Final answer:
Deep ocean trenches are related to deep ocean ridges through the process of plate tectonics, with ridges creating new crust and trenches marking where old oceanic crust is subducted and recycled into the mantle.
Explanation:
Deep ocean trenches and deep ocean ridges are related through the process of plate tectonics. A deep ocean ridge, such as the Mid-Atlantic Ridge, is an underwater mountain range formed by plate separation where new oceanic crust is created by upwelling magma. Meanwhile, a deep ocean trench is a very long, narrow depression in the sea floor that is typically associated with a subduction zone, which is a type of convergent plate boundary.
As an oceanic plate moves away from a mid-ocean ridge, it ages and cools. Eventually, it becomes denser than the underlying asthenosphere and can be subducted into the mantle at a trench. This destroys old crust at roughly the same rate as new crust is formed at mid-ocean ridges, maintaining a balance in Earth's crustal budget.
Therefore, subduction at ocean trenches is directly related to spreading at mid-ocean ridges, with trenches marking zones where old crust is recycled into the Earth's mantle. This is part of the global cycle of crustal recycling that shapes the Earth's surface over geological timescales.