This research addresses one of the most important problems in large-scale geodynamics, the fate of subducted lithosphere once it has penetrated below the depths of the deepest earthquakes. The work will investigate deep slab structure from its effects on the waveforms of seismic P and S waves. These effects include travel time advance, defocusing, multipathing, and diffraction. Digitally recorded P and S waves will be analyzed by comparison with seismograms synthesized in three dimensional slab structures computed by theoretical methods. The structure of the descending lithospheric slabs below the cutoff in seismicity at 650 km depth is important to the understanding of the viscosity structure of the mantle and processes of whole mantle convection. Because convection is the driving force behind plate tectonics and the world's earthquake activity, this work is a contribution to the National Earthquake Hazard Reduction Program.