How are the ZNE, ZRT and LQT coordinate systems defined?
Z depends upon convention, but in geophysics we typically use Z=positive downward. R is radial and the positive direction is defined in the direction FROM the source TOWARD the receiver. T polarity can be determined from the right-hand rule once you have Z and R. 

For reference, this is the based on the convention for polarity as described by Aki and Richards (1980).