  We investigate a recent suggestion that the spatial distribution of
earthquake hypocenters makes a fractal set with a structure and fractal
dimensionality close to those of the backbone of critical percolation clusters,
by analyzing four different sets of data for the hypocenter distributions and
calculating the dynamical properties of the geometrical distribution such as
the spectral dimension $d_s$. We find that the value of $d_s$ is consistent
with that of the backbone, thus supporting further the identification of the
hypocenter distribution as having the structure of the percolation backbone.
