What term describes a string of islands formed by volcanoes along a deep ocean trench?

The term that describes a string of islands formed by volcanoes along a deep ocean trench is "island arc." An island arc is a geological formation that occurs primarily at convergent boundaries, where an oceanic plate subducts beneath another oceanic plate. This subduction leads to the melting of the mantle and the generation of magma, which rises to form volcanic islands. These volcanic islands are typically arranged in a curved or arc-like shape due to the geometry of the subduction process.

In contrast, the other options refer to different geographical features. A continental shelf is a submerged border of a continent that slopes gently and can be found near coastlines. An archipelago is a broader term that encompasses a group of islands, but it does not specifically refer to the formation process related to volcanic activity at ocean trenches. An atoll is a ring-shaped coral reef, island, or series of islets that encircle a lagoon partially or completely, typically formed from coral growth around volcanic islands, but it doesn't arise from the subduction processes that create island arcs.