Physics‐reliable frugal local uncertainty analysis for full waveform inversion

Abstract Full waveform inversion stands at the forefront of seismic imaging technologies, pivotal in retrieving high‐resolution subsurface velocity models. Its application is especially profound when imaging complex geologies such as salt bodies, which are regions notoriously challenging, yet essential given their hydrocarbon potential. However, with the power of full waveform inversion comes the intrinsic challenge of estimating the associated uncertainties. Such uncertainties are crucial in understanding the reliability of subsurface models, particularly in terrains like subsalt regions. Addressing this, we advocate for a nuanced approach employing the Stein variational gradient descent algorithm. Through a judicious use of a limited number of velocity model particles and the integration of random field‐based perturbations, our methodology provides a local representation of the uncertainties inherent in full waveform inversion. Our evaluations, based on the Marmousi model, showcase the robustness of the proposed technique. Yet, it is our exploration into salt‐intensive terrains, leveraging data from the Sigsbee 2A synthetic model and the Gulf of Mexico, that emphasizes the method's versatility. Findings indicate pronounced uncertainties along salt boundaries and in the deeper subsalt sediments, contrasting the minimal uncertainties in non‐salt terrains. However, anomalies like salt canyons present unique challenges, potentially due to the interplay of multi‐scattering effects. Emphasizing the scalability and cost‐effectiveness of this approach, we highlight its potential for large‐scale industrial applications in full waveform inversion, while also underscoring the necessity for prudence when integrating these uncertainty insights into subsequent seismic‐driven geological and reservoir modelling.