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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
Articles

Abstract

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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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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