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Journal of the Australian Society of Exploration Geophysicists
RESEARCH ARTICLE

Estimation of reservoir properties from seismic data through a Markov Chain Monte Carlo-AVA inversion algorithm

Mattia Aleardi 1 3 Fabio Ciabarri 2 Alfredo Mazzotti 1
+ Author Affiliations
- Author Affiliations

1 Earth Sciences Department, University of Pisa, via S. Maria 53, 56126, Pisa, Italy.

2 Edison Research, Development and Innovation (RD&I), Foro Bonaparte 31, 20121, Milano, Italy.

3 Corresponding author. Email: mattia.aleardi@dst.unipi.it

Exploration Geophysics 49(5) 688-703 https://doi.org/10.1071/EG17077
Submitted: 2 June 2017  Accepted: 11 October 2017   Published: 1 December 2017

Abstract

We formulate the amplitude versus angle (AVA) inversion in terms of a Markov Chain Monte Carlo (MCMC) algorithm and apply it for reservoir characterisation and litho-fluid facies prediction in offshore Nile Delta. A linear empirical rock physics model is used to link the petrophysical properties (porosity, water saturation and shaliness) to the elastic attributes (P-wave velocity, S-wave velocity and density), whereas the exact Zoeppritz equations are used to convert the elastic properties into AVA responses. The exact Zoeppritz equations allow us to take advantage of the long offset seismic acquisition and thus to consider a wide range of incidence angles in the inversion. The proposed algorithm reliably estimates the non-uniqueness of the solution that is the uncertainties affecting the estimated subsurface characteristics (both in terms of litho-fluid facies and petrophysical properties), taking into consideration the uncertainties in the prior information, the uncertainties in the estimated rock-physics model and the errors affecting the observed AVA responses. A blind test, based on available well log information, demonstrates the applicability of the proposed method and the reliability of the results. In addition, comparisons between the results provided by the implemented MCMC algorithm with those yielded by a linear AVA inversion and an analytical approach to facies prediction, show the benefits introduced by wide-angle reflections in better constraining the inverted parameters and in attenuating the noise in the predicted subsurface models.

Key words: AVO/AVA, reservoir, seismic exploration.


References

Agostinetti, N. P., and Malinverno, A., 2010, Receiver function inversion by trans-dimensional Monte Carlo sampling: Geophysical Journal International, 181, 858–872

Aki, K., and Richards, P. G., 1980, Quantitative seismology: W. H. Freeman & Co.

Aleardi, M., 2016, A Markov Chain Monte Carlo algorithm for litho-fluid facies prediction and petrophysical property estimation: an application for reservoir characterization in offshore Nile Delta: 35th Convegno del Gruppo Nazionale per la Geofisica della Terra Solida, Expanded Abstracts, 490–494.

Aleardi, M., and Ciabarri, F., 2017a, Assessment of different approaches to rock-physics modeling: a case study from offshore Nile Delta: Geophysics, 82, MR15–MR25
Assessment of different approaches to rock-physics modeling: a case study from offshore Nile Delta:Crossref | GoogleScholarGoogle Scholar |

Aleardi, M., and Ciabarri, F., 2017b, Application of different classification methods for litho-fluid facies prediction: a case study from offshore Nile Delta: Journal of Geophysics and Engineering, 14, 1087–1102
Application of different classification methods for litho-fluid facies prediction: a case study from offshore Nile Delta:Crossref | GoogleScholarGoogle Scholar |

Aleardi, M., and Mazzotti, A., 2014, A feasibility study on the expected seismic AVA signatures of deep fractured geothermal reservoirs in an intrusive basement: Journal of Geophysics and Engineering, 11, 065008
A feasibility study on the expected seismic AVA signatures of deep fractured geothermal reservoirs in an intrusive basement:Crossref | GoogleScholarGoogle Scholar |

Aleardi, M., and Mazzotti, A., 2017, 1D elastic full-waveform inversion and uncertainty estimation by means of a hybrid genetic algorithm-Gibbs sampler approach: Geophysical Prospecting, 65, 64–85
1D elastic full-waveform inversion and uncertainty estimation by means of a hybrid genetic algorithm-Gibbs sampler approach:Crossref | GoogleScholarGoogle Scholar |

Aleardi, M., and Tognarelli, A., 2016, The limits of narrow and wide-angle AVA inversions for high Vp/Vs ratios: an application to elastic seabed characterization: Journal of Applied Geophysics, 131, 54–68
The limits of narrow and wide-angle AVA inversions for high Vp/Vs ratios: an application to elastic seabed characterization:Crossref | GoogleScholarGoogle Scholar |

Aleardi, M., Mazzotti, A., Tognarelli, A., Ciuffi, S., and Casini, M., 2015, Seismic and well log characterization of fractures for geothermal exploration in hard rocks: Geophysical Journal International, 203, 270–283
Seismic and well log characterization of fractures for geothermal exploration in hard rocks:Crossref | GoogleScholarGoogle Scholar |

Aleardi, M., Ciabarri, F., Peruzzo, F., Garcea, B., and Mazzotti, A., 2016, Bayesian estimation of reservoir properties by means of wide-angle AVA inversion and a petrophysical Zoeppritz equation: 78th Conference and Exhibition, EAGE, Expanded Abstracts, Th SRS3 02.

Aleardi, M., Ciabarri, F., and Garcea, B., 2017a, Application of a Markov Chain Monte Carlo-AVA inversion algorithm for reservoir characterization in offshore Nile Delta: 79th Conference and Exhibition, EAGE, Expanded Abstracts, Th B1 02.

Aleardi, M., Ciabarri, F., and Mazzotti, A., 2017b, Probabilistic estimation of reservoir properties by means of wide-angle AVA inversion and a petrophysical reformulation of the Zoeppritz equations: Journal of Applied Geophysics, 147, 28–41
Probabilistic estimation of reservoir properties by means of wide-angle AVA inversion and a petrophysical reformulation of the Zoeppritz equations:Crossref | GoogleScholarGoogle Scholar |

Aster, R. C., Borchers, B., and Thurber, C., 2005, Parameter estimation and inverse problems: Elsevier Academic Press.

Avseth, P., Mukerji, T., Jørstad, A., Mavko, G., and Veggeland, T., 2001, Seismic reservoir mapping from 3-D AVO in a North Sea turbidite system: Geophysics, 66, 1157–1176
Seismic reservoir mapping from 3-D AVO in a North Sea turbidite system:Crossref | GoogleScholarGoogle Scholar |

Avseth, P., Flesche, H., and Van Wijngaarden, A. J., 2003, AVO classification of lithology and pore fluids constrained by rock physics depth trends: The Leading Edge, 22, 1004–1011
AVO classification of lithology and pore fluids constrained by rock physics depth trends:Crossref | GoogleScholarGoogle Scholar |

Avseth, P., Mukerji, T., and Mavko, G., 2005, Quantitative seismic interpretation: applying rock physics tools to reduce interpretation risk: Cambridge University Press.

Bosch, M., 2004, The optimization approach to lithological tomography: combining seismic data and petrophysics for porosity prediction: Geophysics, 69, 1272–1282
The optimization approach to lithological tomography: combining seismic data and petrophysics for porosity prediction:Crossref | GoogleScholarGoogle Scholar |

Bosch, M., Mukerji, T., and Gonzalez, E. F., 2010, Seismic inversion for reservoir properties combining statistical rock physics and geostatistics: a review: Geophysics, 75, 75A165–75A176
Seismic inversion for reservoir properties combining statistical rock physics and geostatistics: a review:Crossref | GoogleScholarGoogle Scholar |

Castagna, J. P., and Swan, H. W., 1997, Principles of AVO crossplotting: The Leading Edge, 16, 337–344
Principles of AVO crossplotting:Crossref | GoogleScholarGoogle Scholar |

Chiappa, F., and Mazzotti, A., 2009, Estimation of petrophysical parameters by linearized inversion of angle domain pre‐stack data: Geophysical Prospecting, 57, 413–426
Estimation of petrophysical parameters by linearized inversion of angle domain pre‐stack data:Crossref | GoogleScholarGoogle Scholar |

Doyen, P., 2007, Seismic reservoir characterization: EAGE.

Draper, N. R., and Smith, H. 1985, Applied regression analysis: John Wiley & Sons.

Fernandez Martinez, J. L., Fernandez Muniz, M. Z., and Tompkins, M. J., 2012, On the topography of the cost functional in linear and nonlinear inverse problems: Geophysics, 77, W1–W15
On the topography of the cost functional in linear and nonlinear inverse problems:Crossref | GoogleScholarGoogle Scholar |

Grana, D., and Bronston, M., 2015, Probabilistic formulation of AVO modeling and AVO-attribute-based facies classification using well logs: Geophysics, 80, D343–D354
Probabilistic formulation of AVO modeling and AVO-attribute-based facies classification using well logs:Crossref | GoogleScholarGoogle Scholar |

Grana, D., Mukerji, T., Dvorkin, J., and Mavko, G., 2012, Stochastic inversion of facies from seismic data based on sequential simulations and probability perturbation method: Geophysics, 77, M53–M72
Stochastic inversion of facies from seismic data based on sequential simulations and probability perturbation method:Crossref | GoogleScholarGoogle Scholar |

Hastie, T., Tibshirani, R., and Friedman, J., 2002, The elements of statistical learning: Springer.

Hastings, W. K., 1970, Monte Carlo sampling methods using Markov chains and their applications: Biometrika, 57, 97–109
Monte Carlo sampling methods using Markov chains and their applications:Crossref | GoogleScholarGoogle Scholar |

Larsen, A. L., Ulvmoen, M., Omre, H., and Buland, A., 2006, Bayesian lithology/fluid prediction and simulation on the basis of a Markov-chain prior model: Geophysics, 71, R69–R78
Bayesian lithology/fluid prediction and simulation on the basis of a Markov-chain prior model:Crossref | GoogleScholarGoogle Scholar |

Li, D., and Zhang, F., 2015, Direct estimation of petrophysical properties based on AVO inversion: 85th Annual International Meeting, SEG, Expanded Abstracts, 2886–2890.

Mavko, G., and Mukerji, T., 1998, A rock physics strategy for quantifying uncertainty in common hydrocarbon indicators: Geophysics, 63, 1997–2008
A rock physics strategy for quantifying uncertainty in common hydrocarbon indicators:Crossref | GoogleScholarGoogle Scholar |

Mavko, G., Mukerji, T., and Dvorkin, J., 2009, The rock physics handbook: tools for seismic analysis of porous media: Cambridge University Press.

Mazzotti, A., 1990, Prestack amplitude analysis methodology and application to seismic bright spots in the Po Valley, Italy: Geophysics, 55, 157–166
Prestack amplitude analysis methodology and application to seismic bright spots in the Po Valley, Italy:Crossref | GoogleScholarGoogle Scholar |

Mazzotti, A., and Zamboni, E., 2003, Petrophysical inversion of AVA data: Geophysical Prospecting, 51, 517–530
Petrophysical inversion of AVA data:Crossref | GoogleScholarGoogle Scholar |

Mosegaard, K., 2006, Monte Carlo analysis of inverse problem: Ph.D. thesis, Copenhagen University.

Mosegaard, K., and Tarantola, A., 1995, Monte Carlo sampling of solutions to inverse problems: Journal of Geophysical Research: Solid Earth, 100, 12431–12447
Monte Carlo sampling of solutions to inverse problems:Crossref | GoogleScholarGoogle Scholar |

Ostrander, W., 1984, Plane-wave reflection coefficients for gas sands at non-normal angles of incidence: Geophysics, 49, 1637–1648
Plane-wave reflection coefficients for gas sands at non-normal angles of incidence:Crossref | GoogleScholarGoogle Scholar |

Riedel, M., and Theilen, F., 2001, AVO investigations of shallow marine sediments: Geophysical Prospecting, 49, 198–212
AVO investigations of shallow marine sediments:Crossref | GoogleScholarGoogle Scholar |

Riedel, M., Dosso, S. E., and Beran, L., 2003, Uncertainty estimation for amplitude variation with offset (AVO) inversion: Geophysics, 68, 1485–1496
Uncertainty estimation for amplitude variation with offset (AVO) inversion:Crossref | GoogleScholarGoogle Scholar |

Rutherford, S. R., and Williams, R. H., 1989, Amplitude-versus-offset variations in gas sands: Geophysics, 54, 680–688
Amplitude-versus-offset variations in gas sands:Crossref | GoogleScholarGoogle Scholar |

Sajeva, A., Aleardi, M., and Mazzotti, A., 2016, Combining genetic algorithms, Gibbs sampler, and gradient-based inversion to estimate uncertainty in 2D FWI: 78th Conference and Exhibition, EAGE, Expanded Abstracts, Th SRS2 10.

Sambridge, M., 1999, Geophysical inversion with a neighbourhood algorithm—II. Appraising the ensemble: Geophysical Journal International, 138, 727–746
Geophysical inversion with a neighbourhood algorithm—II. Appraising the ensemble:Crossref | GoogleScholarGoogle Scholar |

Sambridge, M., and Mosegaard, K., 2002, Monte Carlo methods in geophysical inverse problems: Reviews of Geophysics, 40, 3-1–3-29
Monte Carlo methods in geophysical inverse problems:Crossref | GoogleScholarGoogle Scholar |

Shuey, R. T., 1985, A simplification of the Zoeppritz equations: Geophysics, 50, 609–614
A simplification of the Zoeppritz equations:Crossref | GoogleScholarGoogle Scholar |

Tarantola, A., 2005, Inverse problem theory and methods for model parameter estimation: SIAM.

Zhu, X., and McMechan, G. A., 2012, Elastic inversion of near-and postcritical reflections using phase variation with angle: Geophysics, 77, R149–R159
Elastic inversion of near-and postcritical reflections using phase variation with angle:Crossref | GoogleScholarGoogle Scholar |

Zunino, A., Mosegaard, K., Lange, K., Melnikova, Y., and Mejer Hansen, T., 2015, Monte Carlo reservoir analysis combining seismic reflection data and informed priors: Geophysics, 80, R31–R41
Monte Carlo reservoir analysis combining seismic reflection data and informed priors:Crossref | GoogleScholarGoogle Scholar |