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<p>This study introduces a transdimensional inversion framework to quantify stratigraphic uncertainties in layered reservoir models from well data. The goal is to adaptively determine the appropriate number of subsurface model parameters. The parameters to infer correspond to (1) the number of layers <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(n_L\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>n</mi> <mi>L</mi> </msub> </math></EquationSource> </InlineEquation>, (2) the average permeability for each layer, (3) the horizontal gradient of permeability in each layer, (4) <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(n_L-1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>n</mi> <mi>L</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> interface depths, and (5) interface slope angles. The inverse problem is formulated within a Bayesian framework, and a reversible-jump Markov chain Monte Carlo algorithm is employed to determine both the optimal number of layers and their properties. This approach is first applied to a synthetic case aiming to reconstruct a two-dimensional continuous field from two well logs of permeability, demonstrating the ability of the method to retrieve a posterior density close to the reference solution. The method is then successfully applied to real data from three well logs in the Teapot Dome oilfield, Wyoming, USA. Overall, the proposed methodology provides a unified framework through which to infer geological parameters and can be extended to integrate seismic inversion, flow data inversion (e.g., for well test interpretation), or other types of geophysical data.</p>

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Transdimensional Inversion of Well Log Data for a Two-Dimensional Geological Model with Inclined Layers and Petrophysical Lateral Variability

  • 期刊论文

  • 发表日期：

    2026年1月8日

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  • Julien Herrero,
  • Guillaume Caumon,
  • Thomas Bodin

摘要

This study introduces a transdimensional inversion framework to quantify stratigraphic uncertainties in layered reservoir models from well data. The goal is to adaptively determine the appropriate number of subsurface model parameters. The parameters to infer correspond to (1) the number of layers \(n_L\) n L , (2) the average permeability for each layer, (3) the horizontal gradient of permeability in each layer, (4) \(n_L-1\) n L - 1 interface depths, and (5) interface slope angles. The inverse problem is formulated within a Bayesian framework, and a reversible-jump Markov chain Monte Carlo algorithm is employed to determine both the optimal number of layers and their properties. This approach is first applied to a synthetic case aiming to reconstruct a two-dimensional continuous field from two well logs of permeability, demonstrating the ability of the method to retrieve a posterior density close to the reference solution. The method is then successfully applied to real data from three well logs in the Teapot Dome oilfield, Wyoming, USA. Overall, the proposed methodology provides a unified framework through which to infer geological parameters and can be extended to integrate seismic inversion, flow data inversion (e.g., for well test interpretation), or other types of geophysical data.