Is there a subterranean SOFAR channel After discovering the SOFAR channel in water at a depth which the speed of sound is at its minimum and acts as a waveguide, it was postulated that a similar channel existed in the atmosphere and indeed was found and put to somewhat practical use in Project Mogul.
What I haven't been able to find is if there exists, or if it's possible to have a similar channel in the earth.
 A: The type of sound channel you are asking about is caused by a position dependent sound speed profile, which causes a position dependent refractive index.  Sound waves will tend to travel into regions of low sound speed, this is most easily seen from a ray trace.  In the pacific ocean higher temperatures at the surface and higher pressures at the bottom cause higher sound speeds in those regions.  There is a minimum at approximately 1000 - 1300m under the surface.  Rays from a spherical source will still hit the floor and surface but a large bundle of rays in the horizontal plane will be trapped in the channel.  Hard boundary reflections can also cause wave guide behavior but the sound channel is purely refractive.  This can happen anywhere and in any medium in theory.  Whether or not it happens in practice is another story.  It is no surprise that such effects occur in aeroacoustic environments.  There is a famous double channel over wallops island that is in the hand book of physics (I think).  As for such channels existing in bedrock or other earth materials I am not sure.  As I said it is possible but you'd need a working model of how temperature gradients build up in the earth and how these affect the bulk material locally and by extension the local SSP.  There is a very comprehensive text by Cerveny called Seismic Ray Theory that discusses reflections from interfaces between different stratum and may discuss refractive ray bending in the earth in general.  Since that text focuses on seismology I'd think it would be a good starting point for investigating your question.  The references may point to books and articles about this.  
A: From the link you give and searching, it appears to be an effect in fluids which have a uniform behavior to pressure and temperature changes.


Cutaway diagram of Earth's internal structure (to scale) with inset showing detailed breakdown of structure (not to scale)

The only fluids are the oceans, the atmosphere you already mention, and the liquid core. I do not know whether the conditions of changes in sound velocity exist in the liquid core so as to allow a SOFAR channel, but you  must agree it is irrelevant, since one cannot reach the core. 
