Fractures and faults within a reservoir can provide important pathways for the movement of reservoir fluids. Understanding the character and properties of these features on a range of length scales can be vital for the efficient exploitation of natural resources, whether it be enhanced oil and gas recovery, the safe storage of CO2, or better exploitation of geothermal heat. The monitoring of microseismicity within a reservoir illuminates active faults, but these events can be also used to characterize fracture networks through measurements of seismic anisotropy. In this study we use microseismic data acquired over an 18-day period in April 1997 at the Ekofisk oil field in the North Sea. Using the analysis of seismic multiplets we delineate a number of sub-vertical tectonic faults, which are consistent with previous core data analysis and seismic reflection work. We use shear wave splitting measurements, which are indicative of fracture-induced seismic anisotropy, to infer the orientation of aligned aseismic fracture sets within the reservoir. The estimated fracture dip and strike from the shear wave splitting analysis are consistent with the active tectonic fractures characterized by the multiplets, but this analysis also illuminates spatial variations in fracture properties. Such monitoring on a longer term and with multiple wells is a promising tool for better understanding fracture and fault-controlled flow within reservoirs.