TY - JOUR
AU - Xu,, Minqiang
AB - Summary Large-amplitude collar wave covering formation signals is still a tough problem in acoustic logging-while-drilling (LWD) measurements. In this study, we investigate the propagation and energy radiation characteristics of the monopole collar wave and the effects of grooves on reducing the interference to formation waves by finite-difference calculations. We found that the collar wave radiates significant energy into the formation by comparing the waveforms between a collar within an infinite fluid, and the acoustic LWD in different formations with either an intact or a truncated collar. The collar wave recorded on the outer surface of the collar consists of the outward-radiated energy direct from the collar (direct collar wave) and that reflected back from the borehole wall (reflected collar wave). All these indicate that the significant effects of the borehole-formation structure on collar wave were underestimated in previous studies. From the simulations of acoustic LWD with a grooved collar, we found that grooves broaden the frequency region of low collar-wave excitation and attenuate most of the energy of the interference waves by multireflections. However, grooves extend the duration of the collar wave and convert part of the collar-wave energy originally kept in the collar into long-duration Stoneley wave. Interior grooves are preferable to exterior ones because both the low-frequency and the high-frequency parts of the collar wave can be reduced and the converted inner Stoneley wave is relatively difficult to be recorded on the outer surface of the collar. Deeper grooves weaken the collar wave more greatly, but they result in larger converted Stoneley wave especially for the exterior ones. The interference waves, not only the direct collar wave but also the reflected collar wave and the converted Stoneley waves, should be overall considered for tool design. Downhole methods, Guided waves, Wave propagation 1 INTRODUCTION Acoustic logging-while-drilling (LWD) has grown in popularity for oil-gas exploration, due to a number of outstanding advantages over the traditional wireline acoustic logging. It aims at detecting formation information such as the P- and S-wave velocities during drilling (Tang et al.2002a). Acoustic LWD can guide the well trajectory through the reservoir to a great extent in real time and make the measurements convenient in highly deviated and horizontal wells and offshore regions. Although various acoustic LWD tools have been commercially employed (e.g. Hsu et al.2007; Nakajima et al.2012; Pabon 2014), there are still some tough problems to solve, one of which is the collar-wave interference to formation waves. Unlike the wireline logging, a ‘collar wave’ appears in the acoustic LWD signals, owing to the heavy thick-walled drill collar occupying a large portion of borehole. This collar wave, with strong amplitude and long duration, covers formation signals and makes it difficult to extract formation P- and S-wave velocities. In order to eliminate the collar wave, many attempts have been made at clarifying such details as the wave components caused by the drill collar, the excitation, dispersion and attenuation characteristics and the interactions with the formation waves (e.g. Hsu et al.1997; Rama Rao & Vandiver 1999; Tang et al.2002b; Cui 2004; Sinha et al.2009; Wang & Tao 2009; Su et al. 2011, 2015; Wang et al.2016; Zheng & Hu 2017). From these studies on the waves excited by monopole, dipole and quadrupole in the acoustic LWD environment, it has been acknowledged that there is a collar wave for the monopole or dipole acoustic LWD. While the quadrupole collar wave theoretically vanishes at low frequencies due to its cut-off frequency (Tang et al.2002b; Hsu et al.2007), a pure quadrupole signal is not available in practice, especially in deviated and horizontal wells, owing to the source eccentricity (Zheng et al.2004; Wang et al.2015a). Because significant energy from the collar wave was found to go into the formation around the borehole (Guan et al.2013; Zheng et al.2015), the effects of the borehole-formation structure and its properties on collar wave might have been underestimated previously. To clarify the collar wave characteristics, one should investigate the waves in the entire cylindrically layered structure of the acoustic LWD model, including those in the formation around the borehole. However, in most previous literatures the authors focused on the collar wave on the outer surface of the drill collar where to mount the receivers in real acoustic LWD tools, but they did not investigate how the collar wave arrives at the receivers. Sinha et al. (2009) calculated the wave amplitudes in the formation of the acoustic LWD by a mode wave calculation algorithm. While they analysed the amplitude variations of the two Stoneley waves by amplitude profiles, they did not calculate that of the collar wave and did not present the waveforms in the temporal and spatial domain. Most recently, Wang et al. (2015b) presented the snapshots of the wavefield distribution in the entire model of the acoustic LWD including in the formation by finite-difference simulations. Their purpose was to illustrate the multipole modes when the source deviates from the borehole axis, thus they did not analyse the collar wave in the formation around the borehole and the effects of the borehole-formation structure on collar wave. Inspired by wireline acoustic logging tools, the collar wave in real acoustic LWD tools is suppressed by virtue of an acoustic-isolation zone between source and receiver array. This zone is generally realised by carving some grooves on the collar surfaces and filling the grooves with acoustic absorbing materials (Kinoshita et al.2010; Nakajima et al.2012; Pabon 2014). Experiments measurements have indicated that grooves attenuate the collar wave effectively (Joyce et al.2001; Leggett et al.2001). The collar-wave attenuation, which is estimated by measuring the collar-wave amplitudes respectively before and after the transmission across the grooves, has been regarded as a performance index of the acoustic-isolation zone. Nevertheless, this collar-wave attenuation measurement is generally implemented in laboratory for the drill collar itself or the drill collar within the fluid. Because the significant effects of the borehole-formation structure on collar wave were not considered, the measured collar wave in these cases may be appreciably different from that in real acoustic LWD measurements. For better suppression of the collar wave, numerical simulations are worthwhile to assess the effects of the borehole-formation structure quantitatively and to further optimize the grooving design. In most previous literatures, the acoustic LWD waves were calculated for the models with a smooth collar. Although there were some numerical studies on the collar wave for the model with a grooved collar, the relatively simple model of the grooved collar within the infinite fluid was employed. Su et al. (2015) studied the optimal design of the acoustic-isolation zone by numerical simulations and experimental measurements. Nevertheless, their designs were based on the model of the drill collar within an infinite fluid and focused only on how to broaden the frequency region of relatively low collar-wave excitation. The variation of the collar-wave excitation with frequency is significantly different between the models with and without a formation (Zheng & Hu 2017) due to the effects of the borehole-formation structure. The collar-wave amplitude within the low excitation region for the model with the formation is not as small as that for the model without the formation (Zheng & Hu 2017). While Matuszyk & Torres-Verdín (2014) presented finite-element simulations of the acoustic LWD with a grooved collar by employing the model with formation, they did not make a comparative calculation and analysis for different grooving positions and groove parameters. In this study, we investigate the propagation and energy radiation characteristics of the collar wave in monopole acoustic LWD by finite-difference time-domain (FDTD) simulations. Unlike previous studies, we give special attention to the energy radiation of the collar wave to the formation around the borehole for analysing the effects of the borehole-formation structure on both the amplitude and phase of collar wave. We also investigate the effects of grooves on weakening the undesired waves by the simulations of the acoustic LWD with a grooved collar. The rest of the paper is organised as follows: Following a brief introduction of the FDTD implementation, we firstly present the simulated full waveforms of the acoustic LWD with a smooth collar for a fast and a slow formation, respectively, in order to verify the correctness of our algorithm and illustrate the wave characteristics for different kinds of formations. We then calculate the wavefields for the collar within an infinite fluid and the acoustic LWDs with either an intact or a truncated collar. By comparative analysis, we reveal the propagation and energy-radiation mechanisms of collar wave. On this basis, we then simulate the acoustic LWD with a grooved collar and compare the results between different grooving manners, and between different groove parameters. According to the comparisons, we analyse the effects of grooves on reducing the interference waves and propose the optimal grooving manner and better groove parameters. Finally, we conclude this study. 2 FULL WAVEFORMS OF THE ACOUSTIC LWD A typical acoustic LWD configuration can be simplified as the cylindrically layered structure as shown in Fig. 1. From inner to outer, these layers are sequentially the inner fluid (the fluid inside the drill collar), the drill collar, the outer fluid (the fluid outside the drill collar), and the formation surrounding the borehole. The collar and the formation are considered as elastic solids. Without special explanation, the medium and geometric parameters in Table 1 are employed for our simulations. In real acoustic LWD tools (e.g. Joyce et al.2001; Leggett et al.2001; Kinoshita et al.2010; Nakajima et al.2012; Pabon 2014), the source and the receiver array are normally mounted on the outer surface of the collar as shown in Fig. 1, and there are some grooves on the outer and/or the inner surfaces between the source and the receiver array to reduce the interference waves. The grooves are not shown in Fig. 1 but shown in Fig. 10 for investigating the cases with a grooved collar later in this study. For all the simulations, we suppose the source to be a cosine enveloped pulse as in Guan et al. (2009). Figure 1. Open in new tabDownload slide Schematic view of the acoustic LWD model. Figure 1. Open in new tabDownload slide Schematic view of the acoustic LWD model. Table 1. The medium and geometric parameters of acoustic LWD. . P-wave velocity . S-wave velocity . Density . Radius . . (m s−1) . (m s−1) . (kg m−3) . (m) . Inner fluid 1470 – 1000 0.027 Drill collar 5860 3130 7800 0.09 Outer fluid 1470 – 1000 0.117 Formation I (fast formation) 3000 1800 2320 – Formation II (slow formation) 2485 1067 2000 – Formation III 4000 2000 2320 . P-wave velocity . S-wave velocity . Density . Radius . . (m s−1) . (m s−1) . (kg m−3) . (m) . Inner fluid 1470 – 1000 0.027 Drill collar 5860 3130 7800 0.09 Outer fluid 1470 – 1000 0.117 Formation I (fast formation) 3000 1800 2320 – Formation II (slow formation) 2485 1067 2000 – Formation III 4000 2000 2320 Open in new tab Table 1. The medium and geometric parameters of acoustic LWD. . P-wave velocity . S-wave velocity . Density . Radius . . (m s−1) . (m s−1) . (kg m−3) . (m) . Inner fluid 1470 – 1000 0.027 Drill collar 5860 3130 7800 0.09 Outer fluid 1470 – 1000 0.117 Formation I (fast formation) 3000 1800 2320 – Formation II (slow formation) 2485 1067 2000 – Formation III 4000 2000 2320 . P-wave velocity . S-wave velocity . Density . Radius . . (m s−1) . (m s−1) . (kg m−3) . (m) . Inner fluid 1470 – 1000 0.027 Drill collar 5860 3130 7800 0.09 Outer fluid 1470 – 1000 0.117 Formation I (fast formation) 3000 1800 2320 – Formation II (slow formation) 2485 1067 2000 – Formation III 4000 2000 2320 Open in new tab The 2.5-D FDTD scheme with a velocity-stress staggered grid for calculating multipole borehole acoustic waves (Randall et al.1991; Wang & Tang 2003) is applied to the wave simulations in this study. In the scheme, the perfect matched layer (PML) without splitting the fields (Wang & Tang 2003; Guan et al.2009) is used to truncate the computational region. The problem of inner boundaries between different media is solved by the parameter averaging technique (Guan et al.2009; Guan & Hu 2011). The FDTD formulas on inner boundaries are identical with those in homogeneous media. Nevertheless, the average parameters, specifically harmonic average of the shear modulus and arithmetic averages of other parameters, are employed instead. More details about the FDTD scheme can be found in Wang & Tang (2003), Guan et al. (2009) and Guan & Hu (2011). In Figs 2 and 3, we simulated the full waveforms of the monopole acoustic LWD with a smooth collar for Formations I and II, respectively, by the FDTD scheme. Formation I is a fast formation whose S-wave velocity is higher than the sound speed in borehole fluid, while Formation II is a slow formation whose S-wave velocity is lower than that. As given in Table 1, we employ a fast formation (Formation I) with a relative slower P-wave velocity (3000 m s−1) slower than those in previous numerical studies. The purpose is to separate the formation P-wave from the collar wave as far as possible for ensuring a reliable collar wave in the following analysis. The source has a centre frequency of 8.0 kHz. Figs 2(a) and 3(a) are the amplitude-normalized waveforms of the source-to-receiver axial distances from z = 3.6 to 4.2 m with an equal interval of 0.1 m. The close-ups of the waveforms at z = 4.0 m are shown in Figs 2(b) and 3(b). To check the FDTD scheme, the waveforms calculated by real axis integration (RAI) method (Tsang & Rader 1979) are also presented in Figs 2 and 3. The red solid and the black dash-dot lines are the FDTD and the RAI results, respectively. The phenomenological agreements between the two methods, including both the amplitudes and phases of the waveforms at all the receivers, confirm the correctness of our FDTD algorithm. Figure 2. Open in new tabDownload slide Comparisons of the waveforms of the acoustic LWD in Formation I between FDTD (red solid line) and RAI (black dash-dot line). The receivers are on the outer surface of the collar. (a) Normalized waveforms from z = 3.6 to 4.2 m with an equal interval of 0.1 m. (b) Waveforms at z = 4.0 m. Figure 2. Open in new tabDownload slide Comparisons of the waveforms of the acoustic LWD in Formation I between FDTD (red solid line) and RAI (black dash-dot line). The receivers are on the outer surface of the collar. (a) Normalized waveforms from z = 3.6 to 4.2 m with an equal interval of 0.1 m. (b) Waveforms at z = 4.0 m. Figure 3. Open in new tabDownload slide Same as Fig. 2 except that the formation is Formation II. (a) Normalized waveforms from z = 3.6 to 4.2 m with an equal interval of 0.1 m. (b) Waveforms at z = 4.0 m. Figure 3. Open in new tabDownload slide Same as Fig. 2 except that the formation is Formation II. (a) Normalized waveforms from z = 3.6 to 4.2 m with an equal interval of 0.1 m. (b) Waveforms at z = 4.0 m. In Fig. 2(a), the first wave group labelled by the dashed line a-a has a velocity of about 4940 m s−1 according to the slowness-time coherence (STC) processing of the waveforms. Since its velocity is between the P-wave and S-wave velocities in the collar, and significantly higher than the formation P-wave velocity (3000 m s−1), a-a group is the collar wave dependent on the collar properties rather than the formation P-wave. The subsequent b-b and c-c groups are the formation S- and pseudo Rayleigh wave, and the Stoneley wave, respectively. The small-amplitude formation P-wave is covered by the large-amplitude collar wave thereby it is not observable in Fig. 2. At this case of the smooth collar, the formation P-wave velocity is unable to be extracted by signal processing methods such as STC. In real acoustic LWD tools, a grooved drill collar is normally employed to reduce the collar wave. Even so, it is still difficult to extract the formation P-wave, as will be shown in this study. In Fig. 3 for the slow formation, the earliest arrival group, a-a, is the collar wave, like in Fig. 2. The subsequent b-b, c-c and d-d groups are the formation P-wave and two Stoneley waves, respectively. The formation S-wave is absent from the full waveform for the slow formation. In order to differentiate between the two Stoneley waves, they are referred to as the inner Stoneley wave and the outer Stoneley wave, respectively (Cui 2004). The outer Stoneley wave (d-d group) originates from the borehole wall due to the borehole-formation structure. The inner Stoneley wave (c-c group) originates from the inner surface of the collar between the inner fluid and the collar. The inner Stoneley wave propagates obviously faster than the outer one, because the shear modulus of the collar is much larger than that of the slow formation. This can be explained according to the approximate phase velocity formula of Stoneley wave given by White (1983). There is only one Stoneley wave group in Fig. 2 for the fast formation, because the velocities of the inner and the outer Stoneley waves are close to each other. Furthermore, the amplitude of the inner Stoneley wave is much smaller than that of the outer one. The reason is that the energy radiation in the radial direction of the inner Stoneley wave is obstructed by the collar, making it relatively difficult for the wave to arrive at the receivers on the outer surface of the collar. Due to more formation-wave attenuation in the slow formation, the collar-wave amplitude relative to those of the formation waves in Fig. 2 is obviously larger than that in Fig. 3 for the fast formation. In real measurement environments, the formation waves could be much smaller because the borehole mud and the formation are dissipative media. 3 PROPAGATION AND RADIATION CHARACTERISTICS OF COLLAR WAVE Having restated the wave components in the full waveforms of the acoustic LWD, we now investigate the propagation and energy radiation characteristics of the monopole collar wave. Unlike most previous studies only interested in the waves on the outer surface of the collar, we also pay special attention to the waves in the formation around the borehole. The purpose is to analyse the effects of the borehole-formation structure on collar wave, which is motivated by the recent studies of our research group as follows. Firstly, it was found that significant collar wave energy goes into the formation when simulating the seismoelectric LWD fields (Guan et al.2013; Zheng et al.2015). Then the collar wave characteristics such as the attenuation and excitation have significant differences between the drill collar within an infinite fluid and that within a fluid-filled borehole surrounded by the formation when calculating the individual component waves of the acoustic LWD (Zheng & Hu 2017). In this section, we compare the wavefields between the models of a drill collar within an infinite fluid and the acoustic LWDs in a fast and a slow formation with an intact or a truncated collar. 3.1 Effects of borehole-formation structure on collar wave Fig. 4 shows the comparisons of the waveforms for the acoustic LWD in Formation I between different radial locations. Figs 4(b) and (c) show the waveforms in the formation, specifically at the radial distances of 0.123 and 0.423 m outside the borehole wall, respectively. For comparison, the waveforms on the outer surface of the drill collar are given in Fig. 4(a). The source-to-receiver axial distance z is from 0.6 to 4.2 m with an equal interval of 0.06 m, and the waveforms are amplitude-normalized with respect to the peak value of that at z = 0.6 m in Fig. 4(a). Figure 4. Open in new tabDownload slide The normalized waveforms at various radial locations of the acoustic LWD. (a) On the outer surface of the collar. (b) At 0.123 m outside the borehole wall. (c) At 0.423 m outside the borehole wall. Figure 4. Open in new tabDownload slide The normalized waveforms at various radial locations of the acoustic LWD. (a) On the outer surface of the collar. (b) At 0.123 m outside the borehole wall. (c) At 0.423 m outside the borehole wall. All the input parameters employed in Fig. 4 are identical with those in Fig. 2, including the medium and geometric parameters and the centre frequency of the source. Thus the three visible groups respectively labelled as ‘C’, ‘S’ and ‘ST’ in Fig. 4(a) are the collar wave, the shear and pseudo-Rayleigh wave, and the Stoneley wave, as is stated for Fig. 2. The arrow with label ‘P’ in Fig. 4 denotes the arrival time of the formation P-wave which is covered by the collar wave. By comparison, the three groups in Figs 4(b) and (c) are the same as those in Fig. 4(a). With the increase of the radial distance, the Stoneley wave weakens so obviously and it is scarcely visible in Fig. 4(c) of 0.423 m outside the borehole wall. In contrast, the collar wave weakens not so much within the radial-distance scope of investigation and it is still visible and dominates the full waveforms in Fig. 4(c). Furthermore, the collar-wave amplitude at 0.123 m outside the borehole wall seems larger than that on the outer surface of the collar (we will confirm this and explain the reason by Fig. 5). This indicates that the collar wave can radiate energy to deeper formation compared with the Stoneley wave and undoubtedly the collar wave is influenced by the borehole-formation structure. Figure 5. Open in new tabDownload slide Comparisons of the collar waves between the collar within an infinite fluid (blue solid line), and the acoustic LWDs in Formation I (black dash-dot line) and in Formation II (red dash-dot line). (a) At the outer surface of the collar. (b) At 0.117 m away from the borehole axis (At the borehole wall for the two formation cases). Figure 5. Open in new tabDownload slide Comparisons of the collar waves between the collar within an infinite fluid (blue solid line), and the acoustic LWDs in Formation I (black dash-dot line) and in Formation II (red dash-dot line). (a) At the outer surface of the collar. (b) At 0.117 m away from the borehole axis (At the borehole wall for the two formation cases). To analyse the energy radiation characteristics of the collar wave quantitatively, the waveforms at z = 4.0 m for three models are depicted together in Fig. 5 by different coloured lines. The three models are the collar within an infinite fluid (blue solid line), the acoustic LWDs in the fast formation (black dash-dot line) and in the slow formation (red dash-dot line). Figs 5(a) and (b) are the waveforms at two different radial locations: 0.09 m (on the outer surface of the collar) and 0.117 m away from the borehole axis, respectively. For the formation cases, the location of 0.117 m is at the borehole wall. Only the first 2.5 ms of the waveforms are given in Fig. 5, to clearly display the differences in the collar-wave amplitude and phase between different cases. For the infinite-fluid case, the amplitude as well as the phase of the collar wave in Fig. 5(a) is not much different from that in Fig. 5(b) because of the very close locations, and the peak amplitudes are 0.0427 and 0.0363 kPa, respectively. It is not like that for the formation cases. On the outer surface of the collar, the peak amplitudes for the fast and the slow formations are 0.0213 and 0.0267 kPa, respectively, and they are obviously smaller than that for the infinite-fluid case. At the borehole wall, the results are opposite that the peak amplitudes for the fast and the slow formations are 0.0544 and 0.0537 kPa, respectively, and they are obviously larger than that for the infinite-fluid case. While the collar-wave phases for the formation cases are almost the same as that for the infinite-fluid case at the borehole wall, there is an obvious deviation on the outer surface of the collar. These phenomena are not caused by the formation P-wave, because the larger amplitude collar wave is scarcely influenced by the small amplitude and unobvious formation P-wave. In fact, the arrival time of the formation P-wave is behind the peak amplitude of the collar wave. As shown in Fig. 5, the arrival time of the P-wave in the fast formation signalled by an arrow is later than that of the peak amplitudes. The real reason is the effects of borehole-formation structure on collar wave. Part of the collar-wave energy going outward from the drill collar is reflected back by the borehole wall. The reflected collar wave is superposed with the outward-going collar wave itself (direct collar wave). At the borehole wall, the reflected collar wave has no difference in phase with the direct one, resulting in an in-phase and amplitude-enhanced superposition as shown in Fig. 5(b). On the outer surface, the reflected collar wave has a phase delay to the direct one, resulting in a phase-delayed and amplitude-decreased superposition as shown in Fig. 5(a). The reflected collar wave is about 50 per cent of the direct collar wave for different formations, indicating that the effects of the borehole-formation structure on the collar wave is significant and should not be ignored. The effect of the formation parameters on the collar wave is relatively small because there are no distinct differences in both the amplitude and phase of the collar wave between the fast and slow formation cases as shown in Fig. 5. Therefore the collar wave recorded by the receiver arrays on the outer surface of the collar in real acoustic LWD tool consists of the outward-going collar wave direct from the drill collar and the inward-going collar wave reflected by the borehole wall. Fig. 6 shows the variations of the collar-wave amplitude with the radial distance within the scope of 0.1 m from the outer surface of the collar to the fast formation (Formation I) around the borehole. The peak amplitudes are extracted from the simulated full waveforms at z = 4.0 m. We present the variations for different borehole radii (the collar radii are same) of 0.105, 0.111, 0.117, 0.129 and 0.141 m, respectively labelled as ‘R1’, ‘R2’, ‘R3’, ‘R4’ and ‘R5’ and depicted by different coloured lines. The label ‘F’ represents the result for the infinite-fluid case. For convenience, the horizontal ordinate begins from the outer surface of the collar. It is seen that the amplitude of the infinite-fluid case decreases monotonically with radial distance as expected, while those of the formation cases are maximal at the borehole wall regardless of the borehole radii. In the formation, the variation tendencies of the amplitude are same for all the formation cases. They decrease monotonically with the radial distance. In the outer fluid, the amplitude variations are different between formation cases with various borehole radii. The amplitude increases with radial distance for smaller radii (0.105 m, 0.111 m and 0.117 m), while it decreases first and then increases with radial distance for bigger radii (0.129 m and 0.141 m). That is due to the phase delay of the inward-going collar wave to the outward-going one mentioned above. The delay time equals to twice the distance from the borehole wall to the investigation position in the outer fluid divided by the fluid sound velocity. With the increase of the distance, the delay time increases and thus the amplitude decreases. If the borehole is big enough that it makes the delay time possible to be larger than the peak-to-valley time of the collar wave, the amplitude decrease has a minimum and then the amplitude changes to increase with the increase of the distance. When the delay time equals to the peak-to-valley time, the amplitude achieves the minimum. Furthermore, the maximum amplitude at the borehole wall of the formation case significantly decreases with the increase of the borehole radius. This reconfirms the significant effects of the borehole-formation structure on collar wave. In general, to drill a bigger-radius borehole can cause a smaller-amplitude collar wave without considering the drilling cost and the size limitation of the drilling bit. Nevertheless it is not always this case. It can be found from Fig. 6 that the amplitude at the outer surface of the collar for ‘R5’ is larger than that for the smaller radius ‘R3’. Moreover, the time span of the collar wave is longer for bigger-radius boreholes due to the larger delay time, which intensifies the interference to formation waves. Figure 6. Open in new tabDownload slide Variations of the collar-wave amplitude with radial location. Labels ‘R1’, ‘R2’, ‘R3’ ‘R4’ and ‘R5’ denote the acoustic LWD cases with different borehole radii of 0.105, 0.111, 0.117, 0.129 and 0.141 m, respectively, while Label ‘F’ represents the infinite-fluid case. The amplitudes are extracted from the peak values of the collar waves in the full waveforms at z = 4.0 m. The horizontal ordinate starts from the outer surface of the collar. Figure 6. Open in new tabDownload slide Variations of the collar-wave amplitude with radial location. Labels ‘R1’, ‘R2’, ‘R3’ ‘R4’ and ‘R5’ denote the acoustic LWD cases with different borehole radii of 0.105, 0.111, 0.117, 0.129 and 0.141 m, respectively, while Label ‘F’ represents the infinite-fluid case. The amplitudes are extracted from the peak values of the collar waves in the full waveforms at z = 4.0 m. The horizontal ordinate starts from the outer surface of the collar. 3.2 Collar wave for the case of a truncated collar In this subsection, we further analyse the propagation and energy radiation characteristics of collar wave and the effects of borehole-formation structure. Supposing that the drill collar is truncated at its end part from z = 3.6 m as shown in Fig. 7, we simulate the acoustic LWD with the truncated collar. Fig. 8 shows the normalized waveforms at the outer surface of the collar from z = 0.6 to 4.2 m with an equal interval of 0.04 m. Figs 9(a) and (b) respectively display the STC plot for the upgoing waveforms from z = 1.8 to 2.88 m and that for the waveforms after the truncation surface from z = 3.72 to 4.2 m. The white horizontal lines labelled as ‘Sp’, ‘Ss’ and ‘Sf’ in Fig. 9 represent the slownesses of the formation P-wave, the formation S-wave and the fluid sound wave, respectively. Figure 7. Open in new tabDownload slide Schematic view of the acoustic LWD with a drill collar truncated at z = 3.6 m. Figure 7. Open in new tabDownload slide Schematic view of the acoustic LWD with a drill collar truncated at z = 3.6 m. Figure 8. Open in new tabDownload slide Normalized waveforms from z = 0.6 to 4.2 m on the outer surface of the collar for the truncated collar model in Fig. 7. Figure 8. Open in new tabDownload slide Normalized waveforms from z = 0.6 to 4.2 m on the outer surface of the collar for the truncated collar model in Fig. 7. Figure 9. Open in new tabDownload slide STC plots extracted from the waveforms in Fig. 8. (a) From the upgoing waves between z = 1.8 and 2.88 m in Fig. 8(b) From the waves between 3.72 and 4.2 m in Fig. 8. Figure 9. Open in new tabDownload slide STC plots extracted from the waveforms in Fig. 8. (a) From the upgoing waves between z = 1.8 and 2.88 m in Fig. 8(b) From the waves between 3.72 and 4.2 m in Fig. 8. In Fig. 8, the three upgoing waves labelled as ‘C’, ‘S’ and ‘ST’ are the collar wave, the formation S-wave and the Stoneley wave, respectively, according to their slownesses given in Fig. 9(a) of the STC plot. In fact, these three waves are the same as those in Fig. 4, because the model before the truncation surface is identical with that for Fig. 4. Then we analyse how the three upgoing waves encounter with the truncation surface. It is seen that the formation S-wave remains unchanged when propagating across the truncation surface, because the truncated collar which is a model change in the borehole does not influence the formation waves basically. However, this is not the case for both the Stoneley wave and the collar wave. The case of the Stoneley wave is comparatively simple. As an interface in the propagation way of the Stoneley wave, the truncation surface reflects part of the Stoneley wave energy back. Thus the upgoing Stoneley wave separates into the reflected Stoneley wave (ST-rST) and the transmitted Stoneley wave (ST-tST). However, the upgoing collar wave separates into two reflected waves and a transmitted wave. According to the slopes, the two reflected waves are sequentially the reflected collar wave (C-rC) and the reflected Stoneley wave (C-rST), and the transmitted wave is the transmitted Stoneley wave (C-tST) rather than the transmitted collar wave. It can be confirmed from the slowness in Fig. 9(b) that there is no transmitted collar wave across the truncation surface. Because the cylindrical waveguide structure to maintain the collar wave is absent, except for the energy of the reflected collar wave, all the rest of the collar wave energy can only come out of the collar at the truncation surface and converts to the Stoneley wave. The converted Stoneley wave also separates into the reflected and the transmitted parts at the truncation surface. Furthermore, it is found from Fig. 8 that the amplitudes of both the two parts of the converted Stoneley wave are significantly larger than that of the upgoing collar wave. The reason is as follows. Before the collar wave arrives at truncation surface, most of the collar wave energy is kept within the drill collar and only small part of it can radiate out of the collar to be the upgoing collar wave. After that, the energy originally kept in the drill collar comes out to be the converted Stoneley wave. We give a brief summary of the propagation and energy radiation characteristics of the collar wave as follows. The collar wave is a kind of cylindrical guided wave relied on the whole cylindrical-layered acoustic LWD structure. Although the collar wave originates from the annular drill collar and most of its energy is hold within the collar, the borehole-formation structure contributes significant effects to the collar wave. When the collar wave propagates along the collar, it radiates energy out of the collar. The radiated energy goes into the outer fluid and can arrive at the borehole wall. Part of the energy arriving at the borehole wall is reflected back and the rest of it goes into the formation. The inward-going energy reflected by the borehole wall is significant by comparison with the outward-going energy direct from the collar. Thus the collar wave recorded by real acoustic LWD tools is not exactly the radiation energy direct from the collar but is composed by the direct and the reflected parts. The collar wave propagates out of the collar and converts to Stoneley waves at the places where the geometrical structure of the drill collar is destroyed or changed, such as the truncated collar argued in this section, the collar with variable inner radii in Su et al. (2015), and the grooved collar to be analysed in the next section. 4 EFFECTS OF GROOVES ON COLLAR WAVE In real acoustic LWD tools, the interference to formation waves can be reduced by cutting some grooves periodically on the surfaces of the collar between the source and receiver sections. One of the three manners is generally implemented in real tools (e.g. Kinoshita et al.2010; Nakajima et al.2012; Pabon 2014), including grooving only on the outer surface (exterior grooves), only on the inner surface (interior grooves), and staggered on both the outer and inner surfaces (staggered grooves). As an example, Fig. 10 gives a schematic view of the acoustic LWD with interior grooves. The close-up of the annular grooves is also present in Fig. 10 in order to illustrate the relevant parameters, including the groove width L, the groove depth H and the separation of adjacent grooves W, where a denotes the inner radius of the collar. Figure 10. Open in new tabDownload slide Schematic view of the acoustic LWD with a collar periodically grooved on the inner surface. The close-up of the grooves is also given, where L, H and W denote the groove width, the groove depth and the separation of adjacent grooves, respectively. Figure 10. Open in new tabDownload slide Schematic view of the acoustic LWD with a collar periodically grooved on the inner surface. The close-up of the grooves is also given, where L, H and W denote the groove width, the groove depth and the separation of adjacent grooves, respectively. In order to better use the grooves, we compare the collar waves between different grooving manners and groove parameters in this section. According to the results, we analyse the effects of grooves on reducing the interference to formation waves and present the optimal grooving manner and groove parameters. In the following simulations, we use Formation III that listed in Table 1 for a better illustration of the contrast in the interferences to formation waves especially to the formation P-wave between different grooving cases. Formation III has a P-wave velocity faster than that of Formation I and is more close to the velocity of the collar wave. By comparison, Formation III makes the interference stronger and thus it is more difficult to extract the formation P-wave. Without special explanations, we suppose that there are ten exterior, interior or staggered grooves and the three groove parameters mentioned above are L = 0.12 m, W = 0.12 m and H = 0.021 m, respectively. The ten staggered grooves are actually composed by ten grooves on the outer surface and ten grooves on the inner surface. 4.1 Effect of grooving manner In Fig. 11, we compare the collar wave for the smooth collar (red solid line) respectively with those for the three grooving manners mentioned above (black dashed-dot line) under various source centre frequencies from 9.0 to 15.0 kHz. Figs 11(a)–(c) are sequentially the comparisons with the exterior grooves, the interior grooves and the staggered grooves. All the waveforms in Fig. 11 are at the same location of z = 4.0 m on the outer surface of the collar. Only the first 2.0 ms of them are given in order to clearly show the collar wave. For the smooth collar, the arrival times of the collar wave and the formation P-wave are about 0.8 and 1.1 ms, marked by the vertical dash lines ‘C’ and ‘P’, respectively. The formation P-wave is covered by the large-amplitude collar wave. By comparison with the smooth collar, the amplitudes of the collar waves for the grooved collars are much smaller, whatever the grooving manner and the source centre frequency. The reason is as follows. The grooves act as a series of small interfaces. The collar wave is reflected back and forth at the grooves, during which part of the wave energy scatters off. Nevertheless, this multireflection extends the duration of the collar wave, which is harmful to the extraction of formation waves especially the formation P-wave. Figure 11. Open in new tabDownload slide Comparisons of the first 2.0 ms of the acoustic LWD waveforms between the grooved collar (black dash-dot line) and the smooth collar (red solid line) under various source centre frequencies from 9.0 to 15.0 kHz. (a) Exterior grooves. (b) Interior grooves. (c) Staggered grooves. Figure 11. Open in new tabDownload slide Comparisons of the first 2.0 ms of the acoustic LWD waveforms between the grooved collar (black dash-dot line) and the smooth collar (red solid line) under various source centre frequencies from 9.0 to 15.0 kHz. (a) Exterior grooves. (b) Interior grooves. (c) Staggered grooves. The collar-wave velocity decreases with the frequency increasing and this decrease is sharp within the frequency region of 10–15 kHz (Zheng & Hu 2017). In this study, we divide the collar wave into two parts: the earlier arriving collar wave in low frequencies (about from 0.8 to 1.3 ms in Fig. 11) and the later arriving collar wave in high frequencies (about from 1.3 from 1.8 ms in Fig. 11). By comparison, the exterior grooves weaken the low-frequency collar wave well but do not seem to weaken the high-frequency collar wave, while the interior ones weaken both the low-frequency and the high-frequency collar waves well. We found that the reason is because the high-frequency collar wave is focused on the inter surface of the collar. Furthermore, the amplitude of the wave behind the collar wave for grooved collars significantly increases by comparison with that for the smooth collar, whatever the grooving manner and the source centre frequency. The reason can be explained according to the analysis of the simulations of a truncated collar. The truncated collar can be imagined as a peculiar grooved collar, where the only groove is too deep that the collar is cut off. The collar-wave energy comes out of the collar from the truncation surface and converts to the Stoneley wave. Similarly, energy can come out from the exterior and interior grooves and convert to the outer and inner Stoneley waves, respectively. These converted Stoneley waves are superposed onto the wave behind of the collar wave. For further analysis, in Fig. 12 we present the STC plots obtained from the waveforms for different grooving manners of 13.0 kHz in Fig. 11. Figs 12(a) and (b) are the STC plots for the exterior grooves and the interior grooves, respectively. The STC plot for the staggered grooves is not given because it is similar to that for the exterior grooves. In Fig. 12(a), the wave behind the collar wave has a velocity slightly slower than the sound velocity in borehole fluid (the slowness is slightly higher than the line labelled as ‘Sf’). This confirms the conversion from the collar wave to the outer Stoneley wave at the exterior grooves. Because of the multireflection by the grooves, the collar wave and especially the converted outer Stoneley wave have long durations. Compared with the collar wave, the converted outer Stoneley wave has larger amplitude and longer duration. Consequently, not only the formation P-waves is fully covered but also the formation S-wave is significantly interfered. In Fig. 12(a), the formation P-wave is absent and the formation P-wave is not particularly clear because the multireflected Stoneley wave interferes in their time-slowness correlations. In summary, while grooves indeed weaken the collar wave effectively, they generate the converted Stoneley wave with long duration and extend the duration of the collar wave. Figure 12. Open in new tabDownload slide STC plots extracted from the waveforms for 13.0 kHz in Fig. 11. (a) From Fig. 11(a) for the exterior grooves. (b) From Fig. 11(b) for the interior grooves. Figure 12. Open in new tabDownload slide STC plots extracted from the waveforms for 13.0 kHz in Fig. 11. (a) From Fig. 11(a) for the exterior grooves. (b) From Fig. 11(b) for the interior grooves. For the case of interior grooves, however, the collar wave converts to the inner Stoneley wave. The converted inner Stoneley wave is smaller than the converted outer Stoneley wave and is absent in Fig. 12(b), because the converted inner Stoneley wave is relatively difficult to go out of the collar and arrive in the receivers on the outer surface of the collar by comparison. The slowness of the formation P-wave seems present in Fig. 12(b) between the low-frequency and the high-frequency parts of the collar wave, although it is still not clear. The slowness of formation S-wave in Fig. 12(b) is clearer than that in Fig. 12(a). Therefore, interior groove is optimal among the three manners, because it weakens both the two parts of the collar wave and converts small-amplitude inner Stoneley wave. 4.2 Effects of groove parameters We have argued that grooving on the inner surface of the collar is optimal for reducing the interference to formation waves. Although interior grooves are carved, it is still difficult to extract the formation P-wave from the STC plot. It is unable to confirm that the suspected unclear slowness between those of the low-frequency and high-frequency parts of the collar wave in Fig. 12(b) is the formation P-wave slowness. In this subsection, we calculate and compare the results for the models with different interior groove parameters for greater reducing the interference to formation waves. Firstly we increase the groove number from ten to eleven, meanwhile decrease both the groove width L and the groove separation W from 0.12 to 0.102 m, in order to keep the length of the grooving zone between source and receiver section basically unchanged. For this case, the groove depth remains unchanged. In Fig. 13 we present the simulated results for the altered grooves. The source with centre frequency of 13.0 kHz is employed. The medium parameters are the same as that employed for calculating Fig. 11. Figs 13(a) and (b) are the full waveform at z = 4.0 m on the outer surface of the collar and its corresponding STC plot, respectively. The first 2.5 ms of the waveform in Fig. 13(a) are enlarged for the following analysis. At this case, both the low-frequency and the high-frequency parts of the collar wave are extremely smaller than before. As a result, the formation P-wave whose expected arrival time is about 1.1 ms seems present in Fig. 13(a). It can be confirmed from Fig. 13(b) of the STC plot where the high-frequency part of the collar wave is absent while formation P-wave is clearly present. Furthermore, it is found from the enlarged panel in Fig. 13(a) that the formation P-wave is obviously larger than the collar wave as well as the converted inner Stoneley wave. Although the amplitude of the collar wave has become so small, its low-frequency part is still present in Fig. 13(b) because of not be interfered by other waves. Figure 13. Open in new tabDownload slide Simulation results of the acoustic LWD with interior grooves when the groove parameters are altered. By comparison with Fig. 11(b), the groove number increases from ten to eleven and the groove width L and the groove separation W decrease from 0.12 to 0.102 m. The source centre frequency is 13.0 kHz. (a) Waveform at z = 4.0 m on the outer surface of the collar (b) STC plot. Figure 13. Open in new tabDownload slide Simulation results of the acoustic LWD with interior grooves when the groove parameters are altered. By comparison with Fig. 11(b), the groove number increases from ten to eleven and the groove width L and the groove separation W decrease from 0.12 to 0.102 m. The source centre frequency is 13.0 kHz. (a) Waveform at z = 4.0 m on the outer surface of the collar (b) STC plot. Then we analyse the effects of the groove depth. Fig. 14 shows the results for alternative groove depths of H = 0.012 and 0.027 m against that in Fig. 13 for H = 0.021 m. All the other parameters are identical with those employed in Fig. 13. Figs 14(a) and (b) show the full waveforms and the corresponding STC plots, respectively. The upper panels of Figs 14(a) and (b) are the results for H = 0.012 m, while the lower panels are those for H = 0.027 m. It is found from Figs 13(b) and 14(b) that both the collar wave and the converted inner Stoneley wave are small enough that the formation P-wave is present in the every STC plot whatever the groove depth. By comparison between the STC plots, the resolutions of the formation waves as well as the collar wave decrease with the increase of the groove depth. The STC plot for H = 0.012 m has the highest resolution probably because the converted inner Stoneley wave is weakest. Although deeper grooves weaken the collar wave greater, more collar-wave energy goes out of the collar and converts to Stoneley wave. Because the converted Stoneley wave with low velocity has extremely long duration caused by the multireflection by the grooves, it interferes with not only the formation P-wave but also the formation S-wave. If exterior grooves are carved, this kind of interference might be more serious because of the larger amplitude of the converted outer Stoneley wave. Figure 14. Open in new tabDownload slide Same as Fig. 13 except that the groove depth H changes from 0.021 to 0.012 m (upper panels) and 0.027 m (lower panels), respectively. (a) Waveforms at z = 4.0 m on the outer surface of the collar (b) STC plot. Figure 14. Open in new tabDownload slide Same as Fig. 13 except that the groove depth H changes from 0.021 to 0.012 m (upper panels) and 0.027 m (lower panels), respectively. (a) Waveforms at z = 4.0 m on the outer surface of the collar (b) STC plot. 4.3 Effect of source frequency As has been argued in previous studies (Su et al. 2011, 2015), there is a frequency region of several kilohertz in which the collar-wave excitation is relatively low. This region is dependent on the collar geometry such as the inner and outer radii. Su et al. (2011, 2015) argued that the frequency region of low collar-wave excitation for a grooved collar or a collar with varied inner radii is obviously broader than that for a smooth collar, and thereby a smaller collar wave is excited. Real acoustic transmitters excite a collar wave with various frequency components within its bandwidth. A broader frequency region brings about more frequency components of the collar wave especially those with large energy to be low excited. Nevertheless, their investigation is mainly based on the simulations for the collar within an infinite fluid. In view of the significant effects of the borehole-formation structure on collar wave argued in this study, the characteristics of the low collar-wave excitation region might be different between the models with and without the formation. In this subsection, we compare the collar waves excited by different source centre frequencies and calculate the amplitude spectrums of the interference waves to formation P-wave, from which we present the optimal source frequency that the weakest interference waves can be obtained. We recalculate Fig. 13(a) by employing alternative source centre frequencies of 11.0, 12.0, 14.0 and 15.0 kHz, respectively, where the other input parameters such as the medium and groove parameters remain unchanged as those in Fig. 13. Similar to that in Fig. 13 for 13.0 kHz, we found that the collar wave as well as the converted Stoneley wave for 12.0 or 14.0 kHz is still small enough that the formation P- and S-wave velocities can be extracted by STC. The results for 12.0 and 14.0 kHz are not given because of the limited space of this paper. Nevertheless, it is not the case for 11.0 and 15.0 kHz. Fig. 15 shows the first 2.0 ms of the waveforms for 11.0 and 15.0 kHz (black dash-dot line) by the upper and lower panels, respectively. For comparison, the result for 13.0 kHz is also given in the two panels. The formation P-wave velocity cannot be extracted from the STC plot for 15.0 kHz, because the collar wave and the converted Stoneley wave are obviously larger than those for 13.0 kHz. Although the collar wave for 11.0 kHz is slightly larger than that for 13.0 kHz, the formation P-wave velocity also cannot be extracted from the STC plot for 11.0 kHz owing to the significantly larger converted Stoneley wave. Figure 15. Open in new tabDownload slide Comparisons of the first 2.0 ms of the waveform in Fig. 13(a) for source centre frequency of 13.0 kHz (red solid line) with those (black dash-dot line) for 11.0 kHz (the upper panel) and 15.0 kHz (the lower panel), respectively. Figure 15. Open in new tabDownload slide Comparisons of the first 2.0 ms of the waveform in Fig. 13(a) for source centre frequency of 13.0 kHz (red solid line) with those (black dash-dot line) for 11.0 kHz (the upper panel) and 15.0 kHz (the lower panel), respectively. To further explain the wave comparisons in Fig. 15, we calculate the amplitude spectrums of the first 2.0 ms of the waveforms and compare them between the smooth collar (black dash-dot line) and the two different grooved collars (red and blue solid lines, respectively) in Fig. 16. The red solid line is for ten grooves and L = W = 0.12 m (sparse grooves), while the blue one is for eleven grooves and L = W = 0.102 m (dense grooves). Note that this amplitude spectrum is not exactly that of the collar wave, because part of the collar wave arriving late is not included in the time window of 2.0 ms (Zheng & Hu 2017) while the formation P- wave is included. For the model with a grooved collar, part of the converted Stoneley wave energy is also included. The contribution of the formation is relatively small, thus we term the amplitude spectrum as the amplitude spectrum of the interference waves with regard to the formation P-wave, which reflects the variation of the interference to formation P-wave with frequency. It is seen that the curve for the smooth collar has a minimum at about 14.0 kHz, where the interference waves have lowest excitation intensity. Nevertheless, this low-excitation region is extremely narrow, where the excitation intensity increases sharply before and after the frequency of the minimum. As a result, it is unpractical to record a collar wave small enough in real measurements by employing a source with such a narrow bandwidth. For the cases of a grooved collar, the low-excitation region is about between 10.0 and 16.0 kHz and is obviously broader by comparison with that for the smooth collar. That is the reason why the formation P-wave cannot be extracted when the source centre frequency is out of the range of 12–14.0 kHz. Furthermore, the frequency regions for the dense and sparse grooves are almost the same size and that for the sparse grooves (the red line) seems slightly larger. Nevertheless, as has been illustrated that the formation P-wave can be extracted under the dense grooves but not under the sparse grooves. Thus not only to obtain a broader low-excitation should be considered when designing the acoustic-isolation zone. By Comparison, the excitation intensities for the model with formation are not as low as that for the model without formation given by Su et al. (2011), owing to the reflected collar wave by the borehole wall. The amplitude of the interference waves for the dense grooves is smaller than that for the sparse grooves, because more interference wave energy scatters out when reflecting back and forth within the grooves. Figure 16. Open in new tabDownload slide Amplitude spectrums of the first 2.0 ms of the acoustic LWD waveforms for the smooth collar (black dash-dot line) and two different collars with interior grooves (two solid lines). The red solid line is for ten grooves with L = W = 0.12 m, while the blue one is for eleven grooves with L = W = 0.102 m. Figure 16. Open in new tabDownload slide Amplitude spectrums of the first 2.0 ms of the acoustic LWD waveforms for the smooth collar (black dash-dot line) and two different collars with interior grooves (two solid lines). The red solid line is for ten grooves with L = W = 0.12 m, while the blue one is for eleven grooves with L = W = 0.102 m. 5 CONCLUSIONS We have investigated the wavefields of the monopole acoustic LWD by FDTD calculations, in the view of basic wave principles, for better recognitions of the collar wave characteristics, the effects of borehole-formation structure on the collar wave and the effects of grooves on reducing the interference to formation waves. We have analysed the propagation and energy radiation characteristics of the collar wave according to the comparisons of the simulated wavefields in the formation around the borehole between different models, including a collar within an infinite fluid, acoustic LWDs respectively with an intact and a truncated collar. We have found that the collar wave is a kind of guided wave arising from the annular drill collar structure, which propagates along the collar but radiates significant energy in the radial direction to the outer fluid and even to the formation. Moreover, the collar wave recorded on the outer surface of the collar by real acoustic LWD tools consists of two components: the direct collar wave (outward-radiated energy arrives at the receivers direct from the collar) and the reflected collar wave (outward-radiated energy reflected back from the borehole wall). Whatever the formations, the reflected collar wave is about 50 per cent of the direct collar wave. It indicates that the effects of the borehole-formation structure on collar wave are underestimated in previous studies and they are significant and thus should not be ignored. We have analysed the effects of grooves on reducing the interference to formation waves by comparing the simulations of the acoustic LWDs between different grooved collars. Grooving reduces the collar wave as well as other interference waves by virtue of the multiple-reflection at the grooves. It also broadens the frequency region of low collar-wave excitation. As a result, more frequency components within the source bandwidth can be low excited by comparison with the smooth collar. Nevertheless, the amplitude of the interference waves within the low-excitation frequency region for the model with the formation is not as low as that for the model of a collar within an infinite fluid, owing to the effects of the borehole-formation structure on collar wave. Despite the virtues of reducing the interference waves, grooving leads to the collar-wave energy originally kept in the collar coming out at the grooves and converting to long-duration inner and/or outer Stoneley waves. Besides, grooving extends the duration of the collar wave. The converted inner Stoneley wave at the exterior grooves is smaller because it is relatively difficult to arrive at the receivers on the outer surface of the collar. Therefore, for design of acoustic LWD tools of smaller interference to formation waves, it is better to employ the model with the borehole-formation structure. Moreover, it is better to overall consider the collar-wave energy kept in the collar, the direct and reflected parts of the outward-radiated collar-wave energy and the converted Stoneley wave. Grooving on the inner interface is optimal by comparison, because it reduces both the low-frequency and high-frequency parts of the collar wave, generates a smaller converted Stoneley wave, and less influence the Stoneley wave along the borehole wall. If the mechanical requirements are allowed, increase the groove number appropriately meanwhile decrease the groove width within the fixed the length of the acoustic-isolation zone can reduce the interference waves. While deeper grooves reduce the collar wave greater, they result in larger converted Stoneley wave especially for the exterior ones. Acknowledgments We are grateful to the editor Xiaofei Chen and two anonymous reviewers for their comments and constructive suggestions, to Yubao Zhen who helped to use the high-speed cluster for the numerical calculations and to Zak Kornberg who helped to polish the language. This work is jointly supported by National Natural Science Foundations of China (41574112, 11372091 and 41674121), Natural Science Foundation of Heilongjiang Province of China (D2015001), Foundation of Key Laboratory of Harbin Institute of Technology (30620150260) and Research Fund of Heilongjiang Provincial Education (12541610). 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Published by Oxford University Press on behalf of The Royal Astronomical Society.
TI - Numerical study of the collar wave characteristics and the effects of grooves in acoustic logging while drilling
JO - Geophysical Journal International
DO - 10.1093/gji/ggx044
DA - 2017-05-01
UR - https://www.deepdyve.com/lp/oxford-university-press/numerical-study-of-the-collar-wave-characteristics-and-the-effects-of-MD8YCJl4VM
SP - 749
VL - 209
IS - 2
DP - DeepDyve
ER -