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Volume 21, Issue 1
  • E-ISSN: 1365-2117

Abstract

ABSTRACT

The inference of ancient environmental conditions from their preserved response in the sedimentary record still remains an outstanding issue in stratigraphy. Since the 1970s, conceptual stratigraphic models (e.g. sequence stratigraphy) based on the underlying assumption that accommodation space is the critical control on stratigraphic architecture have been widely used. Although these methods considered more recently other possible parameters such as sediment supply and transport efficiency, they still lack in taking into account the full range of possible parameters, processes, and their complex interactions that control stratigraphic architecture. In this contribution, we present a new quantitative method for the inference of key environmental parameters (specifically sediment supply and relative sea level) that control stratigraphy. The approach combines a fully non‐linear inversion scheme with a ‘process–response’ forward model of stratigraphy. We formulate the inverse problem using a Bayesian framework in order to sample the full range of possible solutions and explicitly build in prior geological knowledge. Our methodology combines Reversible Jump Markov chain Monte Carlo and Simulated Tempering algorithms which are able to deal with variable‐dimensional inverse problems and multi‐modal posterior probability distributions, respectively. The inverse scheme has been linked to a forward stratigraphic model, BARSIM (developed by Joep Storms, University of Delft), which simulates shallow‐marine wave/storm‐dominated systems over geological timescales. This link requires the construction of a likelihood function to quantify the agreement between simulated and observed data of different types (e.g. sediment age and thickness, grain size distributions). The technique has been tested and validated with synthetic data, in which all the parameters are specified to produce a ‘perfect’ simulation, although we add noise to these synthetic data for subsequent testing of the inverse modelling approach. These tests addressed convergence and computational‐overhead issues, and highlight the robustness of the inverse scheme, which is able to assess the full range of uncertainties on the inferred environmental parameters and facies distributions.

© 2009 The Authors. Journal Compilation © Blackwell Publishing Ltd, European Association of Geoscientists & Engineers and International Association of Sedimentologists
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References

  1. Al‐Awadhi, F., Horn, M. & Jennison, C. (2002) Improving the acceptance rate of reversible jump MCMC proposals. Stat. Prob. Lett., 69 (2), 189–198.
    [Google Scholar]
  2. Bernardo, J. & Smith, A.F.M. (1994) Bayesian Theory. John Wiley and Sons Ltd, Chichester.
    [Google Scholar]
  3. Beard, D.C. & Weyl, P.K. (1973) Influence of texture on porosity and permeability of unconsolidated sand. AAPG Bull., 572, 349–369.
    [Google Scholar]
  4. Bornholdt, S., Nordlund, U. & Westphal, H. (1999) Inverse stratigraphic modelling using genetic algorithms. In: Numerical Experiments in Stratigraphy: Recent Advances in Stratigraphic and Sedimentologic Computer Simulations, Vol. 62 (Ed. by J.Harbaugh , W.Watney , E.Rankey , R.Slingerland , R.Goldstein & E.Franseen ), pp. 85–90. SEPM (Society for Sedimentary Geology), SEPM Spec. Publ., 62.
    [Google Scholar]
  5. Bowman, S.A. & Vail, P.R. (1999) Interpreting the stratigraphy of the Baltimore canyon Section, offshore New Jersey with PHIL, a stratigraphic simulator. In: Numerical Experiments in Stratigraphy: Recent Advances in Stratigraphic and Sedimentologic Computer Simulations, Vol. 62 (Ed. by J.Harbaugh , W.Watney , E.Rankey , R.Slingerland , R.Goldstein & E.Franseen ), pp. 117–138. SEPM (Society for Sedimentary Geology), SEPM Spec. Publ., 62.
    [Google Scholar]
  6. Brooks, S.P., Fan, Y. & Rosenthal, J.S. (2006) Perfect forward simulation via simulated tempering. Commun. Statist.-Simulat. Comput., 35, 683–713.
    [Google Scholar]
  7. Brooks, S.P., Giudici, P. & Roberts, G.O. (2003) Efficient construction of reversible jump Markov chain Monte Carlo proposal distribution. J. R. Stat. Soc., Ser. B90 J. Stat. Methodol., 65, 3–39.
    [Google Scholar]
  8. Burgess, P.M. (2001) Modelling carbonate sequence development without relative sea‐level oscillations. Geology, 29, 1127–1130.
    [Google Scholar]
  9. Burgess, P.M., Lammers, H., Van Oosterhout, C. & Granjeon, D. (2006) Multivariate sequence stratigraphy: tackling complexity and uncertainty with stratigraphic forward modelling, multiple scenarios, and conditional frequency maps. AAPG Bull., 90 (12), 1883–1901.
    [Google Scholar]
  10. Carey, J.S., Swift, D.P., Steckler, M., Reed, C.W. & Niedoroda, A. (1999) High‐resolution sequence stratigraphic modeling 2: effects of sedimentation processes. In: Numerical Experiments in Stratigraphy: Recent Advances in Stratigraphic and Sedimentologic Computer Simulations, Vol. 62 (Ed. by J.Harbaugh , W.Watney , E.Rankey , R.Slingerland , R.Goldstein & E.Franseen ), pp. 151–164. SEPM (Society for Sedimentary Geology), SEPM Spec. Publ .
    [Google Scholar]
  11. Caroll, A.R., Chetel, L.M. & Elliot Smith, M. (2006) Feast to famine: sediment supply control on Laramide basin fill. Geology, 34, 197–200.
    [Google Scholar]
  12. Charvin, K., Hampson, G.L., Gallagher, K. & Labourdette, R. (2008) A Bayesian approach to inverse modelling of stratigraphy, part 2: validation and sensitivity tests. Basin Research, in press. doi: 10.1111/j.1365–2117.2008.00370.x
  13. Clevis, Q.J.W.A., Boer, P.L. & De Nijman, W. (2004) Differentiating the effect of episodic tectonism and eustatic sea‐level fluctuations in foreland basins filled by alluvial fans and axial deltaic systems: insights from a three-dimensional stratigraphic forward model. Sedimentology, 51 (4), 809–835.
    [Google Scholar]
  14. Cross, T. & Lessenger, M. (1999) Construction and application of stratigraphic inverse model. In: Numerical Experiments in Stratigraphy: Recent Advances in Stratigraphic and Sedimentologic Computer Simulations, Vol. 62 (Ed. by J.Harbaugh , W.Watney , E.Rankey , R.Slingerland , R.Goldstein & E.Franseen ), pp. 69–83. SEPM (Society for Sedimentary Geology), SEPM Spec. Publ .
    [Google Scholar]
  15. Den Bezemer, T., Kooi, H. & Cloetingh, S. (1999) Numerical modeling of fault‐related sedimentation. In: Numerical Experiments in Stratigraphy: Recent Advances in Stratigraphic and Sedimentologic Computer Simulations, Vol. 62 (Ed. by J.Harbaugh , W.Watney , E.Rankey , R.Slingerland , R.Goldstein & E.Franseen ), pp. 177–196. SEPM (Society for Sedimentary Geology), SEPM Spec. Publ .
    [Google Scholar]
  16. Denison, D.G.T., Holmes, C.C., Mallick, B.K. & Smith, A.F.M. (2002) Bayesian Methods for Nonlinear Classification and Regression. Wiley, Chichester.
    [Google Scholar]
  17. Deutsch, C.V. (2002) Geostatistical Reservoir Modeling (Applied Geostatistics). Oxford University Press, Oxford, 384p.
    [Google Scholar]
  18. De Wet, C.B. (1998) Deciphering the sedimentological expression of tectonics, eustasy and climate: a basin-wide study of the Corallian Formation, southern England. J. Sediment. Res., 68, 653–667.
    [Google Scholar]
  19. Eberli, G.P., Kendall, C.G.St.C, Moore, P., Whittle, G.L. & Cannon, R. (1994) Testing a seismic interpretation of great Bahama Bank with a computer simulation. AAPG Bull., 98 (6), 981–1004.
    [Google Scholar]
  20. Flemings, P.B. & Grotzinger, J.P. (1996) STRATA: freeware for analyzing classic stratigraphy problems. GSA Today, 6 (12), 1–7.
    [Google Scholar]
  21. Galloway, W.E. (1989) Genetic stratigraphy sequences in basin analysis 1: architecture and genesis of flooding-surface bounded depositional units. AAPG Bull., 73, 125–142.
    [Google Scholar]
  22. Gawthorpe, R.L., Fraser, A.J. & Collier, R.E.L (1994) Sequence stratigraphy in active extensional basins: implication for the interpretation of ancient basin fills. Mar. Petrol. Geol., 11, 642–658.
    [Google Scholar]
  23. Geyer, C. (1991) Markov Chain Monte Carlo maximum Likelihood. Computing science and statistics. Proceedings of the 23rd Symposium on the Interface, 156–163
  24. Geyer, C.J. & Thompson, E.A. (1995) Annealing Markov chain Monte Carlo with applications to ancestral inference. J. Am. Statist. Assoc., 90, 909–920.
    [Google Scholar]
  25. Gilks, W.R., Richardson, S. & Spiegelhalter, D.J. (1996) Markov Chain Monte Carlo in Practice. Chapman & Hall, London.
    [Google Scholar]
  26. Granjeon, D. & Joseph, P. (1999) Concepts and applications of a 3‐D multiple lithology, diffusive model in stratigraphic modeling. In: Numerical Experiments in Stratigraphy: Recent Advances in Stratigraphic and Sedimentologic Computer Simulations, Vol. 62 (Ed. by J.Harbaugh , W.Watney , E.Rankey , R.Slingerland , R.Goldstein & E.Franseen ), pp. 197–210. SEPM (Society for Sedimentary Geology), SEPM Spec. Publ .
    [Google Scholar]
  27. Green, P.J. (1995) Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika, 82 (4), 711–732.
    [Google Scholar]
  28. Green, P.J. (2001) A primer on Markov chain Monte Carlo. In: Complex Stochastic Systems (Ed. by O.L.Barndorff‐Nielsen , D.R.Cox & C.Kluppelberg ) Chapman & Hall, London.
    [Google Scholar]
  29. Green, P.J. (2003) Trans‐dimensional MCMC. In: Highly Structured Stochastic Systems (Ed. by P.J.Green , N.Hjort & S.Richardson ), pp. 179–196. Oxford Statistical Sciences Series, Chapter 6. Oxford University Press, Oxford.
    [Google Scholar]
  30. Griffiths, C.M., Dyt, C., Paraschivoiu, E. & Liu, K. (2001) Sedsim in hydrocarbon exploration. In: Geologic Modeling and Simulation (Ed. by D.Merriam & J.C.Davis ), pp. 71–97. Kluwer Academic, New York.
    [Google Scholar]
  31. Guillen, J. & Hoekstra, P. (1996) The “equilibrium” distribution of grain size fractions and its implications for cross‐shore sediment transport: a conceptual model. Mar. Geol., 135, 15–33.
    [Google Scholar]
  32. Hampson, G.J. & Howell, J.A. (2005) Sedimentologic and geomorphic characterization of ancient wave‐dominated shorelines: examples from the Late Cretaceous Blackhawk Formation, Book Cliffs, Utah. In: Deltas Old and New, Vol. 83 (Ed. by J.P.Bhattacharya & L.Giosan ), pp. 133–154SEPM, Spec. Publ .
    [Google Scholar]
  33. Hampson, G.J. & Storms, J.E.A. (2003) Geometric and sequence stratigraphic variability in wave‐dominated, shoreface‐shelf parasequences. Sedimentology, 50, 667–701.
    [Google Scholar]
  34. Hastings, W.K. (1970) Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57, 97–109.
    [Google Scholar]
  35. Houston, W.S., Hunton, J.E. & Kamola, D.L. (2000) Modelling of Cretaceous foreland‐basin parasequences, Utah, with implications for timing Servier thrusting. Geology, 28, 267–270.
    [Google Scholar]
  36. Jackson, M.D., Yoshida, S. & Muggeridge, A.H. (2005) Three‐dimensional reservoir characterization and flow simulation of heterolithic tidal sandstones. AAPG Bull., 89, 507–528.
    [Google Scholar]
  37. Kerler, W. & Rehberg, P. (1994) Simulated‐tempering procedure for spin‐glass simulations. Phys. Rev., E50, 4220–4225.
    [Google Scholar]
  38. Leeder, M., Harris, T. & Kirkby, M. (1998) Sediment supply and climate change: implications for basin stratigraphy. Basin Res., 10, 7–18.
    [Google Scholar]
  39. Lerche, I. (1996) An inverse method for determining parameters for folded structures. Quart. Appl. Math., 54, 625–636.
    [Google Scholar]
  40. Lessenger, M. & Cross, T.A. (1996) Is stratigraphic inversion possible?Energy Explorat. Exploit., 14 (6), 627–637.
    [Google Scholar]
  41. Lessenger, M. & Lerche, I. (1999) White paper in inverse modeling. In: Numerical Experiments in Stratigraphy: Recent Advances in Stratigraphic and Sedimentologic Computer Simulations, Vol. 62 (Ed. by J.W.Harbaugh , W.L.Watney , E.C.Rankey , R.Slingerland , R.H.Goldstein & E.K.Franseen ), pp. 29–31. SEPM (Society for Sedimentary Geology)SEPM Spec. Publ .
    [Google Scholar]
  42. Liu, J.S. & Sabatti, C. (1999) Simulated sintering: Markov chain Monte Carlo with spaces of varying dimension. In: Bayesian Statistics, Vol. 6 (Ed. by J.M.Bernardo , A.F.M.Smith , A.P.Dawid & J.O.Berger ), pp. 389–414. Oxford University Press, New York.
    [Google Scholar]
  43. Malinverno, A. (2002) Parsimonious Bayesian Markov chain Monte Carlo inversion in a non linear geophysical problem. Geophys. J. Int., 151, 675–688.
    [Google Scholar]
  44. Marinari, E. & Parisi, G. (1992) Simulated tempering: a new Monte Carlo scheme. Europhys. Lett., 19, 451–458.
    [Google Scholar]
  45. Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H. & Teller, E. (1953) Equations of state calculations by fast computing machines. J. Chem. Phys., 21, 1087–1091.
    [Google Scholar]
  46. Miall, A.D. (1986) Eustatic sea level changes interpreted from Seismic Stratigraphy: a critique of the methodology with particular reference to the North Sea Jurassic record. AAPG Bull., 70, 131–137.
    [Google Scholar]
  47. Miall, A.D. (1991) Stratigraphic sequences and their Chronostratigraphic correlation. J. Sediment. Petrol., 61, 497–505.
    [Google Scholar]
  48. Miall, A.D. (1992) Exxon global cycle chart: an event for every occasion? Geology, 20, 787–790.
    [Google Scholar]
  49. Miall, A.D. & Miall, C. (2001) Sequence Stratigraphy as a scientific enterprise: the evolution and persistence of conflicting paradigms. Earth Sci. Rev., 54, 321–348.
    [Google Scholar]
  50. Mosegaard, K. & Sambridge, M. (2002) Monte Carlo analysis of inverse problems. Inverse Problems, 18, R29–R54.
    [Google Scholar]
  51. Mosegaard, K. & Tarantola, A. (1995) Monte Carlo sampling of solutions to inverse problems. J. Geophys. Res., 100 (B7), 12431–12447.
    [Google Scholar]
  52. Niedoroda, A. & Kravitz, J.H. (1996) STRATAFORM: a program to study the creation and interpretation of sedimentary strata on continental margin. Oceanorgraphy, 9 (3), 146–152.
    [Google Scholar]
  53. Niedoroda, A.M., Reed, C.W., Swift, D.J.P., Arata, H. & Hoyanagi, K. (1995) Modeling shore‐normal large‐scale coastal evolution. Mar. Geol., 126, 181–199.
    [Google Scholar]
  54. Nordlund, U. (1999) FUZZIM: forward stratigraphic modeling made simple. Comput. Geosci., 25 (4), 449–456 (8).
    [Google Scholar]
  55. Paola, C. (2000) Quantitative models of sedimentary basin filling. Sedimentology, 47 (Suppl. 1), 121–178.
    [Google Scholar]
  56. Posamentier, H.W. & Allen, G.P. (1993) Variability of the sequence stratigraphy model: effects of local basins factors. Sediment. Geol., 86, 91–109.
    [Google Scholar]
  57. Rasmussen, E.S. & Dybkjaer, K. (2005) Sequence stratigraphy of the Upper Oligocene‐Lower Miocene of eastern Jylland, Denmark: role of structural relief and variable sediment supply in controlling sequence development. Sedimentology, 52, 25–63.
    [Google Scholar]
  58. Rivenaes, J.C. (1992) Application of a dual lithology, depth‐dependent diffusion equation in stratigraphic simulation. Basin Res., 4, 133–146. Blackwell Sciences Ltd.
    [Google Scholar]
  59. Rivenaes, J.C. (1997) Impact of sediment transport efficiency on large‐scale sequence architecture: results from stratigraphic computer simulation. Basin Res., 9/2, 91–105.
    [Google Scholar]
  60. Rotondi, R. (2002) On the influence of the proposal distribution on a reversible jump MCMC algorithm applied to the detection of multiple change‐points. Computat. Statist. Data Anal., 40, 633–653.
    [Google Scholar]
  61. Sambridge, M., Gallagher, K., Jackson, A. & Rickwood, P. (2006) Trans‐dimensional inverse problems, Model comparison and the Evidence. Geophys. J. Int., 167, 528–542.
    [Google Scholar]
  62. Schlager, W. (1993) Accommodation and supply – a dual control on stratigraphic sequences. Sediment. Geol., 86, 111–136.
    [Google Scholar]
  63. Sivia, D. & Skilling, J. (2006) Data analysis: A Bayesian tutorial. Oxford University Press, Oxford 246p.
    [Google Scholar]
  64. Steckler, M.S., Reynolds, D.J., Coakley, B.J., Swift, B.A. & Jarrad, R.D. (1993) Modeling passive margin sequence stratigraphy. In: Sequence Stratigraphy and Facies Associations (Ed. by H.W.Posamentier , C.P.Summerhayes , B.U.Haq & G.P.Allen ) International Association of Sedimentologists Special Publication, 18.
    [Google Scholar]
  65. Storms, J.E.A. (2003) Simulating event‐based shallow marine deposition over geological timescales. Mar. Geol., 199, 83–100.
    [Google Scholar]
  66. Storms, J.E.A. & Hampson, G.J. (2005) Mechanisms for forming discontinuity surfaces within Shoreface – shelf Parasequences: sea level, sediment supply, or Wave regime? J. Sediment. Res., 75, 67–81.
    [Google Scholar]
  67. Storms, J.E.A. & Swift, D.J.P. (2003) Shallow marine sequences as the building blocks of stratigraphy: insights from numerical modelling. Basin Res., 15, 287–303.
    [Google Scholar]
  68. Storms, J.E.A., Weltje, G.J., Van Dijke, J.J., Geel, C.R. & Kroonenberg, S.B. (2002) Process‐response modeling of wave‐dominated coastal systems: simulating evolution and stratigraphy on geological time scales. J. Sediment. Res., 72 (2), 226–239.
    [Google Scholar]
  69. Syvitski, J.P., Pratson, L. & O'Grady, D. (1999) Stratigraphic predictions of continental margins for the U.S. Navy. In: Numerical Experiments in Stratigraphy: Recent Advances in Stratigraphic and Sedimentologic Computer Simulations, Vol. 62 (Ed. by J.Harbaugh , W.Watney , E.Rankey , R.Slingerland , R.Goldstein & E.Franseen ), pp. 219–236. SEPM (Society for Sedimentary Geology), SEPM Spec. Publ .
    [Google Scholar]
  70. Syvitski, J.P.M. & Andrews, J.T. (1994) Climate change: numerical modelling of sedimentation and coastal processes, Eastern Canadian Arctic. Arctic Alpine Res., 26, 199–212.
    [Google Scholar]
  71. Tarantola, A. (2005) Inverse problem theory and methods for models parameter estimation. SIAM 342 p.
  72. Tetzlaff, D.M. & Harbaugh, J.W. (1989) Simulating Clastic Sedimentation. Van Nostrand Reinhold, New York.
    [Google Scholar]
  73. Thorne, J.A. (1992) An analysis of the implicit assumptions of the methodology of seismic sequence stratigraphy. In: Geology and Geophysics of Continental Margins, Vol. 53 (Ed. by J.S.Watkins ), pp. 375–394. AAPG Memoir.
    [Google Scholar]
  74. Thorne, J.A. & Swift, D.J.P. (1991) Sedimentation on continental margins: II. Application of the regime concept. In: Shelf sand and sandstone bodies: Geometry, Facies and Sequence Stratigraphy, Vol. 14 (Ed. by D.J.P.Swift , G.F.Oertel , R.W.Tillman & J.A.Thorne ), pp. 33–58. International Association of Sedimentologists Special Publication.
    [Google Scholar]
  75. Thomsen, R.O. & Lerche, I. (1997) Relative contributions to uncertainties in reserve estimates. Mar. Petrol. Geol., 14 (1), 65–74 (10).
    [Google Scholar]
  76. Ulicny, D., Nichols, G. & Waltham, D. (2002) Role of initial depth at basin margins in sequence architecture: field examples and computer models. Basin Res., 14, 347–360.
    [Google Scholar]
  77. Vail, P.R., Audmard, F., Bowman, S.A., Eisner, P.N. & Perez‐Cruz, G. (1991) The stratigraphic signature of tectonics, Eustarys and Sedimentology. In: An Overview: Cycles and Events in Stratigraphy (Ed. by G.Einsele , W.Rickeng & A.Sielacher ) Springer‐Verlag, Berlin, Heidelberg.
    [Google Scholar]
  78. Vail, P.R., Mitchum, R.M.Jr. & Thompson, S.III (1977) Seismic stratigraphy and global changes of sea level, Part 4: global cycles of relative changes of sea level. In: Seismic Stratigraphy‐Applications to Hydrocarbon Exploration, Vol. 26 (Ed. by C.E.Payton ), pp. 83–97. AAPG, Memoir.
    [Google Scholar]
  79. Watney, W.L., Rankey, E.C. & Harbaugh, J. (1999) Perspectives on stratigraphic simulation models: current approaches and future opportunities. In: Numerical Experiments in Stratigraphy: Recent Advances in Stratigraphic and Sedimentologic Computer Simulations, Vol. 62 (Ed. by J.W.Harbaugh , W.L.Watney , E.C.Rankey , R.Slingerland , R.H.Goldstein & E.K.Franseen ), pp. 3–21. SEPM (Society for Sedimentary Geology)SEPM Spec. Publ .
    [Google Scholar]
  80. Wijns, C., Poulet, T., Boschetti, F., Dyt, C. & Griffiths, C.M. (2004) Interactive inverse methodology applied to stratigraphic forward modelling. In: Geological Prior Information Informing Science and Engineering, Vol. 239 (Ed. by A.Curtis & R.Wood ), pp. 147–156. Geological Society, London Spec. Publ .
    [Google Scholar]
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A Bayesian approach to inverse modelling of stratigraphy, part 1: method
Basin Research 21, 5 (2009); https://doi.org/10.1111/j.1365-2117.2008.00369.x
/content/journals/10.1111/j.1365-2117.2008.00369.x
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