1. A method of determining an azimuth and a direction of first motion of a fault or fracture plane in a subsurface of the earth by optimizing at least one azimuthally-dependent attribute of microseismic signals generated by one or more microseismic sources within the earth's subsurface, comprising: recording microseismic data traces corresponding to the generated microseismic signals detected by plurality of sensors located at a plurality of sensor positions at or near the earth's surface, the recorded microseismic data traces being at least one of electrical, magnetic or optical signals generated by said sensors and recorded by a recording unit, the microseismic signals originating within a volume of the subsurface of the earth, located at least one of near and in the fault or fracture; subdividing the subsurface volume into a plurality of spatial volumes, each spatial volume corresponding to a selected time interval, each spatial volume comprising a plurality of voxels corresponding thereto; for each voxel within a selected spatial volume, applying a time shift to recorded microseismic data traces corresponding thereto, wherein the time shift is substantially equal to a travel time from each voxel to the sensor position corresponding thereto, thereby transforming the recorded microseismic data traces into a time shifted microseismic data trace for each combination of voxel and sensor position; selecting a subset of the voxels corresponding to the selected spatial volume for determination of the azimuth and direction of first motion, and for a selected voxel within the selected subset, determining for the voxel the azimuth of the fault or fracture plane and the direction of first motion of the fault or fracture corresponding to a maximum value of at least one azimuthally-dependent attribute of the microseismic data traces.