Disclosed herein are various embodiments of methods and systems for determining the orientation and direction of first motion of a fault or fracture by optimizing an azimuthally-dependent attribute of signals generated by microseismic sources, comprising: recording microseismic data traces using a of sensors located at a plurality of sensor positions; subdividing the subsurface volume into spatial volumes corresponding to selected time intervals and comprising a plurality of voxels; for each voxel, applying a time shift to the microseismic data traces that is substantially equal to a travel time from each voxel to the corresponding sensor position, and determining for the voxel the orientation and direction of first motion of the fault or fracture corresponding to a maximum value for the voxel of at least one azimuthally-dependent attribute of the microseismic data traces.