Where an ocean plate meets another plate head-on, the denser one sinks into the mantle at a subduction zone. Subduction zones make the deepest trenches, the largest earthquakes and chains of explosive volcanoes, all from the same sinking slab.
Why it works
Old ocean lithosphere is cold and dense (oceanic crust about $3.0\,\text{g/cm}^3$, continental about $2.7$), so it sinks beneath a continent or younger ocean plate. As the slab descends it stays cold and brittle, so it breaks in earthquakes far deeper than anywhere else, down to about 700 km. Plotted on a cross-section, those earthquakes trace the slab: a Wadati–Benioff zone. At about 100 km depth, heat and pressure drive water out of the slab's minerals. The water rises into the hot mantle wedge above and lowers its melting point: flux melting. The magma rises to build a volcanic arc.
Key idea
At a subduction zone the denser plate sinks; earthquakes trace the slab hundreds of kilometers down, and water released at about 100 km melts the mantle above it to feed arc volcanoes. The slab's dip sets how far inland the volcanoes stand: distance $= 100\,\text{km} \div \tan(\text{dip})$.
Worked examples
Worked example: Slab dip from earthquakes
Earthquakes 150 km deep lie 200 km inland from the trench. What is the slab's dip?
- $\tan(\text{dip}) = \dfrac{150}{200} = 0.75$.
- Dip $= \tan^{-1}(0.75) \approx 37^\circ$.
Answer: About $37^\circ$.
Worked example: Where are the volcanoes?
A slab dips $30^\circ$. Where do arc volcanoes form?
- Above the point where the slab is about 100 km deep.
- Distance $= \dfrac{100}{\tan 30^\circ} = \dfrac{100}{0.577} \approx 173\,\text{km}$ from the trench.
- A gentler slab puts its volcanoes farther inland; a steeper one brings them closer to the trench.
Answer: About $173\,\text{km}$ from the trench.
Common mistake
It is natural to think the sinking plate melts to make the arc's magma. Mostly it doesn't: the slab is cold and stays solid. The water it gives off lowers the melting point of the mantle above it, and that mantle melts. Check with temperatures: the slab is hundreds of degrees cooler than the mantle around it, which is why it can still break in earthquakes at 600 km.