Trans-conceptual sampling in geophysical inverse problems

Jinji Li, Ivan Sanchez, Kristopher A. Innanen

Bayesian methods that explicitly account for uncertainty in model parameters have become a key tool for quantifying uncertainty in geophysical inversion. An important extension is trans-dimensional (trans-D) Bayesian sampling, in which even the number of model parameters is treated as unknown. Most trans-D studies employ the reversible-jump Markov chain Monte Carlo (MCMC) algorithm, which can sample across models of different dimensionality but only under specific conditions that successive models must differ in a simple, sequential way, and the method depends on carefully crafted, application- specific mathematical transformations to move between dimensions. Recently, a more general framework called trans-conceptual (trans-C) Bayesian sampling has been introduced to geophysics. Instead of merely changing the number of free parameters, trans-C sampling explores a predefined set of alternative conceptual models. These models may vary not only in dimensionality, but also in their underlying physical assumptions, forward-model formulations, or the statistical description of measurement noise. Crucially, the trans-C framework dispenses with the complex, case-dependent parameter-space transformations required by reversible-jump methods, making it possible to develop fully automated MCMC schemes that do not depend on detailed knowledge of how the data is generated. In this study, we review the trans-C sampling algorithm and assess its feasibility using synthetic examples from amplitude-versus-offset (AVO) inversion and surface-wave inversion. The results show that the sampler can effectively identify suitable forward-model assumptions and remains robust in scenarios where conventional reversible-jump methods would be difficult or impractical to implement.