easily imported to a variety of signal processing software packages Time Step Scale A time step scale parameter is utilized to control the time step of the simulation. The software internally computes the time step, based on grid element size and wave velocities within defined materials. However, this time step does not account for changes required due to specific boundary conditions, attenuation settings, source signals, and other model settings. Therefore, to ensure the stability of the simulation, the internally computed time step is adjusted using a time step scale. The actual time step is then determined by the product of the time step scale and internally computed time step Maximum Frequency The maximum frequency parameter is an important parameter to calculate the minimum wavelength and the resolving wavelength. The resolving wavelength and the points/cycle determine the grid size of the numerical model. Maximum frequency is

71 57 calculated based on the highest frequency content of the source signal, which results in the lowest resolving wavelength and highest spectral resolution. 4.3 Numerical Simulation of Wave Propagation in Layered Media Dimension of the problem are 7.2m x 1.5m ( 23 7 x4 11 ). Resolution of the image was fixed at 0.2 pixels/mm to reduce problem size. The shear wave velocity distribution in the soil box was determined using a refraction test conducted in two sets on the soil box. Setup of the refraction tests is discussed in Chapter 3 and results are listed in Chapter 5. The model was divided into eight layers with the shear wave velocity distribution as shown in Figure 4.1. This distribution was established from the output graph of the shear wave velocity from both refraction tests. Figure 4.1. Numerical Model Setup This model simulated three infinite boundary conditions imposed on the left, right, and bottom boundary, and one free boundary condition at the top boundary to simulate the actual ground conditions. The left and right boundaries were treated as an infinite boundary, but, due to limitations of the software in modeling infinite boundary conditions, these conditions were not the perfect infinite boundary condition. Due to this imperfection, the boundaries produced some reflections. To reduced the effect of these reflections on the receivers, the length of the problem was increased from 4.57m (15 ) to

72 (23 ) so that reflections are delayed and had a minimum effect on the receivers. Even though the length was increased, the reflections were not eliminated completely and the effect could be seen in the time-frequency plot of the receivers. The loading pulse was simulated using a point source function acting on the top surface given by Zerwer, Cascante, and Hutchinson (2002): Fbt δ( t ) = (4.3) 2 2 π( t + ψ ) where F b alters the magnitude of the excitation; ψ controls the frequency content of the excitation, and t represents time. Source and receiver locations in the numerical model were the same as the geophone locations in the soil box test (Figure 3.5). The test set up consisted of eleven receivers with a receiver spacing of 0.3m (1 ) from receiver 1 to 9. Receiver 10 is 0.914m (3 ) from receiver 9 and 1.22m ( 4 ) from the receiver 11. The source was at the same location as receiver 1. To insure numerical stability of the simulation, the time step scale factor was established as 0.9. During the simulation the source was active for 2.5ms and total simulation time was 50ms. The source signal was analyzed in the frequency domain and maximum frequency was established at 0.2 Khz, resulting in the grid size of 5 mm and 5 grids/pixel. The center of the void was placed at the same location as shown in Figure 3.4.

73 Summary This chapter summarized the various aspects of numerical modeling of the wave propagation problem in a soil box, using Wave2000 Pro Version 2.2 software. All parameters related to the numerical modeling and their applicability was discussed in detail.

74 60 Chapter 5 Results and Discussion 5.1 Introduction Seismic ground motion data requires specialized interpretation techniques to extract required information about the ground medium because information from the propagation of all types of waves is included. This chapter reviews techniques used in this study to analyze the seismic test data collected from laboratory test in the soil box and a corresponding numerical simulation. This chapter reviews the results from two refraction tests conducted on soil media in a soil box to determine shear wave velocity profile of the soil mass in the box and also the results from the wavelet analysis of the data from the soil box seismic tests. 5.2 Data Processing Data obtained from soil box tests were analyzed using the MATLAB 7.0 wavelet toolbox and MATLAB 7.0 programming platform. Codes were written using the MATLAB 7.0 programming platform to plot the time-history of the signals from all geophones to perform wavelet analysis and to construct time-frequency plots of the geophone data. Data obtained from the refraction test was processed using Seisimager 2D, a data processing software for seismic refraction survey test data.

75 Data Processing Software MATLAB 7.0 Programming Platform and Wavelet Toolbox MATLAB 7.0 is a computing environment and programming language created by Math Works, Inc. MATLAB 7.0 that allows matrix manipulation, plotting of functions and data, implementation of algorithms, graphic user interface creation, and interfacing with programs in other languages. The programming platform comes with a built-in library of functions for typical programming processes that would otherwise require function call codes. MATLAB 7.0 has a powerful base for input/output file processing that makes it very efficient for reading data stored in ASCII format. The MATLAB Wavelet Toolbox is a collection of built-in functions written on the MATLAB 7.0 Technical Computing Environment. This provides tools for analysis and synthesis of signals and images, statistical applications, as well as wavelets and wavelet packets within the framework of MATLAB 7.0. In this study, the toolbox was used to remove noise from the data and to construct a time-frequency plot of the signal to study it in both time and frequency domains simultaneously Seisimager 2D SeisImager 2D from Geometrics, Inc. provides data processing and analysis for refraction tests. It can perform comprehensive refraction modeling using ray tracing for both P-wave and shear wave refraction surveys. The software reads seismic trace data obtained from refraction survey tests in a general format for seismic data analysis, also known as the SEG-2 or SEG-Y format. The signal analyzer exports data in ASCII format that is then converted to SEG-2 format by the program IXSeg2Segy.

76 Data Processing Protocol A step-by-step protocol was developed for data processing to ensure that information regarding the soil medium could be efficiently extracted from seismic test data. The data processing protocol is shown in Figure 5.1. Both numerical simulation and experimental test data were processed using the same protocol. Figure 5.1. Protocol for Data Processing This data processing protocol includes two main steps: 1) removal of noise from the raw data; 2) performs CWT on the processed data. MATLAB 7.0 wavelet based inbuilt

77 functions were used for the noise removal from the seismic data. The second step consists of several sub-steps: 63 i. Select a mother wavelet. ii. Select a scale range and scale interval. Because scales are inversely related to the frequency, this sub-step is based on the interested frequency range. iii. Perform the CWT using the selected wavelet over the selected scale range and interval. Codes were written in MATLAB 7.0 to perform this sub-step. iv. Construct time-frequency plots from the wavelet coefficients calculated from CWT. v. Accept the time-frequency plot if the features such as ripples and undulations in the high and low scale regions are distinct. If the features are not distinct select another mother wavelet and repeat the steps 2-5. The selection of final mother wavelet relies on the user s judgment as explained in sub-step 5 of the second step. Thus, for different applications, different families of wavelets might be more efficient.

78 Data Processing Results In-situ Refraction Survey for In-situ Shear Wave Velocity Profile The refraction tests were conducted on the soil box to determine the shear wave velocity distribution in the media. This property was required for the numerical simulation material model. Refraction test setup details are shown in Figure 3.5(a) and 3.5(b). Seismic data was analyzed using SeisImager 2D. Results for the refraction tests conducted in the soil box are shown in Figure 5.2(a) and 5.2(b). Results show some localized variations in the shear wave velocity profile (Figure 5.2) that may be the result of non-uniform compaction of the soil mass. For the numerical simulation material model input, soil mass was divided into eight layers, with shear wave velocity and thickness, as shown in Figure 4.1. C ft/sec Local shear wave velocity variation 0.0' 1.0' 2.0' 3.0' 4.0' 5.0' 6.0' 7.0' 7.5' Distance from the left edge of the soil box Figure 5.2 (a). Shear Wave Velocity Profile for Refraction Test #1 Conducted on Full Length Soil Box

79 C 65 ft/sec Local shear wave velocity variation 7.5' 8.5' 9.5' 10.5' 11.5' 12.5' 13.5' 14.5' 15' Distance from the left edge of the soil box Figure 5.2 (b). Shear Wave Velocity Profile for Refraction Test #2 Conducted on Full Length Soil Box Wavelet Analysis of the Experimental Data Analysis Using Different Wavelet Families Seismic test data was analyzed using different wavelets from MATLAB 7.0. Wavelet toolbox built-in wavelet families were used to investigate the effect of different types of wavelets on time-frequency maps. Selection of wavelets during the continuous wavelet transformation is an important step in the data processing procedure. If the shape of the mother wavelet is out of phase with the original signal then the different timefrequency plot features (variation of wave strength in scales, time-localization of frequency content) are not distinct (the contours are not clearly visible), resulting in high smoothing. However, if the shape of the mother wavelet is in-phase with the signal, then the time-frequency plot features are distinct and can be interpreted. Often, high smoothing is not desired as it eliminates minor details of signals but no smoothing will

80 c) c) 66 result in unnecessary details due to inherent noise, and thus contaminates the timefrequency plot. To study the effects of different kinds of wavelets on continuous wavelet transformation, channel 6 signal of the soil box test setup with a void (Figure 3.4(b)) generated from 7.25kg (16 lb) sledge hammer) was analyzed with several different wavelets. The time-frequency plots are shown in Figures 5.3(a) through Figure 5.3(e) Ripples in the signal x(t) Sample# a) Signal from Channel 6 Low strength ripples in high scale regions are not clearly visible Sample# b) Time-Frequency Plot of the Signal from Channel 6 Using Gauss 1 Wavelet Low strength ripples in high scale regions are not clearly visible Sample# Time-Frequency Plot of the Signal from Channel 6 Using Mexican Hat Wavelet d) Figure 5.3. Time-Frequency Plot for Channel 6 Generated with 7.25kg (16 lb) Sledgehammer on Soil Box with Void Using Different Types of Wavelets (cont d)

81 67 The peaks in low and high scale regions are not distinct Minor Details e) Time-Frequency Plot of the Signal Sample# from Channel 6 Using db1 Wavelet Minor Details The peaks in both high scale and low scale regions are very close to each other and thus are not distinct Sample# f) Time-Frequency Plot of the Signal from Channel 6 Using Symlet2 Wavelet Clear low strength ripples in high and low scale region. Sample# g) Time-Frequency Plot of the Signal from Channel 6 Using db10 Wavelet Figure 5.3. Time-Frequency Plot for Channel 6 Generated with 7.25kg (16 lb) Sledgehammer on Soil Box with Void Using Different Types of Wavelets The first two time-frequency plots (Figure 5.3(b) and 5.3(c)) were generated using the Gaussian and Mexican hat wavelets. The supported width of these wavelets varies from - to + and has a bell shape. However, the signal from the geophone is localized in time, consists of numerous ripples, and is not smooth. Due to differences in the shape of the original signal and the mother wavelet, the CWT eliminates minor details of the

82 68 signal, and thus high scale (scale ) peaks are not distinct in the time-frequency maps. db1 and symlet2 wavelets have small supported width and large vanishing points for the supported width and their shape resembles the original signal. Due to the similarity between the properties of the original signal and these wavelets, the CWT resulted in minor details in the time-frequency maps including the noise embedded with the system. These details contaminated the time-frequency map and made the data interpretation task more difficult. A db10 wavelet was used in the final wavelet transformation (Figure 5.3(f)) because the db10 mother wavelet shape resembles the shape of the original geophone signal and also the properties of the signal. The db10 wavelet resulted in filtering of small ripples caused by noise in the time-frequency plots and thus all the features of the signals in the high scale and low scale regions are distinct (Figure 5.3(f)). Thus, this wavelet was used in the final data analysis of the signals from soil box test with and without a void Wavelet Analysis of Soil Box Test Data Seismic tests were conducted on the soil box shown in Figure 3.3(b). For these tests, a soft impact produced with a small swing of the sledge hammer on a steel plate was used to generate low frequency waves (frequency 10 hertz). Also, a hard impact produced with a large swing of a rubber mallet was used to generate a high frequency (frequency 500 hertz) signal. A surface wave traveling in an elastic media, with material properties as a function of depth, experiences dispersion and material and geometric damping phenomenon. Material and geometrical damping results in signal power loss that is directly proportional to the distance traveled by the surface wave. In the absence of anomalies

83 69 like voids, surface waves do not encounter an obstruction in the wave path, therefore, any observation made in a time-frequency plot of the receiver signal under such conditions can be marked as a signature of surface wave damped and dispersive behavior. In the setup shown in Figure 3.4(a) for the laboratory test without a void, channel 1 is at the source location and was selected for data analysis because it provides the closet approximation of the impact properties. However, the distance between the source and channel 1 is insufficient to produce any damping or dispersive behavior. Therefore, channel 10 was selected for analysis as it is located at the maximum distance from the source. Thus, seismic waves can experience sufficient dispersion and damping phenomenon before it reaches channel 10 and thus can be studied. Also, channel 4, located near the center of the soil box, was selected for analysis to observe the change in the dispersion and damping behavior as seismic waves travel across the box. The signals from both channels 4 and 10 were analyzed in the time-frequency domain to study the effects of dispersion and damping in order to mark the signature of dispersion and damping behavior. MATLAB 7.0 was used to remove noise from the data, perform continuous wavelet transformation analysis on the data, and construct time-frequency plots. Time-frequency plots were generated with db10 wavelets for scales from 2 to 128 with a scale interval of 2. Time-frequency plots for channels 1, 4, and 10 are shown in Figure 5.4.

84 70 No damp undulations present in this region Sample# (a) Time-frequency Plot of Channel 1 Damped undulation Sample# (b) Time-frequency Plot of Channel 4 Damped undulation Sample# (c) Time-frequency Plot of Channel 10 Figure 5.4. Time-Frequency Plot for Channels 1, 4, and 10 Generated from 7.25kg (16 lb) Sledgehammer on Soil Box without Void Figures 5.4(a), 5.4(b) and 5.4(c) illustrate time-frequency plots of channels 1, 4, and 10 test setups without a void, and were generated using a 7.25kg (16 lb) sledgehammer. Channel 4 and channel 10 signal time-frequency plot show uniform damped undulations

85 71 (see Figure 5.3(b) and 5.3(c)). However, these undulation are absent in the channel 1 signal time-frequency plot (see Figure 5.3(a)). In the absence of any sub-surface anomalies between channel 1 and channel 4 and 10, only dispersion and damping will effect the wave propagation. Thus, it can be concluded that damped uniform undulations in time-frequency plots of the signals from the seismic wave tests is due to dispersion and thus can be marked as the signature of surface wave dispersive behavior. This observation was used in this research to investigate the effect of voids on the signal properties obtained from seismic test on soil box with a void. For the laboratory test with a void (Figure 3.4(b)), the same set of channels (1, 4 and 10) was selected for analysis so that the time-frequency plot of the signal from these channels can be compared for both cases. Channels 4 and 10 are at a sufficient distance from the source so that waves can experience dispersion and damping behavior. Channel 4 is also at a sufficient distance from the void to capture surface wave reflections from the void. MATLAB 7.0 was used to perform continuous wavelet transformation analysis on the data, and construct time-frequency plots. Time-frequency plots were generated with db10 wavelets for scales from 1 to 128 with a scale interval of 2. Time-frequency plots for channels 1, 4, and 10 generated by a 7.25 kg (16 lb) sledgehammer for the test setup with a void are shown in Figure 5.5.

86 72 The strength of signal is distributed from low to high scale. No damp undulations present in this region Sample# (a) Time-frequency Plot of Channel 1 Low strength ripples in high scale region Damped undulation Sample# (b) Time-frequency Plot of Channel 4 No low strength ripples in high scale region as observed in time-frequency map of channel 4 signal Damped undulation (c) Time-frequency Plot of Channel 10 Figure 5.5. Time-frequency Plot for Channels 1, 4, and 10 Generated from 7.25kg (16 lb) Sledgehammer on Soil Box with Void Figures 5.5(a), 5.5(b) and 5.5(c) show channels 1, 4, and 10 time-frequency plot generated with a 7.25kg (16 lb) sledgehammer on the soil medium with a void. The channel 4 signal time-frequency plot shows the signature of dispersion behavior as damped uniform undulations (see Figure 5.5(b)), the same as concluded from the seismic

87 73 test in the soil box without a void. Unique low strength ripples in the high scale (low frequency) region between samples 300 and 700 can also be observed in this timefrequency plot. However, these low strength ripples are not present in the channel 4 signal time-frequency plot obtained from the soil box test without the void (Figure 5.4(b)). Therefore, it can be concluded that low strength and high scale ripples are occurring due to the reflections from the surface from the void because it is the only difference in both test setup and thus, can be marked as the signature of the void-like anomaly. Channel 10 signal time-frequency plot (Figure 5.5(c)) also shows the same damped uniform undulations as observed in the channel 10 signal time-frequency plot (Figure 5.4(c)) obtained from the soil test without the void. However, low strength, low frequency ripples as observed in the channel 4 signal time-frequency plot (Figure 5.5(b)) are absent. From this observation it can be concluded that the void or anomalies do not disrupt the time-frequency spectrum of the signals from geophones placed after the void or anomalies. A final set of tests were conducted on the laboratory soil box test setup with a void. A rubber mallet was used as the energy source. MATLAB 7.0 was used to perform continuous wavelet transformation analysis on the data and construct time-frequency plots. Time-frequency plots were generated with db10 wavelets for scales from 1 to 128 with a scale interval of 2. Time-frequency plots for channels 1, 4, and 10 signal generated by a rubber mallet for the test setup with a void are presented in Figures 5.6.

88 74 The strength of signal is concentrated in low scale region. No damp undulations present in this region Sample# a) Time-frequency Plot of Channel 1 Low strength ripples in high scale region Damped undulation Sample# b) Time-frequency Plot of Channel 4 No low strength ripples in high scale region as observed in time-frequency map of channel 4 signal Damped undulation Sample# (c) Time-frequency Plot of Channel 10 Figure 5.6. Time-frequency Plot for Channels 1, 4, and 10 Generated from Rubber Mallet on Soil Box with Void Apart from the similarities, time-frequency plots of the signals generated using rubber mallets also shows some different features from the plots generated using a 7.25kg (16 lb) sledgehammer.

89 75 Figures 5.5(a) and 5.6(a) presents the time-frequency plots of the signal from channel 1, located at the source, generated by the 7.25kg (16 lb) sledgehammer and a rubber mallet respectively. Under a 7.25kg (16 lb) sledgehammer the major portion of energy lies between 2 to 85, however under the rubber mallet the maximum energy lays between scales 2 to 57. Thus, impact from the rubber mallet produces waves with a major portion of energy in the high frequency (low scale) region. However, the high frequency waves have a higher attenuation rate than the low frequency waves (Zerwer, 2002). Thus, the dispersion phenomenon decay at a higher rate in the plots generated using a rubber mallet than in the plots generated using a 16 lb sledgehammer (Figure 5.5(b) and Figure 5.6(b)). Channel 4 signal time-frequency plot generated by the rubber mallet (Figure 5.6(b)) shows the same characteristics as the channel 4 signal time-frequency plot generated by the sledgehammer (Figure 5.5(b)). Also, these low strength, high scale ripples are absent from the channel 10 signal time-frequency plot generated by the rubber mallet (Figure 5.5(c)) and time-frequency plot of channel 10 signal generated by the sledgehammer (Figure 5.5(c)). Thus, time-frequency plots of channel 1, 4 and 10 signal generated with a rubber mallet on the test setup with void (Figure 5.6(a), 5.6(b) and 5.6(c)) confirm the conclusions from the data analysis of the signals generated with a 7.25kg (16 lb) sledgehammer. From this data analysis, it can also be concluded that the dispersion or damping behavior signature and void signature in the time-frequency domain do not change with source weight Wavelet Analysis of the Numerical Simulation Data Seismic tests conducted on the soil box were simulated using Wave2000 Pro Version 2.2 and the receiver data was processed using the same protocol that was used for the

90 76 experimental test data. Time-frequency plots were generated with db10 wavelets for scales from 1 to 128 with a scale interval of 2. Plots for receivers 1, 4, and 10 are shown in Figure 5.7. No damp undulations present in this region Sample# (a) Time-frequency Plot of Receiver 1 Damped undulation Low strength ripples in high scale region Reflections from the boundary Sample# (b) Time-frequency Plot of Receiver 4 Reflections from the boundary No low strength ripples in high scale region as observed in time-frequency map of channel 4 signal Sample# Damped undulation (c) Time-frequency Plot of Receiver 10 Figure 5.7. Time-frequency Plot of Receivers 1, 4, and 10 Generated from Numerical Simulation