  We use three-dimensional magnetohydrodynamical (MHD) simulations to study the
formation of a corona above an initially weakly magnetized, isothermal
accretion disk. We also describe a modification to time-explicit numerical
algorithms for MHD which enables us to evolve highly stratified disks for many
orbital times. We find that MHD turbulence driven by the magnetorotational
instability (MRI) produces strong amplification of weak fields within two scale
heights of the disk midplane in a few orbital times. About 25 % of the magnetic
energy generated by the MRI within two scale heights escapes due to buoyancy,
producing a strongly magnetized corona above the disk. Most of the buoyantly
rising magnetic energy is dissipated between 3 and 5 scale heights, suggesting
the corona will also be hot. The average vertical disk structure consists of a
weakly magnetized turbulent core below a strongly magnetized corona which is
stable to the MRI. The largescale field structure in both the disk and corona
is toroidal. The functional form of the stress is flat within two scale
heights, but proportional to the density above two scale heights.
  For initially weak uniform vertical fields, we find the exponential growth of
magnetic field via axisymmetric vertical modes of the MRI produces strongly
buoyant sheets of magnetic energy which break the disk apart into horizontal
channels. These channels rise several scale heights vertically before the onset
of the Parker instability distorts the sheets and allows matter to flow back
towards the midplane and reform a disk. We suggest this evolution may be
relevant to the dynamical processes which disrupt the inner regions of a disk
when it interacts with a strongly magnetized central object.
