Transdimensional joint inversion of flow and well log data using a cascaded Metropolis sampler on a layer-cake model

History matching is a type of inverse problem for subsurface georesource evaluation that adjusts the geological and petrophysical properties of a reservoir from dynamic data. Here, we aim to infer the geological structures and the associated permeability values of a model in a joint inversion using observed production data (pressure and fluid saturation) and permeability log data. To determine the appropriate level of complexity in the unknown model, we introduce a transdimensional Monte Carlo method applied to a one-dimensional layered reservoir model. In contrast to classical Bayesian modeling in which permeability values are predicted in a fixed reservoir geometry, the number of layers is treated as an unknown variable in the inversion. Layers remain horizontal for simplicity and are characterized only by their number, thickness, interface depth, and constant isotropic permeability values. Our method employs a cascaded Metropolis sampler based on a two-step sequential acceptance criterion in the Markov chain to reduce computational costs. The likelihood probability of well log data is first quickly computed as in a standard regression problem, and flow simulations are performed only on candidate models accepted by this first regression step to further reduce the uncertainty. Numerical flow simulations are solved on a mesh conformal to horizons, which is locally updated at each iteration. Synthetic tests on a simple reference model highlight the capability of the transdimensional cascaded Metropolis algorithm, which jointly uses flow and well log data, to recover a parsimonious representation of the subsurface. Results show that the proposed approach is able to successfully locate major geological discontinuities, quantify uncertainty, and spatially capture the level of information brought by different datasets in the joint inversion process. This suggests potential applicability to real data, more complex reservoir geometries, and other physics. • Introduces a transdimensional Monte Carlo method for layered reservoir models. • Combines flow data and well log data in a joint inversion framework. • Relies on local mesh updating and flow simulation for efficient history matching. • Utilizes a cascaded Metropolis sampler to reduce the computational time. • Characterizes structural uncertainty and recovers geometry of a synthetic solution.