Skip to main content

Advertisement

Log in

Comparison of Recursive Neural Network and Markov Chain Models in Facies Inversion

  • Special Issue
  • Published:
Mathematical Geosciences Aims and scope Submit manuscript

Abstract

Predicting the spatial configuration of geological facies is a key step in the reservoir modeling process. The productivity of a reservoir depends not only on the facies proportions but also on the spatial patterns of the facies sequence. The recent developments in seismic to facies inversion techniques use \(1\mathrm{st}\)-order Markov models to improve the geological realism of the inferred facies profiles. However, the emergence of deep learning techniques such as recursive neural networks shows promising results in predictive modeling of event sequences as shown by the successful applications in complex modeling problems, such as natural language processing. In this work, a comparison between hidden Markov models and recursive neural networks is presented to highlight their advantages and disadvantages. The results are discussed according to the prior assumptions related to facies proportions and sequence patterns. Then, an innovative approach integrating recursive neural networks and the state-of-the-art seismic to facies inversion, known as the convolutional hidden Markov model, is proposed in order to predict geologically more realistic facies sequences based on seismic data. The proposed inversion technique is validated using synthetic seismic data in the context of a complex geological environment.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  • Bishop CM (2006) Pattern recognition and machine learning. Springer, Berlin

    Google Scholar 

  • Bortfeld R (1961) Approximations to the reflection and transmission coefficients of plane longitudinal and transverse waves. Geophys Prospect 9:485–502

    Article  Google Scholar 

  • Buland A, Omre H (2003) Bayesian linearized avo inversion. Geophysics 68(1):185–198

    Article  Google Scholar 

  • Caers J, Ma X (2002) Modeling conditional distributions of facies from seismic using neural nets. Math Geol 34(2):143–167

    Article  Google Scholar 

  • Chen C, Hiscott RN (1999) Statistical analysis of facies clustering in submarine-fan turbidite successions. J Sediment Res 69(2):505–517

    Article  Google Scholar 

  • Cong S, Liang Y (2009) Pid-like neural network nonlinear adaptive control for uncertain multivariable motion control systems. IEEE Trans Industr Electron 56(10):3872–3879

    Article  Google Scholar 

  • Connolly PA, Hughes MJ (2016) Stochastic inversion by matching to large numbers of pseudo-wells. Geophysics 81:M7–M22

    Article  Google Scholar 

  • Da Veiga S, Le Ravalec M (2012) Maximum likelihood classification for facies inference from reservoir attributes. Comput Geosci 16(3):709–722

    Article  Google Scholar 

  • Doyen P (2007) Seismic reservoir characterization: an earth modelling perspective, vol 2. EAGE Publications, Houten

    Google Scholar 

  • Dubois MK, Bohling GC, Chakrabarti S (2007) Comparison of four approaches to a rock facies classification problem. Comput Geosci 33(5):599–617

    Article  Google Scholar 

  • Dubrule O (2003) Geostatistics for seismic data integration in earth models. SEG Distinguished Instructor Short Course

  • Eidsvik J, Mukerji T, Switzer P (2004) Estimation of geological attributes from a well log, an application of hidden Markov chains. Math Geol 36(3):379–397

    Article  Google Scholar 

  • Elfeki A, Dekking M (2001) A markov chain model for subsurface characterization: theory and applications. Math Geol 33(5):569–589

    Article  Google Scholar 

  • Fan L, Poh KL (2007) A comparative study of pca, ica and class-conditional ica for naïve Bayes classifier. In: International work-conference on artificial neural networks, Springer, pp 16–22

  • de Figueiredo LP, Grana D, Roisenberg M, Rodrigues BB (2019a) Gaussian mixture markov chain monte carlo method for linear seismic inversion. Geophysics 84(3):R463–R476

    Article  Google Scholar 

  • de Figueiredo LP, Grana D, Roisenberg M, Rodrigues BB (2019b) Multimodal markov chain monte carlo method for nonlinear petrophysical seismic inversion. Geophysics 84(5):M1–M13

    Article  Google Scholar 

  • Fjeldstad T (2015) Bayesian inversion and inference of categorical markov models with likelihood functions including dependence and convolution. Master’s thesis, Norwegian University of Science and Technology

  • Fjeldstad T, Grana D (2017) Joint probabilistic petrophysics-seismic inversion based on gaussian mixture and markov chain prior models. Geophysics 83:1–46

    Google Scholar 

  • Goodfellow I, Bengio Y, Courville A, Bengio Y (2016) Deep learning, vol 1. MIT Press, Cambridge

    Google Scholar 

  • Graf W, Freitag S, Kaliske M, Sickert JU (2010) Recurrent neural networks for uncertain time-dependent structural behavior. Comput Aided Civil Infrast Eng 25(5):322–323

    Article  Google Scholar 

  • Grana D, Pirrone M, Mukerji T (2012) Quantitative log interpretation and uncertainty propagation of petrophysical properties and facies classification from rock-physics modeling and formation evaluation analysis. Geophysics 77(3):WA45–WA63

    Article  Google Scholar 

  • Grana D, Fjeldstad T, Omre H (2017) Bayesian gaussian mixture linear inversion for geophysical inverse problems. Math Geosci 49:493–515

    Article  Google Scholar 

  • Guo C, Pleiss A, Sun Y, Weinberger KQ (2017) On calibration of modern neural networks. In: 34th international conference on machine learning, pp 1321–1330

  • Hall B (2016) Facies classification using machine learning. Lead Edge 35(10):906–909

    Article  Google Scholar 

  • Hall M, Hall B (2017) Distributed collaborative prediction: results of the machine learning contest. Lead Edge 36(3):267–269

    Article  Google Scholar 

  • Hastie T, Tibshirani R, Friedman J (2009) The elements of statistical learning: data mining, inference, and prediction. Springer, Berlin

    Google Scholar 

  • Hochreiter S, Schmidhuber J (1997a) Long short-term memory. Neural Comput 9(8):1735–1780. https://doi.org/10.1162/neco.1997.9.8.1735

    Article  Google Scholar 

  • Hochreiter S, Schmidhuber J (1997b) Long short-term memory. Neural Comput 9(8):1735–1780

    Article  Google Scholar 

  • Krumbein WC, Dacey MF (1969) Markov chains and embedded Markov chains in geology. J Int Assoc Math Geol 1(1):79–96

    Article  Google Scholar 

  • Larsen AL, Ulvmoen M, Omre H, Buland A (2006) Bayesian lithology fluid prediction and simulation on the basis of a markov-chain prior model. Geophysics 71(5):R69–R78

    Article  Google Scholar 

  • Li Y, Anderson-Sprecher R (2006) Facies identification from well logs: A comparison of discriminant analysis and naïve Bayes classifier. J Petrol Sci Eng 53(3–4):149–157

    Article  Google Scholar 

  • Lin FJ, Wai RJ, Chou WD, Hsu SP (2002) Adaptive backstepping control using recurrent neural network for linear induction motor drive. IEEE Trans Industr Electron 49(1):134–146

    Article  Google Scholar 

  • Lindberg DV, Grana D (2015) Petro-elastic log-facies classification using the Expectation Maximization algorithm and hidden Markov models. Math Geosci 47(6):719–752

    Article  Google Scholar 

  • Maniar H, Ryali S, Kulkarni MS, Abubakar A (2018) Machine-learning methods in geoscience. In: SEG Technical Program Expanded Abstracts 2018, Society of Exploration Geophysicists, pp 4638–4642

  • Mozafari A, Gomes H, Leão W, Janny S, Gagné C (2019) Attended temperature scaling: a practical approach for calibrating deep neural networks. Mach Learn

  • Mukerji T, Jørstad A, Avseth P, Mavko G, Granli J (2001) Mapping lithofacies and pore-fluid probabilities in a north sea reservoir: seismic inversions and statistical rock physics. Geophysics 66(4):988–1001

    Article  Google Scholar 

  • Park BS, Yoo SJ, Park JB, Choi YH (2008) Adaptive neural sliding mode control of nonholonomic wheeled mobile robots with model uncertainty. IEEE Trans Control Syst Technol 17(1):207–214

    Article  Google Scholar 

  • Rimstad K, Omre H (2013) Approximate posterior distributions for convolutional two-level hidden markov models. Comput Stat Data Anal 53:187–200

    Article  Google Scholar 

  • Sak H, Senior A, Beaufays F (2014) Long short-term memory recurrent neural network architectures for large scale acoustic modeling. In: Fifteenth annual conference of the international speech communication association, pp 347–352

  • Scheidt C, Caers J (2009) Representing spatial uncertainty using distances and kernels. Math Geosci 41(4):397

    Article  Google Scholar 

  • Sherstinsky A (2020) Fundamentals of recurrent neural network (rnn) and long short-term memory (lstm) network. Physica D: Nonlinear Phenomena 404:132306. https://doi.org/10.1016/j.physd.2019.132306. http://www.sciencedirect.com/science/article/pii/S0167278919305974

  • Stolt R, Weglein A (1985) Migration and inversion of seismic data. Geophysics 50:2458–2472

    Article  Google Scholar 

  • Talarico E (2018) Seismic to facies inversion using convolved hidden markov model. Master’s thesis, Pontifical Catholic University of Rio de Janeiro

  • Tian M, Omre H, Xu H (2021) Inversion of well logs into lithology classes accounting for spatial dependencies by using hidden markov models and recurrent neural networks. Journal of Petroleum Science and Engineering 196:107598.https://doi.org/10.1016/j.petrol.2020.107598. http://www.sciencedirect.com/science/article/pii/S0920410520306665

  • Ulvmoen M, Omre H (2010) Improved resolution in bayesian lithology/fluid inversion from prestack seismic data and well observations: Part 1 - methodology. Geophysics 75(2):R21–R35

    Article  Google Scholar 

  • Ulvmoen M, Omre H, Buland A (2010) Improved resolution in bayesian lithology/fluid inversion from prestack seismic data and well observations: Part 2 - real case study. Geophysics 75(2):B73–B82

    Article  Google Scholar 

  • Wang G, Carr TR, Ju Y, Li C (2014) Identifying organic-rich Marcellus Shale lithofacies by support vector machine classifier in the Appalachian basin. Comput Geosci 64:52–60

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Erick Talarico.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Talarico, E., Leão, W. & Grana, D. Comparison of Recursive Neural Network and Markov Chain Models in Facies Inversion. Math Geosci 53, 395–413 (2021). https://doi.org/10.1007/s11004-020-09914-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11004-020-09914-w

Keywords

Navigation