Mathematical Geology

, Volume 23, Issue 6, pp 817–832 | Cite as

Inversion of dynamical indicators in quantitative basin analysis models. I. Theoretical considerations

  • I. Lerche


Present-day observed downhole quantities, which a dynamical model of basin evolution should account for, include: total depth drilled, formation thicknesses, variations of porosity, permeability and total fluid pressure with depth, and depths of unconformities. Following a line of logic previously employed with multiple thermal indicators, it is shown how the observed quantities can be used in a nonlinear inverse sense to determine, or at least constrain, parameters and functions entering quantitative models of dyanmical sedimentary evolution. A procedure is given so that the inverse methods can be used: (a) with single well data; (b) with multiple well data; and (c) simultaneously with thermal indicator data, which have already been previously successfully inverted using a tomographic procedure. Parameters that can be evaluated using the dynamical indicator inversion (dynamical tomography) include, but are not limited to, values dealing with geological events (such as unconformity timing and amount of material eroded, the “openness” or “shutness” of faults; critical fracture pressure, etc.), as well as values dealing with intrinsic, or assumed, lithologic equations of state (such as power law values in connections between permeability and void ratio, or between frame pressure and void ratio). The dynamical tomography procedure can be used with or without weighting the data and/or the dynamical indicators; is guaranteed to produce a closer correspondence between predicted and observed behaviors at each nonlinear iteration; and is guaranteed to keep all parameters within any chosen domain. When used in a multiple well setting, the dynamical tomography method enables an assessment to be made of the assumed invariance to spatial location of parameters in equations of state, as well as allowing geologic process parameters to vary with well location. The procedure also automatically incorporates the ability to determine precision, resolution, sensitivity, and uniqueness of any or all parameters, both associated with equations of state and associated with geological processes. Thus, a sharper understanding is achieved of the trustworthiness and uncertainty of quantitative basin analysis models in respect of: (i) intrinsic assumptions of a model; (ii) implicit or explicit parameter dependences for both geological events and imposed functional dependences of variables; (iii) resolution with respect to finite sampling and measurement error or uncertainty in the quality and quantity of observed data.

Key words

basin analysis inverse methods dynamics 


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  1. Aki, K., and Lee, W. H. K., 1976, Determination of Three-Dimensional Anomalies under a Seismic Array Using FirstP Arrival Times from Local Earthquakes: A Homogeneous Initial Model: J. Geophys. Res., v. 81, p. 4381–4399.Google Scholar
  2. Armagnac, C., 1985, Thermal History of the National Petroleum Reserve, Alaska: M.S. thesis, University of South Carolina.Google Scholar
  3. Armagnac, C., Bucci, J., Kendall, C. G. St. C., and Lerche, I., 1989, Estimating the Thickness of Sediment Removed at an Unconformity Using Vitrinite Reflectance Data, in N. Naeser and T. H. McCulloh (Eds.), Thermal History of Sedimentary Basins: Springer-Verlag, Berlin, Ch. 13, p. 217–238.Google Scholar
  4. Bethke, C. M., 1985, A Numerical Model of Compaction-Driven Groundwater Flow and Heat Transfer and Its Application to the Paleohydrology of Intracratonic Sedimentary Basins: J. Geophys. Res., v. 90, p. 6817–6829.Google Scholar
  5. Cao, S., Glezen, W. H., and Lerche, I., 1986, Fluid, Flow, Hydrocarbon Generation and Migration: A Quantitative Model of Dynamical Evolution in Sedimentary Basins: Proc. Offshore Technol. Conf., v. 2, p. 267–276.Google Scholar
  6. Cao, S., and Lerche, I., 1989, One-Dimensional Modelilng of Episodic Fracturing: A Sensitivity Study: Terra Nova, v. 1, p. 177–181.Google Scholar
  7. Cao, S., and Lerche, I., 1990, Basin Modelling: Applications of Sensitivity Analysis: J. Pet. Sci. Eng., v. 4, p. 83–104.Google Scholar
  8. Dutta, N., 1987, Fluid Flow in Low Permeable Porous Media, in B. Doligetz (Ed.), Migration of Hydrocarbons in Sedimentary Basins: Editions Technip, Paris, p. 567–596.Google Scholar
  9. Freeze, R. A. 1975. A Stochastic Conceptual Analysis of One-Dimensional Groundwater in Non-uniform Homogeneous Media: Water Resour. Res., v. 11, p. 725–741.Google Scholar
  10. Glezen, W. H., and Lerche, I., 1985, A Model of Regional Fluid Flow: Sand Concentration Factors and Effective Lateral and Vertical Permeabilities: Math. Geol., v. 17, p. 297–315.Google Scholar
  11. Hawley, B. W., Zandt, G., and Smith, R. B., 1981, Simultaneous Inversion for Hypocenters and Lateral Velocity Variations: An Iterative Solution with a Layered Model: J. Geophys. Res., v. 86, p. 7073–7086.Google Scholar
  12. He, Z., and Lerche, I., 1989, Inversion of Multiple Thermal Indicators: Quantitative Methods of Determining Paleoheat Flux and Geological Parameters IV. Case Histories Using Thermal Indicator Tomography: Math. Geol., v. 21, p. 523–542.Google Scholar
  13. Kuckelkorn, K., Wang, X., and Lerche, I., 1990. Overthrusting History in the Austrian Alps: Case Study of Oberhofen 1: J. Geodynamics (June 1990).Google Scholar
  14. Lerche, I., 1988a, Inversion of Multiple Thermal Indicators: Qunatitative Methods of Determining Paleoheat Flux and Geological Parameters. I. The Theoretical Development for Paleoheat Flux: Math. Geol., v. 20, p. 1–36.Google Scholar
  15. Lerche, I., 1988b, Inversion of Multiple Thermal Indicators: Quantitative Methods of Determining Paleoheat Flux and Geological Parameters. II. The Theoretical Development for Chemical, Physical, and Geological Parameters: Math. Geol., v. 20, p. 73–96.Google Scholar
  16. Lerche, I., 1990a, Basin Analysis: Quantitative Methods, Vol. 1: Academic Press, Orlando, 562 p.Google Scholar
  17. Lerche, I., 1990b, Basin Analysis: Quantitative Methods, Vol. 2: Academic Press, San Diego, 614 p.Google Scholar
  18. Menke, W., 1984, Geophysical Data Analysis: Discrete Inverse Theory: Academic Press, Orlando.Google Scholar
  19. Palicianskas, V. V., and Domenico, P. A., 1980, Microfracture Development in Compacting Sediments: A Relation to Hydrocarbon Maturation Kinetics: Am. Assoc. Pet. Geol. Bull., v. 64, p. 927–937.Google Scholar
  20. Pantano, J., and Lerche, I., 1990, Inversion of Multiple Thermal Indicators: Quantitative Methods of Determining Paleoheat Flux and Geological Parameters. III. Stratigraphic Age Determination from Inversion of Vitrinite Reflectance Data and Sterane Isomerization Data: Math. Geol., v. 22, p. 281–307.Google Scholar
  21. Warren, J., and Price, H. S., 1961, Flow in Heterogenous Porous Media: Soc. Pet. Eng. J., v. 1, p. 153–169.Google Scholar
  22. Wei, Z. P., and Lerche, I., 1988, Quantitative Dynamical Geology of the Pinedale Anticline, Wyoming, U.S.A.: An Application of a Two-Dimensional Simulation Model: Appl. Geochem., v. 3, p. 423–440.Google Scholar
  23. Welte, D. H., and Yukler, M. A., 1981, Petroleum Origin and Accumulation in Basin Evolution—A Quantitative Model: Am. Assoc. Pet. Geol. Bull., v. 65, p. 1387–1396.Google Scholar
  24. Yukler, M. A., 1979, Sensitivity Analysis of Groundwater Flow System and an Application to a Real Case,In D. F. Merriam, (Ed.), Geomathematical and Petrophysical Studies in Sedimentology (Computer Geology): Pergamon Press, New York.Google Scholar

Copyright information

© International Association for Mathematical Geology 1991

Authors and Affiliations

  • I. Lerche
    • 1
  1. 1.Department of Geological SciencesUniversity of South CarolinaColumbia

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