Dipole Sonic Log Calibration using Walkaway VSP data S. Horne*, P. Primiero, A. Donald, E. Knight, C. Sayers (Schlumberger); K. Koster, Donald Keir (Apache). Summary In this paper, we describe how one can use anisotropy estimates derived from walkaway VSPs as a constraint on upscaled sonic log data recorded in a deviated well to derive a ‘calibration’ relationship between the anisotropic parameters measured from the sonic logs. One can apply this calibration to the dipole sonic log data to extract all Transverse Isotropy parameters. Introduction A common form of anisotropy often observed in the earth is Transverse Isotropy (TI) in which properties change only with respect to a single direction. If this direction is vertical five elastic constants (C11, C33, C13, C44 and C66) describe the Transverse Isotropy. Thomsen (1986) introduced a more convenient parameterization, which the seismic industry has widely adopted. The Thomsen parameters include Vp0 and Vs0, which are the compressional and shear wave velocities along the symmetry axis; and dimensionless parameters ε, δ and γ, which describe anisotropic (directional) variations.
Liu, 1997; Sondergeld et al. 2000; Wang, 2002; Tsuneyama and Mavko, 2005; Sayers, 2005). We also note that the correlation coefficient is formation dependent. One may also use walkaway VSPs to measure elastic anisotropy parameters. In general, there are two methods of deriving the elastic constants around the downhole receiver array. The first is the slowness technique (e.g. Miller, Leaney and Borland, 1994), which requires a near horizontally layered overburden. The second method is slowness-polarization (e.g. de Parscau, 1991), which does not require structural simplicity in the overburden like the slowness method. In general, these methods extract only four of the Thomsen anisotropy parameters—Vp0, Vs0, ε and δ. Thomsen’s γ is not typically measured with conventional VSPs because it describes the behaviour of horizontally polarized shear waves (SH), which conventional seismic sources do not usually generate.
In deviated wells, modern sonic logs accurately measure four wave types from which one can compute two elastic constants (C44 and C66), and two other parameters (M, N) that represent a combination of the other elastic constants, which Norris and Sinha (1993) defined as 2 4
sin cos To resolve all the Thomsen parameters from these four parameters, one could use the ANNIE model (Schoenberg, Muir and Sayers, 1996). The ANNIE model implies that Thomsen’s δ is zero and can sometimes be a good approximation for shale anisotropy. However, this approximation may not always be appropriate, as Figure 1 demonstrates. These plots show reported measurements of the Thomsen anisotropic parameters of ε, δ and γ for two shales. For these shales, the Thomsen’s δ parameter is generally not zero. This suggests that in these cases the ANNIE model is not appropriate, which is not unexpected because the primary purpose of the ANNIE model is to enable accurate prediction of a shale’s anellipticity, given an incomplete dataset. However, we observe that Thomsen’s anisotropy parameters of ε and γ are strongly correlated, as many authors have observed (e.g. Vernik and
Figure 1: Laboratory measurements of anisotropy for Kimmeridge Shale (top, modified from Sondergeld et al., 2000) and Bakken Shale (bottom, modified from Vernik & Liu, 1997). The ANNIE model implies a Thomsen’s δ of zero (red line). Note the correlation of Thomsen’s γ and ε (green line).
© 2010 SEG SEG Denver 2010 Annual Meeting Downloaded 25 Dec 2010 to 199.6.131.16. Redistribution subject to SEG license or copyright; see Terms of Use at http://segdl.org/
4334
Dipole Sonic Log Calibration Using VSPs
One obtains the elastic properties derived from dipole sonic logs using high frequency seismic sources in the well and recording the resulting waves with receivers also deployed in the well. Such sonic logs measure high spatial resolution estimates of the elastic properties around the wellbore. One obtains the elastic anisotropy estimates derived from walkaway VSPs using receivers placed in the well that measure seismic waves generated by a remote seismic source. VSP measurements are of a lower spatial resolution than sonic log measurements because the frequencies of their measurements differ. This scale difference makes direct comparison of dipole sonic log and VSP data difficult. One means of reconciling the two scale lengths is through a process known as upscaling. Below, we describe how one can use anisotropy estimates derived from walkaway VSPs as a constraint on the upscaled sonic log data to derive a ‘calibration’ relationship between the anisotropic parameters measured from sonic logs. Then one can apply this calibration to the dipole sonic log data to extract all of the TI parameters.
types in which frequency dependence due, for example, to fluid effects, is unlikely to be an issue.
Example: Application to North Sea shale The Sele Shale formation is a regional sealing unit in the North Sea that is known to be elastically anisotropic. Failure to accurately account for elastic anisotropy can lead to poor seismic images, which, in turn, can lead to incorrect well placements. Furthermore, if one neglects anisotropy, one may not correctly anticipate geomechanical effects, which can lead to well failures. To address these problems, we obtained a suite of geophysical and geological measurements over the Forties field with the specific purpose of understanding the elastic anisotropy of the Sele formation. This measurement program included dipole and Stoneley shear sonic logs, walkaway VSP and geomechanical measurements on recovered cores (Donald et al., 2009).
Calibration Algorithm The calibration process proceeds as follows: 1. Process the dipole and Stoneley shear sonic logs recorded in the deviated well to obtain the parameters C44Log, C66Log, MLog and NLog; 2. Process the walkaway VSP to derive anisotropy parameters (i.e. Thomsen’s εVSP and δVSP); 3. Assume a relationship between Thomsen’s εLog and γLog; 4. Compute the elastic constants(C11Log, C33Log, C13Log) from MLog and NLog; 5. Upscale the logs and compute the Thomsen anisotropy parameters; 6. Modify the proposed relationship in (Step 3) until there is a good agreement between the VSP (from Step 2) and the upscaled log anisotropy parameters (from Step 5). 7. Use the anisotropy parameters to output a calibrated log for the 5 elastic constants. Note that we do not attempt to directly match the elastic constants, or velocities, but only the dimensionless anisotropic parameters. We do this because it is well known that the velocities derived from high frequency log measurements differ from those derived from lower frequency seismic measurements such as VSPs. For this reason, we choose to match the dimensionless anisotropic parameters that one would expect to be less sensitive to these frequency-dependent effects. The technique is intended for relatively homogeneous impermeable rock
2.0
1.5
Misfit 1.0
0.5
0 0
0.5
1.0
1.5
2.0
2.5
Calibration Coefficient
Figure 2: Top: Calibration results comparing walkaway VSP inversion results (colored squares) with anisotropy parameters from the upscaled log data (grey line) as the relationship between Thomsen’s εLog and γLog changes. Bottom: The objective function measuring the difference between the upscaled logs and the walkaway VSP anisotropy parameters.
© 2010 SEG SEG Denver 2010 Annual Meeting Downloaded 25 Dec 2010 to 199.6.131.16. Redistribution subject to SEG license or copyright; see Terms of Use at http://segdl.org/
4335
Dipole Sonic Log Calibration Using VSPs
The walkaway VSP was acquired using an 8-level receiver array in a deviated well section. Since the overburden was essentially flat, we used the slowness curve method to estimate the elastic anisotropy parameters. We constructed a slowness curve using only the receivers located within the Sele formation. Then we inverted the slowness curve to obtain Thomsen parameter anisotropy estimates of εVSP=0.15 and δVSP=0.02, which indicated moderate anelliptical anisotropy. We acquired dipole sonic log data over the Sele formation in a well close to the location of the walkaway VSP. The data were of good quality, and were processed to extract the elastic parameters C44 and C66 and the parameters N and M.
between Thomsen’s γ and ε, and, 3) that both the VSP and sonic measurements are taken over a reasonably homogenous formation in a deviated well. Applying the procedure to dipole sonic data validates the approach and shows good agreement with a priori measurements. Acknowledgments The authors gratefully acknowledge Apache North Sea Limited and the Schlumberger Technology Corporation for permission to present this paper.
Figure 2 shows a summary of the calibration process results. The background image composed of colored squares represents anisotropic models sampled by the walkaway VSP inversion, in which colors correspond to the quality of fit. Also marked is the result obtained using the ANNIE model (εLog=0.07 and δLog=-0.02). Note that the ANNIE model under predicts the ε and δ anisotropy parameters observed with the walkaway VSP anisotropy measurements. Overlain on this plot is a gray line showing the track of the upscaled anisotropy parameters as the relationship between Thomsen’s γ and ε is modified. Note how the track passes very close to the peak solution for the walkaway VSP-derived anisotropy measurements. The optimal match occurs with a calibration coefficient of 1.03. This value is in good agreement with the linear relationship found by Wang (2002), who determined a value of 1.05. We applied this calibration coefficient to the log data (Figure 3). We gained further confidence in these results by comparing the anisotropy parameters from these calibrated logs with the core results (Figure 4). Figure 4 also shows the Thomsen anisotropy parameters ε and δ that we obtained using the ANNIE model. Whilst the ANNIE results do not agree well with the core measurements, a comparison of the anellipticity parameter η = (ε-δ)/(1+2δ) derived using the ANNIE model and the VSP calibrated logs show good agreement (Figure 5). This suggests that whilst ANNIE may not be appropriate for predicting the elastic constants or the Thomsen’s ε and δ, it may still be appropriate for computing the anellipticity parameter η from dipole sonic log data. Conclusions We have outlined a procedure whereby one can use walkaway VSP anisotropy estimates as a constraint for dipole sonic log measurements to derive all five TI elastic constants. Such a procedure assumes 1) that the anisotropic parameters are less sensitive to scale effects than the elastic constants themselves, 2) that there is a linear relationship
Figure 3: Logs calibrated in terms of the elastic constants (top) and in terms of the anisotropy parameters (bottom). Curves are color-coded according to the objective function measuring the similarity between the upscaled logs and the VSP derived anisotropy values.
© 2010 SEG SEG Denver 2010 Annual Meeting Downloaded 25 Dec 2010 to 199.6.131.16. Redistribution subject to SEG license or copyright; see Terms of Use at http://segdl.org/
4336
Dipole Sonic Log Calibration Using VSPs
VSP Calibrated
ANNIE
Figure 4: Cross plots of anisotropy parameters derived from the logs (red) and core measurements (black) using (left) walkaway VSP data and (right) the ANNIE model.
Figure 5: Cross plots of the anellipticity parameter η computed using the ANNIE model plotted against η computed from the VSP calibrated logs.
© 2010 SEG SEG Denver 2010 Annual Meeting Downloaded 25 Dec 2010 to 199.6.131.16. Redistribution subject to SEG license or copyright; see Terms of Use at http://segdl.org/
4337
EDITED REFERENCES Note: This reference list is a copy-edited version of the reference list submitted by the author. Reference lists for the 2010 SEG Technical Program Expanded Abstracts have been copy edited so that references provided with the online metadata for each paper will achieve a high degree of linking to cited sources that appear on the Web. REFERENCES
Donald, A., A. Paxton, D. Keir, and K. Koster, 2009, Improving seismic calibration and geomechanical models through characterization of anisotropy using single and multi well data: Case Study in Forties Field, UK: SEG Expanded Abstracts, 28, no. 1, 557–561. Miller, D., W. Leaney, and W. Borland, 1994, An in situ estimation of anisotropic elastic moduli for a submarine shale : Journal of Geophysical Research, 99, B11, 21659–21665, doi:10.1029/94JB01849. Norris, A., and B. Sinha, 1993, Weak elastic anisotropy and the tube wave: Geophysics, 58, 1091–1098, doi:10.1190/1.1443493. de Parscau, J., 1991, P- and SV-wave transversely isotropic phase velocity analysis from VSP data : Geophysical Journal International, 107, no. 3, 629–638, doi:10.1111/j.1365-246X.1991.tb01422.x. Sayers, C. M., 2005, Seismic anisotropy of shales: Geophysical Prospecting, 53, no. 5, 667–676, doi:10.1111/j.1365-2478.2005.00495.x. Schoenberg, M., F. Muir, and C. M. Sayers, 1996, Introducing ANNIE: A simple three-parameter anisotropic velocity model for shales: Journal of Seismic Exploration, 5, 35–49. Sondergeld, C. H., S. R. Chandra, R. W. Margesson, and K. J. Whidden, 2000, Ultrasonic measurement of anisotropy on the Kimmeridge Shale : SEG Expanded Abstracts, 19, no. 1, 1858–1861, doi:10.1190/1.1815791. Thomsen, L., 1986, Weak elastic anisotropy: Geophysics, 51, 1954–1966, doi:10.1190/1.1442051. Tsuneyama, F., and G. Mavko, 2005, Velocity anisotropy estimation for brine-saturated sandstone and shale: The Leading Edge, 24, no. 9, 882–888, doi:10.1190/1.2056371. Vernik, L., and X. Liu, 1997, Velocity anisotropy in shales: A petrophysical study: Geophysics, 62, 521– 532, doi:10.1190/1.1444162. Wang, Z., 2002, Seismic anisotropy in sedimentary rocks, part 2: Laboratory data: Geophysics, 67, 1423– 1440, doi:10.1190/1.1512743.
© 2010 SEG SEG Denver 2010 Annual Meeting Downloaded 25 Dec 2010 to 199.6.131.16. Redistribution subject to SEG license or copyright; see Terms of Use at http://segdl.org/
4338
