  Monitoring changes inside a reservoir in real time is crucial for the success
of CO2 injection and long-term storage. Machine learning (ML) is well-suited
for real-time CO2 monitoring because of its computational efficiency. However,
most existing applications of ML yield only one prediction (i.e., the
expectation) for a given input, which may not properly reflect the distribution
of the testing data, if it has a shift with respect to that of the training
data. The Simultaneous Quantile Regression (SQR) method can estimate the entire
conditional distribution of the target variable of a neural network via pinball
loss. Here, we incorporate this technique into seismic inversion for purposes
of CO2 monitoring. The uncertainty map is then calculated pixel by pixel from a
particular prediction interval around the median. We also propose a novel
data-augmentation method by sampling the uncertainty to further improve
prediction accuracy. The developed methodology is tested on synthetic
Kimberlina data, which are created by the Department of Energy and based on a
CO2 capture and sequestration (CCS) project in California. The results prove
that the proposed network can estimate the subsurface velocity rapidly and with
sufficient resolution. Furthermore, the computed uncertainty quantifies the
prediction accuracy. The method remains robust even if the testing data are
distorted due to problems in the field data acquisition. Another test
demonstrates the effectiveness of the developed data-augmentation method in
increasing the spatial resolution of the estimated velocity field and in
reducing the prediction error.
