Skip to main content

Forward and Inverse Stratigraphic Models

  • Living reference work entry
  • First Online:
Encyclopedia of Mathematical Geosciences

Part of the book series: Encyclopedia of Earth Sciences Series ((EESS))

  • 40 Accesses

Synonyms

Optimization; Simulation

Definition

A stratigraphic model is a conceptual, physical or mathematical representation of the succession of sedimentary layers beneath the surface of the Earth. Historically such models were static representations of the shape, location, and content of existing layers. Such models were initially built through observation of outcrops, drill holes, and excavations, and have been supplemented since the 1920s by remote petro- and geophysical measurements.

Stratigraphic models have formed the basis not only of academic studies, but a significant proportion of the global economy since pre-Roman times, with rock quarrying, gold, copper, and lead mining, and more recently hydrocarbon extraction and carbon sequestration.

“Forward” and “inverse” models can be both intuitive and formal, mathematical, ways of examining and testing the inductive and deductive reasoning behind stratigraphic model building.

The traditional “inductive” process of geological...

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

Access this chapter

Institutional subscriptions

Bibliography

  • Ager DV (1973) The nature of the Stratigraphical record. Wiley, p 114

    Google Scholar 

  • Alazzam A, Lewis HW (2013) A new optimization algorithm for combinatorial problems. Int J Adv Res Artif Intell 2(5):63–68

    Article  Google Scholar 

  • Alt H, Godau M (1995) Computing the Fréchet distance between two polygonal curves. Int J Comput Geom Appl 5(1–2):75–91

    Article  Google Scholar 

  • Angevine CL, Heller PL, Paola C (1990) Quantitative sedimentary basin modeling. Continuing Education Course Note Series 32 AAPG, Tulsa

    Google Scholar 

  • Baker MR (1988) Quantitative interpretation of geological and geophysical well data, Ph.D. Dissertation, The University of Texas at El Paso, El Paso, Texas, p 145

    Google Scholar 

  • Bates CC (1953) Rational theory of delta formation. AAPG 37:2119–2162

    Google Scholar 

  • Blum J, Dobranszky G, Eymard R, Masson R (2006) Identification of a stratigraphic model with seismic constraints. Inverse Prob 22(4):1207–1226

    Article  Google Scholar 

  • Bonham-Carter GF, Harbaugh JW (1968) Simulation of Geologic Systems, an overview. Computer contribution 22, Kansas Geological Survey

    Google Scholar 

  • Bonham-Carter GF, Sutherland AJ (1967) Diffusion and settling of sediments at river mouths: a computer simulation model. Gulf Coast Assoc Geol Soc Trans 17:326–338

    Google Scholar 

  • Bonham-Carter GF, Sutherland AJ (1968) Mathematical model and Fortran IV program for computer simulation of deltaic sedimentation, Computer Contribution 24, Kansas Geological Survey

    Google Scholar 

  • Bornholdt S, Westphal H (1998) Automation of stratigraphic simulations: quasi-backward modelling using genetic algorithms. In: Mascle A, Puigdefabregas C, Luterbacher HP, Fernandez M (eds) Cenozoic Foreland Basins of Western Europe, vol 134. Geological Society Special Publications, pp 371–379

    Google Scholar 

  • Bornholdt S, Nordlund U, Westphal H (1999) Inverse stratigraphic modelling using genetic algorithms. In: Harbaugh JW, Watney WL, Rankey EC, Slingerland RL, Goldstein RH, Franseen EK (eds) Numerical experiments in stratigraphy: recent advances in stratigraphic and sedimentologic computer simulations, vol 62. SEPM Society for Sedimentary Geology, pp 85–90. https://doi.org/10.2110/pec.99.62.0069

    Chapter  Google Scholar 

  • Boschetti F, Moresi L (2001) Interactive inversion in geosciences. Geophysics 66(4):1226–1234

    Article  Google Scholar 

  • Boschetti F, Wijns C, Moresi L (2002) Effective exploration and visualisation of geological parameter space. Geochem Geophys Geosyst 4:10

    Google Scholar 

  • Bovy B, Braun J, Cordonnier G, Lange R, Yuan X (2020) The FastScape software stack: reusable tools for landscape evolution modelling. In EGU General Assembly Conference Abstracts

    Google Scholar 

  • Burgess PM (2012) A brief review of developments in stratigraphic forward modelling, 2000–2009. In: Regional geology and tectonics: principles of geologic analysis. Elsevier, Amsterdam/Boston

    Google Scholar 

  • Burton R, Kendall CGStC, Lerche I (1987) Out of our depth: on the impossibility of fathoming eustasy from the stratigraphic record. Earth Sci Rev 4:237–277

    Article  Google Scholar 

  • Cancès C, Granjeon D, Peton N, Tran QH, Wolf S (2017) Numerical scheme for a stratigraphic model with erosion constraint and nonlinear gravity flux. FVCA 8 International Conference on Finite Volumes for Complex Applications VIII, Jun 2017, Lille, France. pp 327–335

    Google Scholar 

  • Carson R (1951) The sea around us. Oxford University Press, New York

    Book  Google Scholar 

  • Charvin K, Hampson GL, Gallagher K, Labourdette R (2009a) A Bayesian approach to inverse modelling of stratigraphy, part 1. Basin Res 21:5–25

    Article  Google Scholar 

  • Charvin K, Hampson GL, Gallagher K, Labourdette R (2009b) A Bayesian approach to inverse modelling of stratigraphy, part 2: validation and sensitivity tests. Basin Res 21:27–45

    Article  Google Scholar 

  • Craig RG (1979) A simulation model of landform erosion. Phd The Pennsylvania State University

    Google Scholar 

  • Cross TA (1988) Controls on coal distribution in transgressive-regressive cycles, Upper Cretaceous, Western Interior, U.S.A. In: Wilgus CK et al (eds) Sea-level changes – an integrated approach, vol 42. Society of Economic Paleontologists and Mineralogists Special Publication, pp 371–380

    Chapter  Google Scholar 

  • Cross TA, Lessenger MA (1997) Sediment volume partitioning: rationale for stratigraphic model evaluation and high-resolution stratigraphic correlation. In: Sandvik KO et al (eds) Predictive high-resolution stratigraphic sequence stratigraphy

    Google Scholar 

  • Cross TA, Lessenger MA (1999) Construction and application of a stratigraphic inverse model. In: Harbaugh JW, Watney WL, Rankey EC, Slingerland RL, Goldstein RH, Franseen EK (eds) Numerical experiments in stratigraphy: recent advances in stratigraphic and Sedimentologic computer simulations, vol 62. SEPM Society for Sedimentary Geology, pp 69–84

    Google Scholar 

  • Culling WEH (1960) Analytical theory of erosion. J Geol 68:3

    Article  Google Scholar 

  • Denison DGT, Holmes CC, Mallick BK, Smith AFM (2002) Bayesian methods for nonlinear classification and regression. Wiley, Chichester

    Google Scholar 

  • Duan T (2017) Similarity measure of sedimentary successions and its application in inverse stratigraphic modeling. Pet Sci 14:484–492

    Article  Google Scholar 

  • Duan T, Griffiths CM, Cross TA (1998) Adaptive stratigraphic forward modeling: making forward modeling adapt to conditional data. AAPG Annual convention and exhibition, Salt Lake City

    Google Scholar 

  • Duan T, Griffiths CM, Johnsen SO (1999) Conditional simulation of 2-D parasequences in shallow marine depositional systems by using attributed controlled grammar. Comput Geosci 25(6):667–681

    Article  Google Scholar 

  • Duan T, Cross TA, Lessenger MA (2001) Reservoir- and exploration-scale stratigraphic prediction using a 3-D inverse carbonate model. AAPG annual convention, Denver

    Google Scholar 

  • Flores JS (2011) Process-based modelling of the Brent delta: influence of paleobathymetry from the Oseberg Fm. pinch out on the wave dominated Brent delta progradation. North Sea Norwegian sector – Huldra field. Delft University of Technology, MSc thesis

    Google Scholar 

  • Gervais V, Ducros M, Granjeon D (2018) Probability maps of reservoir presence and sensitivity analysis in stratigraphic forward modeling. AAPG Bull 102(4):613–628

    Article  Google Scholar 

  • Gilks WR, Roberts GO, George EI (1992) Adaptive direction sampling. Journal of the Royal Statistical Society. Series D (the statistician) 43, 1, special issue: conference on practical Bayesian. Statistics 1992(3):179–189

    Google Scholar 

  • Gilks WR, Richardson S, Spiegelhalter DJ (1996) Markov chain Monte Carlo in practice. Chapman & Hall, London

    Google Scholar 

  • Granjeon D (1996) Modélisation stratigraphique déterministe: Conception et applications d’un modèle diffusif 3D multilithologique.. Stratigraphie. Université Rennes 1, PhD 1996. Français. Access through HAL 2011 Id: tel-00648827 https://tel.archives-ouvertes.fr/tel-00648827

  • Griffiths CM, Duan T (2000) Quantitative comparison of observed stratigraphy and that predicted from forward modelling. In: Proceedings of the 31st IGC, Rio de Janeiro, August 2000

    Google Scholar 

  • Griffiths CM, Duan T, Mitchell A (1996) How to know when you get it right: a solution to the section comparison problem in forward modelling. In: Proceedings numerical experiments in sedimentology conference, 15–17 May 1996. University of Kansas

    Google Scholar 

  • Harbaugh JW (1966) Mathematical simulation of marine sedimentation with IBM 7090/7094 computers. Computer Contribution 1, Kansas Geological Survey

    Google Scholar 

  • Harbaugh JW, Bonham-Carter GF (1970) Computer simulation in geology. Wiley Interscience, p 575

    Google Scholar 

  • Harlow FH (1964) The particle-in-cell computer method for fluid dynamics. In B Alder (ed). Comput Phys 3:319–343

    Google Scholar 

  • Hern C, Nordlund U, van der Zwan K, Ladipo K (2001) Forward prediction of Aeolian systems using fuzzy logic, constrained by data from recent and ancient analogues. Geologie en Mijnbouw/Netherlands J Geosci 80(1):53–70

    Article  Google Scholar 

  • King CAM (1968) SPITSIM. In: The use of computers in geomorphological research, British geomorphological research group symposium, Occ Paper 6. Geo Abstracts, Norwich, pp 63–72

    Google Scholar 

  • Krumbein WC (1947) Shore processes and beach characteristics. United States Beach Erosion Board, Technical memorandum #3

    Google Scholar 

  • Krumbein WC (1968) Fortran IV computer program for simulation of transgression and regression with continuous-time Markov models. Computer Contribution 26, Kansas Geological Survey

    Google Scholar 

  • Krumbein WC, Hall JV (1964) A geological process-response model for analysis of beach phenomena, Northwestern University Technology Report 8, ONR Contract 1228(26). Northwestern University, Evanston

    Google Scholar 

  • Lawrence DT, Doyle M, Snelson S, Horsfield WT (1987) Stratigraphic modeling of sedimentary basins. SEG Technical Program Expanded Abstracts: 407–408

    Google Scholar 

  • Lessenger MA (1989) A stratigraphic inverse simulation model. In: Proceedings from the American Geophysical Union Chapman conference on sea level estimation (abstr)

    Google Scholar 

  • Lessenger MA (1993) Forward and inverse simulation models of Stratal architecture and facies distributions in marine shelf to coastal plain environments, Ph.D. Dissertation, Colorado School of Mines, Golden, Colorado, p 182

    Google Scholar 

  • Lessenger MA, Cross TA (1991) A stratigraphic inverse simulation model. AAPG Bull 75(3):7–10

    Google Scholar 

  • Lessenger MA, Cross TA (1996) An inverse stratigraphic simulation model – is stratigraphic inversion possible? Energy Explor Exploit 14(6):627–637

    Google Scholar 

  • Lessenger MA, Lerche I (1999) Inverse modeling. In: Harbaugh JW, Watney WL, Rankey EC, Slingerland RL, Goldstein RH, Franseen EK (eds) Numerical experiments in stratigraphy: recent advances in stratigraphic and sedimentologic computer simulations, vol 62. SEPM Society for Sedimentary Geology, pp 29–31

    Google Scholar 

  • Lesser GR, Roelvink JA, van Kester JATM, Stelling GS (2004) Development and validation of a three-dimensional morphological model. Coast Eng 51:883–915

    Article  Google Scholar 

  • Levenshtein VI (1966) Binary codes capable of correcting deletions, insertions and reversals. Cybern Control Theory 10(8):707–710

    Google Scholar 

  • Martinez PA, Harbaugh JW (1993) Simulating nearshore environments, Computer methods in the geosciences 12. Pergamon Press, p 265

    Google Scholar 

  • Nordlund U (1996) Formalizing geological knowledge; with an example of modeling stratigraphy using fuzzy logic. J Sediment Res 66(4):689–698. https://doi.org/10.1306/D42683E2-2B26-11D7-8648000102C1865D

    Article  Google Scholar 

  • Nordlund U (1999a) FUZZIM: forward stratigraphic modeling made simple. Comput Geosci 25(4):449–456

    Article  Google Scholar 

  • Nordlund U (1999b) Stratigraphic modeling using common sense rules. In: Harbaugh JW, Watney WL, Rankey EC, Slingerland RL, Goldstein RH, Franseen EK (eds) Numerical experiments in stratigraphy: recent advances in stratigraphic and sedimentologic computer simulations, vol 62. SEPM Society for Sedimentary Geology, pp 85–90

    Google Scholar 

  • Nordlund U, Silfversparre M (1994) Fuzzy logic – a means for incorporating qualitative data in dynamic stratigraphic modeling. In: International association for mathematical geology, … conferences and proceedings, pp 265–266

    Google Scholar 

  • Oertel G, Walton EK (1967) Lessons for a feasibility study for computer models of coal-bearing deltas. Sedimentology 9:157–168

    Google Scholar 

  • Oldenburg DW (1974) The inversion and interpretation of gravity anomalies. Geophysics 39(4):389–581

    Article  Google Scholar 

  • Paola C (2000) Quantitative models of sedimentary basin filling. Sedimentology 47(1):121–178

    Article  Google Scholar 

  • Plotnick RE (1986) A fractal model for the distribution of stratigraphic hiatuses. J Geol 94(6):885–890

    Article  Google Scholar 

  • Revil A, Jardani A (2013) Forward and inverse modeling. In: The self-potential method: theory and applications in environmental geosciences. Cambridge University Press, Cambridge, pp 110–153

    Chapter  Google Scholar 

  • Ritchie BD, Hardy S, Gawthorpe RL (1999) Three-dimensional numerical modeling of coarse-grained clastic deposition in sedimentary basins. J Geophys Res 104:17759–17780

    Google Scholar 

  • Rivenaes JC (1992) Application of a dual-lithology, depth-dependent diffusion equation in stratigraphic simulation. Basin Res 4:133–146

    Article  Google Scholar 

  • Salles T, Duclaux G (2014) Combined hillslope diffusion and sediment transport simulation applied to landscape dynamics modelling. Earth Surf Process Landf 40:823–839

    Article  Google Scholar 

  • Salles T, Hardiman L (2016) Badlands: an open-source, flexible and parallel framework to study landscape dynamics. Comput Geosci 91:77–89

    Article  Google Scholar 

  • Salles T, Griffiths CM, Dyt C (2011) Aeolian sediment transport integration in general stratigraphic forward modeling. J Geol Res 2011:1–12

    Google Scholar 

  • Salles T, Ding X, Brocard G (2018a) pyBadlands: a framework to simulate sediment transport, landscape dynamics and basin stratigraphic evolution through space and time. PLoS One 13(4):e0195557

    Article  Google Scholar 

  • Salles T, Pall J, Webster JM, Dechnik B (2018b) Exploring coral reef responses to millennial-scale climatic forcings: insights from the 1-D numerical tool pyReef-Core v1.0. Geosci Model Dev 11:2093–2110

    Article  Google Scholar 

  • Sambridge M (1999) Geophysical inversion with a neighbourhood algorithm—I. Searching a parameter space. Geophys J Int 138(2):479–494

    Article  Google Scholar 

  • Schwarzacher W (1966) Sedimentation in subsiding basins. Nature 210:1349–1350

    Google Scholar 

  • Sloss LL (1962) Stratigraphic models in exploration. J Sediment Petrol 32(3):415–422

    Google Scholar 

  • Straub KM, Duller RA, Foreman BZ, Hajek EA (2020) Buffered, incomplete, and shredded: the challenges of reading an imperfect stratigraphic record. J Geophys Res Earth 125:1–44

    Google Scholar 

  • Tetzlaff DM (1987) A simulation model of clastic sedimentary processe.s [unpublished PhD dissertation] Dept. Applied Earth Sciences, Stanford University, Stanford, California. p 345

    Google Scholar 

  • Tetzlaff DM, Harbaugh JW (1989) Simulating clastic sedimentation, Computer methods in the geosciences 8. Van Nostrand, New York, p 202

    Book  Google Scholar 

  • Tucker GE, Hutton E, Piper MD, Campforts B, Gan T, Barnhart KR, Kettner A, Overeem I, Peckham SD, McCready L, Syvitski J (2021) Numerical modeling of Earths dynamic surface: a community approach. Community Surface Dynamics Modeling System (CSDMS) Technical Report & Preprint submitted to EarthArXiv

    Google Scholar 

  • Wan L, Bianchi V, Hurter S, Salles T (2020) Evolution of a delta-canyon-fan system on a typical passive margin using stratigraphic forward modelling. Mar Geol 429(106310):1–18

    Google Scholar 

  • White N, Bellingham P (2002) A two-dimensional inverse model for extensional sedimentary basins 1. Theory J Geophys Res 107(B10):2259

    Google Scholar 

  • Whitten EHT (1964) Process-response models in geology. GSA Bull 75(5):455–464

    Article  Google Scholar 

  • Wijns C, Poulet T, Boschetti F, Dyt C, Griffiths CM (2004) Interactive inverse methodology applied to stratigraphic forward modelling. Geological Society of London Special Publication, Geological Prior Information, pp 147–156

    Google Scholar 

  • Zhang J, Flaig P, Wartes M, Aschoff J, Shuster M. (2021) Integrating stratigraphic modelling, inversion analysis, and shelf-margin records to guide provenance analysis: An example from the Cretaceous Colville Basin, Arctic Alaska. Basin Research 24;33(3):1954–66

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Cedric M. Griffiths .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2022 Springer Nature Switzerland AG

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Griffiths, C.M. (2022). Forward and Inverse Stratigraphic Models. In: Daya Sagar, B.S., Cheng, Q., McKinley, J., Agterberg, F. (eds) Encyclopedia of Mathematical Geosciences. Encyclopedia of Earth Sciences Series. Springer, Cham. https://doi.org/10.1007/978-3-030-26050-7_117-1

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-26050-7_117-1

  • Received:

  • Accepted:

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-26050-7

  • Online ISBN: 978-3-030-26050-7

  • eBook Packages: Springer Reference Earth and Environm. ScienceReference Module Physical and Materials ScienceReference Module Earth and Environmental Sciences

Publish with us

Policies and ethics