Are there any techniques for imaging the deep Earth besides seismic waves?
Gravity can be used to investigate the lower crust and upper mantle (see for example Fullea et al, 2014). Satellite measurements of gravity could even be to investigate deeper structures in the mantle, like subducting slaps (Panet, 2014). However, I couldn't find any use of gravity data to probe deeper, into the core for example.

The magnetotelluric method is sometimes used for deep crustal structure. And features of the geomagnetic field, like secular variation, can be inverted to investigate as far down as the outer core (Gubbins, 1996).

However, the most common and well developed method to image the lower mantle and core is still through seismic waves.