Abstract

Azimuthal elastic inversion (AVO/AVA analysis) has a large potential for fracture characterization in the productive fractured strata of the shale gas and oil reservoirs. «Looseness» of the geological medium, caused by fracturing, including normal and tangential looseness, in accordance with «theory of surfaces with a linear slip» is a bridge between the seismic data and fracture characteristics. However, stability of the azimuthal elastic inversion methods for assessment of the anisotropy parameters and/or fracturing parameters using seismic data is debatable. This study explores an amplitude variation with incident angle and azimuth (AVAZ) inversion approach with model constraint for fracture weaknesses in Bayesian inversion scheme. Based on perturbation theory and stable phase approximation, the fracture medium can be considered as the superimposition of background medium and perturbation medium, and then the seismic scattering coefficient of fracture media can be derived. This equation establishes the relationship between seismic data and fracture weakness together with elastic parameters like P-wave and S-wave moduli and weaknesses. With this equation, an inversion approach in Bayesian scheme is proposed. This method implements the estimation of P-wave modulus, S-wave modulus, density, normal weakness and tangential weakness simultaneously. And the constraint from initial model enhances the stability of this method. In this approach, Gaussian and Cauchy distributions are explored for the likelihood and a priori probability distributions, respectively.

Keywords

AVAZ, AVAZ, Formation weaknesses, Seismic scattering coefficient, Stable phase approximation,

Reference

  •  1) Glubokovskih S.M., Kaplan S.A., Rok V.E., Titova Yu.A. Teoreticheskoe i eksperimentalnoe issledovaniya vliyaniya orientirovannoy vertikalnoy treschinovatosti na effektivnye seysmoakusticheskie svoystva gornyh porod // Tehnologii seysmorazvedki. 2011. №4. S. 62-69.

  •  2) Aki K. andP.G. Richards. 1980, Quantitative seismology, vol. 1: NY: WH Freeman and Company.

  •  3) Bakulin A., V. Grechka and I. Tsvankin. 2000, Estimation of fracture parameters from reflection seismic data. Part I: HTI model due to a single fracture set: Geophysics, 65, 1788-1802.

  •  4) Cerveny V. and J. Berryman. 2002, Seismic ray theory: Applied Mechanics Reviews, 55, B118.

  •  5) Chen H., R.L. Brown and J.P. Castagna, 2005. AVO for one- and two-fracture set models: Geophysics, 70, 1.

  •  6) Chen H., G. Zhang and X. Yin. 2012, AVAZ inversion for elastic parameter and fracture fluid factor, SEG Technical Program Expanded Abstracts 2012: Society of Exploration Geophysicists, 1-5.

  •  7) Corrigan D., R. Withers J. Darnall and T. Skopinski. 1996, Fracture mapping from azimuthal velocity analysis using 3-D surface seismic data: 66th Annual International Meeting: SEG, Expanded Abstracts.

  •  8) Downton J. and B. Roure. Year, Azimuthal simultaneous elastic inversion for fracture detection: SEG Annual Meeting.

  •  9) Downton J. and H. Russel. 2011, Azimuthal fourier coefficients: A simple method to estimate fracture parameters: SEG Technical Program Expanded Abstracts, 30, 269-273.

  •  10) Far M., L. Thomsen and C. Sayers. 2013, Seismic characterization of reservoirs with asymmetric fractures: Geophysics, 78, N1-N10.

  •  11) Fryer G.J. and L.N. Frazer. 1984, Seismic waves in stratified anisotropic media: Geophysical Journal of the Royal Astronomical Society, 78, 691-710.

  •  12) Gray D., G. Roberts andK. Head. 2002, Recent advances in determination of fracture strike and crack density from P-wave seismic data: The Leading Edge, 21, 280-285.

  •  13) Grechka V. and I. Tsvankin. 1998, 3-D description of normal moveout in anisotropic inhomogeneous media: Geophysics, 63, 1079-1092.

  •  14) Grechka V., I. Tsvankin and Lai Zhongkang. 1999, 3-D moveout inversion in azimuthally anisotropic media with lateral velocity variation; theory and a case study: Geophysics, 64, 1202-1218.

  •  15) Hall S.A., J.-M. Kendall and O.I. Barkved. 2002, Fractured reservoir characterization using P-wave AVOA analysis of 3D OBC data: The Leading Edge, 21, 777-781.

  •  16) Hudson J. 1980, Overall properties of a cracked solid, Cambridge Univ Press, 371-384.

  •  17) Hudson J. 1981, Wave speeds and attenuation of elastic waves in material containing cracks: Geophysical Journal of the Royal Astronomical Society, 64, 133-150.

  •  18) Jech J. and I. Psencik. 1989, First-order perturbation method for anisotropic media: Geophysical Journal International, 99, 369-376.

  •  19) Jenner E. 2001, Azimuthal anisotropy of 3-D com-pressional wave seismic data, Weyburn field, Saskatchewan, Canada, Colorado School of Mines.

  •  20) Lynn H., W. Beckham, K. Simon, C. Bates, M. Layman and M. Jones. 1999, P-wave and S-wave azimuthal anisotropy at a naturally fractured gas reservoir, Bluebell - Altamont Field, Utah: Geophysics, 64, 1312-1328.

  •  21) MacBeth C. 1999, Azimuthal variation in P-wave signatures due to fluid flow: Geophysics, 64, 1181-1192.

  •  22) Ruger A. 1997, P-wave reflection coefficients for transversely isotropic models with vertical and horizontal axis of symmetry: Geophysics, 62, 713-722.

  •  23) Ruger A. 1998, Variation of P-wave reflectivity with offset and azimuth in anisotropic media: Geophysics, 63, 935-947.

  •  24) Sayers C.M. and J.E. Rickett. 1997, Azimuthal variation in AVO response for fractured gas sands: Geophysical Prospecting, 45, 165-182.

  •  25) Schoenberg M. 1980, Elastic wave behavior across linear slip interfaces: The Journal of the Acoustical Society of America, 68, 1516.

  •  26) Shaw R.K. andM.K. Sen. 2004, Born integral, stationary phase and linearized reflection coefficients in weak anisotropic media: Geophysical Journal International, 158, 225-238.

  •  27) Shaw R.K. and M.K. Sen. 2006, Use of AVOA data to estimate fluid indicator in a vertically fractured medium: Geophysics, 71, C15.

  •  28) Sil S., M. Davidson, C. Zhou, R. Olson, H. Swan, J. Howell, S. Chiu and M. Willis. 2011, Effect of near-surface anisotropy on a deep anisotropic target layer: 81st Annual International Meeting, SEG, Expanded Abstracts, 305-308.

  •  29) Thomsen L. 1986, Weak elastic anisotropy: Geophysics, 51, 1954-1966.

  •  30) Thomsen L. 1995, Elastic anisotropy due to aligned cracks in porous rock: Geophysical Prospecting, 43, 805-829.

  •  31) Tsvankin I. 1997, Anisotropic parameters and P-wave velocity for orthorhombic media: Geophysics, 62, 1292-1309.

  •  32) Xu Y., X.-Y. Li and H. Dai. 2010, Azimuthal AVO and seismic scattering attenuation in 3D fractured media: a numerical simulation study on the Discrete Fracture Model: SEG Technical Program Expanded Abstracts, 29, 483-487.

  •  33) Zhu P., J. Wang, W. Yu and G. Zhu. 2004, Inverting reservoir crack density from P-wave AVOA data: Journal of Geophysics and Engineering, 1, 168.

  •  34) ZongZ., X. Yin andG. Wu. 2013, AVO inversion and stress evaluation in heterogeneous medium: SEG Houston,Annual Meeting, 428-432.

Avaz-инверсия по схеме Байеса с ограничением модели для изучения зон трещиноватости

Чжаоюнь Цзун Синяо Инь Гочэнь У Лаптев А.П.

Аннотация

Азимутальная упругая инверсия, или анализ AVO/AVA, имеет огромный потенциал для описания трещин в продуктивных толщах с трещинными коллекторами в резервуарах сланцевого газа и нефти. «Ослабленность» геологической среды, вызванная трещинами, включающая нормальную и тангенциальную ослабленности, в соответствии с «теорией поверхностей с линейным проскальзыванием» (ТПЛП) служит мостом между сейсмическими данными и параметрами трещиноватости [1]. Однако устойчивость методов азимутальной упругой инверсии для оценки анизотропных параметров или параметров трещиноватости с использованием полевых сейсмических данных остается спорной. В данной работе используется Байесовская схема инверсии с ограничениями модели для изучения изменений амплитуд с углом и азимутом падения (AVAZ) с получением параметров трещинной ослабленности. В соответствии с теорией приближений и аппроксимации устойчивой фазы среда с трещинами может рассматриваться как суперпозиция вмещающей среды и среды возмущения, и может быть получен коэффициент отражения сейсмической волны для среды с трещинами. Это уравнение устанавливает связь между сейсмическими данными и плотностью трещин, а также между упругими параметрами, такими как модули P- и S-волн (модули объемного сжатия и сдвига) и плотностью трещин. На основе этого уравнения предлагается метод инверсии по схеме Байеса. Этот метод включает одновременную оценку модулей P-, S-волн, плотности, вертикальной и касательной трещинной ослабленности. И ограничения исходной модели увеличивают устойчивость этого метода. В этом подходе распределения Гаусса и Коши исследуются на подобие и априорное распределение вероятности соответственно.

Финансирование

Авторы выражают благодарность за спонсорство Национальной 973 Программе Китая (2013CB228604), Научному фонду для ученых с докторской степенью Китая и Кингдао, Фонда естественных наук Китая, геофизической лаборатории Синопек (WTYJY-WX2013-04-01).

Ключевые слова

трещинные ослабленности, коэффициент отражения сейсмической волны, аппроксимация устойчивой фазы,

Информация об авторах

Библиографическая ссылка

Чжаоюнь Цзун Синяо Инь Гочэнь У Лаптев А.П. Avaz-инверсия по схеме Байеса с ограничением модели для изучения зон трещиноватости // Геофизика. 2014. № 5. С. 83-87.

Список литературы

  •  1) Глубоковских С.М., Каплан С.А., Рок В.Е., Титова Ю.А. Теоретическое и экспериментальное исследования влияния ориентированной вертикальной трещиноватости на эффективные сейсмоакустические свойства горных пород // Технологии сейсморазведки. 2011. №4. С. 62-69.

  •  2) Aki K. andP.G. Richards. 1980, Quantitative seismology, vol. 1: NY: WH Freeman and Company.

  •  3) Bakulin A., V. Grechka and I. Tsvankin. 2000, Estimation of fracture parameters from reflection seismic data. Part I: HTI model due to a single fracture set: Geophysics, 65, 1788-1802.

  •  4) Cerveny V. and J. Berryman. 2002, Seismic ray theory: Applied Mechanics Reviews, 55, B118.

  •  5) Chen H., R.L. Brown and J.P. Castagna, 2005. AVO for one- and two-fracture set models: Geophysics, 70, 1.

  •  6) Chen H., G. Zhang and X. Yin. 2012, AVAZ inversion for elastic parameter and fracture fluid factor, SEG Technical Program Expanded Abstracts 2012: Society of Exploration Geophysicists, 1-5.

  •  7) Corrigan D., R. Withers J. Darnall and T. Skopinski. 1996, Fracture mapping from azimuthal velocity analysis using 3-D surface seismic data: 66th Annual International Meeting: SEG, Expanded Abstracts.

  •  8) Downton J. and B. Roure. Year, Azimuthal simultaneous elastic inversion for fracture detection: SEG Annual Meeting.

  •  9) Downton J. and H. Russel. 2011, Azimuthal fourier coefficients: A simple method to estimate fracture parameters: SEG Technical Program Expanded Abstracts, 30, 269-273.

  •  10) Far M., L. Thomsen and C. Sayers. 2013, Seismic characterization of reservoirs with asymmetric fractures: Geophysics, 78, N1-N10.

  •  11) Fryer G.J. and L.N. Frazer. 1984, Seismic waves in stratified anisotropic media: Geophysical Journal of the Royal Astronomical Society, 78, 691-710.

  •  12) Gray D., G. Roberts andK. Head. 2002, Recent advances in determination of fracture strike and crack density from P-wave seismic data: The Leading Edge, 21, 280-285.

  •  13) Grechka V. and I. Tsvankin. 1998, 3-D description of normal moveout in anisotropic inhomogeneous media: Geophysics, 63, 1079-1092.

  •  14) Grechka V., I. Tsvankin and Lai Zhongkang. 1999, 3-D moveout inversion in azimuthally anisotropic media with lateral velocity variation; theory and a case study: Geophysics, 64, 1202-1218.

  •  15) Hall S.A., J.-M. Kendall and O.I. Barkved. 2002, Fractured reservoir characterization using P-wave AVOA analysis of 3D OBC data: The Leading Edge, 21, 777-781.

  •  16) Hudson J. 1980, Overall properties of a cracked solid, Cambridge Univ Press, 371-384.

  •  17) Hudson J. 1981, Wave speeds and attenuation of elastic waves in material containing cracks: Geophysical Journal of the Royal Astronomical Society, 64, 133-150.

  •  18) Jech J. and I. Psencik. 1989, First-order perturbation method for anisotropic media: Geophysical Journal International, 99, 369-376.

  •  19) Jenner E. 2001, Azimuthal anisotropy of 3-D com-pressional wave seismic data, Weyburn field, Saskatchewan, Canada, Colorado School of Mines.

  •  20) Lynn H., W. Beckham, K. Simon, C. Bates, M. Layman and M. Jones. 1999, P-wave and S-wave azimuthal anisotropy at a naturally fractured gas reservoir, Bluebell - Altamont Field, Utah: Geophysics, 64, 1312-1328.

  •  21) MacBeth C. 1999, Azimuthal variation in P-wave signatures due to fluid flow: Geophysics, 64, 1181-1192.

  •  22) Ruger A. 1997, P-wave reflection coefficients for transversely isotropic models with vertical and horizontal axis of symmetry: Geophysics, 62, 713-722.

  •  23) Ruger A. 1998, Variation of P-wave reflectivity with offset and azimuth in anisotropic media: Geophysics, 63, 935-947.

  •  24) Sayers C.M. and J.E. Rickett. 1997, Azimuthal variation in AVO response for fractured gas sands: Geophysical Prospecting, 45, 165-182.

  •  25) Schoenberg M. 1980, Elastic wave behavior across linear slip interfaces: The Journal of the Acoustical Society of America, 68, 1516.

  •  26) Shaw R.K. andM.K. Sen. 2004, Born integral, stationary phase and linearized reflection coefficients in weak anisotropic media: Geophysical Journal International, 158, 225-238.

  •  27) Shaw R.K. and M.K. Sen. 2006, Use of AVOA data to estimate fluid indicator in a vertically fractured medium: Geophysics, 71, C15.

  •  28) Sil S., M. Davidson, C. Zhou, R. Olson, H. Swan, J. Howell, S. Chiu and M. Willis. 2011, Effect of near-surface anisotropy on a deep anisotropic target layer: 81st Annual International Meeting, SEG, Expanded Abstracts, 305-308.

  •  29) Thomsen L. 1986, Weak elastic anisotropy: Geophysics, 51, 1954-1966.

  •  30) Thomsen L. 1995, Elastic anisotropy due to aligned cracks in porous rock: Geophysical Prospecting, 43, 805-829.

  •  31) Tsvankin I. 1997, Anisotropic parameters and P-wave velocity for orthorhombic media: Geophysics, 62, 1292-1309.

  •  32) Xu Y., X.-Y. Li and H. Dai. 2010, Azimuthal AVO and seismic scattering attenuation in 3D fractured media: a numerical simulation study on the Discrete Fracture Model: SEG Technical Program Expanded Abstracts, 29, 483-487.

  •  33) Zhu P., J. Wang, W. Yu and G. Zhu. 2004, Inverting reservoir crack density from P-wave AVOA data: Journal of Geophysics and Engineering, 1, 168.

  •  34) ZongZ., X. Yin andG. Wu. 2013, AVO inversion and stress evaluation in heterogeneous medium: SEG Houston,Annual Meeting, 428-432.