  Seismic imaging is an ill-posed inverse problem that is challenged by noisy
data and modeling inaccuracies -- due to errors in the background
squared-slowness model. Uncertainty quantification is essential for determining
how variability in the background models affects seismic imaging. Due to the
costs associated with the forward Born modeling operator as well as the high
dimensionality of seismic images, quantification of uncertainty is
computationally expensive. As such, the main contribution of this work is a
survey-specific Fourier neural operator surrogate to velocity continuation that
maps seismic images associated with one background model to another virtually
for free. While being trained with only 200 background and seismic image pairs,
this surrogate is able to accurately predict seismic images associated with new
background models, thus accelerating seismic imaging uncertainty
quantification. We support our method with a realistic data example in which we
quantify seismic imaging uncertainties using a Fourier neural operator
surrogate, illustrating how variations in background models affect the position
of reflectors in a seismic image.
