Estimation of the spatial statistics of subsurface velocity heterogeneity
from surface-based geophysical reflection survey data is a problem
of significant interest in seismic and ground-penetrating radar (GPR)
research. A method to effectively address this problem has been recently
presented, but our knowledge regarding the resolution of the estimated
parameters is still inadequate. Here we examine this issue using
an analytical approach that is based on the realistic assumption
that the subsurface velocity structure can be characterized as a
band-limited scale-invariant medium. Our work importantly confirms
recent numerical findings that the inversion of seismic or GPR reflection
data for the geostatistical properties of the probed 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.