  We prove observability estimates for oscillatory Cauchy data modulo a small
kernel for $n$-dimensional wave equations with space and time dependent $C^2$
and $C^{1,1}$ coefficients using Gaussian beams. We assume the domains and
observability regions are in $\mathbb{R}^n$, and the GCC applies. This work
generalizes previous observability estimates to higher dimensions and time
dependent coefficients. The construction for the Gaussian beamlets solving
$C^{1,1}$ wave equations represents an improvement and simplification over
Waters (2011).
