The Domo de San Pedro Geothermal field, located in the westernmost part of the trans-Mexican volcanic belt, is part of a silicic volcanic complex. Geothermal energy is produced since 2015 from 9 wells as deep as 3 km. We monitor geothermal operations using a continuous seismic dataset from a temporary network of 20 broadband stations from March 2021 to January 2022. The well logs describing the geothermal operations allow us to investigate the seismic response of the geothermal field to fluid extraction and re-injection across the geothermal wells. We produced a catalog of 217 local earthquakes and derive an optimized 1D velocity model for the geothermal field between 1.2 m above the sea level (masl) and 12 km depth. Apparent velocity changes (dv/v) are measured using seismic ambient noise interferometry from the coda of noise cross-correlations. Next, we identify and locate subsurface velocity anomalies, combining the methods of station collapse sensitivity and ambient noise imaging applied to the continuous seismic noise records. We distinguish three periods of seismic activity where prominent changes in velocity coincide with the re-injection of fluids and significant variation in the production rate of the geothermal wells. We determine the distribution of these velocity transients inside the geothermal field and propose that they are associated with variations in reservoir fluid content and effective stress changes beneath the volcanic system and are responsible for induced microseismicity. Our study shows that implementing dv/v quantification as an additional tool for geothermal seismic monitoring can lead to an improved understanding of the behavior of the geothermal system over time and ultimately de-risk geothermal operations.