  Measuring and calibrating relations between cluster observables is critical
for resource-limited studies. The mass-richness relation of clusters offers an
observationally inexpensive way of estimating masses. Its calibration is
essential for cluster and cosmological studies, especially for high-redshift
clusters. Weak gravitational lensing magnification is a promising and
complementary method to shear studies, that can be applied at higher redshifts.
We employed the weak lensing magnification method to calibrate the
mass-richness relation up to a redshift of 1.4. We used the Spitzer Adaptation
of the Red-Sequence Cluster Survey (SpARCS) galaxy cluster candidates
($0.2<z<1.4$) and optical data from the Canada France Hawaii Telescope (CFHT)
to test whether magnification can be effectively used to constrain the mass of
high-redshift clusters. Lyman-Break Galaxies (LBGs) selected using the $u$-band
dropout technique and their colours were used as a background sample of
sources. LBG positions were cross-correlated with the centres of the sample of
SpARCS clusters to estimate the magnification signal measured for cluster
sub-samples, binned in both redshift and richness. We detected a weak lensing
magnification signal for all bins at a detection significance of
2.6-5.5$\sigma$. In particular, the significance of the measurement for
clusters with $z>1.0$ is 4.1$\sigma$; for the entire cluster sample we obtained
an average M$_{200}$ of $1.28^{+0.23}_{-0.21}$ $\times 10^{14} \,
\textrm{M}_{\odot}$. Our measurements demonstrated the feasibility of using
weak lensing magnification as a viable tool for determining the average halo
masses for samples of high redshift galaxy clusters. The results also
established the success of using galaxy over-densities to select massive
clusters at $z > 1$. Additional studies are necessary for further modelling of
the various systematic effects we discussed.
