  In the present work, we report a comprehensive theoretical study of the $\log
ft$ values for the allowed and forbidden $\beta^-$ decay transitions of
$^{46}$K and $^{47}$K corresponding to recently available experimental data
from the GRIFFIN spectrometer at TRIUMF-ISAC [Phys. Rev. C {\bf 100}, 054327
(2019); Phys. Rev. C {\bf 102}, 054314 (2020)]. We perform the nuclear
shell-model calculation in $sdpf$-valence space, with the SDPF-MU interaction,
to calculate low-lying energy spectra of $^{46,47}$K and $^{46,47}$Ca. For
further investigation, we also calculate spectroscopic properties of
$^{46,47}$K, $^{46,47}$Ca and compare the results with the experimental data.
We suggest spin-parity of several levels, which were previously tentative, in
both the calcium isotopes. Based on the energy and $\log ft$ values, we
conclude that the state at 3.984 MeV in $^{46}$Ca could be either $3^{-}$ or
$2^{+}$ and a state at 4.432 MeV might be $3^{-}$. The spin-parity of the
states at 2.875, 3.951 and 4.453 MeV are predicted to be $1/2^-$, $3/2^-$ and
$1/2^-$ or $1/2^+$, respectively, in $^{47}$Ca. We also give the confirmation
to spin-parity of 2.850, 3.889 and 4.606 MeV states for $^{47}$Ca. Our results
of level schemes of $^{46,47}$K are in a reasonable agreement with the
experimental data, while the agreement of calculated $\log ft$ values for the
$\beta^-$ decay with the experimental data is limited.
