  We study a variant of the searching problem where the environment consists of
a known terrain and the goal is to obtain visibility of an unknown target point
on the surface of the terrain. The searcher starts on the surface of the
terrain and is allowed to fly above the terrain. The goal is to devise a
searching strategy that minimizes the competitive ratio, that is, the
worst-case ratio between the distance traveled by the searching strategy and
the minimum travel distance needed to detect the target. For $1.5$D terrains we
show that any searching strategy has a competitive ratio of at least
$\sqrt{82}$ and we present a nearly-optimal searching strategy that achieves a
competitive ratio of $3\sqrt{19/2} \approx \sqrt{82} + 0.19$. This strategy
extends directly to the case where the searcher has no knowledge of the terrain
beforehand. For $2.5$D terrains we show that the optimal competitive ratio
depends on the maximum slope $\lambda$ of the terrain, and is hence unbounded
in general. Specifically, we provide a lower bound on the competitive ratio of
$\Omega(\sqrt{\lambda})$. Finally, we complement the lower bound with a
searching strategy based on the maximum slope of the known terrain, which
achieves a competitive ratio of $O(\sqrt{\lambda})$.
