Estimation of the spatial statistics of subsurface velocity heterogeneity
from surface-based reflection data is a problem of significant interest
in seismic and groundpenetrating radar (GPR) studies. A method to
effectively address this problem has been recently presented, but
our knowledge regarding the resolution of the corresponding inverse
problem is still patchy. Here, we address this issue through an analytical
approach based on the realistic assumption that the underlying velocity
structure can be characterized as a scale-invariant medium. We then
test these analytical findings on pertinent depth-migrated synthetic
seismic images. In doing so, we also relax our original assumption
that scale-invariance prevails over the entire bandwidth of the source
signal. The numerical results fully confirm our analytical findings,
which indicate that the inversion of surface-based seismic or GPR
reflection data for the geostatistical properties of the imaged subsurface
region is sensitive to the aspect ratio of the velocity heterogeneity
and to the decay of its power spectrum, but not to the individual
values of the horizontal and vertical correlation lengths.