To improve our understanding of the Canoe Reach Geothermal Field in the Rocky Mountain Trench of western Canada, we examine the distribution of local earthquakes using a network of 10 broadband seismometers deployed over a 40 by 60 km area across the trench. The Canoe Reach area exhibits strong cultural noise from communities, roads and trains that makes detecting earthquake signals challenging. We propose detecting earthquakes in the area of the trench by measuring the kurtosis of the seismic signal, which is a statistical moment representing the distribution tail and is insensitive to emerging signals but more sensitive to impulsive earthquake onsets. Examining the kurtosis of the three-component seismograms for four months of data, we identified eight local earthquakes. An earthquake catalog produced by STA/LTA detections found 11 events for the same four-month period, four of which were detected through our kurtosis approach. By further exploring the kurtosis detections, we are refining our catalog to identify the source of discrepancies between it and the STA/LTA catalog. We then estimated locations of our detected events, and the uncertainties of those locations, through nonlinear Bayesian sampling. This method treats the origin times, half-space velocities, and the picking noise for P and S arrivals as unknowns. We employed this parameterization to test whether Bayesian sampling could account for the challenging noise environment. Locating our detected events found that five events occurred outside the seismic network and three events occurred inside. The average horizontal and vertical uncertainty is 28 and 19 km respectively for the outside events. These uncertainties are lower at 7 and 9 km for the inside events. While the inside events exhibit lower spatial uncertainties than the outside events, their uncertainties remain large. We then examined whether the uncertainties could be further improved by jointly locating multiple events. Jointly inverting two of the events from within the array decreased their average horizontal uncertainty from 6.5 to 2.5 km and the vertical from 14 to 7 km. Reducing uncertainties in the locations of the events in this manner will clarify their distribution and all for an improved understanding of the seismicity and structure of the Rocky Mountain Trench.