Quantifying fault-related uncertainty with inverse homogenization

Although the ease and accuracy of seismic interpretation are continually increasing thanks to the increasing amount of available data, computing power and new automatic interpretation techniques, it is still challenging to resolve fine-scale geological features at depth (e.g. faults) because of physical limitations. Indeed, seismic imaging techniques are based on frequency band-limited seismic data, and therefore they can only recover a smooth version of the true Earth, which is not suited for a proper geological interpretation below the decametric scale. Uncertainties and pitfalls in the interpretation of these fine-scale features can affect natural hazard mitigation strategies, and lead to overly optimistic model-based forecasts. To make sure that such subtle features are appropriately considered in subsurface uncertainty studies, we propose the use of a downscaling (or inverse homogenization) approach.

In this work, the downscaling is used to properly detect faults and quantify the uncertainty associated to fault parameters geometry and displacement. In particular, from a smooth representation of the real complex structures, obtained through seismic techniques, such as the well-known Full Waveform Inversion (FWI), the downscaling inversion aims to recover all the finer scale fault models compatible with the FWI solution. Because this is an ill-posed inverse problem, the inversion is cast into a Bayesian framework, which combines the information at larger scale coming from the data (FWI model) with some a priori knowledge on the fault structures in order to retrieve a probability distribution over the possible fine-scale models. A Markov Chain Monte Carlo (MCMC) algorithm is adopted to sample the model space and numerically evaluate the posterior probability distribution. This involves the stochastic generation of velocity model realizations where fault displacement is computed using a kinematic modeling approach and the fine-layering velocity is obtained through geostatistical simulations.

A significant advantage of this technique is that it can be applied to downscale a localized area of interest within a larger FWI dataset, consequently reducing memory consumption and computational cost. This latter is also reduced thanks to the inexpensive forward modeling operator (i.e., the non-periodic homogenization), making the stochastic inversion feasible compared to standard MCMC-based seismic inversion methods. The proposed methodology, validated on a synthetic data-case example, proves to be a reliable approach to resolve and quantify fault-related uncertainty.