  We present an approach based on machine learning (ML) to distinguish eruption
and precursory signals of Chimay\'{o} geyser (New Mexico, USA) under noisy
environments. This geyser can be considered as a natural analog of
$\mathrm{CO}_2$ intrusion into shallow water aquifers. By studying this geyser,
we can understand upwelling of $\mathrm{CO}_2$-rich fluids from depth, which
has relevance to leak monitoring in a $\mathrm{CO}_2$ sequestration project. ML
methods such as Random Forests (RF) are known to be robust multi-class
classifiers and perform well under unfavorable noisy conditions. However, the
extent of the RF method's accuracy is poorly understood for this
$\mathrm{CO}_2$-driven geysering application. The current study aims to
quantify the performance of RF-classifiers to discern the geyser state. Towards
this goal, we first present the data collected from the seismometer that is
installed near the Chimay\'{o} geyser. The seismic signals collected at this
site contain different types of noises such as daily temperature variations,
seasonal trends, animal movement near the geyser, and human activity. First, we
filter the signals from these noises by combining the Butterworth-Highpass
filter and an Autoregressive method in a multi-level fashion. We show that by
combining these filtering techniques, in a hierarchical fashion, leads to
reduction in the noise in the seismic data without removing the precursors and
eruption event signals. We then use RF on the filtered data to classify the
state of geyser into three classes -- remnant noise, precursor, and eruption
states. We show that the classification accuracy using RF on the filtered data
is greater than 90\%.These aspects make the proposed ML framework attractive
for event discrimination and signal enhancement under noisy conditions, with
strong potential for application to monitoring leaks in $\mathrm{CO}_2$
sequestration.
