A solution to the class of problems in which an SH line source is operating in a medium consisting of two quarter spaces with an arbitrary number of semi infinite vertical layers in between is given in a frequency-wavenumber domain. The general result is applied to a model with a single vertical layer, and synthetic seismograms are calculated for a source specified as an SH line dislocation at the interface between the vertical layer and the faster quarter space. The numerical examples demonstrate that moderate fault-normal material heterogeneity can have significant effects on the seismic response of a medium. The overall distribution of travel times, amplitudes, and motion polarities in the presence of fault zone material heterogeneity is different from a corresponding distribution in a homogeneous half space. The effects are most prominent near the fault zone, where head waves, surface waves, and trapped modes result in waveform complexities, large amplifications (over an order of magnitude in the fault zone itself), and first-motion polarities which are reversed from homogeneous medium predictions. The results imply that material heterogeneity should be included in fault zone models which are used for the interpretation of observed seismic data and theoretical calculations of near fault responses. Such models can be utilized to obtain important fault zone and earthquake source parameters.