Block sparse Bayesian learning based prestack seismic inversion with the correlation of velocities and density

• Autorzy: Ma Ming , Zhang Rui

Identyfikatory

DOI

10.1007/s11600-022-00914-4

• Języki publikacji: EN

Abstrakty

EN

Prestack seismic inversion has been widely used around the seismic exploration. It can precisely output the elastic properties of layers in subsurface, e.g., P-wave velocity (V_ρ), S-wave velocity (V R_s), and density (ρ). These are utilized further to extract many reservoir properties, like saturation and porosity, which are very helpful for the successful oil field development. The accuracy of prestack inversion result could play a critical role for the evaluation of reservoir characterization and the quantitative interpretation. It has been observed the existing relationships among velocities and density (V_ρ, V_s, and R_ρ) lead to the correlations of three reflectivities (Rp, Rs, and R _ρ). In this paper, we establish a new formulation for amplitude-versus-angle (AVA) inversion incorporating these correlations. A machine learning technique—block sparse Bayesian learning, has been implemented as the inversion engine to solve R_ρ, R_s, and R_ρ and to estimate the correlations described as the covariance matrix automatically. Due to the contribution of relationship between velocities and density, the performance of proposed AVA inversion is superior to the conventional technique in denoising and highlighting small-scale reflections. Three reflectivities are finally converted into velocities and density via an optimal multi-trace algorithm L-BFGS, which can mighty mitigate the lateral discontinuity of inverted results. The proposed approach has been tested on the synthetic examples. It shows a good consistence between inverted and true elastic properties. Field data test with the seismic profiles in Ordos basin area has demonstrated its high feasibility and efficiency for practical applications.

Słowa kluczowe

EN

bSBL; prestack inversion; correlation of elastic parameters

PL

bSBL

• Wydawca: Instytut Geofizyki PAN ; Springer
• Czasopismo: Acta Geophysica
• Rocznik: 2023
• Tom: Vol. 71, no. 1
• Strony: 261--274
• Opis fizyczny: Bibliogr. 44 poz.

Twórcy

autor

Ma Ming

• School of Geological Engineering and Geomatics, Chang’an University, Xi’an, China
• School of Geosciences, University of Louisiana at Lafayette, Lafayette, LA, USA

autor

Zhang Rui

• School of Geosciences, University of Louisiana at Lafayette, Lafayette, LA, USA

Bibliografia

• 1. Aki K, Richards PG (1980) Quantitative seismology. Theory and Method pp 304–308
• 2. Bortfeld R (1961) Approximations to the reflection and transmission coefficients of plane longitudinal and transverse waves. Geophys Prospect 9(4):485–502
• 3. Buland A, Omre H (2003) Bayesian linearized AVO inversion. Geophysics 68(1):185–198
• 4. Chen SS, Donoho DL, Saunders MA (2001) Atomic decomposition by basis pursuit. SIAM Rev 43(1):129–159
• 5. Chopra S, Castagna JP (2007) Introduction to this special section-AVO. Lead Edge 26(12):1506–1507
• 6. Du Q, Zhang B, Meng X et al (2016) Two-step joint pp-and ps-wave three-term amplitude-variation with offset inversion. Interpretation 4(4):T613–T625
• 7. Fatti JL, Smith GC, Vail PJ et al (1994) Detection of gas in sandstone reservoirs using AVO analysis: a 3-D seismic case history using the Geostack technique. Geophysics 59(9):1362–1376
• 8. Foucart S, Lai MJ (2009) Sparsest solutions of underdetermined linear systems via lq-minimization for 0 < q ≤ 1. Appl Comput Harmon Anal 26(3):395–407
• 9. Gholami A, Siahkoohi H (2010) Regularization of linear and non-linear geophysical ill-posed problems with joint sparsity constraints. Geophys J Int 180(2):871–882
• 10. Gorodnitsky IF, Rao BD (1997) Sparse signal reconstruction from limited data using FOCUSS: a re-weighted minimum norm algorithm. IEEE Trans Sig Process 45(3):600–616
• 11. Gouveia WP, Scales JA (1998) Bayesian seismic waveform inversion: parameter estimation and uncertainty analysis. J Geophys Res: Solid Earth 103(B2):2759–2779
• 12. Gray D, Goodway B, Chen T (1999) Bridging the gap: using AVO to detect changes in fundamental elastic constants. In: SEG technical program expanded abstracts 1999. Society of Exploration Geophysicists, pp 852–855
• 13. Horn RA, Horn RA, Johnson CR (1994) Topics in matrix analysis. Cambridge University Press
• 14. Ji S, Xue Y, Carin L (2008) Bayesian compressive sensing. IEEE Trans Sig Process 56(6):2346–2356
• 15. Levy S, Fullagar PK (1981) Reconstruction of a sparse spike train from a portion of its spectrum and application to high-resolution deconvolution. Geophysics 46(9):1235–1243
• 16. Li C, Zhang J, Zhu Z (2017) Bayesian AVO inversion with consistent angle parameters. J Appl Geophys 139:246–256
• 17. Lin J, Dyer C (2010) Data-intensive text processing with MapReduce. Synthesis lectures on human language technologies 3(1):1–177
• 18. Longbottom J, Walden A, White R (1988) Principles and application of maximum kurtosis phase estimation. Geophys Prospect 36(2):115–138
• 19. Lörtzer G, Berkhout A (1992) An integrated approach to lithologic inversion-part I: theory. Geophysics 57(2):233–244
• 20. Lyu Q, Lin Z, She Y et al (2013) A comparison of typical l_ρ minimization algorithms. Neurocomputing 119:413–424
• 21. Ma M, Wang S, Yuan S et al (2017) Multichannel spatially correlated reflectivity inversion using block sparse Bayesian learning. Geophysics 82(4):V191–V199
• 22. Mazumder R, Friedman JH, Hastie T (2011) Sparsenet: coordinate descent with nonconvex penalties. J Am Stat Assoc 106(495):1125–1138
• 23. Moré JJ, Thuente DJ (1994) Line search algorithms with guaranteed sufficient decrease. ACM Trans Math Softw (TOMS) 20(3):286–307
• 24. Pérez DO, Velis DR, Sacchi MD (2013) High-resolution prestack seismic inversion using a hybrid FISTA least-squares strategy. Geophysics 78(5):R185–R195
• 25. Richards PG (1976) On the adequacy of plane-wave reflection/transmission coefficients in the analysis of seismic body waves. Bull Seismol Soc Am 66(3):701–717
• 26. Rogers S, Girolami M (2016) A first course in machine learning. CRC Press
• 27. Sacchi MD (1997) Reweighting strategies in seismic deconvolution. Geophys J Int 129(3):651–656
• 28. Sen MK, Roy IG (2003) Computation of differential seismograms and iteration adaptive regularization in prestack waveform inversion. Geophysics 68(6):2026–2039
• 29. She B, Wang Y, Liang J et al (2018) A data-driven amplitude variation with offset inversion method via learned dictionaries and sparse representation. Geophysics 83(6):R725–R748
• 30. Shuey R (1985) A simplification of the Zoeppritz equations. Geophysics 50(4):609–614
• 31. Tarantola A (2005) Inverse problem theory and methods for model parameter estimation. SIAM
• 32. Tihonov AN (1963) Solution of incorrectly formulated problems and the regularization method. Soviet Math 4:1035–1038
• 33. Tipping ME (2001) Sparse Bayesian learning and the relevance vector machine. J Mach Learn Res 1:211–244
• 34. Ulrych TJ, Sacchi MD (2005) Information-based inversion and processing with applications. Elsevier
• 35. Varela OJ, Torres-Verdín C, Sen MK (2006) Enforcing smoothness and assessing uncertainty in non-linear one-dimensional prestack seismic inversion. Geophys Prospect 54(3):239–259
• 36. Wipf DP, Rao BD (2004) Sparse Bayesian learning for basis selection. IEEE Trans Sig Process 52(8):2153–2164
• 37. Wipf DP, Rao BD (2007) An empirical Bayesian strategy for solving the simultaneous sparse approximation problem. IEEE Trans Sig Process 55(7):3704–3716
• 38. Yin X, Zhang S (2014) Bayesian inversion for effective pore-fluid bulk modulus based on fluid-matrix decoupled amplitude variation with offset approximation. Geophysics 79(5):R221–R232
• 39. Zhang Z, Rao BD (2011) Sparse signal recovery with temporally correlated source vectors using sparse Bayesian learning. IEEE J Sel Top Sig Process 5(5):912–926
• 40. Zhang Z, Rao BD (2013) Extension of SBL algorithms for the recovery of block sparse signals with intra-block correlation. IEEE Trans Sig Process 61(8):2009–2015
• 41. Zhang R, Sen MK, Srinivasan S (2013) A prestack basis pursuit seismic inversion. Geophysics 78(1):R1–R11
• 42. Zhang B, Chang D, Lin T et al (2015) Improving the quality of prestack inversion by prestack data conditioning. Interpretation 3(1):T5–T12
• 43. Zoeppritz K (1919) On the reflection and propagation of seismic waves. Gott Nachr 1(5):66–84
• 44. Zong Z, Yin X, Wu G (2013) Multi-parameter nonlinear inversion with exact reflection coefficient equation. J Appl Geophys 98:21–32

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).