Method for characterizing a subterranean formation includes: obtaining azimuth-dependent observed travel-times from measured seismic data; inverting observed travel-times to calculate a fracture attribute selected from the group consisting of: magnitude and orientation; identifying presence of fracture based on calculated fracture magnitude; identifying fracture direction based on calculated fracture orientation; calculating predicted travel-times; calculating differences or residual errors between observed travel-times and predicted travel-times; identifying potential fault locations based on residual errors; inverting fracture magnitude and orientation using travel-time differences between a shallower horizon to a deeper horizon of interest to minimize overburden artifacts.