  Phase referencing is a standard calibration procedure in radio
interferometry. It allows to detect weak sources by using quasi-simultaneous
observations of closeby sources acting as calibrators. Therefore, it is assumed
that, for each antenna, the optical paths of the signals from both sources are
similar. However, atmospheric turbulence may introduce strong differences in
the optical paths of the signals and affect, or even waste, phase referencing
for cases of relatively large calibrator-to-target separations and/or bad
weather. The situation is similar in wide-field observations, since the random
deformations of the images, mostly caused by atmospheric turbulence, have
essentially the same origin as the random astrometric variations of
phase-referenced sources with respect to the phase center of their calibrators.
In this paper, we present the results of a Monte Carlo study of the astrometric
precision and sensitivity of an interferometric array (a realization of the
Square Kilometre Array, SKA) in phase-referenced and wide-field observations.
These simulations can be extrapolated to other arrays by applying the
corresponding corrections. We consider several effects from the turbulent
atmosphere (i.e., ionosphere and wet component of the troposphere) and also
from the antenna receivers. We study the changes in dynamic range and
astrometric precision as a function of observing frequency, source separation,
and strength of the turbulence. We find that, for frequencies between 1 and 10
GHz, it is possible to obtain images with high fidelity, although the
atmosphere strongly limits the sensitivity of the instrument compared to the
case with no atmosphere. Outside this frequency window, the dynamic range of
the images and the accuracy of the source positions decrease. [...] (Incomplete
abstract. Please read manuscript.)
