  One of the risks of large-scale geologic carbon sequestration is the
potential migration of fluids out of the storage formations. Accurate and fast
detection of this fluids migration is not only important but also challenging,
due to the large subsurface uncertainty and complex governing physics.
Traditional leakage detection and monitoring techniques rely on geophysical
observations including seismic. However, the resulting accuracy of these
methods is limited because of indirect information they provide requiring
expert interpretation, therefore yielding in-accurate estimates of leakage
rates and locations. In this work, we develop a novel machine-learning
detection package, named "Seismic-Net", which is based on the deep densely
connected neural network. To validate the performance of our proposed leakage
detection method, we employ our method to a natural analog site at Chimay\'o,
New Mexico. The seismic events in the data sets are generated because of the
eruptions of geysers, which is due to the leakage of $\mathrm{CO}_\mathrm{2}$.
In particular, we demonstrate the efficacy of our Seismic-Net by formulating
our detection problem as an event detection problem with time series data. A
fixed-length window is slid throughout the time series data and we build a deep
densely connected network to classify each window to determine if a geyser
event is included. Through our numerical tests, we show that our model achieves
precision/recall as high as 0.889/0.923. Therefore, our Seismic-Net has a great
potential for detection of $\mathrm{CO}_\mathrm{2}$ leakage.
