  We investigate how the divergence-free property of magnetic fields can be
exploited to resolve the azimuthal ambiguity present in solar vector
magnetogram data, by using line-of-sight and horizontal heliographic derivative
information as approximated from discrete measurements. Using synthetic data we
test several methods that each make different assumptions about how the
divergence-free property can be used to resolve the ambiguity. We find that the
most robust algorithm involves the minimisation of the absolute value of the
divergence summed over the entire field of view. Away from disk centre this
method requires the sign and magnitude of the line-of-sight derivatives of all
three components of the magnetic field vector.
