  In this work we construct holographic boundary theories for linearized 3D
gravity, for a general family of finite or quasi-local boundaries. These
boundary theories are directly derived from the dynamics of 3D gravity by
computing the effective action for a geometric boundary observable, which
measures the geodesic length from a given boundary point to some centre in the
bulk manifold. We identify the general form for these boundary theories and
find that these are Liouville like with a coupling to the boundary Ricci
scalar. This is illustrated with various examples, which each offer interesting
insights into the structure of holographic boundary theories.
