1887
Volume 73, Issue 6
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

Deep‐strata high‐pressure reservoirs are a key research area in subsurface resource exploration. The complex mix of in situ pressure, anisotropy and fluid saturation in rocks leads to unclear seismic responses and uncertainties in wave propagation. Using acoustoelasticity theory and assuming weak anisotropy, we derived equations for the elastic parameters of stressed orthotropic media. These equations use anisotropic parameters to describe the unstressed elastic properties of orthotropic media. Then, using the Gassmann equation and low‐frequency poro‐elasticity, we found elastic parameters for single fluid‐saturated orthotropic media. Non‐welded interfaces serve as a reasonable approximation for tiny fractures and are ubiquitous in subsurface formations, and the viscous fluid present within these interfaces contributes to the observable attenuation of seismic waves. Using elastic parameters of stressed, fluid‐saturated orthotropic media, we formulated reflection and transmission coefficient equations for these interfaces based on linear‐slip theory. Using these equations, we analysed how stress, fluid saturation and interface changes affect seismic response and wave propagation. We then analysed how frequency, porosity, viscosity, fracture weakness and other physical properties affect seismic behaviour within and at the medium's interface. By constructing exact equations, we have achieved a more realistic simulation of subsurface seismic response. This enhancement in simulation accuracy facilitates a deeper understanding of the seismic response patterns observed in deep and complex subsurface reservoirs. Furthermore, it provides a solid theoretical foundation for fluid identification and reservoir prediction in actual subsurface reservoir scenarios.

Loading

Article metrics loading...

/content/journals/10.1111/1365-2478.70052
2025-07-15
2026-02-11
Loading full text...

Full text loading...

References

  1. Aki, K., and P. G.Richards. 2002. Quantitative Seismology. University Science Books.
    [Google Scholar]
  2. Belyaev, A. K., V. A.Polyanskiy, A. M.Lobachev, et al. 2016. “Propagation of Sound Waves in Stressed Elasto‐Plastic Material.” In 2016 Days on Diffraction (DD). IEEE.
  3. Brown, R. J. S., and J.Korringa. 1975. “On the Dependence of the Elastic Properties of a Porous Rock on the Compressibility of the Pore Fluid.” Geophysics40: 608–616.
    [Google Scholar]
  4. Carcione, J. M., and S.Picotti. 2012. “Reflection and Transmission Coefficients of a Fracture in Transversely Isotropic Media.” Studia Geophysica Et Geodaetica56: 307–322.
    [Google Scholar]
  5. Chaisri, S., and E.Krebes. 2000. “Exact and Approximate Formulas for P‐SV Reflection and Transmission Coefficients for a Nonwelded Contact Interface.” Journal of Geophysical Research: Solid Earth105, no. B12: 28045–28054.
    [Google Scholar]
  6. Chen, F. B., and Z. Y.Zong. 2022. “PP‐Wave Reflection Coefficient in Stress‐Induced Anisotropic Media and Amplitude Variation With Incident Angle and Azimuth Inversion.” Geophysics87, no. 6: C155–C172.
    [Google Scholar]
  7. Chen, F. B., Z. Y.Zong, and M.Jiang. 2021. “Seismic Reflectivity and Transmissivity Parametrization With the Effect of Normal In Situ Stress.” Geophysical Journal International226, no. 3: 1599–1614.
    [Google Scholar]
  8. Chen, F. B., Z. Y.Zong, R.Rezaee, et al. 2024. “Pressure Effects on Plane Wave Reflection and Transmission in Fluid‐Saturated Porous Media.” Surveys in Geophysics45: 1245–1290.
    [Google Scholar]
  9. Chen, F. B., Z. Y.Zong, A.Stovas, et al. 2023. “Wave Reflection and Transmission Coefficients for Layered Transversely Isotropic Media With Vertical Symmetry Axis Under Initial Stress.” Geophysical Journal International233, no. 3: 1580–1595.
    [Google Scholar]
  10. Chen, F. B., Z. Y.Zong, and X. Y.Yin. 2022. “Acoustothermoelasticity for Joint Effects of Stress and Thermal Fields on Wave Dispersion and Attenuation.” Journal of Geophysical Research: Solid Earth127, no. 4: e2021JB023671.
    [Google Scholar]
  11. Chen, F. B., Z. Y.Zong, X. Y.Yin, et al. 2022. “Accurate Formulae for P‐Wave Reflectivity and Transmissivity for a Non‐Welded Contact Interface With the Effect of In Situ Vertical Stress.” Geophysical Journal International229, no. 1: 311–327.
    [Google Scholar]
  12. Chen, F. B., Z. Y.Zong, and X. Y.Yin. 2024. “Seismic Scattering Inversion for Multiple Parameters of Overburden‐Stressed Isotropic Media.” Geophysics89, no. 6: T319–T336.
    [Google Scholar]
  13. Crecraft, D.1967. “The Measurement of Applied and Residual Stresses in Metals Using Ultrasonic Waves.” Journal of Sound and Vibration5, no. 1: 173–192.
    [Google Scholar]
  14. Cui, X., and L. R.Lines. 2011. “PP, PS Reflection And Transmission Coefficients For a Non‐Welded Interface Contact With Anisotropic Media.” In SEG Technical Program Expanded Abstracts. SEG.
  15. Fan, Z. H., Z. Y.Zong, and F. B.Chen. 2023. “Accurate P‐Wave Reflection and Transmission Coefficients for Non‐Welded Interface Incorporating Elasto‐Plastic Deformation.” Annals of Geophysics66: PE322.
    [Google Scholar]
  16. Fan, Z. H., Z. Y.Zong, F. B.Chen, and D.Qin. 2025. “Reflection Coefficients for Non‐Welded Interface Between Orthorhombic Half‐Spaces Under Initial Stress.” Geophysical Journal International240: 233–248.
    [Google Scholar]
  17. Fang, X. D., Y. C.Zheng, C.Michael, et al. 2017. “Fracture Clustering Effect on Amplitude Variation With Offset and Azimuth Analyses.” Geophysics82: N13–N25.
    [Google Scholar]
  18. Gassmann, F.1951. “Uber Die Elastizitat Poroser Medien.” Veirteljahrsschrift Der Naturforschenden Gesellschaft in Zzirich96: 1–23.
    [Google Scholar]
  19. Gurevich, B.2003. “Elastic Properties of Saturated Porous Rocks With Aligned Fractures.” Journal of Applied Geophysics54, no. 3–4: 203–218.
    [Google Scholar]
  20. Holbrook, R. D.1948. “A Pulse Method for Measuring Small Changes in Ultrasonic Velocity in Solids With Temperature.” Journal of the Acoustical Society of America20, no. 4_S: 590–590.
    [Google Scholar]
  21. Hudson, J., T.Pointer, and E.Liu. 2001. “Effective‐Medium Theories for Fluid‐Saturated Materials With Aligned Cracks.” Geophysical Prospecting49: 509–522.
    [Google Scholar]
  22. Hudson, J. A., E.Liu, and S.Crampin. 1996. “The Mechanical Properties of Materials With Interconnected Cracks and Pores.” Geophysical Journal International124, no. 1: 105–112.
    [Google Scholar]
  23. Iwashimizu, Y.1971. “Ultrasonic Wave Propagation in Deformed Isotropic Elastic Materials.” International Journal of Solids and Structures7, no. 4: 419–429.
    [Google Scholar]
  24. Johnson, G. C.1981. “Acoustoelastic Theory for Elastic–Plastic Materials.” Journal of the Acoustical Society of America70, no. 2: 591–595.
    [Google Scholar]
  25. Lan, T., Z.Zong, and W.Jia. 2024. “Fluid Identification by Nonlinear Frequency‐Dependent Amplitude Variation With Offset Inversion Based on Scattering Theory.” Geophysical Prospecting72, no. 2: 657–674.
    [Google Scholar]
  26. Li, L., G.Zhang, X.Pan, et al. 2022. “Anisotropic Poroelasticity and AVAZ Inversion for In Situ Stress Estimate in Fractured Shale‐Gas Reservoirs.” IEEE Transactions on Geoscience and Remote Sensing60: 1–13.
    [Google Scholar]
  27. Liu, J. X., Z. W.Cui, and K. X.Wang. 2007. “Reflection and Transmission of Acoustic Waves at the Interface Between Rocks in the Presence of Elastic–Plastic Deformations.” Journal of Geophysics and Engineering4, no. 2: 232–241.
    [Google Scholar]
  28. Minato, S., R.Ghose, and G.Osukuku. 2018. “Experimental Verification of Spatially Varying Fracture‐Compliance Estimates Obtained From Amplitude Variation With Offset Inversion Coupled With Linear Slip Theory.” Geophysics83, no. 1: WA1–WA8.
    [Google Scholar]
  29. Pan, X. P., L.Huang, and J.Liu. 2024. “P‐Wave Amplitude Versus Offset and Azimuth and Low‐Frequency Anisotropic Poro‐Acoustoelasticity.” In IEEE Transactions on Geoscience and Remote Sensing. IEEE.
  30. Pan, X. P., C.Lu, Z. Y.Zhao, et al. 2024. “Characteristics of Orthorhombic Anisotropic Seismic Response Induced by Horizontal In Situ Stress in Vertical Transversely Isotropic Media.” Science China Earth Sciences67: 2291–2310.
    [Google Scholar]
  31. Pan, X. P., G. Z.Zhang, and Y.Cui. 2020. “Matrix‐Fluid‐Fracture Decoupled‐Based Elastic Impedance Variation With Angle and Azimuth Inversion for Fluid Modulus and Fracture Weaknesses.” Journal of Petroleum Science and Engineering189: 106974.
    [Google Scholar]
  32. Pan, X. P., G. Z.Zhang, and X. Y.Yin. 2018. “Azimuthal Seismic Amplitude Variation With Offset and Azimuth Inversion in Weakly Anisotropic Media With Orthorhombic Symmetry.” Surveys in Geophysics39: 99–123.
    [Google Scholar]
  33. Pan, X. P., and Z. Y.Zhao. 2024. “A Decoupled Fracture‐and Stress‐Induced PP‐Wave Reflection Coefficient Approximation for Azimuthal Seismic Inversion in Stressed Horizontal Transversely Isotropic Media.” Surveys in Geophysics45, no. 1: 151–182.
    [Google Scholar]
  34. Pan, X. P., Z. Y.Zhao, and D. Z.Zhang. 2023. “Characteristics of Azimuthal Seismic Reflection Response in Horizontal Transversely Isotropic Media Under Horizontal In Situ Stress.” Surveys in Geophysics44, no. 2: 387–423.
    [Google Scholar]
  35. Pang, S., and A.Stovas. 2020. “Frequency‐Dependent PP and PS Reflection Coefficients in Fractured Media.” Geophysical Prospecting68, no. 3: 926–940.
    [Google Scholar]
  36. Pao, Y. H.1984. “Acoustoelasticity and Ultrasonic Measurements of Residual Stresses.” Physical AcousticsXVII: 61–143.
    [Google Scholar]
  37. Prioul, R., A.Bakulin, and V.Bakulin. 2004. “Nonlinear Rock Physics Model for Estimation of 3D Subsurface Stress in Anisotropic Formations: Theory and Laboratory Verification.” Geophysics69, no. 2: 415–425.
    [Google Scholar]
  38. Pyrak‐Nolte, L. J., L. R.Myer, and N. G. W.Cook. 1990. “Transmission of Seismic Waves Across Single Natural Fractures.” Journal of Geophysical Research: Solid Earth95, no. B6: 8617–8638.
    [Google Scholar]
  39. Sarkar, D., A.Bakulin, and R. L.Kranz. 2003. “Anisotropic Inversion of Seismic Data for Stressed Media: Theory and a Physical Modeling Study on Berea Sandstone.” Geophysics68, no. 2: 690–704.
    [Google Scholar]
  40. Schoenberg, M.1980. “Elastic Wave Behavior Across Linear Slip Interfaces.” Journal of the Acoustical Society of America68, no. 5: 1516–1521.
    [Google Scholar]
  41. Schoenberg, M., and J.Douma. 1988. “Elastic‐Wave Propagation in Media With Parallel Fractures and Aligned Cracks.” Geophysical Prospecting36, no. 6: 571–590.
    [Google Scholar]
  42. Schoenberg, M., and K.Helbig. 1997. “Orthorhombic Media: Modeling Elastic Wave Behavior in a Vertically Fractured Earth.” Geophysics62, no. 6: 1954–1974.
    [Google Scholar]
  43. Schoenberg, M., and C. M.Sayers. 1995. “Seismic Anisotropy of Fractured Rock.” Geophysics60, no. 1: 204–211.
    [Google Scholar]
  44. Sil, S., M. K.Sen, and B.Gurevich. 2011. “Analysis of Fluid Substitution in a Porous and Fractured Medium.” Geophysics76, no. 3: WA157–WA166.
    [Google Scholar]
  45. Sinha, B. K., and T. J.Plona. 2001. “Wave Propagation in Rocks With Elastic‐Plastic Deformations.” Geophysics66, no. 3: 772–785.
    [Google Scholar]
  46. Stovas, A.2024. “On the Singularity Point in Acoustic Orthorhombic Media.” Journal of Geophysics and Engineering21, no. 3: 993–1007.
    [Google Scholar]
  47. Stovas, A., Y.Roganov, and V.Roganov. 2024. “Degenerate Orthorhombic Models.” Geophysical Journal International236, no. 3: 1405–1423.
    [Google Scholar]
  48. Thomsen, L.1986. “Weak Elastic Anisotropy.” Geophysics51, no. 10: 1954–1966.
    [Google Scholar]
  49. Thomsen, L.1995. “Elastic Anisotropy Due to Aligned Cracks in Porous Rock.” Geophysical Prospecting43: 805–829.
    [Google Scholar]
  50. Thurston, R., and K.Brugger. 1964. “Third‐Order Elastic Constants and the Velocity of Small Amplitude Elastic Waves in Homogeneously Stressed Media.” Physical Review133, no. 6A: A1604.
    [Google Scholar]
  51. Tokuoka, S.1968. “Response of the Uterine Smooth Muscle Cell to Estrogen Stimulation: An Electron Microscopic and Autoradiographic Study.” Acta Pathologica Japonica18, no. 4: 417–430.
    [Google Scholar]
  52. Toupin, R., and B.Bernstein. 1961. “Sound Waves in Deformed Perfectly Elastic Materials. Acoustoelastic Effect.” Journal of the Acoustical Society of America33, no. 2: 216–225.
    [Google Scholar]
  53. Tsvankin, I.1997. “Anisotropic Parameters and P‐Wave Velocity for Orthorhombic Media.” Geophysics62, no. 4: 1292–1309.
    [Google Scholar]
  54. Van Der Neut, J., M. K.Sen, and K.Wapenaar. 2008. “Seismic Reflection Coefficients of Faults at Low Frequencies: A Model Study.” Geophysical Prospecting56, no. 3: 287–292.
    [Google Scholar]
  55. Vidal, C. A., R.Ghose, and J.van der Neut. 2010. “The Seismic Response of a Single Fracture–Synthetic Modelling and Laboratory Measurements.” In 72nd EAGE Conference and Exhibition Incorporating SPE EUROPEC 2010. European Association of Geoscientists & Engineers.
  56. Winkler, K. W.1997. “Acoustic Evidence of Mechanical Damage Surrounding Stressed Boreholes.” Geophysics62, no. 1: 16–22.
    [Google Scholar]
  57. Winkler, K. W., and L.Mcgowan. 2004. “Nonlinear Acoustoelastic Constants of Dry and Saturated Rocks.” Journal of Geophysical Research: Solid Earth109, no. B10.
    [Google Scholar]
  58. Xu, X., and I.Tsvankin. 2007. “A Case Study of Azimuthal AVO Analysis With Anisotropic Spreading Correction.” Leading Edge26, no. 12: 1552–1561.
    [Google Scholar]
  59. Zoeppritz, K.1919. “On the Reflection and Propagation of Seismic Waves.” Gottinger Nachrichten1, no. 5: 66–84.
    [Google Scholar]
/content/journals/10.1111/1365-2478.70052
Loading
/content/journals/10.1111/1365-2478.70052
Loading

Data & Media loading...

  • Article Type: Research Article
Keyword(s): anisotropy; mathematical formulation; modelling; velocity analysis; wave

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