Questions: Lithospheric Cooling and Thermal Evolution of Plates

Question 1

Two oceanic plates are sampled: one is 16 million years old, the other is 64 million years old. According to the half-space cooling model, how do their surface heat flows compare?

• A. The 16 Ma plate has twice the heat flow of the 64 Ma plate
• B. The 64 Ma plate has twice the heat flow of the 16 Ma plate
• C. Their heat flows are equal because both are past the rapid cooling phase
• D. The 16 Ma plate has four times the heat flow of the 64 Ma plate

Answer: (A)

In the half-space model, surface heat flow decreases as 1/√t. For the 16 Ma plate: 1/√16 = 1/4. For the 64 Ma plate: 1/√64 = 1/8. The ratio is (1/4)/(1/8) = 2, so the younger plate has twice the heat flow. The √t scaling governs both heat flow and lithospheric thickness, making age the primary control on thermal structure.

Question 2

Why does the half-space cooling model overpredict both subsidence and heat flow decline for oceanic lithosphere older than about 80 Ma?

• A. The half-space model ignores heat input from the asthenosphere, which prevents indefinite thickening of old plates
• B. Old oceanic lithosphere undergoes radioactive heating that compensates for conductive cooling
• C. The half-space model applies only to continental lithosphere; a different equation governs old oceanic plates
• D. Sediment loading on old plates adds buoyancy that counteracts thermal subsidence

Answer: (A)

The half-space model assumes the lithosphere thickens without limit as cooling progresses. In reality, small-scale convection or heat flux from the underlying asthenosphere limits the thermal boundary layer thickness. The plate model corrects this by imposing a fixed temperature at the base of the lithosphere (~1300°C at ~100–125 km depth), causing heat flow and bathymetry to flatten rather than continue declining at old ages.

Question 3

Mid-ocean ridges stand topographically higher than abyssal plains primarily because young, warm lithosphere is less dense than old, cold lithosphere.

• T. True
• F. False

Answer: True

As oceanic lithosphere cools with age, it contracts and becomes denser. Isostasy requires that denser material sinks lower. Young lithosphere near the ridge is hot and buoyant, so it sits high; old lithosphere far from the ridge is cold and dense, so it subsides to abyssal depths. This is why ocean depth increases as √t with plate age — it's a direct consequence of thermal contraction and isostatic adjustment.

Question 4

The plate model predicts that oceanic lithosphere continues to thicken indefinitely as it ages, but at a progressively slower rate.

• T. True
• F. False

Answer: False

The plate model was specifically developed to correct this prediction of the half-space model. By imposing a fixed temperature boundary at the base of the lithosphere, the plate model predicts that the thermal boundary layer approaches a maximum thickness asymptotically — the lithosphere stops thickening once it reaches thermal equilibrium with the hot asthenosphere beneath. This explains why heat flow and bathymetry flatten for plates older than ~80 Ma.

Question 5

Why does oceanic depth increase as oceanic lithosphere ages, and what is the physical mechanism connecting thermal state to ocean floor depth?

Model answer: As oceanic lithosphere moves away from the mid-ocean ridge, it cools by conduction. Cooler rock is denser than warm rock (thermal contraction). Because the lithosphere floats on the asthenosphere (isostasy), denser lithosphere sinks lower. The half-space model predicts this depth increase follows √t: the thermal boundary layer thickens proportionally to √t, the plate becomes denser, and isostatic equilibrium requires it to sit deeper. This is why the ocean floor is shallow near ridges and deepens progressively toward subduction zones.

The chain is: age → cooling → thermal contraction → increased density → isostatic subsidence → greater ocean depth. The √t dependence emerges because heat diffuses into the plate following the diffusion equation, whose solution for a semi-infinite medium has a characteristic length scale proportional to √(κt), where κ is thermal diffusivity.