Mechanical and electromagnetic interference (process noise) is common in seismic data recorded to monitor and characterize induced microseismicity during industrial injection and production operations. We have developed a case study of adaptive cancellation to reduce observed process noise in passive seismic data recorded during the 2014 injection test at the Lab research site in Spitsbergen. Our results suggest that adaptive cancellation is effective when major sources of interference are readily identifiable. Adaptive cancellation requires these sources to be instrumented separately but conceivably with low-cost sensors. We suggest that adaptive cancellation should be considered routinely when planning microseismic monitoring operations when strong industrial or anthropogenic noise is anticipated. Interference suppression algorithms are sufficiently simple that they could be implemented in acquisition systems to avoid archival of noise reference data.