Use of Surface Wave Techniques for the Identification of Shallow Rock

Knowing the depth to bedrock is important in designing and constructing foundations for buildings and transportation infrastructure. Rock is typically a strong and competent foundation material, however if it is close to the ground surface it can be costly to remove. This is especially true if the presence of shallow rock is not known until construction. In many transportation projects where geotechnical borings are widely spaced along a road alignment, areas of shallow rock can be easily missed until construction of drainage structures beneath the road. More research is needed on the viability of cost effective tools to identify the presence of shallow rock before construction. Non-destructive evaluation (NDE) techniques to characterize the stiffness of soils may be a good tool for this problem. Spectral Analysis of Surface Waves (SASW) is a wave propagation method in which vertical shear wave velocity profiles and elastic moduli of subsurface layers of soil and rock can be estimated. The profiles are obtained from the analysis of surface wave data, usually generated from a falling weight and measured by an array of two or more geophones. The objective of this thesis is to evaluate the efficiency of the SASW system for use in transportation projects in Rhode Island. It will focus on the identification of shallow rock for aid in construction of drainage structures. SASW tests were performed at five different locations. The resulting shear wave velocity profiles were analyzed and evaluated for the following: 1) identification of shallow rock, 2) global vs. array approach for modeling the dispersion curve and 3) influence of the initial layer thickness. The results showed that it was possible to identify the presence of rock layers with the SASW system. However, the SASW system was not that accurate in identifying the depth to rock. A key lesson from this study is that the process to estimate the shear velocity requires considerable experience and personal judgment. There are many factors that affect the prediction of shear wave velocities, including the selection of data for analysis (masking), the type of approach for modeling the dispersion curve, and the steps used in the inversion.


18
Example of seismic data for Line 2, shot at 240 ft. The first arrival refraction data for the four lithologies are shown by the purple, orange and green, and blue lines  . . . . . . 32

21
The MASW derived 2-D S-wave velocity field at the Olathe, Kansas site    Scheme of the forward and reverse testing with the CRMP geometry

Objectives
The first objective of this study is to evaluate the effectiveness of the SASW system for the identification of shallow rock. The shear wave velocity of rock is typically 5-10 times the velocity of soil and may be identifiable in the upper few meters of a soil profile. Four locations at which shallow rock exist will be tested and compared to existing boring logs and previous test results.
In addition to the two main objectives, an ongoing project at the University of Rhode Island (URI) of collecting shear wave velocity data using SASW on coastal beach sites in Rhode Island where coastal erosion occurred is continued in this study. Three beach sites will be examined. At one of these sites, previous SASW tests have been conducted by  which gives the opportunity to compare the results and identify possible changes. The aim of the data collection is to obtain insight into erosion at these sites.

Organization of Thesis
The thesis is organized to give on the one hand an overview about theoretical information of seismic investigation methods and their application in the investigation of shallow rock and on the other hand introduces the procedure and results of tests with the Spectral Analysis of Surface Waves (SASW) system.
Chapter 2 includes a literature review about seismic wave theory and three seismic investigation methods. The SASW system is introduced in this chapter.
Chapter 3 focuses on the application of the three seismic investigation methods for the identification of shallow rock. The commercial SASW system by Olson Instruments, Inc. is discussed in detail in Chapter 4 which includes the equipment and procedure used in the field as well as the software used for data processing. Chapter 5 presents information about the different sites at which tests were conducted.
Details about the reason of the selection, the location and the site conditions are provided. The test results are presented in Chapter 6. The last chapter, Chapter 7, summarizes and compares all the results.

CHAPTER 2
Literature Review

Elastic Wave propagation
When a force is applied to a body, there are resulting stresses (i.e. compression, tension, or shear) and strains (i.e. volumetric, shear) .
In an elastic material, the relationship between stresses and strain is often linear.
Due to their complex mechanical behavior, soils and rocks are generally not described as linear elastic materials. However, for small and rapidly applied forces, a linear elastic constitutive model may be appropriate. In these cases, the applied forces propagate through the material as stress waves. Two different kind of waves are generated, body waves and surface waves. While body waves can propagate in infinite and unbounded mediums, surface waves only exist if a free surface or surface boundary is defined. In the following sections, body and surface waves will be explained in more detail.

Body Waves
Body waves can travel in a homogeneous, infinite and unbounded continuum such as the interior of the earth. Two different kind of body waves exist, primary waves (P-waves) and secondary waves (S-wave). P-waves, also known as compression or longitudinal waves, propagate in compression or extension movements . The particle motion of P-waves travel in the same direction as the wave propagation. The particle motion of S-waves, also known as shear or transverse waves, is perpendicular to the direction of propagation. Since fluids and gases are not able to support shear stresses, shear waves only propagate in solid materials. Both wave motions are illustrated in Figure 1.   The velocity of propagating body waves depends on the density and the elastic properties of the medium. These parameters can be characterized by the density ρ and Lamé s constants λ and µ (or shear modulus, G). P-waves are the fastest traveling body wave. Since P-waves travel through solids by compression and soils and rocks are nearly incompressible, the waves can propagate at relatively high velocities. Additionally, P-waves travel through pore water due to its incompressibility.
In contrast, S-waves can not travel through water and the particle movement is orthogonal to the direction of propagation. Hence, the velocity of the S-waves is slower. The velocities of the P-waves (v P ) and S-waves (v S ) can be obtained using

Surface Waves
In a elastic half-space, waves can travel along the medium's surface in addition to the propagation within the body of the medium. Surface waves are generated by the interaction between compression and shear waves (P-and S-waves) and propagate along the interface between layers. Since shearing can only occur in solids, at least one of the two medias forming the interface has to be a solid Rayleigh waves, named after Lord Rayleigh who first investigated them in 1885, result from the interference of P-and S v -waves (vertical shear waves) with the medium's surface. Figure 2 shows the particle motion associated with Rayleigh waves.
Figure 2: Deformations produced by Rayleigh Waves (top) and Love-waves (bottom)  Near the surface, the particle motion is elliptical and retrograde with respect to the direction of propagation . Particle motion decreases with increasing depth as can be seen in Figure 3. The energy of Rayleigh waves spreads cylindrically from a point load at the surface, which leads to a reduction of the amplitude with travel distance. However, the rate of geometric attenuation is much lower than for body waves whose energy distribution occurs in a hemi-spherical direction. Therefore, for distances of one to two wavelengths from the source, the wave fields are dominated by Rayleigh waves and body waves can be neglected . Orthogonal to the propagation direction no energy is transported, which leads to an exponential decay of the displacement field and wave amplitude ( Figure 3). Within a depth of one wavelength into the soil, most of the energy associated with surface wave motion dissipates. Soils are inhomogeneous, and the material properties (e.g. density, shear wave velocity) vary with depth . Equivalent to surface waves in homogeneous soils, waves with long wavelengths travel deeper into the soil than waves with short wavelengths. However, since the soil is inhomogeneous the velocity with which each wavelength is propagating depends on the mechanical properties of the respective layer ( Figure 4 (right)). Therefore, the different frequency components of the surface wave travel at different velocities, and these are called phase velocities.
This phenomenon is called dispersion, and the relationship between frequency and phase velocity of a Rayleigh wave is called a dispersion curve.

Seismic Refraction
The seismic refraction method is the analysis of artificially created seismic waves. It comprises sending an impulse of energy into the ground which leads to a vibration of particles in the direction of seismic wave propagation and a transmission of mechanical energy . The propagating body waves (mainly P-waves) get reflected and refracted at the subsurface interfaces and return to the surface where their arrival time will be recorded by a line or array of geophones laid out at the surface.
The method is based on Snell's law and the fact that the subsurface consists of layers with different elastic properties. P-waves that are approaching an interface at a slanting angle, termed obliquely incident, get reflected and refracted ( Figure   5). The refracted ray travels through the lower layer with a change of direction.
This phenomena is analogous to the behavior of a light ray obliquely incident on the boundary between for example air and water . In Snell's law the ray parameter is defined by p = sinθ 1 /v, where i is the angle of inclination of the ray and v the velocity the ray is traveling with. Since the ray parameter stays constant over the depth, the following assumption can be made: Figure 5: Snell's law of refraction and reflection  The seismic refraction test uses an impact source to generate the seismic waves and geophones in an array to register them in defined distances. Figure 6 illustrates a schematic diagram of a seismic refraction test in a two-layered model.
Additionally, the propagation path of the seismic waves can be seen. The seismic waves can reach the receivers in three ways with different arrival times and travel paths during a test. Figure 6: Direct and refracted wave rays  The first one is the direct wave which travels straight along the surface with a constant velocity (here v 1 ). At a distance x the travel time can be computed with: In the second way, the seismic waves get reflected at the interface and travel back to the surface. The calculation of the travel time is only dependent on the velocity of the first layer but slightly more complicated than for the direct wave.
It can be determined with the equation of a hyperbola: The third wave form which reaches the geophones is the refracted or head where t i is the intercept time given by: All travel times can be plotted in travel-time curves or time-distance curves. Figure 7 shows plots of the direct and refracted wave. The travel time of the reflected wave is not shown because it is only of minor interest since the distances are so large that the reflected wave has merged with the direct wave .   As mentioned before, the travel time of the refracted wave is divided into two oblique segments. One segment is traveling at v 1 , a lower velocity, and the other one traveling horizontal segment at a higher velocity, v 2 . With increasing distance x, the horizontal ray of the refracted wave traveling at v 2 encounters the possibility to overtake the direct wave traveling at v 1 . Hence, the refracted wave arrives at the receiver before the direct wave. The offset at which the direct waves will be overtaken by the refracted waves is referred to as x cross . In a distance greater than x cross the refracted waves might be recorded first at the receiver Typical applications for the seismic refraction method include the following (RSK Geophysics, 2013) (Geometrics,

Spectral Analysis of Surface Waves
The most commonly used surface wave for the SASW method are Rayleigh waves. By measuring the Rayleigh waves with at least two receivers, typically geophones, the SASW method can determine shear wave velocity profiles of geotechnical sites. SASW tests are based on a two-receiver configuration .
The distance between the two geophones and the distance to the impact source have to be specified. The whole process to create shear wave velocity profiles can be divided into three main steps: Acquisition, Signal processing and Inversion processes.

Acquisition of experimental data
In the first step (acquisition) the surface waves will be generated by an impact source, monitored by receivers and the signal data recorded by dynamic signal analyzer. A typical set up can be seen in Figure 8.  For the SASW method, two receivers are used to measure the propagating surface waves. The most commonly used receivers are vertically orientated accelerometers or geophones. The geophones are connected to a dynamic signal analyzer to record the measured data. The geophones have to be set up in a linear array with a certain spacing between each other and the source and the first geophone. Since it is more reliable to measure waves with shorter wavelengths with smaller spacings and waves with longer wavelengths with bigger spacings, the spacings have to be changed within the SASW testing.
Two different set-up configurations for SASW testing exist: 1) common receivers midpoint geometry and 2) common source geometry ( Figure 10). For the common receivers midpoint geometry (CRMP), the spacing between the two geophones is adjusted around a fixed point located in the middle of the geophones.
In this case the position of both geophones and the source change with increasing spacings. In the common source geometry set-up the source is fixed to one location and only the two geophones change their position with increasing spacing.
Previous studies by  investigated the effect of the two set-up configurations and suggested that the common receivers midpoint geometry yields more reliable results. Therefore, the common receivers midpoint geometry was used for all tests in this study.

.3.2 Signal Processing
From a SASW test a time signal is recorded for each receiver spacing. The receiver closer to the source will record the signal earlier than the receiver located further away which leads to a time difference between them. The generated spectrum of Rayleigh waves consists of a wide range of frequencies which affect different parts of the soil profile . In the second step (processing), the time signals of each receiver spacing are transformed into the frequency domain and the different frequency components are separated using Fourier analysis. For each frequency f, the phase difference φ(f ) between the receivers can be calculated.
Following, the travel time t(f ) of each frequency between the two receivers can then be obtained by the following equation: The phase velocity of the Rayleigh waves depends on the travel time and the distance between the receivers (∆d=d 2 − d 1 ) and can be calculated by The wavelength of the considered frequency can be obtained by The phase velocity and wavelength are determined for each frequency component of the Rayleigh wave. The results are plotted in the form of a f-k spectrum (frequency vs. wavenumber) and a so called dispersion curve (velocity vs. frequency or velocity vs. wavelength). For each spacing an individual dispersion curve is generated. Subsequently, a single composite dispersion curve from all individual curves is created. Figure 11 and 12 show example plots of dispersion curves.  To obtain the shear wave velocity from the phase velocity of the Rayleigh waves a Poisson's ratio has to be assumed. The Poisson's ratio is defined as the "ratio of transverse strain to the axial strain in an elastic material subjected to a uniaxial stress" . The ratio between the velocities of longitudinal waves (or P-waves, V P ) and transversal waves (or S-waves, V S ) can be expressed in terms of the Poisson's ratio.
where: ν =Poisson's ratio Due to the dependency of the surface wave or Rayleigh wave velocity on the two body wave velocities, a ratio of surface wave to shear wave velocity can be defined as a function of the Poisson's ratio . The variation of the V R /V S ratio with the Poisson's ratio can be seen in Figure 13. For a Poisson's ratio ranging from 0 to 0.5, the ratio V R /V S varies from 0.862 to 0.955. A value of 0.92 was defined by  as typical value for ratios between the surface waves velocity and shear wave velocity.

Inversion Process
The last step for the method is the inversion process to evaluate the properties of the soil layers. A theoretical dispersion curve is assumed and iteratively adjusted with respect to the layer thickness, density, Poisson's ratio, and shear wave velocity until it fits the experimental dispersion curve.
To obtain the theoretical response of the soil due to an impact, the stiffness matrix approach by Kausel and Roësset (1981) can be applied. This approach can be adopted to homogeneous and layered systems.
In case of a homogeneous profile the subsurface can be represented by a halfspace with constant stiffness properties . The stiffness matrix [K] for a half-space can be obtained by the following equation: [ In a inhomogeneous or layered subsurface the stiffness properties vary with depth and layer. Hence, the stiffness matrix relates the displacement at the bottom and top of every layer to an applied load at every interface. The stiffness matrix for only one single layer can be expressed by: Further equations for each element can be found in , Kausel and Roësset (1981) and Kausel and Peek (1982). To obtain a dispersion curve out of the approach for homogeneous and layered subsoil, the determinant of the stiffness matrix has to be set to zero and the equation has to be solved for the Rayleigh wave velocity (V R ). Since the Rayleigh wave velocity is mostly dependent on the shear wave velocity, it is an suitable indicator of shear stiffness .
As soon as a matching theoretical dispersion curve to the experimental dispersion curve is obtained, a shear wave velocity profile over the depth corresponding to the assumes shear velocities can be determined. The whole process of the SASW method is illustrated in Figure 14. Schematic Representation of SASW Measurement Process

Typical Applications
The SASW system can be applied to many different purposes. The following applications are suggested by Olson Instruments Inc. (2012) and (2013)

Multi-Channel Analysis of Surface Waves
The Multi-Channel Analysis of Surface Waves (MASW) system was developed by Choon Byong Park at the University of Kansas in 1995  and first introduced in the journal Geophysics in 1999 . Similar to the SASW system, it is also used as a seismic survey method to evaluate the the elastic properties of the ground for geotechnical engineering purposes . To develop shear wave velocity profiles using the MASW system, the same steps used in the SASW approach are followed: 1) Acquisition, 2) Signal processing and 3) Inversion process.

Acquisition
As the name implies, the MASW system uses a series of receivers (usually twelve or more ). Therefore, the whole range of investigation depth can be covered with just one set-up ( Figure 15). The receivers are spaced evenly along an array and the spacings do not have to be changed during testing.  defined the following recommendations for the geophone spacings during a MASW test.
The spacing between the geophones (dx) should be smaller than the one tenth of the maximum investigation depth (Z max ): Moreover, the first geophone closest to the impact source should have a spacing greater than one half of the maximum desired wavelength (λ max ) from the source: The total array length of geophones (X) is defined as the distance between the first and the last geophone. The following condition should be considered: The last recommendation by  covers the total required number of seismograph channels (N ) to investigate the whole depth of interest in just one survey. If the condition can not be met, more surveys are necessary. In this case the total length of the geophone array should be greater than the depth of investigation.
Different types of sources can be used to generate the surface waves. The most common ones are impulsive seismic sources like sledge hammers ( Figure 15) or vibratory sources like Mini-Vibroseis. In a MASW test the spacing between the receivers is fixed and does not have to be changed during the test. Compared to the SASW system, where only two receivers are used and the spacings have to be changed multiple times, the MASW is a more time efficient method.

Signal Processing
Signal processing in MASW testing consists of the same steps used in the SASW testing. However, the approach to calculate the dispersion curves differs.
Here, the transformation theory proposed by  is applied.
Similar to SASW testing, the measured data are recorded as time domain signals u(x, t). To transform them in into frequency domain signals U (x, w) the Fourier transformation is used: Furthermore, the frequency domain signal can be expressed in terms of the phase and amplitude spectrum, P (x, w) and A(x, w). Since the phase spectrum contains information about the attenuation and divergence of the surface wave it can be expressed with regard to φ = w/c w where w is the frequency in radians and c w is the phase velocity. Therefore, the frequency domain signal can be defined as follows: In the next step the following integration transformation is applied to U (x, w) to obtain V (w, φ). It can be interpreted as the summation over offset of wavefields of a frequency after applying an offset-dependent phase shift .
Dispersion curves can be obtained by transforming V (w, φ) into I(w.c w ). Figure 16 shows an experimental dispersion curve, generated by  with the transformation theory.

Inversion Analysis
An inversion analysis is used to generate a shear velocity profile from the dispersion curve. For this, a theoretical dispersion curve is established. Similar to the SASW method, the shear wave velocity can be obtained from the best fit between the experimental and theoretical dispersion curves. An example shear velocity plot computed by  with the software SurfSeis is displayed in Figure 17.

Typical Applications
MASW testing is a seismic survey method, used for geotechnical engineering site classifications. It can also be applied for the following procedures: 1. Void mapping 2. Identification of bedrock 3. Identification of abandoned mine locations 4. Identification of bedrock fracture zones

Summary
Compared to each other, the three seismic methods, seismic refraction, SASW and MASW, have specific advantages and disadvantages.
Advantages of seismic refraction are its cheap, easy and fast data acquisition and processing. Using the travel time to of the propagating waves in the soil, it is possible to pick up distinct transitions between soil layers with different densities.
Disadvantages are for example the large source-receiver distance that is required and that only the first arrival of the wave is considered.
The main advantage of the SASW system is its simplicity in the data acquisition. The high amount of uncertainty and low accuracy in the data processing and analysis is a big disadvantage of the system.
For the data acquisition with the MASW system only one array of geophone is needed, which makes the collection of data very time sufficient. However, multiple receivers have to be used, which makes the MASW system more expensive. The main advantage of the MASW system is the long experience with multi-channel data processing from oil explorations . More accurate and faster results can be obtained. Additionally, it is possible to visualize the results in 2-D shear wave velocity maps.

Investigation of Shallow Rock using Seismic Methods
In this chapter, the suitability of seismic refraction, SASW, and MASW for identifying shallow rock is investigated from a review of the literature. Table 1 shows typical values of shear and compression wave velocities, bulk density, and Poisson's ratio for a range of materials relevant to this study . Table 1: Typical values of shear wave velocity and other properties for a variety geotechnical materials relevant to this study  3.1 Identification of Shallow Rock 3.1.1 Seismic refraction Seismic refraction has been used in several studies for the identification of bedrock,  and .
The aim of the research conducted by  was to investigate the depth of bedrock in Calumet County, Wisconsin using seismic refraction. In previous geotechnical investigations using augers and Geoprobes, a layer of very hard till within the first three feet was misinterpreted as bedrock. Due to the presence of gravel and cobbles in the till layer, hand augers and Geoprobes could not be used for the determination of bedrock depth.
Seismic refraction tests were performed at ten locations with arrays of 48 geophones with a 10-foot (3 m) spacing. Figure 18 shows an example of the data collected at one array with the source located 240 feet along the array. The vertical motions detected by each geophone can be seen as wiggles in the plot.
Additionally, the first arrival times of each layer are marked in red, orange, green and blue lines. An analysis of the data using Seisimagertm by Geomix led to plots as demonstrated in Figure 19. To check the accuracy of the seismic refraction results, backhoe pits were dug at two locations along the array. The differences in the depth of bedrock between the pit and the seismic refraction were only about two feet which supported seismic refraction as a suitable method for the identification of bedrock. However,  additionally tried to map shallow rock layers with less success. Using the same set-up described above, the method overestimated the depth of bedrock. It is likely that a decrease in geophone spacing would have improved the resolution at shallower depths.

SASW
The SASW system is suitable for soil characterization, but has not been used often for the identification of shallow rock or bedrock.  performed a study relating Rock Quality Designation (RQD) with shear wave velocity which included twenty SASW tests on granitic rock and four SASW tests on a cut hill slope of metasedimentary rock to characterize the rock mass at these sites. In the first step Rayleigh waves were generated, measured and processed. WinSASW 3.1.3. was used for the inversion process and to interpreted shear wave velocity profiles ( Figure 20).  assumed shear wave velocities of 366 -610 m/s for highly weathered rock and 610 -2743 m/s for slightly/moderately weathered rock. In the second step the Rock Quality Designation (RQD) value was correlated with the shear wave velocity of intact specimens in the lab and field measurements by:: with:     Summarizing, the results from the surface wave data showed a high accuracy with only less than 1 ft of difference to the results determined through drilling.
Additionally, the MASW method showed an insensitivity to cultural obstacles and noises created by traffic, electrical and mechanical noise from industrial facilities or drilling.
The focus of the study conducted by  was the detection of rock and soil instability zones using hybrid seismic surveying and the MASW approach.
The test site was located in a village in Switzerland, that experienced a sinkhole collapse in a residents' yard. In both test methods the same data acquisition scheme, consisting of a long array of receivers, was used. To cover the area of the sinkhole and be able to detect more instability zones, tests were conducted along three lines ( Figure A.1, Appendix A). The length of each line differed and was adjusted depending on the area and depth of interest. The receiver station spacing also depended on the depth of interest and it was recommended not to exceed 1/50 to 1/30. Using these two rules, the number of receivers was determined. In addition to the seismic transects, two wells were drilled to verify the test results.
Their locations can be seen in Figure    Even though the results showed similarities to the results of the hybrid seis-mic surveying and the well data, it was recommended by Frei (2012)  CHAPTER 4

SASW System
In order to perform the tests for this study a commercial SASW system was provided by Professor James Kaklamanos of Merrimack College. The SASW system was developed by Olson Instruments and consists of several basic components.
The most important components are the following: 1) NDE-360 platform (spectrum analyzer), 2) a pair of 2 Hz geophones, 3) a pair of 4.5 Hz geophones and 4) an impact source (e.g. sledge hammer). All four components can be seen in Figure   23 and Figure 24. According to Olson Instruments, two different SASW configurations are available with their equipment: SASW-G and SASW-S. SASW-G is the geotechnical system and used to assess material properties of soil and rock.
SASW-S is mostly applied to investigate material stiffness and conditions of structures and layer thickness. However, at the time of this study Olson Instruments had not developed the SASW-G system, so only the SASW-S system was used.

NDE-360 platform
The NDE-360 platform is used for data acquisition, initial analysis and display of the data in both the time and frequency domains. To perform a SASW test, the platform has to be properly configured. Although only the SASW-S configuration can be used (Figure 25), it can be adjusted so that geotechnical tests can be performed. In the following sections the different settings and parameters will be explained in detail.    The channel setup at the bottom of the screen (26) shows how many geophones are connected and which channels will be used. The geophone closer the impact source should be connected to the Trigger Channel (TRIG), which is normally set to channel 1.

Figure 26: Parameter setup on NDE platform
As soon as all parameters are adjusted, the SASW test can be conducted.
Once the test surface gets impacted by the source, data will be collected and visualized on the NDE platform screen. Figure 27 shows the screen of the NDE platform during the testing process. The top plot displays the signal in the time domain (amplitude vs. time) measured at the first geophone. The bottom plot shows the phase difference between the two geophones. Each measurement has to be accepted or rejected based on the following two aspects. First, the plot of the phase difference should show a clean saw tooth pattern, as it can be seen in Figure   27. Second, the scale factor of the geophones should lie within a reasonable range.
It represents how strong the recorded signal is. A high scale of around 90 % implies that the signal is very strong and may be clipped. If a low scale of around 35% or less was measured, the signal might not have a good quality and background noise was recorded. A scale of around 75% is preferred to get records with clear saw tooth pattern. To achieve the desired scale the strength of the impact or the gain can be adjusted. If both aspects are satisfied, the data should be accepted. The procedure will be repeated multiple times for each spacing. The number of repetitions is defined by the number of records in the parameter setup. For each spacings an averaged signal is created based on the number of records measured. Therefore, it is desirable to produce similar looking records. The coherence function of the averaged record will be shown after all records of one spacing are accepted. A good correlation with a value close to unity is desired and means that the recorded signal is not affected by background noise . Figure   28 illustrates a measured signal with good coherence. The recorded signals are processed using two different programs: WinTFS and WinSASW, both provided by Olson Instruments Inc. In the first program, WinTFS, the collected data gets windowed (time domain filtering) and reviewed.
Records that show poor quality can be rejected. It is also possible but not mandatory to create dispersion curves for each spacing of the geophones. Afterwards, the reviewed records are imported into the second program, WinSASW. Here, a experimental dispersion curve from the recorded data is generated and a shear velocity profile of the site is estimated by an inversion analysis.

WinTFS
In WinTFS, all collected records from each spacing can be reviewed. Similar to the visual inspection on the NDE platform during the SASW testing, each record can be accepted or rejected. For each spacing a final averaged record will be produced in the end. Additionally, it is possible to window the data. In this process the parts of the record which are not related to the surface wave and do not carry relevant information should be eliminated. Olson Instruments Inc. (2012) recommends no or exponential windowing for SASW-G testing. The exponential windowing should be used with decay factor of 200 or 500. The decay factor is the exponent of an exponential function and represents how fast the signal decreases and gets cut off. Hence, a higher value leads to a faster decrease and cutoff than a lower value.
The aim of the review is to generate an average record out of similar separate records with a good coherence. Figure 29 shows the window of WinTFS with an exemplary output. The top two plots display one measured signal from each geophone in the time domain. The middle graph shows the coherence function of the averaged signal from all accepted measured signals and the bottom graph illustrated the phase difference. Records which lead to a bad coherence should be rejected and not included in the averaged signal. WinTFS is also able to generate dispersion curves from the averaged signals. However, the averaged signal will be imported into WinSASW for the process.

WinSASW
The process to generate a shear wave velocity profile in WinSASW is divided into three main steps. First, irrelevant or scattered data is removed through a process called masking. Second, an combined experimental dispersion curve from the dispersion curves of each spacings is compiled. Third, a theoretical soil profile is assumed and by using an inversion analysis, it gets iteratively adjusted until it's theoretical dispersion curve matches the experimental dispersion curve. With the theoretical soil profile and dispersion curve, a shear wave velocity profile can be determined.
The averaged signals from WinTFS can be uploaded in form of transfer functions into WinSASW. For each spacing a .hyx file has to be uploaded. To be able to distinguish between the different files later on, the files should be named with respect to the particular spacing. In addition, the spacing between the source and the first geophone as well as between the two geophones has to be specified before the file is loaded into the software. After all files are uploaded, masking of the data can begin.

Masking
The first task to generate a dispersion curve from the imported records is to choose which portions of the phase spectrum (phase angle vs. frequency) will be used for further analysis. This procedure is called masking (i.e. eliminating).
Areas within the record get selected or eliminated based on the following criteria: 1. Masking out areas outside the frequency range of interest (based on the geophone spacing, Table 3)  .
3. Masking out areas with backwards sawtooth pattern  4. Areas with low Gabor spectrum frequency have to be eliminated 5. Masking out the near field, defined by λ ≤ 4 * R d where R d is the radius of the geophone (R d = 3.5cm for 4.5 Hz geophone and R d = 5cm for 2 Hz geophones)  6. Masking out area defined by λ ≥ 2 * d where λ is the wavelength and d is the spacing  Additionally to the mentioned masking criteria, the phase spectrum has to be unwrapped. The plot of the frequency response in WinSASW in Figure 30 shows as a wrapped phase with the phase ranging from ± 180 • . However, to The process of masking and the identification of jumps is the part of the postprocessing which has the highest impact on the evaluation of a dispersion curve and therefore on the calculation of the shear wave velocity profile. A high amount of personal judgment and experience is necessary for the masking process which can lead to a source of mistakes and uncertainties.

Dispersion Curve
The second step of the post-processing is the calculation of a composite experimental dispersion curve for each geophone spacing. The following equation using the unwrapped phase spectrum and the receiver spacing is applied: WinSASW plots the composite dispersion curve for each receiver spacing in a different colors or pattern. A dispersion curve which does not match into the course of the other curves can be removed. Figure 32 shows an example of composite experimental dispersion curves.

Inversion Analysis
The inversion analysis in WinSASW to evaluate the shear wave velocity profile from the phase velocity dispersion curve determined in SASW testing is based on the maximum likelihood method . In the procedure the best match between the experimental and a theoretical dispersion curve is to be determined. The theoretical dispersion curve is created by the response of a soil model to an impact established with dynamic stiffness matrix method. A description of the method can be found in Chapter 2.3.3.
The first step of the inversion procedure is to define a soil profile which characterizes the investigated depth of the test site. Two different approaches were considered for the layering of the starting profile in this study. In the first one, at least 10 layers with increasing layer thickness from the top to the bottom were considered. The layer thickness ranged from 0.1 to 0.8 m depending on the investigation depth. Figure 35 shows an example of this layering approach. The second approach used in this study considers an initial layer thickness of 0.5 m.
Depending on the depth of interest, the number of layers can be smaller than 10.
The last layer represents the half space of the dynamic stiffness and has to be set to a value thicker than the maximum wavelength for both approaches. Once the initial layer thickness is set, values for the P-Wave Velocity, S-Wave Velocity, density, Poisson's Ratio and a damping factor have to be defined for each layer.  In the same window, the option to choose an analysis type is given. Two types are available, 2-dimensional and 3-dimensional. In the 2D analysis the wave front is assumed to be planar. For the 3D analysis a cylindrical wavefront of surface waves and a hemispherical wavefront of body waves is assumed. The 3D assumption considers the modes of all stress waves and therefore is recommended by  for the analysis of SASW tests. In this study the 3D analysis type was considered.
In the second step the experimental dispersion curve has to be selected. It can be chosen between a inversion analysis based on a global averaged dispersion curve or an array averaged dispersion curve. As mentioned before, the global averaged dispersion curve consists only of one averaged best-fit curve, while the array averaged dispersion curve is a collection of the best-fit curves for each receiver spacing. Each dispersion curve is suitable under different conditions. In case of scattered data in the dispersion curve resulting from significant lateral variability at the test site, a global inversion analysis should be selected. The wide-banded data gets averaged in one best-fit global dispersion curve. If the layers of the soil profile show significant changes in the stiffness, a averaged inversion analysis leads to more accurate shear wave velocity profiles . In addition, the needed computational power and time to run the inversion has to be considered. Since the average dispersion curve is a composition of multiple global dispersion curves the needed computational time is significantly longer.
The third step of the inversion analysis is to determine starting model parameters with the best match to the experimental dispersion curve. The starting model parameters are an initial guess that should be a reasonable estimate of the expected material properties at the site. The scheme to develop the starting model parameters in form of a preliminary shear wave velocity profile, is divided up into two phases . In the first phase, a soil profile is assumed with a number of layers based on the number of data points of the experimental dispersion curve. However, Stokoe et al. (2005) points out that the change does only have a minor effect on the shear wave velocity. The investigation depth can be adjusted based on the depth resolution analysis. The depth resolution analysis provides a sense of how well the model is resolved and determines the maximum possible investigation depth which can be examined for given experimental data . In WinSASW for each inversion a profile of the model parameter resolution in each layer is plotted. Figure 36 shows an example of the resolution over the depth for one inversion. In this example, the last two layers have a low resolution and can be eliminated for the model profile. The inversion will then be performed with a decreased amount of layers. The last parameter which can be changed is the uncertainty factor of the shear wave velocity or thickness.  defines the uncertainty factor as the ratio of the standard deviation of the model parameter to the standard deviation of the experimental data. The default value in the software is 0.2 for the uncertainty factor of the shear wave velocity and 0.05 for the thickness.
The inversion analysis is repeated until the lowest value of RMS error is reached, preferably under 10, and the experimental and theoretical dispersion match.

CHAPTER 5 Site Descriptions and Test set up
This chapter presents a description of the sites tested for this study. Figure   37 shows a map of Rhode Island with the locations of all the test sites. The test sites for the identification of shallow rock were chosen based on the knowledge of existing rock within the first few meters. The first site, Middleton Building at the Bay Campus of the University of Rhode Island, has been used for previous SASW tests   Figure 38 shows

Middleton Building, URI
The Middleton building is located at the Narragansett Bay Campus of the University of Rhode Island. The tests were conducted on a grassy area next to the Middleton building ( Figure 40). The location was chosen due to its easy access and the possibility to compare the results to previous SASW test results conducted at URI . A 4 kg sledge hammer (Figure 24) was used as an impact source. The previous study by  recommended the use of a steel plate covered with a rubber pad as a striker plate on the ground (Figure 41). Tests with the 4.5 Hz geophones were conducted for spacings of 0.5m, 1m, 1.5m, 2m, 3m, 4m, 5m and 6m, while the 2 Hz geophones were installed for spacings of 5m, 6m, 7m and 8m. In addition, the location of the source was reversed in the second part of the test, so that the test could be performed in forward and reverse direction ( Figure 42). Since the volume of soil tested does not change between the two parts of the test, the reversed testing simply helps to evaluate the accuracy of the results. Figure 42: Scheme of the forward and reverse testing with the CRMP geometry  The second test at the Middleton Building was also performed with 4.5 Hz and 2 Hz geophones, considering the same spacings as in the second test (0.5 m -8 m). Tests in the forward and reversed directions were performed. The tests in the forward directions were repeated five times for each spacings with the purpose to evaluate experimental error between repeated tests.
The testing parameters of both tests are summarized in the Tables 5 to 8 in Chapter 6.

Baker Pines Road Bridge
The preliminary site investigation showed that the locations marked red in Figure 44 were suitable as test sites. Both sites are located within the area of boring 596-5 and close to I-95.  (Figure 45 b)). The 4.5 Hz geophones were arranged with spacings of 0.5m, 1m, 1.5m, 2m, 3m, 4m, 5m and 6m and the 2 Hz geophones with spacings of 5m, 6m, 7m and 8m. Both the small and the large sledge hammer were used. The choice of the source depended on multiple factors, e.g. the spacing and the gain. Table 9 describes details of each spacing.
The second site is a grassy area ( Figure 46). Here, the spikes could be used again for the 4.5 Hz geophone. Similar to the first test at the Baker Pines Road Bridge, the 2 Hz geophones were covered with sand bags. A summary of the parameters are in Table 10.  at spacings of 0.5m, 1m, 1.5m, 2m, 3m, 4m, 5m and 6m and the 2 Hz geophones were placed at spacings of 5m, 6m, 7m and 8m. The values of the applied gain and the choice of the source, small or big sledge hammer, are summarized in Table 11 and 12 for each spacing.

URI main campus
The main campus of the University of Rhode Island is located in South

GZ-4
The test site GZ-4 is a grassy area next to Crawford Hall and the Powerhouse Road on the URI main campus. The boring of GZA was conducted in one of the outside corners of the lawn area and is visible in Figure 51 a) as a light spot.
Multiple trees, one hydrant and three covers of a water main can be found on the lawn area. The location of the array of geophones, illustrated in red in Figure 51 a), was chosen in a way to avoid any interference with these objects. Figure 51 b) shows the position of the 4.5 Hz geophones during a test. The major parts of the testing area consisted of a sandy and grassy surface.
Close to the Crawford Hall a path made out of sand and gravel ran parallel to the building. Along this path only the source but no geophone was positioned.
Hence, 4.5 Hz geophones with spikes could be used for the entire test. Identical to the previous tests, sand bags were used to apply weight on the 2 Hz geophones to ensure a good geophone-ground contact. The test set-up was based on the CRMP geometry with the midpoint located in the middle of the grassy area. The source and the first geophone moved closer to the Crawford Hall with increasing receiver spacing, while the second geophone moved in the opposite direction, closer to the parking lot. Receiver spacings of 0.5, 1, 1.5, 2, 3, 4, 5 and 6 m were applied for the 4.5 Hz geophones and spacings of 5, 6, 7 and 8 m for the 2 Hz geophones.
The applied test parameter such as the gain are summarized in Table 13 for each spacing.

GZ-7
The test site GZ-7 lied on a grassy area in the middle of the Engineering  The set-up is also based on the CRMP geometry with the midpoint right next to the boring location of GZA (Figure 102 b)). 4.5 Hz geophones with a spike were used and set up in spacings of 0.5, 1, 1.5, 2, 3, 4, 5 and 6 m. The 2 Hz geophones were weighted with sand bags in positioned in spacings of 5, 6, 7 and 8 m. Table   14 summarizes the applied test parameter for each spacing.

GZ-8
The last test site on the URI main campus, GZ-8, was also located in the middle of the engineering quad and close to Wales Hall ( Figure 106). The location of the boring conducted by GZA was situated in between two trees without enough space for a SASW test in between. Hence, the position of the array of geophones was moved closer to the sidewalk (Figure 106 b)).   In the first step of the data processing, the signals were reviewed and windowed in the program WinTFS, using an exponential cut filter with a decay of 500. The file NDE 24 with a spacing of 0.5 m did not show a good averaged signal or coherence and was eliminated from further analysis. The other seven files were imported into the program WinSASW. After the masking process, composite dispersion curves for every spacings were determined. They can be seen in Figure   54 (phase velocity vs. wavelength) and Figure 55 (phase velocity vs. frequency).
Based on the composite dispersion curve a averaged global dispersion curve was calculated ( Figure 56, blue solid circles). In the next step the soil profile for the inversion analysis was defined. The depth of investigation depends on the wavelengths of the global dispersion curve and can be assumed to be half of the maximum wavelength. This approach is based on the fact that most of the particle motion occurs at depths less than one-half of the wavelength (Stokoe et al., 2005). In this case the maximum wavelength was 7 m which leads to an investigation depth of 3.5 m.
The layering of the starting soil profile was defined in two different ways (Chapter 4.2.2). For both approaches, a global inversion was performed. However, in this section only the results of the first approach, increasing layer thickness with depth is described.
In the global inversion process, a theoretical dispersion curve with the lowest RMS error and best match to the experimental dispersion curve was calculated.
In Figure 56 the theoretical dispersion curve is illustrated in red empty circles and the experimental dispersion curve in solid blue circles.

Middleton Building, URI Bay Campus, Narragansett
A SASW test was performed at the Middleton Building in a previous study by . Figure 58 shows the shear wave velocity profile from that study. The SASW test on March 31st, 2016 was performed in the forward and reverse direction. The results of both tests will be discussed separately and then compared.
The testing parameters that were used in the forward test are summarized in Table 5. In the first step of the post-processing, the data was reviewed in the program WinTFS. An exponential cut filter with a decay of 500 was used in the windowing process. All 13 recordings showed signals with good quality, hence all were used for further analysis.  Figure 59 (phase velocity vs. wavelength) and Figure   60 (phase velocity vs. frequency). Each spacing is illustrated in a different color. Inversions with two different starting layer thicknesses, which were determined with the two proposed approaches from Chapter 4.2.2, were performed. In the following only the results of the approach with increasing layer thickness over depth in the starting soil profile will be discussed. The results of the other approach can be seen in Figure 116 (a) in Chapter 7. The global inversion analysis was conducted until the best match between the theoretical and experimental dispersion curve was found. An array inversion analysis was not considered due to a high spreading between the composite dispersion curves at a wavelength of about 2 to 3 m ( Figure   61). The result of the best match is displayed in Figure 62 with the theoretical dispersion curve in empty red circles and the experimental dispersion curve in solid blue circles. The shear wave velocity profile corresponding to the determined theoretical dispersion curve is shown in Figure 63. Additionally, typical shear velocity profiles for soft sand, silt and clay as well as for dense gravel can be seen as references .
In the first 3 m the shear wave velocity ranged from 100 to 500 m/s, which are typical values for dense gravel or till. In the deeper layers the velocity increases to a value up to 950 m/s.  Table 6.   The SASW test on April 13th was performed in the forward and reverse direction. Additionally, in the forward test five data sets were recorded for each spacing to demonstrate the experimental error.
The results of the forward test will be discussed first. Table 7 shows the testing parameters for all five records of each spacing. All files showed a good signal and coherence during the review in WinTFS and were used for the further analysis in WinSASW.  Figure 71 shows the global dispersion curve in solid blue circle. A maximum wavelength of the dispersion curve of about 14 m was captured which resolves in a approximate investigation depth of 7 m. The two different processes to determine the starting soil profile have been described in Chapter 4.2.2. Here, the results of the second method will be discussed in detail.
The estimated match of the theoretical (empty red circles) and experimental (solid blue circles) dispersion curves with the global inversion analysis is shown in Figure   71.   The SASW test in the reverse direction was conducted with only one repetition for each spacing. Table 8 shows the parameters for this test. The review of the data in WinTFS showed that the records of the second geophone of the files NDE 282 to 286 were very weak ( Figure 73 (right)). These five data files were excluded from further analysis and not imported in WinSASW.  The global dispersion curve was calculated from the composite dispersion curves and is illustrated in Figure 76. Since only dispersion curves from smaller spacings were considered the maximum wavelength of the averaged dispersion curve was approximately 9 m. The approximate investigation depth is therefore limited to 4.5 m.
Two starting model profiles were created, based on the approaches described in Chapter 4.2.2. In this section the results of the first approach will be evaluated.
A global inversion analysis was performed until the best match between the theoretical and experimental dispersion curve was determine. Figure 76 shows the two dispersion curves with the best alignment. The testing parameters for the test are summarized in Table 9. (phase velocity vs. frequency). As it can be seen in Table 9, a composite dispersion curve for every file was calculated. The composite dispersion curve of each spacing was used for the determination of the representative averaged dispersion curve. A global dispersion curve was calculated and can be seen in Figure 80 in blue solid circles.   The SASW test at the second location next to the Baker Pines Road Bridge was conducted with the equipment and parameters shown in Table 10. The data processing in WinTFS showed, that the coherence and quality of all data files is sufficient enough to import them into WinSASW for further analysis.  In the next step, the global dispersion curve was estimated for the inversion analysis. This can be seen in Figure 84 in solid blue circles. The maximum wavelength of the dispersion curve of 13 m led to the assumption of a approximate investigation depth of 6.5 m. The set up of the starting soil profile followed the same scheme as location 1 and is divided up into two approaches (Chapter 4.2.2). In the section only the results of the first approach will be considered. The theoretical dispersion curve of the inversion with the smallest RMS error is displayed in Figure   84. The SASW test was conducted with the parameters summarized in Table 11. In the first step the data was reviewed and windowed in the program WinTFS  The second step included the calculation of a global dispersion curve from the composite dispersion curves. Figure 88 shows the global dispersion curve with a maximum wavelength of 13 m. Due to Stokoe et al. (2005), the investigation depth can be assumed as half the maximum wavelength which is 6.5 m in this case.
The procedure to determine the starting soil profile was explained in Chapter 4.2.2. The results of the first approach will be described in this section while the results of the second approach can be found in Figure 116   The test site was located between I-95 and RI-3, two high-traffic streets. At larger spacings the gain had to be set to a higher value to be able to record a signal. However, higher gains also caused the system to trigger from vibrations created by passing cars and trucks. Figure 90 (a) shows such a signal. Due the high number of passing cars it was not possible to record four similar signals for one spacing with a gain set to 1000. As you can see in Table 12 the test had to be stopped at 6 m. A review of the recordings for larger spacings on the site showed that those recordings are not usable for further post-processing and analysis. Figure 90: Example of a triggered signal caused by a passing car or truck at the location 2 at the Weaver Hill Road Bridge The composite dispersion curves were used to determine a global dispersion curve as the representative averaged dispersion curve. It is displayed in Figure   93 in solid blue circles. A global inversion analysis was conducted, considering a approximate investigation depth of 4 m due to a maximum wavelength of 8 m of the experimental dispersion curve. The starting soil profile was specified in two ways, as already described in the sections before. The following results are based on the approach for the starting soil parameter with increasing layer thickness over the depth. Figure 93 shows the theoretical dispersion curve (empty red circles) conducted in the global inversion analysis. The results from the other approach are presented in Figure 116 (e) in Chapter 7.  (SPT) value than in the layers above and below was measured, which indicates a less dense or loose material.
The testing parameters which were used during the test at GZA-4 are listed in Table 13.   Two different starting soil profiles were entered in the software, based on the two approaches proposed in Chapter 4.2.2. In both cases the global inversion analysis was performed. The process was the same as described in the previous sections.
The theoretical dispersion curve (empty red circles) with the lowest RMS error and the best match with the experimental dispersion curve is shown in Figure 97 for starting soil profiles with a) increasing thickness over depth and b) constant thickness over depth.   As it can be seen in Figure 101, the maximum wavelength of the global dispersion curve is 10 m and therefore, a investigation depth of 5 m was assumed.
Similar to the evaluations in the previous sections, inversions with different starting soil profiles were conducted. In the following only the results from the first approach, increasing thickness of layers with depth, will be discussed. The theoretical dispersion curve of this approach showed a better match to the experimental dispersion curve and the calculated RMS error was smaller. Figure 101 shows the best matching theoretical dispersion curve in empty red circles. The results of the second approach can be found in Figure 116 (g) in Chapter 7. The SASW tests were conducted with the parameters summarized in Table 15.
The jump in numbering of the NDE files occurred due to a switch of the memory card. As for the other two sites on URI main campus, no data were excluded in WinTFS. Especially in the lower frequencies good signals with high coherence were obtained.  performed. The results, using the first approach with increasing layer thickness over the depth for the starting soil profile, are presented in this section. Figure 105 shows the alignment between the theoretical (empty red circles) and experimental (solid blue circles) dispersion curves. The results of the second approach also showed a good match and a low RMS error (Figure 116 (h), Chapter 7). However, compared to the boring log from GZA the results of the first approach agree more to the boring log. In this chapter the SASW test results from this study are compared to boring logs or other SASW test results. Additionally, the results using global or array inversion and the influence of the initial layer thickness are analyzed.

Middleton Building
The results of all SASW tests on March 31 in forward and reverse direction and the SASW test from  are shown in Figure 107. In all three  For the SASW test performed on April 13, five signals were recorded fore each spacing. Therefore, five dispersion curves and shear wave velocity profiles were calculated for this test. The comparison of the five dispersion curves for each spacing in Figure 68 in Chapter 6 showed a good agreement between the dispersion curves. Figure 108 shows the five shear wave velocities in different colors and the shear wave profiles from the SASW test on March 31st and from  in dashed lines.

Baker Pines Road Bridge
The SASW test results at the Baker Pines Road Bridge were compared to the boring log 595-5 provided by the RIDOT. The boring log in Figure 109   However, during the SASW test very dense topsoil was identified at Location 1 instead of the loose soil indicated in the boring log. In fact, the spikes used to anchor the 4.5 Hz geophones had to be removed because it was not possible to push them into the soil. At both locations rock was identified at depths of around 3 m at the Location 2 and at 3.5 m at the Location 1. Compared to the boring log, the difference to the actual depth of granite is 0.5 to 1 m. However, in general the shear wave velocity profile matches reasonably well with the stratigraphy shown in the boring log.

Weaver Hill Road Bridge
The SASW test results from the Weaver Hill Road Bridge were compared to the boring logs provided by the RIDOT. Figure 110 shows the results of the SASW test at the first location and the corresponding boring log WH-3. In the boring log, top of rock was defined at a depth of 3.35 m, overlaid with a very dense layer of Sand and a layer of topsoil (Figure 110 a)). The shear wave velocity profile in  The shear wave velocity profile of the second location was compared to the boring log WH-8 ( Figure 111). In the boring log a layer of topsoil, followed by a layer of medium dense sand and the top of rock at a depth of 3.35 m was found.
Up to a depth of 2.5 m the shear wave velocity profile in Figure 111 b) shows values typical for dense gravel. For the deeper layers shear wave velocity higher than 500 m/s, typical for rock, were determined. In this SASW test the calculated top of rock was shallower than in the boring log, but again the agreement between the log and the shear wave profile is reasonable..

Blind Prediction of Depth to Rock at the URI Main Campus
The three SASW tests performed on the URI main campus were compared to the corresponding boring logs provided by GZA Geoenvironmental, Inc.  The boring log and shear wave velocity profile for the location GZA-7 can be seen in Figure 113. The shear wave velocity profile shows higher velocities of 100 to 350 m/s within the first meter which can be related to the medium dense gravel and sand layers shown in the boring log. The decrease of the shear wave velocity to a depth of 2.5 m and the following increase of the velocity corresponds to the sand and till layers in the boring log. At a depth of 4.2 m the boring was terminated due to rock. Since the shear wave profile did not reach further than 3.5 m, no rock was identified with the SASW test. At this location, the blind SASW prediction does not match well with the boring log. In particular, the shear wave velocity suggests looser material than indicated in the boring. Of some concern is the very thin "spike" at a depth of 0.4 m and the early reversals in the shear wave velocity at the initial depths.    Additionally, the calculation time of the global inversion was significant lower than with the array inversion.

Influence of the Initial Layer Thickness
Two different approaches were considered for the definition of the initial layer thickness in the starting soil profile. In the first approach the layer thickness increases with depth and in the second approach the initial layer thickness is set to constant value of 0.5 m. To investigate the influence of the initial layer thickness on the shear wave velocity profile, inversions with both approaches were performed for every test. Figure 116 shows the shear wave velocity profiles for both approaches for every test.   Two different approaches for determining the starting soil profile for the inversion analysis were introduced. The first one (using initial layers of increasing thickness with depth) was based on previous studies (e.g.  and the second one (using an initial layer thickness of 0.5 m) related to a typical layout of boring logs or soil profiles. The shear wave profiles determined with the first approach resolved in more accurate results in the majority of the tests. Since the second approach did not improve the calculation time, the first approach should be used in future studies.
In summary, it was possible to determine rock layers with the SASW system.
The process to reach the shear velocity requires considerable experience and personal judgment and especially the masking procedure is a source of mistakes and uncertainty. Three beach sites have been added to this study to continue an ongoing collection of shear wave velocity data on coastal beach sites in Rhode Island where coastal erosion occurred.

URI Bay Campus beach
The first site is the beach at the URI Bay Campus in Narragansett facing the Narragansett bay. In 1690's the area of the URI Bay Campus Beach was called South Ferry and was used as a pier for a ferry service to Jamestown (Rhode Island Historical Preservation Commission, 1999).
The SASW test was conducted on May 12th, 2016. The position of the array of geophones used for the test is shown in Figure C.1. The array ran parallel and in a distance of about 4 m to the Narragansett Bay. The CRMP geometry, with a south moving source and first geophone and a north moving second geophone, was used. The spacing for the 4.5 Hz geophones were set to 0.5, 1, 1.5, 2, 3, 4, 5 and 6 m and for the 2 Hz geophones to 5, 6,7 and 8 m. Further informations about the applied test parameters can be found in The first SASW test on Matunuck Beach was conducted on June 5th, 2016. The test site was located in front of a sand notch at the east end of the beach ( Figure   C.2). The array ran parallel the to the shoreline and was set up based on the CRMP geometry ( Figure C.3). In the test receiver spacings of 0.5, 1, 1.5, 2, 3, 4, 5 and 6 m for the 4.5 Hz geophones and to 5, 6, 7 and 8 m for the 2 Hz geophones were used. Table C.2 summarizes the applied test parameter fore each spacing.

Test results
At the beach sites shear velocities of soft to dense sand are expected. In the literature, for example ,  and Stokoe et al. (2005), shear wave velocities of 100 to 500 m/s are assumed for sand. An estimation of the shear wave velocities of soft sand, silt and clay according to  will be included in the results.

URI Bay Campus Beach, Narragansett
The Beach at the URI Bay Campus has not been investigated with the SASW system before and therefore, no soil profiles or shear wave velocity data exist. The testing parameters and equipment of the first SASW test on the URI Bay Campus Beach can be seen in Table C.1. The composite dispersion curves were used to compute the global averaged dispersion curve with a maximum wavelength of 14 m. Due to Stokoe et al. (2005), an investigation depth half of the maximum wavelength can be assumed, hence 7 m.
Two inversion analysis were performed for the calculated global dispersion curve. The difference between the two analysis was the starting soil profile. The specification of the starting soil profile was based on two approaches which are explained in Chapter 4.2.2. In the following only the results of the first case will be considered.
The theoretical dispersion curve was computed with the global inversion analysis. In Figure C.8 the theoretical dispersion curve is displayed in empty red circles.
Additionally, the experimental dispersion curve can be seen (solid blue circles) to show the match between the two curves.     The SASW test for this study has been performed at exact the same location and the parameters and equipment from Table C.3. In the next step, the global dispersion curve was determined. Figure