  We present a high angular resolution (0.3" = 40 AU) SMA survey of the 870
micron thermal continuum emission from 9 of the brightest, and therefore most
massive, circumstellar disks in the ~1 Myr-old Ophiuchus star-forming region.
Using 2-D radiative transfer calculations, we simultaneously fit the observed
continuum visibilities and broadband spectral energy distribution for each disk
with a parametric structure model. Compared to previous millimeter studies,
this survey includes significant upgrades in modeling, data quality, and
angular resolution that provide improved constraints on key structure
parameters, particularly those that characterize the spatial distribution of
mass in the disks. In the context of a surface density profile motivated by
similarity solutions for viscous accretion disks, the best-fit models for the
sample disks have characteristic radii R_c = 20-200 AU, high disk masses M_d =
0.005-0.14 M_sun, and a narrow range of radial surface density gradients around
a median $\gamma$ = 0.9. These density structures are used in conjunction with
accretion rate estimates from the literature to help characterize the viscous
evolution of the disk material. Using the standard prescription for disk
viscosities, those combined constraints indicate that $\alpha$ = 0.0005-0.08.
Three of the sample disks show large (R = 20-40 AU) central cavities in their
continuum emission morphologies, marking extensive zones where dust has been
physically removed and/or has significantly diminished opacities. Based on the
current requirements of planet formation models, these emission cavities and
the structure constraints for the sample as a whole suggest that these young
disks may eventually produce planetary systems, and have perhaps already
started. (abridged)
