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Phase velocity approach for Suspension P–S Logging data analysis
Phase velocity approach for Suspension P–S Logging data analysis Chun-Hung Lin, Chih-Ping Lin PII: DOI: Reference:
S0926-9851(16)30094-5 doi: 10.1016/j.jappgeo.2016.04.001 APPGEO 2966
To appear in:
Journal of Applied Geophysics
Received date: Revised date: Accepted date:
10 January 2016 19 March 2016 1 April 2016
Please cite this article as: Lin, Chun-Hung, Lin, Chih-Ping, Phase velocity approach for Suspension P–S Logging data analysis, Journal of Applied Geophysics (2016), doi: 10.1016/j.jappgeo.2016.04.001
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ACCEPTED MANUSCRIPT Phase Velocity Approach for Suspension P-S Logging Data Analysis
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Chun-Hung Lin1 and Chih-Ping Lin2
Assistant Researcher, Disaster Prevention and Water Environment Research Center, National
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Chiao Tung University, 1001 Ta-Hsueh Road, Hsinchu, Taiwan. E-mail: [email protected]
Professor, Department of Civil Engineering, National Chiao Tung University, 1001 Ta-Hsueh
*Corresponding Author Chih-Ping Lin
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Road, Hsinchu, Taiwan. E-mail: [email protected]
Professor, Department of Civil Engineering National Chiao Tung University
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1001 Ta-Hsueh Road, Hisnchu, Taiwan. Tel. +886-3-513-1574
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Fax. +886-3-571-6257
Email: [email protected]
ACCEPTED MANUSCRIPT Phase Velocity Approach for Suspension P-S Logging Data Analysis
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Abstract: Due to the short receiver interval, results of Suspension P-S Logging are sensitive to
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the picking of first arrivals, which is currently carried out by manual picking in the time domain. However, manual picking can be ambiguous and depends heavily on the data quality and
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analysts’ experiences. Furthermore, no information regarding the effective frequency is obtained
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from first arrival times. A data reduction method based on phase velocity analysis of borehole acoustic waves is proposed herein. The aim is to provide an automatic procedure for more
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objective velocity analysis. The procedure utilizes the two-channel dispersion curve analysis, but becomes semi-empirical because an additional assumption is made to simplify the calculation
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and avoid the phase un-wrapping problem associated with the lack of low-frequency information. Some field data were used to evaluate the empirical parameter for calculating the shear wave velocity. Results show that the velocity difference between the proposed method and the
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conventional method based on manually-picked first arrivals are mostly within 15%. The
wave velocity.
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proposed method can be automated and provide the effective frequency of the obtained shear
Keywords: Suspension P-S Logging, Phase Velocity, Dispersion Analysis, Shear Wave Velocity
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ACCEPTED MANUSCRIPT 1. Introduction Evaluation of shear (S) wave velocity in actual field condition has important meaning in
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many fields of applied and pure geophysics. S-wave velocity (VS) within several hundred meters
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of the Earth’s surface is essential in specifying earthquake ground motions for earthquake engineering. In smaller scale, it is also important and useful for geotechnical problems, such as
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site characterization, liquefaction analysis, settlement analysis, and quality control of ground
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improvement, etc(Stokoe et al., 2004). Methods for measuring subsurface Vs can be divided into two major groups: non-invasive surface methods (e.g., surface wave method and seismic
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refraction method) and invasive borehole methods (e.g., down-hole method, cross-hole method, and Suspension P-S logging) (Luna and Jadi, 2000; Stokoe et al., 2004; Boore and Asten, 2008).
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While non-invasive surface methods are advancing and gaining popularity, direct measurements of waves in boreholes by logging remain to be the most effective means. Among the borehole methods, the Suspension P-S Logging is efficient and advantageous in that it only requires one
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borehole (uncased or PVC cased) and its measurement depth can be up to more than 200 meters
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without losing its spatial resolution and signal strength. The Suspension P-S Logging system is a velocity logging system based on the principles of unlocking type receivers and indirect excitation type sources (Kitsunezaki, 1978; Kitsunezaki 1980; Ogura et al., 1980). Since its invention, it has been increasingly used in geotechnical engineering for shallow depth investigation (Diehl et al. 2006; Borre and Asten, 2008; Biringen and Davie, 2010). More recently, other more advanced sonic well logging methods have been developed for deeper applications in oilfield (Arroyo Franco et al., 2006). However, these advanced tools have not been adapted for shallow and smaller diameter boreholes and made readily available for engineering applications. The Suspension P-S Logger has accumulated tremendous amount of 2
ACCEPTED MANUSCRIPT experiences in the past 20 years and continues to be a popular tool for seismic microzonation and other geotechnical engineering studies.
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In a Suspension P-S Logger, a non-symmetric seismic source and two receivers spaced 1 m apart are built into a single probe suspended by a cable. The source exerts pressure on the
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borehole wall via borehole water and the pressure wave is converted to seismic waves (P and S) at the borehole wall. The propagation of P wave and S wave along the wall is measured by
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detecting the behavior of the borehole water through receivers (a combination of hydrophone and
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geophone) of floating type. In this study, we focus on S wave since it is most relevant in earthquake and geotechnical engineering. The elapsed time between arrivals of the waves at the
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receivers is used to determine the average velocity of a 1-meter-high column of geomaterials around the borehole (Ohya, 1986; Nigbor and Imai, 1994). Currently, the data reduction of Suspension P-S Logging is based on the travel-time analysis by manually picking the first-arrival
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times of the seismograms (i.e. by visual inspection of the amplitudes and waveform changes). The estimated shear wave velocity is subjective, particularly in noisy data, and very sensitive to
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the picked arrival times because the two receivers is only 1 m apart. When large amount of seismograms are involved, picking of first arrivals is time-consuming and the uncertainty of Vs estimation can be very large. Several automatic first break picking methods were proposed to increase the efficiency of data processing, such as STA/LTA method (Anderson, 1978; Earle and Shearer, 1994), Akaike Information Criterion(AIC) method (Maeda, 1985; Zhang et al. , 2003), Artificial Neural Network method (Zhao and Takano, 1999), Modified Energy Ratio method (Wong et al. , 2009), etc. However, in the context of Suspension P-S Logging, none of them is practically robust and large bias from the desired picks is often encountered. Most techniques work in the time domain 3
ACCEPTED MANUSCRIPT to determine the transition between noise and noise plus signal by detecting rapid changes in a certain attribute (e.g. energy ratio, entropy, and fractal dimension). The spectral characteristic of
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the signal is not considered and the effective frequency of the measurement is unknown. In the Suspension P-S Logging, the ultimate goal is to obtain the S wave velocity from each
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paired measurements. In this study, we proposed a new approach based on phase velocity analysis of borehole acoustic waves. The aim was to provide a somewhat automatic procedure
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that avoids determining the onset of the first break and achieves more objective velocity
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estimation. First the fundamental of Suspension P-S Logging and characteristics of borehole acoustic waves are examined. Then the procedure based on the two-channel dispersion curve
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analysis is introduced. The validity of the proposed approach is investigated using some field data.
2. Suspension P-S Logging
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The principle of suspension S-wave logging was first introduced in Kitsunezake (1978,
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1980). It dwells upon the working of an indirect-type source effective in radiating shear wave and suspension type receivers of neutral buoyancy. A common available system is shown in Fig. 1. The system consists of a source, a pair of receivers, and a winch unit. The source is connected to the two receivers with a rubber tube in between and suspended by a cable lowered by the winch. It can operate either in un-cased or in PVC-cased borehole but must be in fluid-filled condition. In its early developments, the source was designed to effectively radiate only shear waves while minimizing radiation of P waves. The force is applied to a borehole wall indirectly by producing pressure changes of plus and minus in front and rear sides of the impact body in motion, resulting in indirect excitation on the borehole wall through consequent water motion 4
ACCEPTED MANUSCRIPT (Kitsunezake, 1978, 1980). To increase the radiation power and allow generation of P wave as well, current Suspension P-S Logging system uses fixed solenoid coils to drive a metal hammer
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to strike the inner surface of a thin walled cylindrical sleeve surrounding the sonde body, sending
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a pressure pulse out into the borehole fluid (Tanaka et al., 1985). After the probe is lowered to the specific depth for testing, the solenoid source generates a pulse (typically several hundred Hz to
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a few kHz) and the propagating waves are received by the lower and upper receivers spaced 1 m
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apart. Each suspension type receiver is composed of a two-directional horizontal geophone and a hydrophone. It detects horizontal motion of the borehole wall (ground motion of shear wave)
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through corresponding water motion. The seismograms from the horizontal geophones are used for S-wave velocity analysis. To facilitate shear wave identification, a reversed pulse is generated
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to produce another set of seismograms with 180 degree phase difference. The S-wave velocity is determined by the time difference between the arrivals of shear waves at the upper and lower
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geophones.
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3. Waves in a fluid-filled borehole The wave field generated in a Suspension P-S logger was treated approximately as that of a point single force in an infinite homogeneous medium, if the wavelength is much longer than the borehole diameter (Kitsunezake, 1980). However, the acoustic waves in a borehole are actually quite complex, depending on the energy source and the properties of the formation and the borehole (Haldorsen et al. 2006). When a monopole source is used, the transducer produces spherically symmetrical outgoing compressional waves in the borehole fluid, which in turn excite P and S head waves in the formation. According to the Snell’s law of refraction, the shear head waves generated as shear waves traveling up the borehole are only measurable in fast
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ACCEPTED MANUSCRIPT formations, in which S-wave velocity of the formation is higher than the fluid velocity. In addition to body waves, the interface (or surface) wave, known as Stoneley wave appears in
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nearly every monopole sonic log. Its speed is slower than the S wave and fluid velocity, and it is
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dispersive, which means different frequencies of Stoneley wave propagate at different speeds. In order to measure S-wave velocity in slow formations (with S wave velocity lower than the fluid
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velocity), a dipolar source is used to displace the borehole wall horizontally to generate shear
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waves. Arriving with shear waves, and spreading out behind it, is the dipole-generated flexural waves, which propagates sinuously up the borehole like a wave traveling along a rope fixed at
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one end. The flexural wave is also slightly dispersive, with the lowest frequencies travel fastest at the same speed as the nondispersive shear wave, when the wavelength is much longer than
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borehole diameter. In the Suspension P-S logging frequency range (several hundred Hz to a few kHz), the velocity difference between shear and flexural waves normally can be considered
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insignificant.
As pointed out in Hoyle et al. (1989), the dipole radiation pattern from the struck sleeve in
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the Suspension P-S Logging system is not symmetrical and, as a result, the transmitter will produce a large, undesirable monopole component. Furthermore, the frequency response of the system is not controllable and is likely to be dominated by the resonant frequencies of the sleeve. Therefore, the recorded waveforms in a Suspension P-S Logger may contain a significant amount of Stoneley waves. The effect of Stoneley wave and the effective frequency of the measurement should be examined. Other than direct determination of shear wave travel times, the dispersive analysis of interface waves is an alternative approach (Cheng and Toksoz, 1983). Two factors may contribute to the dispersion characteristics of Stoneley waves. One is the possible concentric variation of S-wave velocity in the formation caused by drilling disturbance. 6
ACCEPTED MANUSCRIPT The other is the geometry-induced dispersion, in which apparent velocity along the interface varies with frequency even though the intrinsic shear wave velocity does not. According to
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Cheng and Toksoz(1981), the relationship between the phase velocity of Stoneley waves and
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frequency in slow formations with homogeneous and isotropic condition is given by the implicit
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equation:
;
is
the
angular
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where,
(1)
frequency; Vph is the phase velocity of Stoneley wave, Vp and Vs are respectively the velocity of
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compression wave and shear wave of the material surrounding the borehole; Vf is the compression wave velocity of the borehole fluid; f and are the density of the fluid and formation, respectively; R is the borehole radius; Ii and Ki are the modified Bessel functions of
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the ith order of first kind and the second kind.
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The shaded area in Fig. 2 is the possible range of geometry-induced dispersion in cases where S-wave velocity is 350m/s, fluid velocity is 1500m/s, density of fluid is 1.2g/cm3, density of soils ranges from 1.5 to 2.1g/cm3, and Poisson’s ratio ranges from 0.25 to 0.4. The wavelength in abscissa is normalized to the radius of borehole and the phase velocity in ordinate is normalized to the S-wave velocity of the formation. By this normalization, the parameters in Eq. (1) are reduced to only two variables, namely the Poisson’s ratio and the ratio of formation density to fluid density /f. From the five cases A1-A5 in Fig. 2, it can be observed that Stoneley waves of short wavelength wave propagate in lower phase velocities due to the geometric dispersion. As the wavelength increases, the phase velocity would increase and 7
ACCEPTED MANUSCRIPT approach 0.98Vs. It also needs to be recognized that larger wavelength would be required to avoid the geometric dispersion in larger boreholes.
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Taking A3 as the reference case, increasing in A2 would only slightly reduce the extent
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and range of the geometric dispersion. On the contrary, decreasing /f in A4 would significantly
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aggravate the dispersive extent and range. This also can be observed from the comparison between A1 and A2. The results show that /f is the dominant factor to affect the geometric
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dispersion. The relative insensitivity of Stoneley wave dispersion to also implies that the phase
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velocity of Stoneley waves strongly depends on Vs rather than Vp. Utilizing this property, we can estimate Vs from the Stoneley waves in the slow formation. However, the effect of the density
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ratio /f still needs to be considered. The five cases A1-A5 in Fig. 2 cover almost all possible density range for soils. The velocity ratio Vph /Vs falls within a small range between 0.89 to 0.98. Although /f is the most sensitive factor of the Stoneley wave dispersion, the error can be
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limited within a tolerable range even if the estimation of Vs from Stoneley wave phase velocity is made without the information about /f. It is noted that above discussion on borehole geometric
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dispersion assumes homogenous condition. In additional to the borehole geometric dispersion, heterogeneity in the radial direction (perpendicular to the propagation direction of the Stonleley wave) will introduce dispersion in a similar way to surface wave dispersion.
4. Analysis of P-S Logging Data based on Phase Velocity To account for Stoneley waves generated by asymmetric dipole radiation pattern in the Suspension P-S Logging system, a phase velocity approach is proposed to analyze the Suspension P-S Logging data. The new method includes three procedures: (1) time window pre-processing, (2) dispersion analysis for phase velocity, and (3) shear wave velocity 8
ACCEPTED MANUSCRIPT computation. The last step involves an empirical parameter. The suggested value was statistically determined by analyzing 52 pair seismograms of P-S Logging data gathered in western Taiwan.
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These Suspension P-S Logging data are all of high signal to noise ratio and their arrival times
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could be easily manually picked. Details of each step are described as follows:
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4.1 Pre-processing
A time window is applied before conducting the dispersion analysis to minimize possible
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distortion by different propagating modes. The Tukey Window (Tukey, 1967) with 60% of the
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window to be 1 was adopted for data pre-processing. As shown in Fig. 3, sometimes two or more wave packets appear at different times in the field data. The two-channel dispersion analysis to
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be introduced is incapable of separating different modes (Lin and Chang, 2004; Lin and Lin, 2012). It may induce some errors if time window is not applied to the original signal (line with light color in Fig. 3) to keep only the first desired wave packet and eliminate subsequent arriving
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waves. It is suggested that the end cut edge of the window be located in the local minimum of the
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envelope between two wave packets as illustrated in Fig. 3. 4.2 Analysis of Phase Velocity The proposed spectral analysis for Suspension P-S Logging data is based on the two-channel spectral analysis originally introduced in the SASW (Spectral Analysis of Surface Wave) method (Heisey et al., 1982), which has been successfully applied in surface wave testing both on the surface and in the borehole (Kalinski and Stokoe II, 2003). The Suspension P-S Logging is similar to SASW testing in that they both use two separated receivers to record waves generated by an impact source. In the SASW analysis, Fourier transforms are performed on the two signals and the phase difference between the two receivers at each frequency is computed. After unwrapping the folding phase difference, dispersion curve is extracted by the following 9
ACCEPTED MANUSCRIPT relation
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(2)
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where Vph is the phase velocity, f is the frequency, Δϕ is the phase difference after unwrapping and Δx is the distance between the two receivers (=1 m in Suspension P-S Logging). With the
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dispersion relation, shear wave velocity can then be estimated by inverting the dispersion curve.
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One major problem arises when applying this procedure in Suspension P-S Logging data. Unwrapping the phase difference between the two receivers is a tricky task, which directly
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influence the result of dispersion analysis. Unwrapping is an accumulative process from low to high frequencies and should be conducted very carefully for each frequency within the maximum
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frequency of interest. The correctness of the accumulated unwrapping greatly depends on the accuracy of phase at low frequencies. However, as shown in Fig. 4a, the energy of the waveform generated by Suspension P-S logger is quite band limited. The signal to noise ratio is poor below
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300Hz. As a consequence, the unwrapped phase difference between two receivers is corrupted
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due to the lack of information in the low frequency range, as illustrated in Fig. 4b. The resulting phase velocities, shown in Fig. 4c as an example, deviate significantly from the wave velocity determined by the manually arrival picking. In order to deal with this problem, a simplifying assumption was made. Considering that Stoneley wave is not highly dispersive, it is assumed that the phase-frequency (Δϕ-f) curve is linear and approaches the origin at zero frequency. Following this assumption, the formula for calculating phase velocity in Eq. (2) can be simplified as (3)
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ACCEPTED MANUSCRIPT The phase velocity is considered locally a constant and proportional to inverse of the Δϕ-f slope. Comparing to Eq. (2), computation of phase velocity by the proposed method requires only the
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slope in the unwrapped Δϕ-f plot. The correctness of accumulated phase difference is not
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important, as long as a proper frequency range of good data quality is selected for determining the Δϕ-f slope. Field measurements show that most of the Δϕ-f slopes around the peak of cross
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spectrum between two receivers are approximately linear and stable. The proper frequency range
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for determining the slope is suggested to be the linear section around the peak of cross power
area in Fig. 4.
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4.3 Calculation of Shear-wave Velocity
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spectrum (i.e. within 50% of the peak of the cross power spectrum), as illustrated by the shaded
According to the theory of Stoneley wave in a homogeneous and isotropic “slow” formation, the phase velocity for sufficiently long wavelength is 0.98 of S-wave velocity. In such a
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condition, the shear wave velocity can be obtained from the measured phase velocity as
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(4)
where a is a constant equal to 1.02. The error that may result from the geometric dispersion of Stoneley wave and the assumption of Eq. (3) should be examined. The possible range of errors in terms of percentage error in the estimated S-wave velocity is depicted in Fig. 5a. Using any combination of Poisson’s ratio and the ratio of formation density to fluid density /f in the range listed in Fig. 2, the corresponding percentage errors in Vs as a function of the normalized wavelength can be calculated. Lower bound and upper bound of errors from all possible combinations are circumscribed to reveal the possible range of errors in Fig. 5a. As an example to illustrate the error introduced by the proposed method, Fig. 5b shows the theoretical 11
ACCEPTED MANUSCRIPT phase-frequency (Δϕ-f) curve for case A5 and that approximated by Eq. (3) using the slope in the frequency range from 1350 to 1650 Hz. The estimated phase angle by the proposed method
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deviates from the theoretical curve due to dispersion. Overestimation in phase difference results
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in underestimation of phase velocity and negative percentage error in Fig. 5a. Also shown in Fig. 5b is the linear phase-frequency (Δϕ-f) curve for non-dispersive condition with Vph=1.02Vs. At
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lower frequencies, it is not dispersive and Δϕ-f curve is linear. Equation (3) is exact under these
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circumstances. Beyond certain frequency, it becomes dispersive and Δϕ-f curve becomes non-linear. The slope of Δϕ-f curve increases as frequency increases (wavelength decreases). The
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linear assumption in Eq. (3) introduces larger errors in higher frequencies (shorter wavelengths), as shown in Fig. 5a. The part of error due to constant a=1.02 alone, which is equivalent to Fig. 2,
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is also indicated in Fig. 5a for comparison. The error Shown in Fig. 5a may be corrected by applying an appropriate a value in Eq. (4) if information on Poisson’s ratio and densities are available. Possible value of a ranges from 1.02 to 1.2, as shown in Fig. 5c. Without information
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of Poisson’s ratio and densities, the a value in Eq. (4) has to be determined empirically.
5. Empirical Evaluation of Parameter a Fifty two datasets collected at five different sites in western Taiwan were selected for evaluating the proper empirical value for parameter a. The selected data are of high signal to noise ratio and it is relatively easy to manually pick the S-wave arrival times. Boreholes were cased with PVC casings and backfilled with sands, which may not be the best practice but common in the local practice. Phase velocities determined by the proposed method were plotted against the shear wave velocities from manually-picked arrival times in Fig. 6. The results show that the ratio of shear wave velocity to phase velocity ranged from 1.0 to 1.4. In addition to the
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ACCEPTED MANUSCRIPT velocity analysis, the proposed method gives more insight to the data by providing extra information on the effective frequency, as shown in Fig. 7. The gray image in Fig. 7a indicates
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the cross power spectrum amplitude within the selected frequency range, and the stars marked
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the peaks. With information on the effective frequency, the effective wavelength can be further obtained, as shown in Fig. 7b. The dominant frequency of the pulse generated by a P-S Logger is
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typically between several hundred Hz to a few kHz. In the selected data, the effective frequency
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of velocity measurement ranges from 500 Hz to 1500 Hz. The corresponding wavelength is
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between 0.3 m to 0.7 m.
From Fig. 6, the parameter a ranges from 1-1.4. It is not reasonable to have a value smaller
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than 1.02. A couple of data lower than 1 might be caused by some slight errors in the manually-picked arrival times. What is of greater concern is that some a values are greater than 1.25, higher than expected in Fig. 5c. As discussed in the last section, dispersion leads to
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underestimation of phase velocity by the proposed method. Lower phase velocity is estimated in more dispersive case. Therefore, it is speculated that higher a values result from more dispersive
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condition. In addition to the borehole geometric dispersion, other mechanism may contribute to the dispersion. Borehole disturbance and backfill materials outside the PVC casing may form a concentric vertically-layered medium within the influence zone. This layered heterogeneity in the direction perpendicular to the direction of the wave propagation adds additional dispersion in a similar way to surface waves in horizontally layered medium. The dispersion is thus induced not only by the borehole geometry but also by the vertically layered medium. This would increase the dispersive level and result in higher a value. Concentric layer model can be considered and inverted for shear wave velocities. However, as shown in Fig. 4a, the lack of energy in low frequency would cause un-wrapping problem while retrieving the dispersion curve. 13
ACCEPTED MANUSCRIPT Instead, an empirical a value of 1.14 is obtained by linear regression to partially account for the effect of dispersion, as shown in Fig. 6. The difference (error) between the manually-picked
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shear wave velocity and the shear wave velocity from the proposed method using a=1.14 is
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shown in Fig. 8a. Over ninety percent of the estimated shear wave velocities are within 15% error. This is considered quite acceptable for Suspension P-S logging data. The data were
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revisited to gain more insights on the results. Each data point in Fig. 6 can be represented by its
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respective value of parameter a. Combining with the wavelength information in Fig. 7b, the relationship between parameter a and wavelength normalized by borehole radius is presented in
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Fig. 8b. Obviously, some a values are apparently greater than that caused by geometric dispersion in Fig. 5c. It also reveals a trend that errors tend to decrease with increasing
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wavelength. This further supports the speculation that more dispersion is caused by concentric variation of S-wave velocity due to borehole disturbance. The effect of the borehole disturbance is reduced as the wavelength increases. Therefore, better results may be achieved by lowering the
6. Conclusion
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dominant frequencies generated by the Suspension P-S Logger.
A new approach for Suspension P-S Logging data analysis is proposed based on two-channel dispersion curve analysis of borehole acoustic waves. An additional assumption is made to simplify the calculation of shear wave velocity and avoid the phase un-wrapping problem associated with the lack of low-frequency information in the dispersion analysis. The proposed method can be automated and provide the effective frequency of the obtained shear wave velocity. Validity and effect of the simplifying assumption were investigated using some field data. In addition to borehole geometric dispersion, it was found that material dispersion due
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ACCEPTED MANUSCRIPT to borehole disturbance may be the major source of error. The effect of dispersion diminishes as wavelength increases. To partially account for the effect of dispersion, the empirical value for the
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ratio of shear wave velocity to phase velocity was suggested to be 1.14 based on the field data.
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Results show that the velocity difference between the proposed method and the conventional method based on manually-picked first arrivals are mostly within 15%. Better results may be
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achieved by lowering the dominant frequencies generated by the source to meet the long
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wavelength condition.
1.
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SEG Meeting, Houston.
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21. Ohya, S., 1986. In Situ P and S Wave Velocity Measurement. Proceedings of In-Situ ’86, Use of In-Situ Tests In Geotechnical Engineering, an ASCE Specialty Conference sponsored by the Geotechnical Engineering Division of ASCE and co-sponsored by the Civil Engineering Dept of Virginia Tech. 22. OYO Corporation, 1998. Suspension P-S Log 170 Operation Manual. 23. Stokoe II, K.H., John, S.H., and Woods, R.D., 2004. Some contributions of in situ geophysical measurements to solving geotechnical engineering problems. Proceedings of 2nd International Conference on Site Characterization, Porto, Portugal, 97-132. 24. Tanaka, K., Ogura, K., and Miura, H., 1985. Application of Suspension P-S Logging 17
ACCEPTED MANUSCRIPT System to High Velocity Ground. 4th ASEG Conference, 289-291. 25. Tukey, J. W., 1967. An introduction to the calculations of numerical spectrum analysis. In:
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Harris, B. (ed.), Spectral Analysis of Time Series, Wiley, New York, 25-46. 26. Wong, J., Han, L., Stewart, R. R., Bentley, L. R., and Bancroft, J. C., 2009. Geophysical
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Well Logs from a Shallow Test Well and Automatic Determination of Formation Velocities from Full-Waveform Sonic Logs. Canadian Society of Exploration Geophysicists Recorder,
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34(4).
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27. Zhang, H., Thurber, C., and Rowe, C., 2003. Automatic P-wave arrival detection and picking with multiscale wavelet analysis for single-component recording. Bulletin of the
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Seismological Society of America, 93, 1904-1912. 28. Zhao, Y., and Takano, K., 1999. An artificial neural network approach for broadband
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seismic phase picking. Bulletin of the Seismological Society of America, 89, 670-680.
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in “slow” formations. Fig. 3. Pre-processing by time windowing.
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Fig. 4. Illustration of the proposed method: (a) Fourier spectrums of the near and far receivers
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and thieir cross power spectrum, (b)phase difference vs. frequency and the frequency range selected for analysis, and (c) dispersion curve directly from unwrapped phase difference and the
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phase velocity estimated by the proposed method.
Fig. 5. Theoratical evalution of the proposed method: (a) The possible errors based on long
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wavelength assumption(i.e. a=1.02), (b) the source of error illustrated by case A5 in Fig. 2., and (c) the possible value for parameter a to compensate for the effect of geometric dispersion. Fig. 6. Empirical value for parameter a from the manually-picked S-wave velocity and the phase
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velocity from the proposed method.
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Fig. 7. (a) Effective frequency range, in which stars being the peaks of cross power spectrum in the data analysis, and (b) effective wavelengths retrieved from the stars. Fig. 8. (a) Percentage error in Vs of the proposed method compared to the manually-picked Vs; (b) each data point is represented by its respecitve value of parameter a and compared to the theoratical evalution (indicated by the shaded area and lines) in Fig. 5c.
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ACCEPTED MANUSCRIPT Highlights
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Comprehensive review of factors affecting Suspension P-S Logging. A new data reduction method based on borehole acoustic waves is proposed for Suspension P-S Logging data. The proposed method is more objective can be readily automated and provide extra information on the effective frequencies of Vs measurements. The effect of borehole disturbance could be examined based on the proposed method.
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S0926-9851(16)30094-5 doi: 10.1016/j.jappgeo.2016.04.001 APPGEO 2966
To appear in:
Journal of Applied Geophysics
Received date: Revised date: Accepted date:
10 January 2016 19 March 2016 1 April 2016
Please cite this article as: Lin, Chun-Hung, Lin, Chih-Ping, Phase velocity approach for Suspension P–S Logging data analysis, Journal of Applied Geophysics (2016), doi: 10.1016/j.jappgeo.2016.04.001
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT Phase Velocity Approach for Suspension P-S Logging Data Analysis
1
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Chun-Hung Lin1 and Chih-Ping Lin2
Assistant Researcher, Disaster Prevention and Water Environment Research Center, National
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Chiao Tung University, 1001 Ta-Hsueh Road, Hsinchu, Taiwan. E-mail: [email protected]
Professor, Department of Civil Engineering, National Chiao Tung University, 1001 Ta-Hsueh
*Corresponding Author Chih-Ping Lin
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Road, Hsinchu, Taiwan. E-mail: [email protected]
Professor, Department of Civil Engineering National Chiao Tung University
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1001 Ta-Hsueh Road, Hisnchu, Taiwan. Tel. +886-3-513-1574
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Fax. +886-3-571-6257
Email: [email protected]
ACCEPTED MANUSCRIPT Phase Velocity Approach for Suspension P-S Logging Data Analysis
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Abstract: Due to the short receiver interval, results of Suspension P-S Logging are sensitive to
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the picking of first arrivals, which is currently carried out by manual picking in the time domain. However, manual picking can be ambiguous and depends heavily on the data quality and
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analysts’ experiences. Furthermore, no information regarding the effective frequency is obtained
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from first arrival times. A data reduction method based on phase velocity analysis of borehole acoustic waves is proposed herein. The aim is to provide an automatic procedure for more
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objective velocity analysis. The procedure utilizes the two-channel dispersion curve analysis, but becomes semi-empirical because an additional assumption is made to simplify the calculation
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and avoid the phase un-wrapping problem associated with the lack of low-frequency information. Some field data were used to evaluate the empirical parameter for calculating the shear wave velocity. Results show that the velocity difference between the proposed method and the
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conventional method based on manually-picked first arrivals are mostly within 15%. The
wave velocity.
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proposed method can be automated and provide the effective frequency of the obtained shear
Keywords: Suspension P-S Logging, Phase Velocity, Dispersion Analysis, Shear Wave Velocity
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ACCEPTED MANUSCRIPT 1. Introduction Evaluation of shear (S) wave velocity in actual field condition has important meaning in
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many fields of applied and pure geophysics. S-wave velocity (VS) within several hundred meters
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of the Earth’s surface is essential in specifying earthquake ground motions for earthquake engineering. In smaller scale, it is also important and useful for geotechnical problems, such as
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site characterization, liquefaction analysis, settlement analysis, and quality control of ground
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improvement, etc(Stokoe et al., 2004). Methods for measuring subsurface Vs can be divided into two major groups: non-invasive surface methods (e.g., surface wave method and seismic
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refraction method) and invasive borehole methods (e.g., down-hole method, cross-hole method, and Suspension P-S logging) (Luna and Jadi, 2000; Stokoe et al., 2004; Boore and Asten, 2008).
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While non-invasive surface methods are advancing and gaining popularity, direct measurements of waves in boreholes by logging remain to be the most effective means. Among the borehole methods, the Suspension P-S Logging is efficient and advantageous in that it only requires one
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borehole (uncased or PVC cased) and its measurement depth can be up to more than 200 meters
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without losing its spatial resolution and signal strength. The Suspension P-S Logging system is a velocity logging system based on the principles of unlocking type receivers and indirect excitation type sources (Kitsunezaki, 1978; Kitsunezaki 1980; Ogura et al., 1980). Since its invention, it has been increasingly used in geotechnical engineering for shallow depth investigation (Diehl et al. 2006; Borre and Asten, 2008; Biringen and Davie, 2010). More recently, other more advanced sonic well logging methods have been developed for deeper applications in oilfield (Arroyo Franco et al., 2006). However, these advanced tools have not been adapted for shallow and smaller diameter boreholes and made readily available for engineering applications. The Suspension P-S Logger has accumulated tremendous amount of 2
ACCEPTED MANUSCRIPT experiences in the past 20 years and continues to be a popular tool for seismic microzonation and other geotechnical engineering studies.
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In a Suspension P-S Logger, a non-symmetric seismic source and two receivers spaced 1 m apart are built into a single probe suspended by a cable. The source exerts pressure on the
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borehole wall via borehole water and the pressure wave is converted to seismic waves (P and S) at the borehole wall. The propagation of P wave and S wave along the wall is measured by
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detecting the behavior of the borehole water through receivers (a combination of hydrophone and
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geophone) of floating type. In this study, we focus on S wave since it is most relevant in earthquake and geotechnical engineering. The elapsed time between arrivals of the waves at the
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receivers is used to determine the average velocity of a 1-meter-high column of geomaterials around the borehole (Ohya, 1986; Nigbor and Imai, 1994). Currently, the data reduction of Suspension P-S Logging is based on the travel-time analysis by manually picking the first-arrival
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times of the seismograms (i.e. by visual inspection of the amplitudes and waveform changes). The estimated shear wave velocity is subjective, particularly in noisy data, and very sensitive to
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the picked arrival times because the two receivers is only 1 m apart. When large amount of seismograms are involved, picking of first arrivals is time-consuming and the uncertainty of Vs estimation can be very large. Several automatic first break picking methods were proposed to increase the efficiency of data processing, such as STA/LTA method (Anderson, 1978; Earle and Shearer, 1994), Akaike Information Criterion(AIC) method (Maeda, 1985; Zhang et al. , 2003), Artificial Neural Network method (Zhao and Takano, 1999), Modified Energy Ratio method (Wong et al. , 2009), etc. However, in the context of Suspension P-S Logging, none of them is practically robust and large bias from the desired picks is often encountered. Most techniques work in the time domain 3
ACCEPTED MANUSCRIPT to determine the transition between noise and noise plus signal by detecting rapid changes in a certain attribute (e.g. energy ratio, entropy, and fractal dimension). The spectral characteristic of
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the signal is not considered and the effective frequency of the measurement is unknown. In the Suspension P-S Logging, the ultimate goal is to obtain the S wave velocity from each
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paired measurements. In this study, we proposed a new approach based on phase velocity analysis of borehole acoustic waves. The aim was to provide a somewhat automatic procedure
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that avoids determining the onset of the first break and achieves more objective velocity
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estimation. First the fundamental of Suspension P-S Logging and characteristics of borehole acoustic waves are examined. Then the procedure based on the two-channel dispersion curve
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analysis is introduced. The validity of the proposed approach is investigated using some field data.
2. Suspension P-S Logging
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The principle of suspension S-wave logging was first introduced in Kitsunezake (1978,
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1980). It dwells upon the working of an indirect-type source effective in radiating shear wave and suspension type receivers of neutral buoyancy. A common available system is shown in Fig. 1. The system consists of a source, a pair of receivers, and a winch unit. The source is connected to the two receivers with a rubber tube in between and suspended by a cable lowered by the winch. It can operate either in un-cased or in PVC-cased borehole but must be in fluid-filled condition. In its early developments, the source was designed to effectively radiate only shear waves while minimizing radiation of P waves. The force is applied to a borehole wall indirectly by producing pressure changes of plus and minus in front and rear sides of the impact body in motion, resulting in indirect excitation on the borehole wall through consequent water motion 4
ACCEPTED MANUSCRIPT (Kitsunezake, 1978, 1980). To increase the radiation power and allow generation of P wave as well, current Suspension P-S Logging system uses fixed solenoid coils to drive a metal hammer
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to strike the inner surface of a thin walled cylindrical sleeve surrounding the sonde body, sending
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a pressure pulse out into the borehole fluid (Tanaka et al., 1985). After the probe is lowered to the specific depth for testing, the solenoid source generates a pulse (typically several hundred Hz to
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a few kHz) and the propagating waves are received by the lower and upper receivers spaced 1 m
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apart. Each suspension type receiver is composed of a two-directional horizontal geophone and a hydrophone. It detects horizontal motion of the borehole wall (ground motion of shear wave)
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through corresponding water motion. The seismograms from the horizontal geophones are used for S-wave velocity analysis. To facilitate shear wave identification, a reversed pulse is generated
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to produce another set of seismograms with 180 degree phase difference. The S-wave velocity is determined by the time difference between the arrivals of shear waves at the upper and lower
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geophones.
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3. Waves in a fluid-filled borehole The wave field generated in a Suspension P-S logger was treated approximately as that of a point single force in an infinite homogeneous medium, if the wavelength is much longer than the borehole diameter (Kitsunezake, 1980). However, the acoustic waves in a borehole are actually quite complex, depending on the energy source and the properties of the formation and the borehole (Haldorsen et al. 2006). When a monopole source is used, the transducer produces spherically symmetrical outgoing compressional waves in the borehole fluid, which in turn excite P and S head waves in the formation. According to the Snell’s law of refraction, the shear head waves generated as shear waves traveling up the borehole are only measurable in fast
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ACCEPTED MANUSCRIPT formations, in which S-wave velocity of the formation is higher than the fluid velocity. In addition to body waves, the interface (or surface) wave, known as Stoneley wave appears in
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nearly every monopole sonic log. Its speed is slower than the S wave and fluid velocity, and it is
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dispersive, which means different frequencies of Stoneley wave propagate at different speeds. In order to measure S-wave velocity in slow formations (with S wave velocity lower than the fluid
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velocity), a dipolar source is used to displace the borehole wall horizontally to generate shear
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waves. Arriving with shear waves, and spreading out behind it, is the dipole-generated flexural waves, which propagates sinuously up the borehole like a wave traveling along a rope fixed at
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one end. The flexural wave is also slightly dispersive, with the lowest frequencies travel fastest at the same speed as the nondispersive shear wave, when the wavelength is much longer than
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borehole diameter. In the Suspension P-S logging frequency range (several hundred Hz to a few kHz), the velocity difference between shear and flexural waves normally can be considered
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insignificant.
As pointed out in Hoyle et al. (1989), the dipole radiation pattern from the struck sleeve in
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the Suspension P-S Logging system is not symmetrical and, as a result, the transmitter will produce a large, undesirable monopole component. Furthermore, the frequency response of the system is not controllable and is likely to be dominated by the resonant frequencies of the sleeve. Therefore, the recorded waveforms in a Suspension P-S Logger may contain a significant amount of Stoneley waves. The effect of Stoneley wave and the effective frequency of the measurement should be examined. Other than direct determination of shear wave travel times, the dispersive analysis of interface waves is an alternative approach (Cheng and Toksoz, 1983). Two factors may contribute to the dispersion characteristics of Stoneley waves. One is the possible concentric variation of S-wave velocity in the formation caused by drilling disturbance. 6
ACCEPTED MANUSCRIPT The other is the geometry-induced dispersion, in which apparent velocity along the interface varies with frequency even though the intrinsic shear wave velocity does not. According to
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Cheng and Toksoz(1981), the relationship between the phase velocity of Stoneley waves and
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frequency in slow formations with homogeneous and isotropic condition is given by the implicit
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equation:
;
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angular
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where,
(1)
frequency; Vph is the phase velocity of Stoneley wave, Vp and Vs are respectively the velocity of
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compression wave and shear wave of the material surrounding the borehole; Vf is the compression wave velocity of the borehole fluid; f and are the density of the fluid and formation, respectively; R is the borehole radius; Ii and Ki are the modified Bessel functions of
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the ith order of first kind and the second kind.
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The shaded area in Fig. 2 is the possible range of geometry-induced dispersion in cases where S-wave velocity is 350m/s, fluid velocity is 1500m/s, density of fluid is 1.2g/cm3, density of soils ranges from 1.5 to 2.1g/cm3, and Poisson’s ratio ranges from 0.25 to 0.4. The wavelength in abscissa is normalized to the radius of borehole and the phase velocity in ordinate is normalized to the S-wave velocity of the formation. By this normalization, the parameters in Eq. (1) are reduced to only two variables, namely the Poisson’s ratio and the ratio of formation density to fluid density /f. From the five cases A1-A5 in Fig. 2, it can be observed that Stoneley waves of short wavelength wave propagate in lower phase velocities due to the geometric dispersion. As the wavelength increases, the phase velocity would increase and 7
ACCEPTED MANUSCRIPT approach 0.98Vs. It also needs to be recognized that larger wavelength would be required to avoid the geometric dispersion in larger boreholes.
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Taking A3 as the reference case, increasing in A2 would only slightly reduce the extent
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and range of the geometric dispersion. On the contrary, decreasing /f in A4 would significantly
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aggravate the dispersive extent and range. This also can be observed from the comparison between A1 and A2. The results show that /f is the dominant factor to affect the geometric
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dispersion. The relative insensitivity of Stoneley wave dispersion to also implies that the phase
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velocity of Stoneley waves strongly depends on Vs rather than Vp. Utilizing this property, we can estimate Vs from the Stoneley waves in the slow formation. However, the effect of the density
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ratio /f still needs to be considered. The five cases A1-A5 in Fig. 2 cover almost all possible density range for soils. The velocity ratio Vph /Vs falls within a small range between 0.89 to 0.98. Although /f is the most sensitive factor of the Stoneley wave dispersion, the error can be
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limited within a tolerable range even if the estimation of Vs from Stoneley wave phase velocity is made without the information about /f. It is noted that above discussion on borehole geometric
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dispersion assumes homogenous condition. In additional to the borehole geometric dispersion, heterogeneity in the radial direction (perpendicular to the propagation direction of the Stonleley wave) will introduce dispersion in a similar way to surface wave dispersion.
4. Analysis of P-S Logging Data based on Phase Velocity To account for Stoneley waves generated by asymmetric dipole radiation pattern in the Suspension P-S Logging system, a phase velocity approach is proposed to analyze the Suspension P-S Logging data. The new method includes three procedures: (1) time window pre-processing, (2) dispersion analysis for phase velocity, and (3) shear wave velocity 8
ACCEPTED MANUSCRIPT computation. The last step involves an empirical parameter. The suggested value was statistically determined by analyzing 52 pair seismograms of P-S Logging data gathered in western Taiwan.
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These Suspension P-S Logging data are all of high signal to noise ratio and their arrival times
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could be easily manually picked. Details of each step are described as follows:
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4.1 Pre-processing
A time window is applied before conducting the dispersion analysis to minimize possible
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distortion by different propagating modes. The Tukey Window (Tukey, 1967) with 60% of the
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window to be 1 was adopted for data pre-processing. As shown in Fig. 3, sometimes two or more wave packets appear at different times in the field data. The two-channel dispersion analysis to
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be introduced is incapable of separating different modes (Lin and Chang, 2004; Lin and Lin, 2012). It may induce some errors if time window is not applied to the original signal (line with light color in Fig. 3) to keep only the first desired wave packet and eliminate subsequent arriving
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waves. It is suggested that the end cut edge of the window be located in the local minimum of the
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envelope between two wave packets as illustrated in Fig. 3. 4.2 Analysis of Phase Velocity The proposed spectral analysis for Suspension P-S Logging data is based on the two-channel spectral analysis originally introduced in the SASW (Spectral Analysis of Surface Wave) method (Heisey et al., 1982), which has been successfully applied in surface wave testing both on the surface and in the borehole (Kalinski and Stokoe II, 2003). The Suspension P-S Logging is similar to SASW testing in that they both use two separated receivers to record waves generated by an impact source. In the SASW analysis, Fourier transforms are performed on the two signals and the phase difference between the two receivers at each frequency is computed. After unwrapping the folding phase difference, dispersion curve is extracted by the following 9
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(2)
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where Vph is the phase velocity, f is the frequency, Δϕ is the phase difference after unwrapping and Δx is the distance between the two receivers (=1 m in Suspension P-S Logging). With the
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dispersion relation, shear wave velocity can then be estimated by inverting the dispersion curve.
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One major problem arises when applying this procedure in Suspension P-S Logging data. Unwrapping the phase difference between the two receivers is a tricky task, which directly
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influence the result of dispersion analysis. Unwrapping is an accumulative process from low to high frequencies and should be conducted very carefully for each frequency within the maximum
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frequency of interest. The correctness of the accumulated unwrapping greatly depends on the accuracy of phase at low frequencies. However, as shown in Fig. 4a, the energy of the waveform generated by Suspension P-S logger is quite band limited. The signal to noise ratio is poor below
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300Hz. As a consequence, the unwrapped phase difference between two receivers is corrupted
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due to the lack of information in the low frequency range, as illustrated in Fig. 4b. The resulting phase velocities, shown in Fig. 4c as an example, deviate significantly from the wave velocity determined by the manually arrival picking. In order to deal with this problem, a simplifying assumption was made. Considering that Stoneley wave is not highly dispersive, it is assumed that the phase-frequency (Δϕ-f) curve is linear and approaches the origin at zero frequency. Following this assumption, the formula for calculating phase velocity in Eq. (2) can be simplified as (3)
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ACCEPTED MANUSCRIPT The phase velocity is considered locally a constant and proportional to inverse of the Δϕ-f slope. Comparing to Eq. (2), computation of phase velocity by the proposed method requires only the
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slope in the unwrapped Δϕ-f plot. The correctness of accumulated phase difference is not
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important, as long as a proper frequency range of good data quality is selected for determining the Δϕ-f slope. Field measurements show that most of the Δϕ-f slopes around the peak of cross
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spectrum between two receivers are approximately linear and stable. The proper frequency range
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for determining the slope is suggested to be the linear section around the peak of cross power
area in Fig. 4.
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4.3 Calculation of Shear-wave Velocity
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spectrum (i.e. within 50% of the peak of the cross power spectrum), as illustrated by the shaded
According to the theory of Stoneley wave in a homogeneous and isotropic “slow” formation, the phase velocity for sufficiently long wavelength is 0.98 of S-wave velocity. In such a
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condition, the shear wave velocity can be obtained from the measured phase velocity as
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(4)
where a is a constant equal to 1.02. The error that may result from the geometric dispersion of Stoneley wave and the assumption of Eq. (3) should be examined. The possible range of errors in terms of percentage error in the estimated S-wave velocity is depicted in Fig. 5a. Using any combination of Poisson’s ratio and the ratio of formation density to fluid density /f in the range listed in Fig. 2, the corresponding percentage errors in Vs as a function of the normalized wavelength can be calculated. Lower bound and upper bound of errors from all possible combinations are circumscribed to reveal the possible range of errors in Fig. 5a. As an example to illustrate the error introduced by the proposed method, Fig. 5b shows the theoretical 11
ACCEPTED MANUSCRIPT phase-frequency (Δϕ-f) curve for case A5 and that approximated by Eq. (3) using the slope in the frequency range from 1350 to 1650 Hz. The estimated phase angle by the proposed method
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deviates from the theoretical curve due to dispersion. Overestimation in phase difference results
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in underestimation of phase velocity and negative percentage error in Fig. 5a. Also shown in Fig. 5b is the linear phase-frequency (Δϕ-f) curve for non-dispersive condition with Vph=1.02Vs. At
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lower frequencies, it is not dispersive and Δϕ-f curve is linear. Equation (3) is exact under these
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circumstances. Beyond certain frequency, it becomes dispersive and Δϕ-f curve becomes non-linear. The slope of Δϕ-f curve increases as frequency increases (wavelength decreases). The
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linear assumption in Eq. (3) introduces larger errors in higher frequencies (shorter wavelengths), as shown in Fig. 5a. The part of error due to constant a=1.02 alone, which is equivalent to Fig. 2,
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is also indicated in Fig. 5a for comparison. The error Shown in Fig. 5a may be corrected by applying an appropriate a value in Eq. (4) if information on Poisson’s ratio and densities are available. Possible value of a ranges from 1.02 to 1.2, as shown in Fig. 5c. Without information
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of Poisson’s ratio and densities, the a value in Eq. (4) has to be determined empirically.
5. Empirical Evaluation of Parameter a Fifty two datasets collected at five different sites in western Taiwan were selected for evaluating the proper empirical value for parameter a. The selected data are of high signal to noise ratio and it is relatively easy to manually pick the S-wave arrival times. Boreholes were cased with PVC casings and backfilled with sands, which may not be the best practice but common in the local practice. Phase velocities determined by the proposed method were plotted against the shear wave velocities from manually-picked arrival times in Fig. 6. The results show that the ratio of shear wave velocity to phase velocity ranged from 1.0 to 1.4. In addition to the
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the cross power spectrum amplitude within the selected frequency range, and the stars marked
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the peaks. With information on the effective frequency, the effective wavelength can be further obtained, as shown in Fig. 7b. The dominant frequency of the pulse generated by a P-S Logger is
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typically between several hundred Hz to a few kHz. In the selected data, the effective frequency
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of velocity measurement ranges from 500 Hz to 1500 Hz. The corresponding wavelength is
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between 0.3 m to 0.7 m.
From Fig. 6, the parameter a ranges from 1-1.4. It is not reasonable to have a value smaller
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than 1.02. A couple of data lower than 1 might be caused by some slight errors in the manually-picked arrival times. What is of greater concern is that some a values are greater than 1.25, higher than expected in Fig. 5c. As discussed in the last section, dispersion leads to
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underestimation of phase velocity by the proposed method. Lower phase velocity is estimated in more dispersive case. Therefore, it is speculated that higher a values result from more dispersive
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condition. In addition to the borehole geometric dispersion, other mechanism may contribute to the dispersion. Borehole disturbance and backfill materials outside the PVC casing may form a concentric vertically-layered medium within the influence zone. This layered heterogeneity in the direction perpendicular to the direction of the wave propagation adds additional dispersion in a similar way to surface waves in horizontally layered medium. The dispersion is thus induced not only by the borehole geometry but also by the vertically layered medium. This would increase the dispersive level and result in higher a value. Concentric layer model can be considered and inverted for shear wave velocities. However, as shown in Fig. 4a, the lack of energy in low frequency would cause un-wrapping problem while retrieving the dispersion curve. 13
ACCEPTED MANUSCRIPT Instead, an empirical a value of 1.14 is obtained by linear regression to partially account for the effect of dispersion, as shown in Fig. 6. The difference (error) between the manually-picked
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shear wave velocity and the shear wave velocity from the proposed method using a=1.14 is
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shown in Fig. 8a. Over ninety percent of the estimated shear wave velocities are within 15% error. This is considered quite acceptable for Suspension P-S logging data. The data were
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revisited to gain more insights on the results. Each data point in Fig. 6 can be represented by its
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respective value of parameter a. Combining with the wavelength information in Fig. 7b, the relationship between parameter a and wavelength normalized by borehole radius is presented in
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Fig. 8b. Obviously, some a values are apparently greater than that caused by geometric dispersion in Fig. 5c. It also reveals a trend that errors tend to decrease with increasing
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wavelength. This further supports the speculation that more dispersion is caused by concentric variation of S-wave velocity due to borehole disturbance. The effect of the borehole disturbance is reduced as the wavelength increases. Therefore, better results may be achieved by lowering the
6. Conclusion
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dominant frequencies generated by the Suspension P-S Logger.
A new approach for Suspension P-S Logging data analysis is proposed based on two-channel dispersion curve analysis of borehole acoustic waves. An additional assumption is made to simplify the calculation of shear wave velocity and avoid the phase un-wrapping problem associated with the lack of low-frequency information in the dispersion analysis. The proposed method can be automated and provide the effective frequency of the obtained shear wave velocity. Validity and effect of the simplifying assumption were investigated using some field data. In addition to borehole geometric dispersion, it was found that material dispersion due
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ratio of shear wave velocity to phase velocity was suggested to be 1.14 based on the field data.
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Results show that the velocity difference between the proposed method and the conventional method based on manually-picked first arrivals are mostly within 15%. Better results may be
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achieved by lowering the dominant frequencies generated by the source to meet the long
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wavelength condition.
1.
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Reference
Anderson, K. R., 1978. Automatic processing of local earthquake data, Ph.D, Cambridge,
2.
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Massachusetts Institute of Technology.
Arroyo Franco, J.L., Mercado Ortiz, M.A., De, G.S., Renlie, L. and Williams, S. 2006.
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Sonic investigations in and around the borehole. Oilfield Review, 18, 14–33. Biringen, E. and Davie, J., 2010. Suspension P-S Logging for Geophysical Investigation of
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Deep Soil and Bedrock. GeoFlorida 2010, American Society of Civil Engineers, 1037-1048. Boore, D.M., and Asten, M.W., 2008. Comparisons of Shear-Wave Slowness in the Santa Clara Valley, California, Using Blind Interpretations of Data from Invasive and Noninvasive Methods. Bulletin of the Seismological Society of America, 98(4), 1983–2003. 5.
Cheng, C.H., and Toksoz, M.N., 1981. Elastic wave propagation in a fluid-filled borehole and synthetic acoustic logs. Geophysics, 46, 1042-1053.
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Cheng, C.H., and Toksoz, M.N., 1983. Determination of shear wave velocities in "slow" formation. Trans. 24th SPWLA Ann. Logging Symp., Calgary, Canada, Paper V. 15
ACCEPTED MANUSCRIPT 7.
Diehl, J.G., Martin, A.J., and Steller, R.A., 2006. Twenty year retrospective on the OYO P-S suspension logger. Proceedings of the 8th U.S. National Conference on Earthquake
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Engineering, April 18-22, 2006, San Francisco, Paper No. 319. Earle, P.S., and Shearer, P.M., 1994. Characterization of global seismograms using an
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automatic-picking algorithm. Bulletin of the Seismological Society of America, 84, 366-376.
Haldorsen, J.B.U., Johnson, D.L., Sinha, B., Valero, H., and Winkler, K., 2006. Borehole
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9.
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acoustic waves, Oilfield Review, 18(1), 34-43.
10. Heisey JS, Stokoe II KH, Hudson WR, and Meyer AH., 1982. Determination of in situ shear
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wave velocities from spectral analysis of surface waves. Research Report No. 256-2, Center for Transportation Research, The University of Texas at Austin. 11. Hoyle, D.C., Wignall, A.H., and Walulik, J.J., 1989. Sonic well logging tool transmitter. U.S.
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Patent: 4,862,991, Sep. 5, 1989.
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12. Kalinski, M.E. and Stokoe II, K.H., 2003. In situ estimate of shear wave velocity using borehole spectral analysis of surface waves tool. Journal of Geotechnical and Geoenvironmental Engineering, 129, 529-535. 13. Kitsunezaki, C., 1978. A new method for shear-wave logging. 48th SEG Meeting, Oct. 31, 1978, San Francisca, 1489-1506. 14. Kitsunezaki, C., 1980. A new method for shear-wave logging, Geophysics. 45, 1489-1506. 15. Leonard, M., 2000. Comparison of manual and automatic onset time picking. Bulletin of the Seismological Society of America, 90, 1384-1390.
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ACCEPTED MANUSCRIPT 16. Lin, C.-P., and Chang, T.-S., 2004. Multi-station analysis of surface wave dispersion. Soil Dyn. Earthquake Eng., 24(11), 877–886.
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17. Lin, C.-H. and Lin, C.-P., 2012. Metamorphosing the SASW Method by 2-D Wavefield Transformation. Journal of Geotechnical and Geoenvironmental Engineering, 138(8),
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1027~1032.
18. Maeda, N., 1985. A Method for Reading and Checking Phase Time in Auto-Processing
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System of Seismic Wave Data. Zisin (Journal of the Seismological Society of Japan. 2nd
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ser.), 38, 365-379.
19. Nigbor, R.J., and Imai, T., 1994. The Suspension P-S Velocity Logging Method. ISSMFE
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Technical Committee 10 for XIII ICSMFE, Geophysical Characteristics of Sites, A. A. Balkema Publishers/Rotterdam & Brookfield, Netherland. 20. Ogura, K., Nakanishi, S., and Morita, K., 1980. Suspension S wave logging system. 50th
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SEG Meeting, Houston.
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21. Ohya, S., 1986. In Situ P and S Wave Velocity Measurement. Proceedings of In-Situ ’86, Use of In-Situ Tests In Geotechnical Engineering, an ASCE Specialty Conference sponsored by the Geotechnical Engineering Division of ASCE and co-sponsored by the Civil Engineering Dept of Virginia Tech. 22. OYO Corporation, 1998. Suspension P-S Log 170 Operation Manual. 23. Stokoe II, K.H., John, S.H., and Woods, R.D., 2004. Some contributions of in situ geophysical measurements to solving geotechnical engineering problems. Proceedings of 2nd International Conference on Site Characterization, Porto, Portugal, 97-132. 24. Tanaka, K., Ogura, K., and Miura, H., 1985. Application of Suspension P-S Logging 17
ACCEPTED MANUSCRIPT System to High Velocity Ground. 4th ASEG Conference, 289-291. 25. Tukey, J. W., 1967. An introduction to the calculations of numerical spectrum analysis. In:
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Harris, B. (ed.), Spectral Analysis of Time Series, Wiley, New York, 25-46. 26. Wong, J., Han, L., Stewart, R. R., Bentley, L. R., and Bancroft, J. C., 2009. Geophysical
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Well Logs from a Shallow Test Well and Automatic Determination of Formation Velocities from Full-Waveform Sonic Logs. Canadian Society of Exploration Geophysicists Recorder,
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34(4).
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27. Zhang, H., Thurber, C., and Rowe, C., 2003. Automatic P-wave arrival detection and picking with multiscale wavelet analysis for single-component recording. Bulletin of the
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Seismological Society of America, 93, 1904-1912. 28. Zhao, Y., and Takano, K., 1999. An artificial neural network approach for broadband
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seismic phase picking. Bulletin of the Seismological Society of America, 89, 670-680.
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ACCEPTED MANUSCRIPT Fig.1. Schematic of the Suspension P-S Logging system (OYO, 1998). Fig. 2. Geometric dispersion of Stoneley waves propagating along the fluid-filled borehole wall
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in “slow” formations. Fig. 3. Pre-processing by time windowing.
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Fig. 4. Illustration of the proposed method: (a) Fourier spectrums of the near and far receivers
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and thieir cross power spectrum, (b)phase difference vs. frequency and the frequency range selected for analysis, and (c) dispersion curve directly from unwrapped phase difference and the
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phase velocity estimated by the proposed method.
Fig. 5. Theoratical evalution of the proposed method: (a) The possible errors based on long
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wavelength assumption(i.e. a=1.02), (b) the source of error illustrated by case A5 in Fig. 2., and (c) the possible value for parameter a to compensate for the effect of geometric dispersion. Fig. 6. Empirical value for parameter a from the manually-picked S-wave velocity and the phase
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velocity from the proposed method.
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Fig. 7. (a) Effective frequency range, in which stars being the peaks of cross power spectrum in the data analysis, and (b) effective wavelengths retrieved from the stars. Fig. 8. (a) Percentage error in Vs of the proposed method compared to the manually-picked Vs; (b) each data point is represented by its respecitve value of parameter a and compared to the theoratical evalution (indicated by the shaded area and lines) in Fig. 5c.
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Fig. 1
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Fig. 2
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A2 A3
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Vph/Vs
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λ /R
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2.1/1.2
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0.4
1.8/1.2
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0.33
1.8/1.2
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0.33
1.6/1.2
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0.25
1.5/1.2
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λ /R
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Theoretical curve
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Proposed method (Frequency 1350-1650 Hz)
Non-dispersive condition
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Frequency, Hz
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λ, m
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Comprehensive review of factors affecting Suspension P-S Logging. A new data reduction method based on borehole acoustic waves is proposed for Suspension P-S Logging data. The proposed method is more objective can be readily automated and provide extra information on the effective frequencies of Vs measurements. The effect of borehole disturbance could be examined based on the proposed method.
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