  We study curvature invariants in a binary black hole merger. It has been
conjectured that one could define a quasi-local and foliation independent black
hole horizon by finding the level--$0$ set of a suitable curvature invariant of
the Riemann tensor. The conjecture is the geometric horizon conjecture and the
associated horizon is the geometric horizon. We study this conjecture by
tracing the level--$0$ set of the complex scalar polynomial invariant,
$\mathcal{D}$, through a quasi-circular binary black hole merger. We
approximate these level--$0$ sets of $\mathcal{D}$ with level--$\varepsilon$
sets of $|\mathcal{D}|$ for small $\varepsilon$. We locate the local minima of
$|\mathcal{D}|$ and find that the positions of these local minima correspond
closely to the level--$\varepsilon$ sets of $|\mathcal{D}|$ and we also compare
with the level--$0$ sets of $\text{Re}(\mathcal{D})$. The analysis provides
evidence that the level--$\varepsilon$ sets track a unique geometric horizon.
By studying the behaviour of the zero sets of $\text{Re}(\mathcal{D})$ and
$\text{Im}(\mathcal{D})$ and also by studying the MOTSs and apparent horizons
of the initial black holes, we observe that the level--$\varepsilon$ set that
best approximates the geometric horizon is given by $\varepsilon = 10^{-3}$.
