  Spectroastrometry measures source astrometry as a function of
wavelength/velocity. Reverberations of spectroastrometric signals naturally
arise in broad-line regions (BLRs) of active galactic nuclei (AGNs) as a result
of the continuum variations that drive responses of the broad emission lines
with time delays. Such signals provide a new diagnostic for mapping BLR
kinematics and geometry, complementary to the traditional intensity
reverberation mapping (RM) technique. We present the generic mathematical
formalism for spectroastrometric RM and show that under realistic parameters of
a phenomenological BLR model, the spectroastrometric reverberation signals vary
on a level of several to tens of microarcseconds, depending on the BLR size,
continuum variability, and angular-size distance. We also derive the analytical
expressions of spectroastrometric RM for an inclined ring-like BLR. We develop
a Bayesian framework with a sophisticated Monte Carlo sampling technique to
analyze spectroastrometric data and infer the BLR properties, including the
central black hole mass and angular-size distance. We demonstrate the potential
of spectroastrometric RM in spatially resolving BLR kinematics and geometry
through a suite of simulation tests. The application to realistic observation
data of 3C~273 obtains tentative, but enlightening results, reinforcing the
practical feasibility of conducting spectroastrometric RM experiments on bright
AGNs with the operating Very Large Telescope Interferometer as well as possibly
with the planned next-generation 30 m class telescopes.
