Paper submitted to IMAGE 2026, by Fuchun Gao, Carlos Calderon, Faqi Liu (TGS), Yiran Huang (Brown University).
Abstract
Four-dimensional full waveform inversion (4D FWI) has been increasingly applied in recent years in time lapse monitoring projects. Like many geophysical exploration techniques, 4D FWI involves inherent uncertainty because FWI is a non-linear ill-posed problem characterized by null space and non-uniqueness. Quantifying uncertainty of 4D FWI models is essential for informed drilling decisions, particularly in terms of cost efficiency and operational safety. Here we propose a method and workflow to quantify 4D FWI uncertainty using a Joint Stein Variational Gradient Descent (JSVGD) method, a tailored variational inference approach for 4D problems. Numerical tests demonstrate its computational affordability and practicality. For the demonstration of the proposed approach and its usefulness we utilize an example with non-repeatable acquisition geometries.
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