Let's explain the meaning of both variants (a and any) and try to reach a conclusion.
Any specific application
This means that, of a large list of specific applications, any specific application may be selected. In context, this means that treebanks can be be used on an arbitrary, but specific, application. The author clearly does not want to indicate exactly which applications treebanks may be used for, and leaves this up to the imagination of the reader.
A specific application
This means that, of a large list of specific applications, one (or maybe a few) applications may be selected. In context, this means that treebanks can be used on a specific application that are explicitly known. You would expect that the author will elaborate in the next sentence as to what applications he was thinking of.
So, to conclude, any means that the specific applications are not well-defined, and the author feels that there is no need for this either; a means that the author has some (or one) specific applications in mind, and will likely elaborate or assumes the reader is aware of which applications treebanks can be used for.