  Spatially extended emission regions of Active Galactic Nuclei (AGN) respond
to continuum variations, if such emission regions are powered by energy
reprocessing of the continuum. The response from different parts of the
reverberating region arrives at different times lagging behind the continuum
variation. The lags can be used to map the geometry and kinematics of the
emission region (i.e., reverberation mapping, RM). If the extended emission
region is not spherically symmetric in configuration and velocity space,
reverberation may produce astrometric offsets in the emission region
photocenter as a function of time delay and velocity, detectable with future
micro-arcsec to tens of micro-arcsec astrometry. Such astrometric responses
provide independent constraints on the geometric and kinematic structure of the
extended emission region, complementary to traditional reverberation mapping.
In addition, astrometric RM is more sensitive to infer the inclination of a
flattened geometry and the rotation angle of the extended emission region.
