  4D seismic imaging has been widely used in CO$_2$ sequestration projects to
monitor the fluid flow in the volumetric subsurface region that is not sampled
by wells. Ideally, real-time monitoring and near-future forecasting would
provide site operators with great insights to understand the dynamics of the
subsurface reservoir and assess any potential risks. However, due to obstacles
such as high deployment cost, availability of acquisition equipment, exclusion
zones around surface structures, only very sparse seismic imaging data can be
obtained during monitoring. That leads to an unavoidable and growing knowledge
gap over time. The operator needs to understand the fluid flow throughout the
project lifetime and the seismic data are only available at a limited number of
times. This is insufficient for understanding the reservoir behavior. To
overcome those challenges, we have developed spatio-temporal
neural-network-based models that can produce high-fidelity interpolated or
extrapolated images effectively and efficiently. Specifically, our models are
built on an autoencoder, and incorporate the long short-term memory (LSTM)
structure with a new loss function regularized by optical flow. We validate the
performance of our models using real 4D post-stack seismic imaging data
acquired at the Sleipner CO$_2$ sequestration field. We employ two different
strategies in evaluating our models. Numerically, we compare our models with
different baseline approaches using classic pixel-based metrics. We also
conduct a blind survey and collect a total of 20 responses from domain experts
to evaluate the quality of data generated by our models. Via both numerical and
expert evaluation, we conclude that our models can produce high-quality 2D/3D
seismic imaging data at a reasonable cost, offering the possibility of
real-time monitoring or even near-future forecasting of the CO$_2$ storage
reservoir.
