Journal of Testing and Evaluationweb.nchu.edu.tw/Pweb/Users/Feng/Research/13946.Pdf73 CWT on...

Journal ofTesting and Evaluation

P.-H. Tsai,1 Z.-Y. Feng,2 and S.-H. Ni3

DOI: 10.1520/JTE20160100

Using Continuous WaveletTransform to Construct theDispersion Image for Soil Layers

VOL. 45 / NO. 1 / JANUARY 2017

-----Original Message----- From: [email protected] [mailto:[email protected]] Sent: Tuesday, August 02, 2016 9:55 PM To: [email protected] Cc: [email protected]; [email protected]; [email protected] Subject: Decision on Manuscript ID JTE-2016-0100.R1 - Journal of Testing andEvaluation 02-Aug-2016 Dear Dr. Tsai: It is a pleasure to accept your manuscript entitled "Using Continuous Wavelet Transform to Construct the Dispersion Image for Soil Layers" in its current form for publication in the Journal of Testing and Evaluation. Thank you for your fine contribution. On behalf of the Editors of the Journal of Testing and Evaluation, we look forward to your continued contributions to the Journal. Please note that authors must pay for figures to appear in color in print and that cost depends on the number of figures. Please contact the editorial office immediately if you are interested in paying color charges. This invoice must be paid prior to publication. If you are not already a member of ASTM International, we welcome you to join the conversation. Go to http://www.astm.org/MEMBERSHIP/index.html for membership details. With Best Regards, Dr. M.R. Mitchell Editor-in-Chief ASTM International Journal of Testing and Evaluation Editorial Office [email protected]

PROOF COPY [JTE20160100]

TECHNICAL NOTE

1P.-H. Tsai,1 Z.-Y. Feng,2 and S.-H. Ni3 AQ2AQ1

Using Continuous Wavelet Transformto Construct the Dispersion Image forSoil Layers

Reference

Tsai, P.-H., Feng, Z.-Y., and Ni, S.-H. AQ2, “Using Continuous Wavelet Transform to Construct the Dispersion

Image for Soil Layers,” Journal of Testing and Evaluation, Vol. 45, No. 1, 2017, pp. 1–9, doi:10.1520/

JTE20160100. ISSN 0090-3973

2ABSTRACT

3This study used a time-frequency domain analysis for estimating the dispersion curve of a

4Rayleigh wave by using two receivers. The signals were first transformed using continuous

5wavelet transform. A similar slant stack procedure was used to analyze the wavelet

6transform signals and extract a dispersion image. This method is advantageous because it

7requires no empirical judgment in phase unwrapping and few receivers. To examine the

8applicability of the method for evaluating the dispersion curve for soil layers with lateral

9heterogeneity, three synthetic examples and an experience example were investigated. In

10these examples, numerical simulations of the surface wave seismic test were performed

11using the finite difference FLAC code. The results revealed that the estimates of the surface

12wave dispersion curve, obtained using the method, coincide with those of the theoretical

13values. A high-resolution dispersion image is generated by increasing the spacing of

14receivers. The method is applicable for extracting a dispersion image for lateral

15heterogeneous soil layers.

Keywords

16dispersion curve, continuous wavelet transform, shear wave velocity, Rayleigh wave, lateral heterogeneity

17Introduction

18The shear wave velocity profile is a crucial part of seismic risk characterization. The shear wave19velocity profile is usually obtained using the surface wave seismic test because the surface wave is20the predominant wave on the ground surface; additionally, it is the most easily measured wave.21The dispersion characteristic of surface waves in a layered soil stratum is a phenomenon involving

Manuscript received February 23, 2016;

accepted for publication August 2, 2016;

published online xx xx xxxx.

1 Dept. of Construction Engineering,

Chaoyang Univ. of Technology,

Taichung City 41349, Taiwan,

e-mail: [email protected]

2 Dept. of Soil and Water Conservation,

National Chung Hsing Univ.,

Taichung City 40227, Taiwan,

e-mail: [email protected]

3 Dept. of Civil Engineering, National

Cheng Kung Univ., Tainan City 70407,

Taiwan, e-mail: [email protected]

J_ID: JTE DOI: 10.1520/JTE20160100 Date: 29-August-16 Stage: Page: 1 Total Pages: 11

ID: asme3b2server Time: 19:09 I Path: //chenas03/Cenpro/ApplicationFiles/Journals/ASTM/JTE#/Vol04501/160128/Comp/APPFile/AT-JTE#160128

Copyright VC 2016 by ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. 1

Journal of Testing and Evaluation

doi:10.1520/JTE20160100 / Vol. 45 / No. 1 / January 2017 / available online at www.astm.org


22 various wave velocities propagated with different frequencies.23 The dispersion curve of the surface wave represents the rela-24 tionship between wave velocity and frequency. The dispersion25 curve obtained from a surface wave seismic test can be used in26 an inversion algorithm to estimate the shear wave velocity pro-27 file. One such test is by using the spectral analysis of surface28 waves (SASW) method, which involves installing two receivers29 on the ground surface and measuring the phase wave velocity in30 the frequency domain from the phase shifts between the two31 receivers. The SASW method has been implemented success-32 fully in geotechnical and pavement engineering since the33 method was introduced by Nazarian et al. [1]. However, the34 signal-processing procedure is difficult and requires an empiri-35 cal judgment for constructing the dispersion curve from the36 surface wave signals. Furthermore, the dispersion curve may be37 constructed incorrectly because of the spurious 360� cycles dur-38 ing phase unwrapping [2]. Some criteria regarding the feasible39 configuration of receiver to perform SASW were suggested in40 Refs 3–6. Recently, some studies by using the SASW method41 were reported in Refs 7–9.42 To reduce the difficulty of evaluating the dispersion curve43 when using the SASW method, the multichannel analysis of44 surface waves (MASW) technique was developed. In the45 method, which involves increasing a number of receivers along46 a survey line, a spatial resolution is acquired using a substantial47 number of geophones and a shot gather is measured using a48 multichannel recording system. The particle motion velocity49 time histories are transformed and analyzed to extract a disper-50 sion image in the wave velocity–frequency domain. The disper-51 sion curve is designated as the peak of the dispersion image.52 Thorson and Claerbout [10] proposed tau-p transform or the53 so-called slant stack, to perform the velocity spectral analysis.54 This transformation takes multiple seismograms, which takes55 amplitudes related to distance and time (x-t), and converts it56 into amplitudes related to slowness and intercept time. In this57 study, the method was applied to extract a dispersion image58 from time–frequency distribution of seismic data. The MASW59 method can be difficult to manipulate in an urban area because60 it requires a substantial number of receivers with a wide receiver61 spread.62 Time–frequency analysis can be performed with continu-63 ous wavelet transform (CWT) to understand the transient64 changes in spectra. The wavelet transform uses a size-adjustable65 window, ensuring that the duration of the window is short at66 high frequencies and long at low frequencies. Therefore, wavelet67 transform has a high-time resolution at high frequencies, and68 has a high-frequency resolution at low frequencies [11]. The69 transformed figure shows the distribution of the transform sig-70 nal at the time–frequency plane, enabling the simultaneous71 acquisition of the signal characteristics in the time domain and72 frequency domain. In the literature about the application of73 CWT on solution for seismic wave decomposing and denoising

74(e.g., Refs 12–16), Kim and Park [12] used harmonic wavelet75transform to determine the dispersion curve. They concluded76that the proposed method is less affected by noise and near field77effect than the phase unwrapping method. Park and Joh [13]78applied the harmonic wavelet for phase spectrum assessment to79reduce background noise effects. Kim and Kwan [14] proposed80a new technique to compute the Rayleigh wave velocity using a81principal wavelet-component analysis to exclude noise and82reflection waves. Rosyidi and Taha [15] utilized CWT based on83Gaussian derivative wavelet to decompose seismic signals and84filter noise on SASW tests. Golestani et al. [16] used CWT to85localize the recorded seismic signals and applied discrete86wavelet transform to reduce noise on SASW tests.87The present study performed a time–frequency analysis to88extract the dispersion image of the surface wave for lateral89heterogeneous soil layers. This method, based on CWT, supplies90dependable information on the surface wave dispersion curve,91and requires only two receivers. Therefore, this method does92not necessitate the use of numerous geophones and requires lit-93tle time. To transform a signal generated from surface wave94seismic testing, a value of 0.8125Hz was set as the center fre-95quency of the real-valued Morlet wavelet function in the Matlab96wavelet toolbox. A similar slant stack procedure was then used97to analyze the wavelet transform signals and extract a dispersion98image. Three synthetic examples and an experimental example99of surface wave seismic test were examined in this paper to esti-100mate the applicability of the time–frequency analysis for soil101layers with lateral heterogeneity.

102Method

103CONTINUOUSWAVELET TRANSFORM

104To transform an original signal into the form of dilation105parameter and time, a wavelet function wðtÞ is used to perform106the translation and dilation processes. Frequency is inversely107proportional to the dilation parameter; thus, the relationship108between the frequency and dilation parameter is defined as109follows [17]:

f ¼ f0aDt

(1)

110where:111f0¼ the center frequency of a wavelet function,112a¼ dilation parameter, and113Dt¼ the sample period.114To transform a signal generated from surface wave testing,115the value of 0.8125Hz was set as the center frequency of the116real-valued Morlet wavelet function in the MATLAB wavelet117toolbox. The real-valued Morlet wavelet function is defined as118follows [17]:

wðtÞ ¼ C cosð5tÞe�t2=2



Journal of Testing and Evaluation2


119 where:120 C¼ a constant used for normalization to achieve121 reconstruction.122 A surface wave seismic test was simulated using the numer-123 ical software FLAC [18]. The surface wave test in the two-layer124 soil model, the thickness of the upper soil is equal to 5 m. Fig. 1a125 is the vertical-component seismogram of particle motion veloc-126 ity at a source-to-receiver offset of 10m. Fig. 1a shows that the

127arrival time of the Rayleigh wave is approximately 0.05 s. If the128particle motion velocity time history was transformed into the129time–frequency domain with CWT, the frequency and time130content of the seismic signal w(t,f) was obtained simultaneously,131as shown in Fig. 1b. The figure shows that the range of1320.05–0.07 s and 100–250Hz clearly indicates a strong seismic133energy. The temporal information in each signal frequency can134be obtained from Fig. 1b. This procedure is used to extract the135dispersion image in the following paragraphs.

136DISPERSION IMAGE EXTRACTED BY THE CWT

137AND SLANT STACK

138Because surface waves possess a maximum energy density, the139peaks of the wavelet transformed signals may be generated by140surface waves. This characteristic is beneficial in extracting the141surface wave component from a time–frequency distribution142obtained using CWT. The wave travel time between the two143receivers is equal to the receiver spacing divided by wave veloc-144ity. The arrival time of the seismic wave to the first and second145receivers is assumed to be t1 and t1 plus the wave travel time,146respectively. The spectrum value for a certain frequency and147wave velocity was firstly calculated as the product values of the148wavelet transformation signals corresponding to the aforemen-149tioned arrival time of the seismic wave for the two receivers.150The spectrum value was then calculated by summing the151products at all assuming t1. By repeating these procedures for152all wave velocities and frequencies, the dispersion image was153obtained.154The main process for deriving dispersion curves in this155study involved the following steps:

156Step 1: 157Time series data from a pair of receivers are trans-158formed into the signal of the time–frequency domain159by using CWT.160Step 2: 161At a certain frequency, the two transformed signals162are normalized at the maximum transformed values163of each receiver.164Step 3: 165The slant stack summation is applied to the two tem-166poral plots. For a certain wave velocity, the summed167value is assigned to a point in the frequency–wave168velocity plane. This step is repeated until each wave169velocity is analyzed.170Step 4: 171Repeat steps 2 and 3 until each frequency is ana-172lyzed, and a 2D dispersion image of the two receivers173is obtained.174Step 5: 175The peak of the high amplitude distribution of the1762D dispersion image is regarded as the dispersion177curve of the surface wave.

178The time series data from a pair of receivers, s1,t and s2,t,179were obtained by surface wave seismic testing. They were180transformed into the time–frequency data w1,t,f and w2,t,f, respec-181tively. Their temporal plots for a specific frequency are displayed182together, as shown in Fig. 2. The first source-to-receiver offset is

FIG. 1 Synthetic seismic record at a source-to-receiver offset of 10 m during

seismic testing for the thickness of the upper layer soil¼ 5 m:

(a) seismogram and (b) time–frequency distribution by continuous

wavelet transform.



TSAI ET AL. ON DISPERSION IMAGE FOR SOIL LAYERS 3


183 x1, and the second is x2¼ x1þ d. Fig. 2 shows the two wavelet184 transform signals w1,t,fa and w2,t,fa at locations x1 and x2, respec-185 tively, for a specific frequency of fa. To avoid the effect of geo-186 metric attenuation on the transformed signal, the signal was187 normalized by the maximum transformed value wmax,fa of the188 receiver. For example, the transform signal of the first receiver189 w1,t,fa was divided by w1,max,fa to obtain the normalized signal190 W1,t,a. If the arrival time of the surface wave was t1 at the first191 receiver, the time of the monitored surface wave of the second192 receiver would be t1þ d/v, where d is the spacing of the receivers193 and v is the surface wave velocity. The product of W1,fa and194 W2,fa were summed at a certain frequency, fa, with the same195 wave velocity, v, for the duration of the seismic test:

efa;v ¼XT

t1¼0W1;t1;fa �W2;t1þd

v;fa(3)

196 where:197 T¼ the duration of the seismic record.198 These steps were repeated over a specified wave velocity199 range. These procedures were also repeated for all frequencies200 to produce a 2D dispersion image, and the spectral values in the201 f–v domain were mapped. This process was similar to that for202 computing the projection of the transformed plots for the pair203 of receivers by using parallel rays under various angles of inci-204 dence. When the slope of the ray path was close to the wave205 velocity of the surface wave, a larger projection was obtained.206 The band of larger spectral amplitudes of 2D dispersion image207 represented the fundamental mode of Rayleigh wave. The trace208 of the amplitude distribution peak in the 2D dispersion image209 was considered the dispersion curve of the Rayleigh waves.

210 Synthetic Examples

211 NUMERICAL MODEL FOR SURFACEWAVE

212 SEISMIC TESTING

213 Several numerical simulations of the surface wave seismic test214 were performed using the finite difference FLAC code. The215 synthesized seismic records in a two-layer earth model were216 simulated. There were 22,500 elements in the model.

217The numerical models were 30m (horizontally)�30m (verti-218cally) with an element size of 0.2m � 0.2m. The duration of219the seismic records was set to 1 s with a time step of 0.2ms. If220the maximum frequency fmax¼ 100 Hz was considered, the221minimum wavelength kmin ¼ 2m would be obtained because222the shear wave velocity of the upper-layer soil was assumed to223be 200m/s in this study. Therefore, the element size would be224equal to 1/10 kmin. This implies a suitable element size for wave225propagation analysis because it conforms to the criterion [19].226An axisymmetric numerical model was employed, and the227boundary on the left side of the model is a symmetrical axis. A228vertical impulsive load was applied to the intersecting point of229the symmetrical axis and ground surface (Fig. 3). The impulsive230load was assumed as a half sine-square function with a duration231of 5ms. The boundaries on the bottom and right side of the232model were assumed as quiet (viscous) boundaries in the nor-233mal and shear directions to absorb most of the energy in the234wave reflected from the boundaries. Twenty-nine receivers were235placed on the ground surface in a linear array with equidistant236spacing of 1 m in the following synthetic examples. The vertical237particle motion velocity time histories at the receiver locations238were recorded simultaneously. The velocity time histories were239regarded as geophone-measured data in surface wave seismic240testing.241The soils were assumed to be linear elastic materials, and242material damping was neglected. The material parameters of243the upper-layer soil were q¼ 1800 kg/m3, vp¼ 346.4m/s, and244vs¼ 200m/s, where q, vp, and vs¼ the mass density, pressure245wave velocity, and shear wave velocity, respectively. The246bottom-layer soil was a half-space, and its material parameters247were q¼ 2100 kg/m3, vp¼ 866m/s, and vs¼ 500m/s.248To ensure that the dispersion image was contributed by the249surface wave, and to avoid body wave effects, a minimum first250source-to-receiver offset of 5m was applied. If the frequency251range of interest was 10 to 80Hz and the shear wave velocity252of the soil was 200m/s, the corresponding shear wavelength253would be from 2.5 to 20m, which nearly satisfies the filtering254criterion [20].

255MODEL A: TWO-LAYERED HORIZONTAL SOIL MODEL

256A softer soil layer with a thickness of 5m that is overlaid on a257homogeneous half-space in Model A is used to indicate the258applicability of the CWT method when applied onto a horizon-259tally layered model. The simulated model of the surface wave260test is shown in Fig. 4. Fig. 5 shows that the dispersion images261of the first source-to-receiver offsets is 10m with four different262spacing of receivers (d¼ 1, 2, 3, and 4m) to evaluate the263influence of the receiver spacing on the dispersion image. The264dispersion curve is picked from the dark dots (peak values) in265high-amplitude band of the dispersion image. The theoretical266dispersion curve for upper-layer soil thickness of 5m denoted267by a blue dashed line with circles is shown in the figures for

FIG. 2 Typical temporal plots of a pair of receivers for a specific frequency.





268 comparison purposes. From Fig. 5, it can be seen that the esti-269 mates of wave velocity obtained by using the method coincide270 with those of the theoretical values. For small receiver spacing,271 wider distribution of high-amplitude band in low-frequency272 range is shown in Fig. 5. Fig. 5d shows that a narrower

273distribution of high-amplitude band is obtained by considering274the receiver spacing of 4m. This implies that a good resolution275of surface wave velocity is obtained by raising the spacing of276receivers, which may be the reason for the long travel time of277waves between receivers when a large receiver spacing provides278a high-accuracy surface wave velocity.

279MODEL B: TWO-LAYER MODELWITH A VERTICAL FAULT

280The CWT method was used in a vertical fault earth model to281show its applicability regarding the lateral variation in layer282thickness. The two-layer soils were separated by a single step-283shaped line. The distance between the vertical fault and source284was 15m. The thickness of the upper-layer soil on the left side285of the vertical fault was 5m, and on the right side was 3m286(Fig. 6). To simplify the influence of lateral heterogeneity, the287pair of receivers were placed on the same side of the vertical288fault (i.e., both receivers were placed on the surface of a medium289with the same thickness of the upper-layer soil).290For comparison purposes, in Fig. 7, the theoretical291dispersion curves for upper-layer soil thickness are given as2925 and 3m, respectively, denoted by a blue dashed line with293circles and green dashed line with triangles. The theoretical

FIG. 3

A typical FLAC mesh of surface wave testing for this study.

FIG. 4 A two-layer horizontal soil model for the surface wave testing with

the predicted soil layer by CWT (the orangeAQ3 and red colors are used

to to show the upper and lower soil layer, respectively).





294dispersion curves were calculated by assuming the medium to295be a horizontal layered model.296Fig. 7a shows the dispersion image when both receivers are297located on the left side of the vertical fault. The estimated dis-298persion curve was picked from the dark dots (peak values) in a299high-amplitude band of dispersion image. The estimated disper-300sion curve approaches the theoretical curve of the horizontally301layered model with 5-m upper-layer soil thickness. Fig. 7b

302reveals that the theoretical dispersion curve of the horizontally

FIG. 5 Dispersion images of a two-layer horizontal soil model: (a) the first

source-to-receiver offset¼ 10 m and receiver spacing¼ 1 m, (b) the

first source-to-receiver offset¼ 10 m and receiver spacing¼ 2 m, (c)

the first source-to-receiver offset¼ 10 m and receiver spacing¼ 3 m,

and (d) the first source-to-receiver offset¼ 10 m and receiver

spacing¼ 4 m.

FIG. 6 A two-layer model with a vertical fault for the surface wave seismic

testing with the predicted soil layer by CWT (the orange and red

colors are used to show the upper and lower soil layer, respectively).

FIG. 7 Dispersion images of a two-layer model with a vertical fault: (a) the

first source-to-receiver offset¼ 10 m and receiver spacing¼4 m, and

(b) the first source-to-receiver offset¼ 20 m and receiver

spacing¼ 4 m.





303 layered model with the 3-m upper-layer soil thickness closely304 corresponds to the estimated dispersion curve obtained from305 the dispersion image. It can be observed that the dispersion306 image is dependent on the thickness of the upper-layer soil at307 the location of the pair of receivers.

308 MODEL C: TWO-LAYER MODEL WITH AN

309 INCLINING INTERFACE

310 To verify the applicability of the CWT method on a high-lateral311 heterogeneity medium, a two-layer model with an inclining312 interface was examined. The thickness of the upper-layer soil313 varies linearly from 5m (on the left side) to 3m (on the right314 side), as shown in Fig. 8. Because the thickness of the upper-315 layer soil varied depending on the locations of receivers, the316 model had a high lateral heterogeneity. In this model, the317 spacing of the receivers was fixed at 4m, and there were three318 distances (5, 15, and 25m) applied between the first receiver319 and source. Fig. 9 shows the high-amplitude distribution shifts320 along the frequency axis with the varying receiver locations.321 The dispersion image is displayed in Fig. 9a, which shows that322 the estimated dispersion curve, indicated by the peak of the323 high-amplitude distribution, approaches the theoretical curve of324 the 5 -m upper-layer soil. The dispersion curve represents the325 soil stratum on the left side of the model. The dispersion image326 in Fig. 9c shows that the estimated dispersion curve approaches327 the theoretical curve of the 3 -m upper-layer soil because the328 two receivers were close to the right boundary of the model.329 Fig. 9b shows the dispersion image of the first source-to-receiver330 offset of 15m. At this location, the thickness of the upper-layer331 soil is approximately 4m. As expected, the estimated dispersion332 curve is between the theoretical curves for the thicknesses of the333 upper-layer soil of 3 and 5m. Therefore, this method can detect

334the lateral variation of a shear wave velocity profile in a lateral335heterogeneous medium.

336An Experimental Example

337The study area is situated on the campus of the Chaoyang338University of Technology, Taichung, Taiwan. An earthfill of a339thickness of approximately 8.1m detected from a drilled bore-340hole is overlaid on dark gray weathered sandstone. The earthfill341is a layer of gray sandy silt with minute quantities of gravel, and342it can be classified to be sandy silt (SM) according to the United343Soils Classification System. The engineering properties of the344earthfill from the experimental work are as follows: unit weight345c¼ 19.5 kN/m3, natural water content wn¼ 16 %, and friction346angle / ¼ 25�.347The impulsive source was derived by using a weighing10 kg348sledgehammer to beat a 0.2m � 0.2m metal plate with the first349source-to-receiver offset of 5m and a receiver spacing of 4m.

FIG. 8 Two-layer model with an inclining interface for the surface wave

seismic testing with the predicted soil layer by CWT (the orange and

red colors are used to show the upper and lower soil layer,

respectively).

FIG. 9 Dispersion images of a two-layer model with an inclining interface:

(a) the first source-to-receiver offset¼ 5 m and receiver

spacing¼ 4 m, (b) the first source-to-receiver offset¼ 15 m and

receiver spacing¼ 4 m, and (c) the first source-to-receiver

offset¼ 25 m and receiver spacing¼ 4 m.





350 The recording time was only 1 s, with a sampling rate of 5000351 samples per second. The dispersion image extracted using the352 CWT method is shown in Fig. 10. The theoretical dispersion353 curve for upper-layer soil thickness of 8m denoted by a white354 dashed line with circles is shown in the figure. Fig. 10 shows that355 the asymptote at high frequencies approaches the wave veloci-356 ties of the earthfill (190m/s). From Fig. 10, it can be observed357 that the depth of the weathered bedrock estimated from the dis-358 persion curve picked by the dark dots in dispersion image is359 approximately 8m, which coincide with that of the neighboring360 borehole data, as shown in Fig. 11.

361Conclusions

362MASW is one kind of surface seismic test methods and from its363result we can depict dispersion image and decide dispersion364curve. However, it needs 12 or more receivers to determine the365phase velocity for statistical redundancy. Therefore, it is still366attractive when a seismic testing is only two receives required.367In this study, the Morlet wavelet was selected in CWT to per-368form time–frequency analysis of seismic records from the two369receivers; then, the slant stack procedures was performed to370extract the dispersion image and to determine the dispersion371curve for soil layers. These signal-processing procedures of the372method proposed can be programmed. Therefore, the method373has the advantages of using only two receivers and no need to374make empirical judgment for phase unwrapping. The three375numerical examples and an experimental example of seismic376test were examined to evaluate the applicability of the proposed377method for soil layers with lateral heterogeneity. The results378show that the estimates of the wave velocities and the values379from theoretical dispersion curve are in excellent agreement.380This suggests that the method is applicable for extracting dis-381persion images and determining dispersion curves in surface382wave seismic testing. A narrower distribution of high-amplitude383band is obtained by raising spacing of receivers. The dispersion384image is dependent on the thickness of the upper-layer soil at385the center location of the pair of receivers in a lateral heteroge-386neous medium. Therefore, this method can detect the lateral387variation of a shear wave velocity profile in a lateral heteroge-388neous medium. To conclude, we present that the method allows389us to pick a dispersion curve without empirical judgment and390using the seismic data from only two receivers to obtain an391accurate 1D distribution of shear wave velocity versus depth.

392ACKNOWLEDGMENTS

393This study is supported by research funding from the National394Science Council of Taiwan (NSC 96-2622-E-324-012-CC3).395Their support is gratefully appreciated.

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FIG. 10 Dispersion image of the experience work (the first source-to-

receiver offset¼ 5 m and receiver spacing¼ 4 m).

FIG. 11 A comparison of predicted soil layers by CWT and neighboring

borehole data.





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Journal of Testing and Evaluationweb.nchu.edu.tw/Pweb/Users/Feng/Research/13946.Pdf73 CWT on...

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Transcript of Journal of Testing and Evaluationweb.nchu.edu.tw/Pweb/Users/Feng/Research/13946.Pdf73 CWT on...