Bayesian RockAVO: Direct petrophysical inversion with hierarchical conditional GANs

Reservoir characterization is a critical component in any oil and gas, geothermal, and CO2 sequestration project. A fundamental step in the process of characterizing the subsurface is represented by the inversion of petrophysical parameters from seismic data. However, this problem suffers from various uncertainty sources originating from inaccuracies in the measurements, modeling errors, and complex geological processes. Moreover, the non-linearity of the rock-physics model and Zoeppritz equation that constitute the modelling operator, further complicates the inversion process. In this work, we propose a novel data-driven approach where well-log information is used to obtain optimal basis functions that link band-limited petrophysical reflectivities to pre-stack seismic data. Subsequently, the inversion of such band-limited reflectivities for petrophysical parameters is framed in a Bayesian framework where a generative adversarial network is used to produce a geologically realistic prior distribution. The trained prior distribution is updated using the Stein Variational Gradient Descent and a set of representative solutions is produced that is consistent with the uncertainties in the data and the nonlinear operators.