Lecture 3: Sea-floor depth, age, and heat flow¶
- Mid ocean ridges and the topography of the sea-floor
- Boundary layer model
- Plate model
- How do we map the seafloor today?
We acknowledge and respect the lək̓ʷəŋən peoples on whose traditional territory the university stands and the Songhees, Esquimalt and W̱SÁNEĆ peoples whose historical relationships with the land continue to this day.
Boundary Layer Model (cooling of an infinite half-space)¶
Boundary Layer Model (cooling of an infinite half-space)¶
If the sea-floor gets deeper away from a mid-ocean ridge, is the lithosphere density higher or lower than the asthenosphere?
Boundary Layer Model (cooling of an infinite half-space)¶
If the sea-floor gets deeper away from a mid-ocean ridge, is the lithosphere density higher or lower than the asthenosphere?
- Calculate the thickness of the lithosphere
- at 0 Ma (3 km bathymetry)
- at 20 Ma (4 km bathymetry)
- at 50 Ma (5 km bathymetry)
- Using the following densities:
- Cool peridotite (lithosphere): 3400 kg/m$^3$
- Hot peridotite (asthenosphere): 3300 kg/m$^3$
- Water: 1000 kg/m$^3$
Boundary Layer Model (cooling of an infinite half-space)¶
The dashed line is the predicted topography of the sea-floor using the diffusion equation and measured thermal conductivities of mantle material. Why do you think the model fails for older crust?
The denser lithosphere thickness stops increasing (maximum plate thickness). Why?
The denser lithosphere thickness stops increasing (maximum plate thickness). Why?
Plate model¶
"A more realistic model is developed here, based on the idea that the thermal structure of the plate becomes unstable and leads to the development of small-scale convection. Convective heat transport then supplies the heat flux needed to match the observations rather than an artificial constant temperature boundary condition. The temperature dependence of the rheology is represented in a simple manner. Below a given temperature the material is assumed to move rigidly, defining an upper mechanical boundary layer. Beneath this rigid layer, where the temperatures are greater, the material is assumed to have a constant Newtonian viscosity. The part of the viscous region where there are significant vertical temperature gradients, immediately below the mechanical boundary layer, forms a thermal boundary layer. As the plate cools, both the mechanical and thermal boundary layers increase in thickness. A local critical Rayleigh number criterion is used to test the stability of the thermal boundary layer. On this basis a convective instability is predicted, its occurrence coinciding with the breakdown of the linear dependence of the depth of the ocean floor on the square root of age."
Parsons and McKenzie, Mantle Convection and the Thermal Structure of the Plates, 1978
Plate model¶
"A more realistic model is developed here, based on the idea that the thermal structure of the plate becomes unstable and leads to the development of small-scale convection. Convective heat transport then supplies the heat flux needed to match the observations rather than an artificial constant temperature boundary condition. The temperature dependence of the rheology is represented in a simple manner. Below a given temperature the material is assumed to move rigidly, defining an upper mechanical boundary layer. Beneath this rigid layer, where the temperatures are greater, the material is assumed to have a constant Newtonian viscosity. The part of the viscous region where there are significant vertical temperature gradients, immediately below the mechanical boundary layer, forms a thermal boundary layer. As the plate cools, both the mechanical and thermal boundary layers increase in thickness. A local critical Rayleigh number criterion is used to test the stability of the thermal boundary layer. On this basis a convective instability is predicted, its occurrence coinciding with the breakdown of the linear dependence of the depth of the ocean floor on the square root of age."
Parsons and McKenzie, Mantle Convection and the Thermal Structure of the Plates, 1978
Plate model¶
"A more realistic model is developed here, based on the idea that the thermal structure of the plate becomes unstable and leads to the development of small-scale convection. Convective heat transport then supplies the heat flux needed to match the observations rather than an artificial constant temperature boundary condition. The temperature dependence of the rheology is represented in a simple manner. Below a given temperature the material is assumed to move rigidly, defining an upper mechanical boundary layer. Beneath this rigid layer, where the temperatures are greater, the material is assumed to have a constant Newtonian viscosity. The part of the viscous region where there are significant vertical temperature gradients, immediately below the mechanical boundary layer, forms a thermal boundary layer. As the plate cools, both the mechanical and thermal boundary layers increase in thickness. A local critical Rayleigh number criterion is used to test the stability of the thermal boundary layer. On this basis a convective instability is predicted, its occurrence coinciding with the breakdown of the linear dependence of the depth of the ocean floor on the square root of age."
Parsons and McKenzie, Mantle Convection and the Thermal Structure of the Plates, 1978
As the plate cools, both the mechanical and thermal boundary layers increase in thickness¶
What exactly is this thermal boundary layer?¶
"A local critical Rayleigh number criterion is used to test the stability of the thermal boundary layer. On this basis a convective instability is predicted, its occurrence coinciding with the breakdown of the linear dependence of the depth of the ocean floor on the square root of age."
Parsons and McKenzie, Mantle Convection and the Thermal Structure of the Plates, 1978
- Rayleigh number describes how heat is transferred in a material with non-uniform density (often due to temperature differences, ie a function of $\Delta T$)
- Low Rayleigh number: conduction
- High Rayleigh number: convection
Parsons and McKenzie are specifically describing a layer near the lithosphere-asthenosphere boundary where the combined viscosity contrasts and temperature contrasts lead to small scale convection.
Thermal boundary layers¶
What exactly is this thermal boundary layer?
Thermal boundary layers¶
What exactly is this thermal boundary layer?
Thermal boundary layers¶
What exactly is this thermal boundary layer?
Thermal boundary layers¶
How does this thermal instability effect plate (lithosphere) thicknesses?
Does convection increase or decrease heat flux rates?
Higher heat flux to the base of the lithosphere after the instability forms, resulting in a near constant temperature at the base of the lithosphere (the instability delivers heat as fast as conductive cooling above can remove it, a steady state).
Recall our drawings of thermal profiles earlier, how does a fixed boundary condition at 100 km change the temperature profile in the lithosphere?
Mapping the sea-floor¶
Mapping the sea-floor¶
How do we map the bathymetry of the sea-floor?
- A combination of:
- Depth Soundings
- Satellite Altimetry
Bathymetric Prediction From SEASAT Altimeter Data (Dixon et al. 1983)¶
Bathymetric Prediction From SEASAT Altimeter Data (Dixon et al. 1983)¶
Gravitational potential¶
Gravitational potential is the the work (energy transferred) per unit mass that would be needed to move an object to that point from a distance infinitely far away. Recall that: $\mathrm{work = force~\times~displacement}$
The acceleration due to gravity is constant along an equipotential surface. One such surface on Earth is commonly referred to as the geoid. What is the geoid?
The geoid (a model) is the ocean surface elevation if winds and tides were absent.