From layer-cake models to complex subsurface structures: a flexible transdimensional inversion approach

We present a transdimensional inversion to quantify stratigraphic and petrophysical uncertainties in 2D stratified subsurface models. The objective is to infer the number and position of geological units and their associated properties during inversion. The transdimensional framework relies on a reversible jump Markov chain Monte Carlo (RJMCMC) sampler, which provides self-adaptive capabilities for the parameterization to evolve with the data, and converge to parsimonious posterior solutions. These solutions balance model complexity with the information provided by diverse datasets, such as well logs, seismic surveys, and well tests, which can be integrated within a joint inversion framework. Nevertheless, parameterizations must be carefully defined, as ensuring a small number of parameters is required to maintain reasonable computational times. In this talk, we present an overview of the different geometrical and petrophysical parameterizations that can be used for this purpose. Starting from the classical 1D "layer-cake" model with piecewise constant properties, often employed in geophysics, we progressively introduce more complex parameterizations which better approach the complexity of subsurface layers. These include inclined layers, anticlines, synclines, faulted structures, and lateral variability. By moving towards increasingly realistic parameterizations, the methodology aims to improve the estimation of stratified properties while accounting for structural and stratigraphic variability. Synthetic and real-world applications with various data types will be briefly presented to demonstrate the ability of the sampler to recover coherent results when the parameterization and the noise model are appropriately defined. Overall, this approach provides a unified and adaptable framework for geomodeling, paving the way for improved subsurface characterization and uncertainty quantification in 3D.