  We explore the usage of boosted as well as semi-boosted topologies in
all-hadronic $t\bar{t}$ final states in simulated $pp$ collisions at $\sqrt{s}
= 14\,$TeV, with top quarks decaying into a boosted hadronic top-jet or a
$W$-jet and an isolated $b$-jet. Correlations between selected kinematic
variables and their shapes are studied for scalar and vector resonances
decaying to a pair of top quarks, and also for a models of
$t\bar{t}$-associated production with an invisible dark matter particle pair.
Stacked signal$+$background samples have been investigated in terms of the
ability to resolve an excess of events over the Standard Model background in
terms of the $t\bar{t}$ invariant mass, top quark transverse momentum and other
1D and 2D spectra using a parameterized detector simulation. A 2D extension of
the BumpHunter algorithm is proposed, resulting in an improved signal
sensitivity in specific 2D areas. We identify the most promising variables with
the largest signal significance and smaller sensitivity to experimental
uncertainties realated to the jet energy calibration. We compare to statistical
tests computing the background-only hypothesis compatibility and a likelihood
fit of the signal strength.
