1887
  1. Home
  2. A-Z Publications
  3. Geophysical Prospecting
  4. Volume 72, Issue 3
  5. Article
Volume 72, Issue 3
  • E-ISSN: 1365-2478
PDF

Abstract

Abstract

The formations above a producing reservoir can exhibit large mechanical changes, creating a risk of significant subsidence and loss of rock integrity. These changes can be monitored by time‐lapse seismic acquisition, which measures the corresponding velocity changes via time‐shifts. Third‐order elastic theory can be used to connect subsurface strains and stress changes to these seismic attribute changes. Existing models assume isotropic strain dependence of the dynamic stiffness in shales. It is important to re‐evaluate this isotropic assumption considering the inherent anisotropy of shales and their abundance in the overburden. Thus, we instead propose a third‐order elastic model with a transversely isotropic strain dependence of the dynamic stiffness. When calibrated, this new model satisfactorily predicted P‐wave velocity changes determined in undrained laboratory experiments conducted on overburden field shales, covering a wide range of propagation directions and stress variations. The shales exhibit anisotropic dynamic strain sensitivity, resulting in a significantly higher strain sensitivity predicted for Thomsen's anisotropy parameters epsilon and delta subjected to a uniaxial strain parallel to the horizontal bedding plane compared to the vertical direction. Geomechanical modelling, considering a depleting disk‐shaped reservoir surrounded by shales, was employed to predict the dynamic stiffness changes of the overburden using the laboratory‐calibrated third‐order elastic model. The overburden time‐shifts increased with offset angle, peaking at about 45°, suggesting a strong influence of shear strains on the time‐shifts. In contrast, a corresponding model with an isotropic third‐order elastic tensor, calibrated to the same data, exhibited a significantly lower sensitivity to the shear strains. These results underscore the importance of considering the anisotropic strain dependence of the dynamic stiffness when studying shales. Interpreting offset‐dependent trends in pre‐stack time‐lapse seismic data, along with geomechanical modelling and an appropriate strain‐dependent rock physics model, can assist in quantifying subsurface strains and stress changes.

© 2024 European Association of Geoscientists & Engineers. © 2024 The Authors. Geophysical Prospecting published by John Wiley & Sons Ltd on behalf of European Association of Geoscientists & Engineers.
Loading

Article metrics loading...

/content/journals/10.1111/1365-2478.13446
2024-02-21
2025-03-22

  • From This Site

    /content/journals/10.1111/1365-2478.13446
    dcterms_title,dcterms_subject,pub_keyword
    -contentType:Journal -contentType:Contributor -contentType:Concept -contentType:Institution
    10
    5
Loading full text...

Full text loading...

/deliver/fulltext/gpr/72/3/gpr13446.html?itemId=/content/journals/10.1111/1365-2478.13446&mimeType=html&fmt=ahah

References

  1. Angus, D.A., Dutko, M., Kristiansen, T.G., Fisher, Q.J., Kendall, J.‐M., Baird, A.F. et al. (2015) Integrated hydro‐mechanical and seismic modelling of the Valhall reservoir: a case study of predicting subsidence, AVOA and microseismicity. Geomechanics for Energy and the Environment, 2, 32–44. https://doi.org/10.1016/j.gete.2015.05.002
     [Google Scholar]
  2. Asaka, M. (2023) Anisotropic 4D seismic response inferred from ultrasonic laboratory measurements: a direct comparison with the isotropic response. Geophysical Prospecting, 71, 17–28. https://doi.org/10.1111/1365‐2478.13273
     [Google Scholar]
  3. Bakk, A., Holt, R.M., Bauer, A., Dupuy, B. & Romdhane, A. (2020) Offset dependence of overburden time‐shifts from ultrasonic data. Geophysical Prospecting, 68, 1847–1863. https://doi.org/10.1111/1365‐2478.12963
     [Google Scholar]
  4. Bakk, A., Holt, R.M., Duda, M. & MacBeth, C. (2020). The fate of R in light of field shale laboratory tests [Conference proceedings]. EAGE 2020 Conference Online. EAGE. pp. 1–5. https://doi.org/10.3997/2214‐4609.202011500
  5. Barkved, O.I., Kristiansen, T. & Fjær, E. (2005) The 4D seismic response of a compacting reservoir – examples from the Valhall Field, Norway [Expanded abstracts]. 75th SEG Annual Meeting. Houston, TX, USA. SEG. pp. 2508–2511. https://doi.org/10.1190/1.2148232
  6. Bathija, A.P., Batzle, M.L. & Prasad, M. (2009) An experimental study of the dilation factor. Geophysics, 74, E181–E191. https://library.seg.org/doi/abs/10.1190/1.3137060
     [Google Scholar]
  7. Batzle, M.L., Han, D.‐H. & Hofmann, R. (2006) Fluid mobility and frequency‐dependent seismic velocity—direct measurements. Geophysics, 71, N1–N9. https://library.seg.org/doi/10.1190/1.2159053
     [Google Scholar]
  8. Bauer, A., Lehr, C., Korndorffer, F., van der Linden, A., Dudley, J., Addis, T. et al. (2008) Stress and pore‐pressure dependence of sound velocities in shales: poroelastic effects in time‐lapse seismic [Expanded abstracts]. 78th SEG Annual Meeting. Las Vegas, NV, USA. SEG. pp. 1630–1634. https://doi.org/10.1190/1.3059221
  9. Berryman, J.G. (1979) Long‐wave elastic anisotropy in transversely isotropic media. Geophysics, 44, 896–917. https://doi.org/10.1190/1.1440984
     [Google Scholar]
  10. Birch, F. (1947) Finite elastic strain of cubic crystals. Physical Review, 71, 809–824. https://doi.org/10.1103/PhysRev.71.809
     [Google Scholar]
  11. Brugger, K. (1964) Thermodynamic definition of higher order coefficients. Physical Review, 133, A1611–A1612. https://doi.org/10.1103/PhysRev.133.A1611
     [Google Scholar]
  12. Brugger, K. (1965) Pure modes for elastic waves in crystals. Journal of Applied Physics, 36, 759–768. https://doi.org/10.1063/1.1714215
     [Google Scholar]
  13. Cheng, A.H.‐D. (1997) Material coefficients of anisotropic poroelasticity. International Journal of Rock Mechanics and Mining Sciences, 34, 199–205. https://doi.org/10.1016/S0148‐9062(96)00055‐1
     [Google Scholar]
  14. Crampin, S., Chesnokov, E.M. & Hipkin, R.G. (1984) Seismic anisotropy—the state of the art: II. Geophysical Journal International, 76, 1–16. https://doi.org/10.1111/j.1365‐246X.1984.tb05017.x
     [Google Scholar]
  15. De Gennaro, S., Onaisi, A., Grandi, A., Ben‐Brahim, L. & Neillo, V. (2008) 4D reservoir geomechanics: a case study from the HP/HT reservoirs of the Elgin and Franklin fields. First Break, 26, 53–59. https://doi.org/10.3997/1365‐2397.2008019
     [Google Scholar]
  16. Delle Piane, C., Dewhurst, D.N., Siggins, A.F. & Raven, M.D. (2011) Stress‐induced anisotropy in brine saturated shale. Geophysical Journal International, 184, 897–906. https://doi.org/10.1111/j.1365‐246X.2010.04885.x
     [Google Scholar]
  17. Delle Piane, C., Sarout, J., Madonna, C., Saenger, E.H., Dewhurst, D.N. & Raven, M. (2014) Frequency‐dependent seismic attenuation in shales: experimental results and theoretical analysis. Geophysical Journal International, 198, 504–515. https://doi.org/10.1093/gji/ggu148
     [Google Scholar]
  18. Dellinger, J. & Vernik, L. (1994) Do traveltimes in pulse‐transmission experiments yield anisotropic group or phase velocities?Geophysics, 59, 1774–1779. https://doi.org/10.1190/1.1443564
     [Google Scholar]
  19. Dewhurst, D.N. & Siggins, A.F. (2006) Impact of fabric, microcracks and stress field on shale anisotropy. Geophysical Journal International, 165, 135–148. https://doi.org/10.1111/j.1365‐246X.2006.02834.x
     [Google Scholar]
  20. Ditlevsen, F., Bourgeois, F. & Calvert, M. (2018) Handling wellbore instability in overburden Tertiary shales [Conference proceedings]. 80th EAGE Conference & Exhibition. Copenhagen, Denmark. EAGE. pp. 1–5. https://doi.org/10.3997/2214‐4609.201800721
  21. Donald, J.A. & Prioul, R. (2015) In situ calibrated velocity‐to‐stress transforms using shear sonic radial profiles for time‐lapse production analysis. The Leading Edge, 34, 286–294. https://doi.org/10.1190/tle34030286.1
     [Google Scholar]
  22. Duda, M.I., Bakk, A., Holt, R.M. & Stenebråten, J.F. (2023) Anisotropic poroelastic modelling of depletion‐induced pore pressure changes in Valhall overburden. Rock Mechanics and Rock Engineering, 56, 3115–3137. https://doi.org/10.1007/s00603‐022‐03192‐0
     [Google Scholar]
  23. Duda, M.I., Holt, R.M. & Bakk, A. (2020) Third‐order elastic tensor of shales determined through ultrasonic velocity measurements [Conference proceedings]. 54th US Rock Mechanics/Geomechanics Symposium. ARMA‐2020‐1237. https://onepetro.org/ARMAUSRMS/proceedings/ARMA20/All‐ARMA20/ARMA‐2020‐1237/447487
  24. Dudley, J.W., Brignoli, M., Crawford, B.R., Ewy, R.T., Love, D.K., McLennan, J.D. et al. (2016) ISRM suggested method for uniaxial‐strain compressibility testing for reservoir geomechanics. Rock Mechanics and Rock Engineering, 49, 4153–4178. https://doi.org/10.1007/s00603‐016‐1055‐4
     [Google Scholar]
  25. Duranti, L., Ewy, R. & Hofmann, R. (2005) Dispersive and attenuative nature of shales: multiscale and multifrequency observations [Expanded abstracts]. 75th SEG Annual Meeting. Houston, TX, USA. SEG. pp. 1577–1580. https://doi.org/10.1190/1.2147994
  26. Dvorak, I., MacBeth, C. & Amini, H. (2018) Evaluating 4D overburden velocity perturbation for the Shearwater field via pre‐stack time‐shift inversion [Conference proceedings]. 80th EAGE Conference & Exhibition. Copenhagen, Denmark, EAGE. pp. 1–5. https://doi.org/10.3997/2214‐4609.201800699
  27. Evensen, A.K. & Landrø, M. (2010) Time‐lapse tomographic inversion using a Gaussian parameterization of the velocity changes. Geophysics, 75, U29–U38. https://library.seg.org/doi/10.1190/1.3442573
     [Google Scholar]
  28. Ewy, R.T. (2021) Well shear associated with conventional and unconventional operations: diagnosis and mechanisms. SPE Drilling & Completion, 36, 427–444. https://doi.org/10.2118/205007‐PA
     [Google Scholar]
  29. Fedorov, F.I. (1968) Theory of elastic waves in crystals. New York: Springer. https://link.springer.com/book/10.1007/978‐1‐4757‐1275‐9
     [Google Scholar]
  30. Fjær, E. (2019) Relations between static and dynamic moduli of sedimentary rocks. Geophysical Prospecting, 67, 128–139. https://doi.org/10.1111/1365‐2478.12711
     [Google Scholar]
  31. Fjær, E., Holt, R.M., Horsrud, P. & Raaen, A.M. (2021) Petroleum related rock mechanics, 3rd edition.Amsterdam: Elsevier Science. https://www.elsevier.com/books/petroleum‐related‐rock‐mechanics/fjaer/978‐0‐12‐822195‐2
     [Google Scholar]
  32. Fuck, R.F., Bakulin, A. & Tsvankin, I. (2009) Theory of traveltime shifts around compacting reservoirs: 3D solutions for heterogeneous anisotropic media. Geophysics, 74, D25–D36. https://library.seg.org/doi/abs/10.1190/1.3033215
     [Google Scholar]
  33. Fuck, R.F. & Tsvankin, I. (2009) Analysis of the symmetry of a stressed medium using nonlinear elasticity. Geophysics, 74, WB79–WB87. https://library.seg.org/doi/10.1190/1.3157251
     [Google Scholar]
  34. Fumi, F.G. (1951) Third‐order elastic coefficients of crystals. Physical Review, 83, 1274–1275. https://doi.org/10.1103/PhysRev.83.1274
     [Google Scholar]
  35. Fumi, F.G. (1952) Third‐order elastic coefficients in trigonal and hexagonal crystals. Physical Review, 86, 561. https://doi.org/10.1103/PhysRev.86.561
     [Google Scholar]
  36. Geertsma, J. (1973) Land subsidence above compacting oil and gas reservoirs. Journal of Petroleum Technology, 25, 734–744. https://doi.org/10.2118/3730‐PA
     [Google Scholar]
  37. Guilbot, J. & Smith, B. (2002) 4‐D constrained depth conversion for reservoir compaction estimation: application to Ekofisk field. The Leading Edge, 21, 302–308. https://doi.org/10.1190/1.1463782
     [Google Scholar]
  38. Hall, S.A., MacBeth, C., Barkved, O.I. & Wild, P. (2002) Time‐lapse seismic monitoring of compaction and subsidence at Valhall through cross‐matching and interpreted warping of 3D streamer and OBC data [Expanded abstracts]. 72nd SEG Annual Meeting. Salt Lake City, UT, USA. SEG. pp. 1696–1699. https://doi.org/10.1190/1.1817004
  39. Hatchell, P. & Bourne, S. (2005) Rocks under strain: strain‐induced time‐lapse time shifts are observed for depleting reservoirs. The Leading Edge, 24, 1222–1225. https://library.seg.org/doi/abs/10.1190/1.2149624
     [Google Scholar]
  40. Hawkins, K. (2008) Defining the extent of the compacting Elgin reservoir by measuring stress‐induced anisotropy. First Break, 26, 81–88. https://doi.org/10.3997/1365‐2397.26.10.28559
     [Google Scholar]
  41. Hearmon, R.F.S. (1953) ‘Third‐order’ elastic coefficients. Acta Crystallographica, 6, 331–340. https://doi.org/10.1107/S0365110x53000909
     [Google Scholar]
  42. Helbig, K. & Thomsen, L. (2005) 75‐plus years of anisotropy in exploration and reservoir seismics: a historical review of concepts and methods. Geophysics, 70, 9ND–23ND. https://doi.org/10.1190/1.2122407
     [Google Scholar]
  43. Herwanger, J.V. & Horne, S.A. (2009) Linking reservoir geomechanics and time‐lapse seismics: predicting anisotropic velocity changes and seismic attributes. Geophysics, 74, W13–W33. https://library.seg.org/doi/abs/10.1190/1.3122407
     [Google Scholar]
  44. Herwanger, J. & Koutsabeloulis, N. (2011). Seismic geomechanics: how to build and calibrate geomechanical models using 3D and 4D seismic data. Utrecht, The Netherlands; EAGE Publications.
     [Google Scholar]
  45. Hodgson, N. (2009) Inversion for reservoir pressure change using overburden strain measurements determined from 4D seismic (PhD thesis). Scotland, UK: Heriot‐Watt University. https://www.ros.hw.ac.uk/handle/10399/2320
  46. Holt, R.M., Bauer, A. & Bakk, A. (2018) Stress‐path‐dependent velocities in shales: impact on 4D seismic interpretation. Geophysics, 83, MR353–MR367. https://doi.org/10.1190/geo2017‐0652.1
     [Google Scholar]
  47. Hornby, B.E. (1998) Experimental laboratory determination of the dynamic elastic properties of wet, drained shales. Journal of Geophysical Research: Solid Earth, 103, 29945–29964. https://doi.org/10.1029/97JB02380
     [Google Scholar]
  48. Hudson, J.A. (1981) Wave speeds and attenuation of elastic waves in material containing cracks. Geophysical Journal International, 64, 133–150. https://doi.org/10.1111/j.1365‐246X.1981.tb02662.x
     [Google Scholar]
  49. Hughes, D.S. & Kelly, J.L. (1953) Second‐order elastic deformation of solids. Physical Review, 92, 1145–1149. https://doi.org/10.1103/PhysRev.92.1145
     [Google Scholar]
  50. Islam, M.A. & Skalle, P. (2013) An experimental investigation of shale mechanical properties through drained and undrained test mechanisms. Rock Mechanics and Rock Engineering, 46, 1391–1413. https://doi.org/10.1007/s00603‐013‐0377‐8
     [Google Scholar]
  51. Jaeken, J.W. & Cottenier, S. (2016) Solving the Christoffel equation: phase and group velocities. Computer Physics Communications, 207, 445–451. https://doi.org/10.1016/j.cpc.2016.06.014
     [Google Scholar]
  52. Johnston, D.H. (1987) Physical properties of shale at temperature and pressure. Geophysics, 52, 1391–1401, https://doi.org/10.1190/1.1442251
     [Google Scholar]
  53. Jones, L.E.A. & Wang, H.F. (1981) Ultrasonic velocities in Cretaceous shales from the Williston basin, Geophysics, 46, 288–297. https://doi.org/10.1190/1.1441199
     [Google Scholar]
  54. Kenter, C.J., Van den Beukel, A.C., Hatchell, P.J., Maron, K.P., Molenaar, M.M. & Stammeijer, J.G.F. (2004) Geomechanics and 4D: evaluation of reservoir characteristics from timeshifts in the overburden. Gulf Rocks 2004; 6th North America Rock Mechanics Symposium (NARMS), Houston, TX, USA. ARMA‐04‐627. https://onepetro.org/ARMANARMS/proceedings‐abstract/ARMA04/All‐ARMA04/ARMA‐04‐627/117669
  55. Kristiansen, T.G., Barkved, O.I., Buer, K. & Bakke, R. (2005) Production‐induced deformations outside the reservoir and their impact on 4D seismic [Conference proceedings]. International Petroleum Technology Conference, Doha, Qatar. pp. 1–12. https://onepetro.org/IPTCONF/proceedings‐abstract/05IPTC/All‐05IPTC/IPTC‐10818‐MS/30437
  56. Kudarova, A., Hatchell, P., Brain, J. & MacBeth, C. (2016) Offset‐dependence of production‐related 4D time‐shifts: real data examples and modelling [Expanded abstracts]. 86th SEG Annual Meeting. Dallas, TX, USA. SEG. pp. 5395–5399. https://doi.org/10.1190/segam2016‐13611549.1
  57. Landrø, M. & Janssen, R. (2002) Estimating compaction and velocity changes from time‐lapse near and far offset stacks [Conference proceedings]. 64th EAGE Conference & Exhibition. Florence, Italy. EAGE. P036. https://doi.org/10.3997/2214‐4609‐pdb.5.P036
  58. Landrø, M. & Stammeijer, J. (2004) Quantitative estimation of compaction and velocity changes using 4D impedance and traveltime changes. Geophysics, 69, 949–957. https://library.seg.org/doi/10.1190/1.1778238
     [Google Scholar]
  59. Larsen, I., Stenebråten, J.F. & Bakk, A. (2011) Stress dependent dynamic anisotropy in shales [Conference abstracts]. 9th Euroconference on Rock Physics and Geomechanics, Trondheim, Norway. https://www.ntnu.edu/euroconference‐2011/program
  60. Lozovyi, S. (2018) Seismic dispersion and the relation between static and dynamic stiffness of shales (PhD Thesis). Norway: Norwegian University of Science and Technology. https://ntnuopen.ntnu.no/ntnu‐xmlui/handle/11250/2564704
  61. Lozovyi, S. & Bauer, A. (2019) Velocity dispersion in rocks: a laboratory technique for direct measurement of P‐wave modulus at seismic frequencies. Review of Scientific Instruments, 90, 024501. https://doi.org/10.1063/1.5026969
     [Google Scholar]
  62. Lubarda, V.A. (1997) New estimates of the third‐order elastic constants for isotropic aggregates of cubic crystals. Journal of the Mechanics and Physics of Solids, 45, 471–490. https://doi.org/10.1016/S0022‐5096(96)00113‐5
     [Google Scholar]
  63. MacBeth, C. & Bachkheti, S. (2021) A geomechanical correction for time‐lapse amplitude variation with offset. Geophysics, 86, M29–M40. https://library.seg.org/doi/10.1190/geo2020‐0398.1
     [Google Scholar]
  64. MacBeth, C., Kudarova, A. & Hatchell, P. (2018) Review paper: a semi‐empirical model of strain sensitivity for 4D seismic interpretation. Geophysical Prospecting, 66, 1327–1348. https://doi.org/10.1111/1365‐2478.12648
     [Google Scholar]
  65. Mah, M. & Schmitt, D.R. (2003) Determination of the complete elastic stiffnesses from ultrasonic phase velocity measurements. Journal of Geophysical Research: Solid Earth, 108, ECV 6‐1–ECV 6‐11. https://doi.org/10.1029/2001JB001586
     [Google Scholar]
  66. Mavko, G., Mukerji, T. & Godfrey, N. (1995) Predicting stress‐induced velocity anisotropy in rocks. Geophysics, 60, 1081–1087. https://library.seg.org/doi/10.1190/1.1443836
     [Google Scholar]
  67. Mulders, F.M.M. (2003) Modelling of stress development and fault slip in and around a producing gas reservoir (PhD Thesis). Delft, The Netherlands: Delft University of Technology. https://repository.tudelft.nl/islandora/object/uuid%3Abe742135‐10d7‐4d69‐bdee‐f808b5926065
  68. Nye, J.F. (1985) Physical properties of crystals: their representation by tensors and matrices. Oxford: Oxford University Press. https://global.oup.com/academic/product/physical‐properties‐of‐crystals‐9780198511656
     [Google Scholar]
  69. Pervukhina, M., Dewhurst, D., Gurevich, B., Kuila, U., Siggins, T., Raven, M. et al (2008) Stress‐dependent elastic properties of shales: measurement and modelling. The Leading Edge, 27, 772–779. https://library.seg.org/doi/10.1190/1.2944162
     [Google Scholar]
  70. Prioul, R., Bakulin, A. & Bakulin, V. (2004) Nonlinear rock physics model for estimation of 3D subsurface stress in anisotropic formations: theory and laboratory verification. Geophysics, 69, 415–425. https://library.seg.org/doi/10.1190/1.1707061
     [Google Scholar]
  71. Prioul, R. & Lebrat, T. (2004) Calibration of velocity‐stress relationships under hydrostatic stress for their use under non‐hydrostatic stress conditions [Expanded abstracts]. 74th SEG Annual Meeting. Denver, CO, USA. SEG. pp. 1698–1701. https://library.seg.org/doi/10.1190/1.1851153
  72. Rasolofosaon, P. (1998) Stress‐induced seismic anisotropy revisited. Oil & Gas Science and Technology – Revue d'IFP Energies Nouvelles, 53, 679–692. https://doi.org/10.2516/ogst:1998061
     [Google Scholar]
  73. Rickett, J., Duranti, L., Hudson, T., Regel, B. & Hodgson, N. (2007) 4D time strain and the seismic signature of geomechanical compaction at Genesis. The Leading Edge, 26, 644–647. https://doi.org/10.1190/1.2737103
     [Google Scholar]
  74. Røste, T. & Ke, G. (2017) Overburden 4D time shifts—indicating undrained areas and fault transmissibility in the reservoir. The Leading Edge, 36, 423–430. https://library.seg.org/doi/10.1190/tle36050423.1
     [Google Scholar]
  75. Røste, T., Landrø, M. & Hatchell, P. (2007) Monitoring overburden layer changes and fault movements from time‐lapse seismic data on the Valhall Field. Geophysical Journal International, 170, 1100–1118. https://doi.org/10.1111/j.1365‐246X.2007.03369.x
     [Google Scholar]
  76. Røste, T., Stovas, A. & Landrø, M. (2006) Estimation of layer thickness and velocity changes using 4D prestack seismic data. Geophysics, 71, S201–S234. https://library.seg.org/doi/abs/10.1190/1.2335657
     [Google Scholar]
  77. Sarkar, D., Bakulin, A. & Kranz, R.L. (2003) Anisotropic inversion of seismic data for stressed media: theory and a physical modelling study on Berea Sandstone. Geophysics, 68, 690–704. https://doi.org/10.1190/1.1567240
     [Google Scholar]
  78. Sarout, J. & Guéguen, Y. (2008) Anisotropy of elastic wave velocities in deformed shales: Part 1—Experimental results. Geophysics, 73, D75–D89. https://library.seg.org/doi/10.1190/1.2952744
     [Google Scholar]
  79. Sayers, C. M. & Kachanov, M. (1995) Microcrack‐induced elastic wave anisotropy of brittle rocks. Journal of Geophysical Research: Solid Earth, 100, 4149–4156. https://doi.org/10.1029/94JB03134
     [Google Scholar]
  80. Scott, T.E. (2007) The effects of stress paths on acoustic velocities and 4D seismic imaging. The Leading Edge, 26, 602–608. https://library.seg.org/doi/10.1190/1.2737101
     [Google Scholar]
  81. Shapiro, S.A. (2017) Stress impact on elastic anisotropy of triclinic porous and fractured rocks. Journal of Geophysical Research: Solid Earth, 122, 2034–2053. https://doi.org/10.1002/2016JB013378
     [Google Scholar]
  82. Shragge, J. & Lumley, D. (2013) Time‐lapse wave‐equation migration velocity analysis. Geophysics, 78, S69–S79. https://library.seg.org/doi/abs/10.1190/geo2012‐0182.1
     [Google Scholar]
  83. Sinha, B.K., (1982) Elastic waves in crystals under a bias. Ferroelectrics, 41, 61–73. https://doi.org/10.1080/00150198208210610
     [Google Scholar]
  84. Sinha, B.K. & Kostek, S. (1996) Stress‐induced azimuthal anisotropy in borehole flexural waves. Geophysics, 61, 1899–1907. https://library.seg.org/doi/10.1190/1.1444105
     [Google Scholar]
  85. Skempton, A.W. (1954). The Pore‐Pressure Coefficients A and B. Géotechnique, 4, 143–147. https://doi.org/10.1680/geot.1954.4.4.143
     [Google Scholar]
  86. Soldal, M., Skurtveit, E. & Choi, J.C. (2021) Laboratory evaluation of mechanical properties of Draupne shale relevant for CO2 seal integrity. Geosciences, 11, 244. https://doi.org/10.3390/geosciences11060244
     [Google Scholar]
  87. Sripanich, Y., Vasconcelos, I., Tromp, J. & Trampert, J. (2021) Stress‐dependent elasticity and wave propagation—new insights and connections. Geophysics, 86, W47–W64. https://library.seg.org/doi/10.1190/geo2020‐0252.1
     [Google Scholar]
  88. Szewczyk, D., Bauer, A. & Holt, R.M. (2018) Stress‐dependent elastic properties of shales—laboratory experiments at seismic and ultrasonic frequencies. Geophysical Journal International, 212, 189–210. https://doi.org/10.1093/gji/ggx392
     [Google Scholar]
  89. Thompson, N., Andrews, J.S. & Bjørnarå, T.I. (2021) Assessing potential thermo‐mechanical impacts on caprock due to CO2 injection—a case study from Northern Lights CCS. Energies,14, 5054. https://doi.org/10.3390/en14165054
     [Google Scholar]
  90. Thomsen, L. (1986) Weak elastic anisotropy. Geophysics, 51, 1954–1966. https://library.seg.org/doi/10.1190/1.1442051
     [Google Scholar]
  91. Thurston, R.N. (1974) Waves in solids. In: Truesdell, C. (Ed.) Mechanics of solids. In: Flügge, S. (Ed.) Encyclopedia of physics, vol. VI4a. Berlin: Springer‐Verlag, pp. 109–308. https://link.springer.com/book/9783540131632
     [Google Scholar]
  92. Thurston, R.N. & Brugger, K. (1964) Third‐order elastic constants and the velocity of small amplitude elastic waves in homogeneously stressed media. Physical Review, 133, A1604–A1610. https://doi.org/10.1103/PhysRev.133.A1604
     [Google Scholar]
  93. Tsvankin, I. (1997) Anisotropic parameters and P‐wave velocity for orthorhombic media. Geophysics, 62, 1292–1309. https://doi.org/10.1190/1.1444231
     [Google Scholar]
  94. Vernay, M., Morvan, M. & Breul, P. (2019) Evaluation of the degree of saturation using Skempton coefficient B. Geomechanics and Geoengineering, 15, 79–89. https://doi.org/10.1080/17486025.2019.1620349
     [Google Scholar]
  95. Wang, H. & Li, M. (2009) Ab initio calculations of second‐, third‐, and fourth‐order elastic constants for single crystals. Physical Review B, 79, 224102. https://doi.org/10.1103/PhysRevB.79.224102
     [Google Scholar]
  96. Wang, W. & Schmitt, D.R. (2021) Static measurements of the third‐order elastic constants of rocks [Conference proceedings]. 55th US Rock Mechanics/Geomechanics Symposium. ARMA‐2021‐1189. https://onepetro.org/ARMAUSRMS/proceedings‐abstract/ARMA21/All‐ARMA21/ARMA‐2021‐1189/467941
  97. Winkler, K.W. & Liu, X. (1996) Measurements of third‐order elastic constants in rocks. Journal of the Acoustical Society of America, 100, 1392–1397. https://doi.org/10.1121/1.415986
     [Google Scholar]
  98. Zoback, M.D. & Zinke, J.C. (2002) Production‐induced normal faulting in the Valhall and Ekofisk oil fields. Pure & Applied Geophysics, 159, 403–420. https://doi.org/10.1007/PL00001258
     [Google Scholar]
  99. Yan, H., Bakk, A., Duda, M., Holt, R.M. & Lozovyi, S. (2023) Overburden 4D seismic analysis: influence of stress and pore‐pressure changes accounting for elastic contrast between a reservoir and its anisotropic surrounding rocks. Geophysics, 88, 1–14. https://doi.org/10.1190/geo2022‐0033.1
     [Google Scholar]
  100. Yan, H., Bakk, A., Holt, R.M. & Lozovyi, S. (2020) Stress paths and predicted time‐shifts around a depleting reservoir [Expanded abstracts]. 90th SEG Annual Meeting, Houston, TX, USA. SEG. pp. 2464–2468. https://doi.org/10.1190/segam2020‐3420041.1
/content/journals/10.1111/1365-2478.13446
Loading
Third‐order elasticity of transversely isotropic field shales
Geophysical Prospecting 72, 1049 (2024); https://doi.org/10.1111/1365-2478.13446
/content/journals/10.1111/1365-2478.13446
/content/journals/10.1111/1365-2478.13446
Loading

Data & Media loading...

  • Article Type: Research Article
Keyword(s): acoustics; anisotropy; rock physics; seismics; time lapse

Most Cited This Month Most Cited RSS feed

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error