  The optimal source-finding strategy for linear polarization data is an
unsolved problem, with many inhibitive factors imposed by the
technically-challenging nature of polarization observations. Such an algorithm
is essential for Square Kilometre Array (SKA) pathfinder surveys, such as the
Multifrequency Snapshot Sky Survey (MSSS) with the LOw Frequency ARray (LOFAR),
as data volumes are significant enough to prohibit manual inspection. We
present a new strategy of `Faraday Moments' for source-finding in linear
polarization with LOFAR, using the moments of the frequency-dependent
full-Stokes data (i.e. the mean, standard deviation, skewness, and excess
kurtosis). Through simulations of the sky, we find that moments can identify
polarized sources with a high completeness: 98.5% at a signal-to-noise of 5.
While the method has low reliability, Rotation Measure (RM) Synthesis can be
applied per candidate source to filter out instrumental and spurious
detections. This combined strategy will result in a complete and reliable
catalogue of polarized sources that includes the full sensitivity of the
observational bandwidth. We find that the technique can reduce the number of
pixels on which RM Synthesis needs to be performed by a factor of
$\approx1\times10^{5}$ for source distributions anticipated with modern radio
telescopes. Through tests on LOFAR data, we find that the technique works
effectively in the presence of diffuse emission. Extensions of this method are
directly applicable to other upcoming radio surveys such as the POlarization
Sky Survey of the Universe's Magnetism (POSSUM) with the Australia Square
Kilometre Array Pathfinder (ASKAP), and the SKA itself.
