  In this paper, we calculate the differential transverse momentum and
azimuthal decorrelation cross sections,
$\mathrm{d}\sigma_{t\bar{t}}/\mathrm{d}q_{\mathrm{T}}$ and
$\mathrm{d}\sigma_{t\bar{t}}/\mathrm{d}\Delta\phi_{t\bar{t}}$, in top-antitop
pair production at the LHC up to NNLL$+$NNLO accuracy. Due to the emergence of
Coulomb singularities in both the hard sector and the corresponding anomalous
dimension as the relative $t\bar{t}$ pair velocity, $\beta_{t\bar{t}}$,
approaches zero, extrapolating the soft-collinear resummation that is derived
in the domain where the top and antitop quarks are kinematically well-separated
into the full phase space is not trivial. Focussing on two observables that are
insensitive to azimuthal asymmetric divergences, $q_{\mathrm{T}}$ and
$\Delta\phi_{t\bar{t}}$, we will demonstrate that a literal application of a
SCET$+$HQET based resummation onto
$\mathrm{d}\sigma_{t\bar{t}}/\mathrm{d}q_{\mathrm{T}}$ and
$\mathrm{d}\sigma_{t\bar{t}}/\mathrm{d}\Delta\phi_{t\bar{t}}$ is only possible
up to NLL accuracy. Starting at NNLL, however, such a na\"ive procedure will
develop power-like divergences in $\beta_{t\bar{t}}$ in the threshold regime.
To this end, two prescriptions, dubbed the D- and R-schemes, are introduced to
facilitate the extrapolation of the resummation framework from the
well-separated region where $\beta_{t\bar{t}}\sim\mathcal{O}(1)$ to the
threshold regime $\beta_{t\bar{t}}\to0$, enabling us to compute
$\mathrm{d}\sigma_{t\bar{t}}/\mathrm{d}q_{\mathrm{T}}$ and
$\mathrm{d}\sigma_{t\bar{t}}/\mathrm{d}\Delta\phi_{t\bar{t}}$ at NNLL$+$NNLO
accuracy throughout. Further, by comparing the results of both formulations, we
can assess the theoretical uncertainty caused by the truncation of the
Coulomb-enhanced terms in the perturbative series.
