slow formation shear from an lwd tool: quadrupole inversion with a

SPWLA 51st Annual Logging Symposium, June 19-23, 2010

SLOW FORMATION SHEAR FROM AN LWD TOOL: QUADRUPOLE INVERSION WITH A GULF OF MEXICO EXAMPLE

David Scheibner, Shinji Yoneshima, Zhenxin Zhang, Wataru Izuhara, Yuichiro Wada, and Peter Wu, Schlumberger, and Ferdinanda Pampuri and Mauro Pelorosso, Eni

Copyright 2010, held jointly by the Society of Petrophysicists and Well Log Analysts (SPWLA) and the submitting authors.

This paper was prepared for presentation at the SPWLA 51st Annual Logging Symposium held Perth, Australia, June 19-23, 2010.

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ABSTRACT The general consensus in the industry is that the best way to measure slow formation shear in the logging-while-drilling (LWD) environment is by utilizing quadrupole waveforms. The use of quadrupole acoustic logging to determine shear velocities in slow formations requires an inversion method that takes into account the dispersion of the quadrupole mode, including the effects of the tool presence. This implies that the quadrupole shear inversion requires careful and well-validated modeling of the tool acoustics. The impact of the tool presence on the quadrupole dispersion is largest in the smaller boreholes where the tool takes up the largest percentage of hole volume. A log example was obtained using a 4.75-in LWD multipole tool from a 5.75-in hole in the Gulf of Mexico where the slowness ranged from 150 to above 250 us/ft. Monopole shear was available only in short intervals, providing a comparison for the quadrupole log in these intervals, as well as illustrating the need for the quadrupole measurement to fill in the missing depths. The resulting logs must be accompanied by convincing quality control (QC) displays to provide the user with the means to QC the final shear slowness product. Log displays compare the waveform dispersion with the inverted model dispersion and the resulting shear log, and single-depth displays provide details where needed. This quadrupole inversion methodology was used with high-quality, very wideband quadrupole waveforms and dispersion curves from a Gulf of Mexico well. Together they supplied the information needed to produce a set of QC displays that enable the resulting shear slowness log to be judged with confidence. INTRODUCTION Sonic logging while drilling (LWD) was introduced in the 1990s (Aron et al., 1994), with monopole tools

providing formation compressional slowness (P or DTC), and shear slowness (S or DTS) in harder rocks. This enabled real-time sonic applications in support of the drilling process, such as correlation with seismic and estimation of pore pressure anomalies. It also made sonic data more available in highly deviated wells where wireline logs are difficult to obtain. However, the inability to obtain a monopole shear arrival in slower rocks placed a significant limitation on the range of useful applications. Theoretical (Winbow, 1985, Schmitt, 1988) and Laboratory (Chen, 1989) work in the 1980s described the use of quadrupole methods for borehole sonic shear measurement. More recently, the service industry has introduced quadrupole sonic LWD tools (Tang et al., 2002, Market et al., 2007, and Kinoshita et al., 2008) to begin to address the need for a continuous shear measurement in such applications as geomechanics, amplitude versus offset (AVO) modeling and other seismic interpretation, and Vp/Vs to detect the presence of gas. Wireline has very successfully used dipole technology for this purpose, but the presence of the drill collar created a significant barrier to the use of dipole technology for LWD sonic. In wireline, the tool flexural arrival can be made quite slow so as not to interfere with the formation arrival. The heavy, stiff drill collar places the collar flexural arrival in the same slowness-frequency band as important components of the formation flexural arrival. With proper design of the LWD collar, the collar and formation quadrupole arrivals are kept separate, making feasible an accurate formation shear estimate. Similar to the dipole flexural, the quadrupole formation arrival is dispersive, with the lowest frequencies traveling at near the shear slowness and higher frequencies much slower. However, there is a significant difference as the two modes approach the shear slowness: the dipole flexural dispersion slope decreases, and the mode approaches and reaches the shear slowness at low frequencies. The quadrupole mode dispersion maintains a steep slope as it crosses the shear slowness and becomes leaky and highly attenuated at lower frequencies. The differences in the dispersion characteristics means that for the quadrupole, there will be a much narrower band of frequencies traveling at the shear slowness, and what is


traveling at the shear slowness is much lower in energy and may be lost in the drilling noise. To understand the various arrivals that can be seen in quadrupole data, Figure 1 shows model dispersion curves in an intermediate-slowness formation. The size of the dispersion circles is indicative of the energy in the component, and in real LWD sonic data the smaller arrivals are often not seen. In real data we almost always obtain a borehole quadrupole mode, but remnants of the leaky quadrupole and collar quadrupole will be evident or not depending on the noise amplitude and borehole conditions. The leaky quadrupole is attenuating rapidly. Due to their lower energy content, the high and low frequency ends of the borehole quadrupole mode dispersion will degrade first as the noise amplitude becomes stronger. Note that at low frequencies, the quadrupole mode can have energy slightly below the shear slowness. This energy is heavily attenuated as the mode is below cutoff.

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Figure 1: Model quadrupole dispersions for a typical intermediate-slowness formation. The circle sizes indicate relative energy, and the lower energy arrivals may or may not be seen in real LWD data. This example is for a 4.75-in tool in a 6.5-in borehole, with DTS = 170 us/ft and DTmud = 200 us/ft.

In addition to shear slowness, the quadrupole mode dispersion is a function of other formation, borehole, mud, and tool collar characteristics. Our goal is to measure the waveforms and dispersion, and along with knowledge of the other parameters, to estimate, or “invert”, for the shear slowness. The ability to understand how the presence of the collar will shift the quadrupole arrival is critical to making a good shear estimate. The next section of this paper will describe the tool model and the simulation, experimental, and field data used to validate and provide confidence in the model. The following section will describe the inversion processing method used to estimate shear slowness. The inversion uses a

dispersive semblance technique that incorporates the tool model. Then we will present an example from a well logged with a 4.75-in LWD sonic tool in the Gulf of Mexico (GOM), where monopole shear was present only in certain depth intervals. The quadrupole shear slowness compared well to the monopole where monopole shear was available, and filled in the remainder to give a shear slowness log over the entire interval. Methods to quality control (QC) the quadrupole shear estimates are critical, and we present a suite of logs and dispersion plots that can be used to QC various aspects of the data and shear slowness estimate. The 4.75-in LWD sonic tool used for the GOM field data example has a single wideband transmitter in 4 quadrants, to enable monopole or quadrupole firing. The receiver array consists of 48 sensors in a 4 x 12 arrangement with 4 sensors around the tool 90 degrees apart at each of the 12 spacings. The nearest receiver is 7 ft from the transmitter, and the inter-receiver spacing is 4 in. To provide the best acoustic quality, the collar structure was designed to provide as much uniformity and azimuthal symmetry as possible between the transmitter and receivers and along the receiver array. The received signals are digitized at the receiver sensors to reduce electronic noise and crosstalk. The small inter-receiver spacing, clean acoustics and reduction of electronic noise all greatly enhance the ability to provide real-time monopole compressional and shear DT. The monopole STC plane peaks are sent uphole, providing a real-time QC capability and allowing re-labeling of the P & S logs if needed. For recorded-mode acquisition, there is 1 GB of downhole waveform recording memory. Further details about the tool and its design can be found in (Kinoshita et al., 2008). EQUIVALENT TOOL MODEL FOR QUADRUPOLE INVERSION Tool effect on quadrupole dispersion - Due to the stresses and pressures of drilling, the LWD sonic tool’s mass is primarily composed of a rigid drill collar. Just as with the flexural mode in wireline sonic dipole tools, the presence of the LWD tool gives a shift to the quadrupole dispersion. Because the borehole volume taken up by the collar is greater than for the typical wireline tool, a large dispersion shift can be produced, especially in smaller boreholes and faster formations. The magnitude of this tool effect varies depending on borehole parameters, such as the formation, mud characteristics, and borehole diameter. The bias between quadrupole dispersions with and without the


tool is large in a fast formation and slim borehole, but is small in the case of a relatively large hole in a slow formation. Comparison of finite difference model with measured dispersions in a borehole - The tool effect on the quadrupole dispersions varies with borehole conditions and must be accurately predicted in order to properly utilize the dispersion for shear estimation. Finite Difference Method (FDM) modeling has been used to calculate synthetic waveforms while including details of the tool structure. Figure 2 shows an example comparing the dispersion calculated by the synthetic FDM waveforms and the dispersion measured in the tool in a fast cement test well. The pink and blue circles of the modeling and measured dispersion overlay well, and are both quite different from the “no-tool” model dispersion shown with a dashed curve.

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Figure 2: Comparison of dispersions with FDM modeling (magenta) and tool measurement (blue) in a borehole. The dashed curve is the no-tool model.

Equivalent tool model used for rapid inversion - FDM tool modeling provides an excellent prediction of the measured dispersion for specific cases. However, for the inversion processing shear estimation we needed a faster method that allowed dispersions to be computed for large combinations of formation, mud and borehole parameters. For this we developed a simplified pipe model with which model dispersions can be calculated by analytical solution much more quickly. Because we simplified the complex structure of the actual tool in this model, there are some differences between the analytical solution and FDM modeling under certain conditions. In order to match the dispersions from analytical and FDM methods in various borehole conditions, the ID/OD of the pipe and the effective mud density are varied as functions of the borehole parameters, i.e. shear slowness, mud slowness, mud

density and borehole diameter. Using this adaptive model, the dispersion is calculated with inputs of formation compressional and shear slowness, mud slowness, formation density, mud density, and borehole diameter, all assuming a homogeneous isotropic (HI) formation. Figure 3 has a comparison to data obtained under actual logging conditions, where the tool passes through the same formation before and after reaming. The bit size for the initial borehole diameter was 5.75 in, and the reamer diameter was 7 in. The equivalent tool model allows the dispersion to be tracked as the borehole characteristics change.

o FDM Modeling o Experiment

Dashed curve is “no-tool” model

Figure 3: Dispersion curves of the 4.75-in equivalent tool model (red curve) with different borehole diameters: top 5.75 in., lower 7.0 in., before and after reamer in a field test job. INVERSION PROCESSING METHOD The processing method is a 2-parameter inversion (formation shear slowness DTS and a mud slowness DTmud) maximizing the dispersive semblance (Kimball, 1998) over a band of frequencies, assuming a homogeneous-isotropic (HI) formation model with known measured borehole parameters such as compressional slowness, borehole diameter and mud density. However, the second inversion parameter should not be considered an estimate of the true mud slowness, because it incorporates various environmental effects such as a non-HI formation and errors in the other input parameters. Here we call it an “environmental slowness” parameter. The quadrupole dispersion model includes the effect of tool presence as described in the previous section on the equivalent tool model. The inversion method back-propagates quadrupole waveforms in the frequency


domain using the quadrupole dispersion model in the specified frequency band, summing across the array and normalizing by the total energy to calculate a semblance value between 0 and 1:

[ ]

dffW

dfefW

MSlowEnvDTSemblance M

ii

M

i

ifSfji

S

∫∑

∫ ∑

=

=

⋅−⋅⋅⋅=

1

2

2

1

)1()(2

)(

)(1.).,(

δπ

M is the number of the receivers, W(f) is the Fourier transform of the input waveform, δ is the inter-receiver spacing, and S(f) is quadrupole dispersion curve slowness (itself a function of the shear slowness DTS and the environmental slowness parameter, “Env. Slow.” in the equation). In the 2-parameter inversion method, the shear slowness and environmental slowness parameter are varied to obtain the semblance maximum, which determines the shear slowness estimate. A 1-parameter variation can be used by fixing the environmental slowness parameter to an estimated DTmud value and maximizing the semblance as a function of shear slowness alone.

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Figure 4: Semblance map example from field data, where the maximum is near DTS = 210 us/ft, environmental slowness = 240 us/ft. The peak is less well defined in the environmental slowness direction than in the DTS direction, especially in slower formations.

Figure 4 shows an example of a 2-D semblance map from field data, with environmental slowness parameter on the horizontal axis and DTS on the vertical axis. In slower formations the region of higher semblance becomes flatter and the environmental slowness parameter is poorly constrained, a manifestation of the lower dispersion curve sensitivity to mud slowness in

slow formations. The 1-parameter inversion is similar to selecting a specific value of the environmental slowness parameter on this plot and finding the peak in the semblance along that vertical slice. The resulting DTS estimate would change with each choice of the environmental slowness parameter. For the 2-parameter inversion, the semblance is maximized over the 2-D plane. To understand the reason behind using a 2-parameter inversion, consider the plot in Figure 5 of sensitivity of the quadrupole dispersion to changes in the model parameters: compressional slowness, shear slowness, mud slowness, formation density, mud density, and borehole diameter.

Fast Formation

Sensitivity

Slow Formation

Sensitivity

Figure 5: Sensitivity analysis of quadrupole dispersion to changes in borehole parameters. Shown for a 4.75-in tool in a 5.75-in borehole.

The top of Figure 5 shows the sensitivity for a fast formation (DTS = 160 us/ft), and the lower figure a slow formation (DTS = 300 us/ft), both in a small 5.75-in borehole with the same mud slowness and mud density. This sensitivity indicates how much the slowness at frequency f will change due to a small change in the parameter p. If a 1% change in the parameter at some frequency results in a 0.5% change in the dispersion slowness, the sensitivity is 0.5.


Sensitivity is plotted as negative if a positive change the parameter value results in a negative change in the dispersion slowness at that frequency. It is interesting to note that the sign of the sensitivity is negative for changes in borehole diameter, so that an increase in borehole diameter causes a reduction in the dispersion slowness. The sensitivity plots (Fig. 5) show that DTS has the dominant sensitivity among all the borehole parameters in a wide frequency band in a slow formation, and in a low frequency band in a fast formation. In fast formations there is a much stronger sensitivity to mud slowness, increasing at higher frequencies to become the dominant factor. There is also a strong sensitivity to borehole diameter, but for this we often have an estimate from the density caliper (although not in the GOM well later in this paper, where bit size is used). Figure 6 shows examples of dispersions changing with mud slowness. Mud slowness is especially difficult to determine in the LWD environment, where the mud composition frequently changes due to operator mud modifications, cuttings, and changing pore fluids.

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Figure 6: Quadrupole dispersion curves in a 5.75-in borehole in fast and slow formations, indicating the change in dispersion as the mud slowness changes.

As seen in Figure 6, at low frequencies near the quadrupole cutoff frequency (where it crosses the shear slowness, near 5 kHz in the fast example in Fig 6), the dispersion is dominated by the shear slowness. This suggests processing in a very low frequency band to remove errors due to the extraneous parameters. Unfortunately, the amplitude of the quadrupole mode is

dropping quite rapidly as the dispersion approaches the shear slowness, so these frequencies may have a low signal-to-noise ratio, making it dangerous to take the entire processing band too low. We have found that a good default band is from near cutoff frequency to near the Airy frequency where the quadrupole mode maximum amplitude occurs. This band can be estimated in an automated way at each depth by taking into account measurements or estimates of the extraneous parameters, and this is our default method. As an alternative and to check the sensitivity to the processing band, the band can be set by zones by the person doing the processing. The primary intent of the 2-parameter (rather than 1-parameter) inversion is to adapt to changing mud slowness. To see how this works, consider the following examples. Figure 7 shows the result using FDM data, with the shear slowness = 170 us/ft and mud slowness = 210 us/ft in a 5.75-in borehole. For the 1-parameter inversion, we assume we know the correct mud slowness. The green circles are the data dispersion, and the solid curves are the model dispersions using the final estimated slownesses. Here both the 1-parameter and 2-parameter inversions give the same shear estimate of 169 us/ft. The 2-parameter model found a value of the environmental slowness parameter of 209 us/ft, very close to the mud slowness of 210 us/ft, and so the two final model dispersion estimates virtually overlay.

DTmud = 250 us/ft

DTmud = 210 us/ft DTmud = 180 us/ft

DTS = 170 us/ft

Fast Formation DTmud Input Correct

DTmud = 210 us/ft DTmud = 250 us/ft

DTmud = 180 us/ft

DTS = 290 us/ft

Slow Formation

Figure 7: Quadrupole shear estimation for an FDM model dataset. Here we assume we know the correct mud slowness, and so the 1-parameter and 2-parameter dispersion estimates (solid) virtually overlay on the data dispersion (green circles), and give accurate DTS estimates. The value of the 2-parameter inversion becomes apparent when we do not know the correct mud slowness. Figure 8 is the same FDM dataset, with True DTmud = 210 us/ft, but the 1-parameter processing on the top assumes DTmud = 230 us/ft (too slow) and in the lower plot we assume DTmud = 190 us/ft (too fast). In


both cases the 1-parameter shear estimate is significantly in error, but the 2-parameter estimate is the same as in Fig. 7, with < 1% error.

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Figure 8: Quadrupole shear estimation for an FDM model dataset, with errors in the assumed mud slowness (too slow upper plot, too fast lower plot). The 2-parameter inversion, which optimizes over both environmental slowness parameter and shear slowness, provides a shear slowness estimate to within 1% in both cases.

The processing model we are using assumes a Homogeneous Isotropic (HI) formation. The preceding discussion dealt with sensitivity and errors in the model parameters under the HI assumption. Since we don’t always have an HI formation, it is worth considering what happens if the formation is not HI, that is, if the HI model itself is not accurate. The space of non-HI models is infinite, so we will consider two common non-HI cases, near-borehole slowness alteration, and transversely isotropic with a vertical axis of symmetry (TIV) formations such as horizontally layered shale, with a vertical borehole. The altered zone case is shown in Figure 9, where the model data is from a 4-in altered zone with a 10% slowness increase at the borehole wall (HD = 6.5 in.). The alteration has caused the data dispersion shown in green to be much more dispersive than the un-altered

HI model shown with the magenta curve. This is similar to the dipole flexural case where the high frequencies are more affected by the near borehole and the low frequencies see deeper, beyond the alteration. The 1-parameter inversion, which has the correct mud slowness input, will try to maximize the semblance with a dispersion model that is roughly parallel to this HI model dispersion. The maximum semblance will occur near where the model curve passes through the data dispersion with maximum energy, giving a significant error. The 2-parameter estimate uses the environmental slowness parameter to allow the model to adapt to the steeper data dispersion. In this case, the environmental slowness parameter is much slower than the true mud slowness (300 us/ft vs 210 us/ft), but the shear slowness estimate is good.

1-Parameter Dispersion


Figure 9: A model formation with a 4-in, 10% altered zone around the borehole. The 2-parameter inversion allows the environmental slowness parameter to adapt to the non-HI dispersion, and obtain < 1% error in the deep shear slowness.

Figure 10: A TIV model formation with a 20% velocity difference. The 2-parameter inversion allows the environmental slowness parameter to adapt to the TIV dispersion, and obtain a better shear slowness estimate (< 2% vs 5% error).

1-Par. DTS = 154 2-Par. DTS = 169 (Model DTS = 170)

2-Param. Disp.

Data Dispersion, Alt.


1-Param. Disp.

Disp. w/ no Alt.1-Parameter Dispersion

(Model DTS = 170) 2-Par. DTS = 169 1-Par. DTS = 178 (Model DTS = 290)

2-Par. DTS = 291 1-Par. DTS = 303

Disp. w/ no TIV

1-Param. Disp.

2-Param. Disp. Data Dispersion, TIV Formation

2-Par. DTS = 216 (Model DTS = 220)

1-Par. DTS = 209


A similar situation occurs in the TIV case, shown in Figure 10 using model data with a TIV horizontal to vertical shear velocity difference of 20%. The TIV dispersion (green) is less dispersive than the HI model (magenta). The inability of the HI model with the correct mud slowness to match the TIV dispersion in this case results in a 5% error in the 1–parameter shear estimate when the semblance is maximized. The 2-parameter estimate allows the environmental slowness parameter to better adjust to the TIV dispersion, reducing the shear slowness error to less than 2%.

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Figure 11: Modeling (upper) and field data (lower) for centered (blue) and fully eccentered (red) 4.75-in LWD tool in a 7-in borehole (field data not from this paper’s GOM example)

Sensitivity to eccentering - When the tool is not centered in the borehole, the quadrupole mode

dispersion can shift, and interfering monopole and dipole modes can appear. Figure 11 presents an example of this for a centered and fully eccentered 4.75-in tool in a 7-in borehole, for both model data and data from a real well. The quadrupole dispersion from the eccentered tool has shifted slower and to lower frequencies, a shift that will change the shear slowness estimate. This is a relatively fast formation (DTS = 125 us/ft), and modeling shows that the dispersion shift is reduced for slower formations. Through extensive modeling, we determined that if we limited the eccentering to less than 50% of the mud annulus radius, the impact on the dispersion curves and the slowness estimates is less than 1%. As a consequence, we have produced sets of appropriately sized stabilizers to be used depending on the bit size. The stabilizers are placed on the tool below the transmitter and above the receivers to limit the eccentering to 50% of the annulus for an in-gauge borehole.

Quadrupole at Stoneley slowness

Model Data

Dispersion Shift

Quadrupole at Stoneley slowness

GULF OF MEXICO EXAMPLE The 4.75-in LWD sonic tool described in the introduction was run while drilling a Gulf of Mexico well, with an inclination of 27 degrees at the top of the 1650 ft logged interval, down to 10 degrees at TD. Bit size was 5.75 in, and the sonic tool had 5.375-in stabilizers on the upper and lower ends of the tool. (This was early in the field test of the tool. Were this job done today, our procedures call for 5.5-in stabilizers.) The mud was 15.7 ppg OBM. The rate-of-penetration was generally 20-40 ft/hr, and the drillstring rotation 90-120 RPM.

Field Data The monopole P & S log is shown in Figure 12 along with the gamma ray. The target was a Lower Pleistocene delta-sourced sand that had re-deposits into previously cut channels or depressions on the outer slope. The reservoir sand is divided into 3 zones. The shallower unit is characterized by laminated sandstone/shale from X990 ft to Y190 ft. From the correlation wells, various rock facies are present in that interval. The predominant rock types are thinly laminated, moderately well sorted, very fine grained, sandstone/shale. Sandstone laminaes are clean and characterized by development of intergranular porosity. The average log porosity in this zone is 28 pu. The horizontal permeability is relatively good but the vertical permeability is low due to the highly laminated nature of the sandstones. The other rocks types are characterized by shale sandstone, poorly sorted, very fine grained, and containing large amounts of dispersed depositional shale. Above the described laminated sand the interval is predominantly shale. Below that sand the sequence is characterized by a sand shale interval.

Dispersion Shift


The compressional arrival is clear and coherent, ranging from 90 to 110 us/ft. The waveforms have been stacked over 16 firings in order to reduce the drilling noise, and the monopole data is shown after applying a 10-16 kHz filter. The monopole shear is weak and highly attenuated across the array even in the fastest intervals near 165 us/ft, and missing in much of the upper section of the log. The quadrupole shear is needed to fill in the missing monopole shear. No density log was run in this well, and there is no caliper. No wireline measurements were made.

Figure 12: LWD sonic monopole P & S log from the Gulf of Mexico well, with gamma ray. A 10-16 kHz filter has been applied to the waveform data. “S/S” in the label stands for Sandstone and Shale.

The quadrupole data also shows very high signal quality, as seen in Figure 13. The waveforms are a stack of 16 firings, and are shown as recorded, with no additional filtering. The dispersive semblance processing used the adaptive frequency selection described earlier, and was generally about 2.5 – 5 kHz. Comparing to the weak monopole shear in Fig. 12, the signal is much more continuous and coherent.

Figure 13: LWD sonic quadrupole data (waveforms, dispersion, and dispersive semblance projection log), with gamma ray. The waveforms are shown as recorded, with no filter applied.

Figure 14 (following page) presents the quadrupole dispersive processing and quality control (QC) log displays. Each track presents an important aspect of the quadrupole signal or inversion processing. The purpose of the QC log display is to provide a quick overview of the entire logged interval to reveal depths where there may be problems with the data or the processing. After noting such depths, the dispersion plots can be viewed at specific depths to see if there is indeed a problem and to determine options for modifying the processing parameters to make corrections.

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Figure 14: Quadrupole dispersive processing and quality control (QC) log displays. Each track is explained in detail in the main body of the paper (following page).


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The following is an explanation of the individual tracks for the quadrupole QC display in Figure 14: Tracks 1, 2: For GR, caliper, bit size, density, when available, and other non-sonic logs. Here we have bit size and GR only, in Track 2, and LWD resistivity logs in Track 1. For the sonic processing shown in Fig. 14, bit size was used for the caliper input to the processing. Vp/Vs and Poison’s Ratio PR are also displayed in Track 2. Track 3 (Slowness): Monopole 10-16 kHz Slowness-Time (ST) Projection from STC processing, with the monopole P and S curves overlaid in black, and the quadrupole S overlaid in red. In this case, it shows that the P has very good coherence, but that monopole S is not continuous, and when present has fairly low coherence. The monopole S and quadrupole S are in substantial agreement at this depth scale, and the quadrupole S is continuous, filling in for the missing monopole shear. If needed, these two shear logs can be combined or “spliced”, using the curve believed to be most trustworthy at each depth. Track 4 (Frequency): The energy spectrum of the quadrupole receiver #1 waveform. In this case, we see increasing energy (darker) with depth and faster formations, increasing bandwith with depth, and the rapid changes in amplitude in the laminated zone. Track 5 (Slowness): Quadrupole dispersive semblance projection from the inversion processing, with the quadrupole S log overlaid. This shows that the semblance is steady throughout the log, again with more variation in the sand zone where there are many thin beds. The quadrupole semblance is much higher than for the monopole shear, but lower than for the monopole compressional, probably because the quadrupole waveforms have a much stronger attenuation across the array than the compressional (can be seen looking at the waveform display in Figs. 12 & 13). Also in Track 5 is a light grey log of the peak quadrupole coherence. Track 6 (Slowness): This track has the “Slowness-Frequency Analysis” (SFA) log image axis (Plona et al., 2006), which is the projection of the quadrupole dispersion (slowness vs. frequency) estimates onto the slowness. The quadrupole shear log is overlaid in black, and it should lie near the left edge of the SFA image, indicating that the shear log is at the lower (faster) edge of the quadrupole dispersion curve. If this is not the case, it is an indicator to check the full dispersion plot at those depths to understand why. The log may be good and the image to the left of the log may come from other expected arrivals or noise, or perhaps the

processing parameters need adjustment, or maybe there is eccentering, alteration, other modes, etc. Sometimes modifying the frequencies to include in this display can remove a misleading part of the image. In any case, viewing the full dispersion display at particular depths usually makes the reason clear. Track 7 (Frequency): The image in this plot compares at each frequency the data dispersion to the model dispersion from the inversion to see how well the final model fits the data. Grey color indicates that there are no data dispersion values within 25% of the model at those frequencies. White indicates that the difference between the data and model is within 8%. Red indicates that the data is faster than the model by more than 8%, and blue that the data is slower than the model by more than 8% at that frequency. From this plot we see that in general the data dispersion and model dispersion are in reasonable agreement (display is mostly white), but in some spots especially in the sand interval there are places (display is grey) where the data dispersion is not well defined over a wide band. We would want to check those depths in more detail. Also shown on Track 7 are the upper and lower limits of the processing band used for the quadrupole processing. The processing band can be either fixed over depth, or as in this case allowed to be adapted at each depth (based on the input model parameters) to be from near cutoff to near the Airy frequency. For this log, the adaptive band was generally from about 2.5 - 5 kHz. The adaptive processing band does not go to higher frequencies because at these higher frequencies the dispersion can be more influenced by other parameters such as DTmud and caliper or deviations from the HI model. Track 8 (Frequency): This is the “Semblance Spectrum” image log. At each frequency it shows whether the semblance (normalized coherence) is high (red), medium (green), or low (grey or white). This image shows the width of the band of frequencies over which the quadrupole data is coherent. In this case, we see that the semblance is generally high over a band at least as wide as the processing band, again with the exception of the thinly layered interval from Y000 to Y275 ft. Track 9 (Time): This track has the quadrupole waveform variable density log (VDL) from receiver #1. The waveform shown in this track is usually filtered to near the band used for the quadrupole inversion processing, to give a better indication of the data seen by the inversion.


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As mentioned, after observing the QC logs, the next step is to check some individual dispersion plots. One of the slowest depths (X530 ft) is shown in Figure 15. The quadrupole inversion model is an excellent match to the data dispersion, with the resulting shear estimate (dashed red line) near the low frequency end of the dispersion. At the same time, we also observe that the monopole compressional dispersion is flat and in agreement with the estimated slowness (dashed green line). Some of the monopole Stoneley dispersion (green) is seen at the top of Figure 15.

Figure 15: GOM field data dispersion plot at one of the slowest depths. Monopole data dispersion uses the green circles, quadrupole the red circles, and the final 2-parameter quadrupole inversion model is shown with the solid red curve. The slowness estimates are shown by the dashed lines.

The interval with the fastest shear is found just above Y800 ft near the bottom of the logged interval. Although the quadrupole agrees well with the monopole shear, the SFA image (Track 6 of Figure 14) is weak at frequencies just above the shear slowness in this interval, so it is useful to check the result. Figure 16 shows a dispersion plot from this fast zone. The model and measured quadrupole dispersions (red) agree, and the monopole shear (blue dashed) and quadrupole shear slowness estimates are in good agreement, considering the scatter on the monopole shear dispersion. The gap in the quadrupole shear dispersion near 2.75 kHz could be due to the very rapidly changing slowness combined with a reduction in modal energy at the lower frequencies in fast formations. A similar result is seen in the FDM model dispersions in Fig. 7 and 8.

Slowness Dispersion (Depth = Y794 ft)

Mono S Quad S

Slowness Dispersion (Depth = X530 ft)

Monopole (Stoneley) Dispersion Figure 16: Dispersion plot in one of the fastest zones. The solid red curve is the dispersion model obtained from the 2-parameter inversion. Quad.

Dispersion The slow bed near Y756 ft shows some disagreement between monopole and quadrupole shear, so we want to take a look at this in more detail. The monopole shear semblance is seen to be weak at this depth in the ST projection log in Track 3 of Figure 14. Figure 17 has the dispersion plot, which indicates a good agreement between the model and measured quadrupole dispersion, and good placement of the shear estimate (dashed red). The monopole shear estimate (dashed blue) is near to the monopole dispersion (green), but this dispersion is weak and poorly defined when compared for example to the compressional near 100 us/ft.

Monopole (P) DispersionMono P


Mono SQuad S

Figure 17: Dispersion plot where there is disagreement between monopole (blue dashed) and quadrupole shear (red dashed) slowness. The quadrupole shear estimate looks reasonable, given the measured dispersion. The monopole estimate is based on a very weak shear arrival.


Next we shift our attention to the more difficult zone between Y000 and Y200 ft. Although there is reasonable agreement with the monopole shear in this interval, the QC logs indicate significantly reduced signal bandwidth and less well defined quadrupole dispersion. At Y065 ft, the dispersions appear as in Figure 18.

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Figure 18: Quadrupole (red) with some energy along the Stoneley dispersion (300 - 400 us/ft, 2 - 6 kHz) suggests the possibility of eccentering at this depth.

Figure 19: At this depth, a highly dispersive quadrupole mode, a very slow Stoneley, and a dispersive compressional arrival all suggest the possibility of a near-borehole altered zone. The shear estimate (red dashed line) appears to be too slow, so a lower processing frequency band should be considered.

In Fig. 18 we see very little continuous high frequency quadrupole dispersion. There is also a significant Stoneley arrival traveling in the quadrupole data, which can occur when the tool is eccentered. The resulting shear estimate is using the energy near 2.5 kHz, 220 us/ft. This appears reasonable given the dispersion plot, but the confidence in the estimate is reduced under

these conditions. If we had a caliper in this dataset, we would check for an enlarged hole, which would help support the conjecture of eccentering. The final dispersion example comes from a nearby depth, at Y060 ft, shown in Figure 19. Here the quadrupole mode is so dispersive that even with the environmental slowness parameter, limited to 300 us/ft here, the processing does not provide a good dispersion match. The result is a shear slowness estimate that is probably biased slower than the true shear. The very slow Stoneley above 400 us/ft, along with the dispersive monopole compressional, are all indicative of near wellbore slowness alteration.


Quadrupole at Stoneley Slowness

SUMMARY LWD quadrupole sonic data is highly dispersive, with energy decreasing rapidly as the dispersion approaches the shear slowness. In the presence of drilling noise, a technique that makes use of the high amplitude dispersive component can enable a more robust measurement. A critical component of this strategy is the ability to incorporate an accurate, experimentally validated, tool model into the dispersive processing. Slowness Dispersion A semblance-based dispersive processing method to estimate shear slowness from LWD sonic quadrupole waveforms can provide the shear slowness not available from monopole sonic logs in slow formations. The technique provides the option of including an environmental slowness parameter in a 2-parameter inversion in cases where the mud slowness may be unknown or variable. The 2-parameter inversion also provides some degree of robustness in the presence of certain types of non-HI formations such as near-borehole slowness alteration or vertical well TIV anisotropy.

(Depth = Y060 ft)

Very slow Stoneley

Very dispersive quadrupole

Dispersive Compressional

High-fidelity monopole and quadrupole LWD sonic acquisition and dispersive processing in a Gulf of Mexico well produced a continuous shear log where the monopole shear was weak or absent. An important component of the quadrupole processing is a suite of QC logs which allow various aspects of the dispersive processing results to be critically evaluated. Intervals of interest from these logs can be analyzed in detail at individual depths by viewing dispersion plots which include monopole and quadrupole data, the quadrupole inversion model, the monopole P & S slownesses and quadrupole shear slowness estimate. In addition to helping to evaluate the slowness estimates, the dispersion plots can help to provide evidence of tool eccentering and near-borehole slowness alteration.


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ACKNOWLEDGEMENTS The authors wish to thank Eni for permission to publish the data used in this study. REFERENCES Aron, J., Chang, S., Dworak, R., Hsu, K., Lau, T., Masson, J., Mayes, J., McDaniel, G., Randall, C., Kostek, S., Plona, T., Sonic Compressional Measurements While Drilling, SPWLA 35th Annual Logging Symposium, June 19-23, 1994. Chen, S. T., 1989, Shear-wave logging with quadrupole sources: Geophysics, vol. 54, 590-597. Kimball, C.V., 1998, Shear slowness measurement by dispersive processing of the borehole flexural mode: Geophysics, 63, 337-344. Kinoshita, T., Endo, T., Nakajima, H., Yamamoto, H., Dumont, A., and Hawthorn, A., 2008 Next Generation LWD Sonic Tool: The 14th Formation Evaluation Symposium of Japan, Sept. 29-30, 2008. Market, J., Althoff, G., Varsamis, G., 2007, New Broad Frequency LWD Multipole Tool Provides High Quality Compressional and Shear Data in a Wide Variety of Formations: SPWLA 14th Annual Logging Symposium, June 3-6, 2007. Plona, T., Endo, T., Wielemaker, E., Walsh, J., Yamamoto, H., Slowness-Frequency Projection Logs: A QC for Accurate Slowness Estimation and Formation Property Identification: Soc. of Expl. Geophysics Annual Meeting, 2006. Schmitt, D. P., Shear-wave logging in elastic formations: J. Acoust. Soc. Amer., 84, 2215-2229. Tang, X. M., Dubinsky, V., Wang, T., Bolshakov, A., Patterson, D., 2002, Shear-Velocity Measurement In The Logging-While Drilling Environment: Modeling And Field Evaluations: SPWLA 43rd Annual Logging Symposium, June 2-5, 2002. Winbow, G., 1985, Compressional and shear arrivals in a multipole sonic log: Geophysics, vol. 50, 1119-1126, 1988.

ABOUT THE AUTHORS David Scheibner has been with Schlumberger for 24 years, working primarily in Wireline and LWD sonic

tool engineering in Texas and Japan. He holds a BSEE degree from New Mexico State Univ., and MSEE and PhD EE degrees from Rice University in Houston, Texas. Shinji Yoneshima has received M.S. in 1999 for geophysics. After joining Schlumberger, he contributed to the development of sonic data processing algorithms for both LWD and wireline sonic tools at Schlumberger K. K. in Japan. He is currently working in the microseismic domain. Zhenxin Zhang is a processing engineer in the sonic application development group at Schlumberger K.K. in Japan. He joined Schlumberger in 2003 as an engineer in the Petrophysics department in the Beijing Geoscience Center. Then he moved to Sonic Engineering group in Schlumberger K.K. in 2007. Since then he has been working on sonic processing developments. He has an MS degree in physics from Fudan University in Shanghai, China. Wataru Izuhara has been working in Schlumberger for 3 years. He is involved in LWD sonic tool engineering in Japan. He holds Bachelor and Master Degrees of Engineering from Kyoto University in Kyoto, Japan. Yuichiro Wada joined Schlumberger in 2008, and is a physics engineer working on sonic experimental measurement and evaluation in the sonic product discipline at Schlumberger K.K. in Japan. He received a PhD in physics from Tokyo Institute of Technology. Peter Wu received a Ph. D. in Acoustics. He has been working for Schlumberger for 30 years in the areas of Acoustics and Electromagnetics. Ferdinanda Pampuri is currently Senior Advisor Petrophysics in the Reservoir Characterization Department for Eni E&P. In particular she is the focal point for the world wide acoustic acquisition and interpretation activities. She graduated in Geology at the University of Milano, and started her experience in Schlumberger’s wireline department as a log analyst and then as a petrophysicist on standard and high technology measurements for both open hole and cased hole data. Since she joined Eni E&P in 1994 she has worked on high technology measurement interpretation, integrated petrophysical evaluation, reservoir studies as well as R&D projects for Formation Evaluation. She is an author and co-author of a number of papers published by the SPWLA and SPE. Mauro Pelorosso has been with Eni E&P for nearly seven years. In his position as Petrophysicist he worked


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in Ravenna (Italy) and in Hassi Messaoud (Algeria). Starting from 2008 he has been in Houston working on deepwater GOM and Alaska Wells. He has a University

Degree in Structural Geology from the University of Chieti (Italy).

slow formation shear from an lwd tool: quadrupole inversion with a

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