Lecture 2: Sea-floor depth, age, and heat flow

• Why do we have ocean basins?
• Mid ocean ridges and the topography of the sea-floor
• Heat transport in the Earth

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.

What are ocean basins?

"We can only sense that in the deep and turbulent recesses of the sea are hidden mysteries far greater than any we have solved." -Rachel Carson, The Sea Around Us, 1957

Ask the class what we know about oceans, list ideas and topics on the board. Move the discussion towards topography and the why of topography.

What are ocean basins?

• Why does this topography exist?
• Crustal thickness.
  • What is crust? Different rocks than mantle, peridotite vs basalt/andesite
  • often defined by Distance to Mohorovičić discontinuity

Mohorovičić discontinuity

What are the differences between lithosphere and asthenosphere and crust and mantle?

• The Moho marks the transition in composition between the Earth's crust and the lithospheric mantle.
• Defined by wave speed:
  • above moho (P-waves) are consistent with those through basalt (6.7–7.2 km/s)
  • below they are similar to those through peridotite or dunite (7.6–8.6 km/s).
  • commonly accepted as the lower limit of the Earth's crust.
  • lith/astheno boundary at mid ocean ridge

Mohorovičić discontinuity

What are the differences between lithosphere and asthenosphere and crust and mantle?

Mohorovičić discontinuity

"Seismic evidence shows that the so-called crustal thickness-depth to the M discontinuity-is 6 km under oceans and 34 km under continents on the average." Gravity data prove that these two types of crustal columns have the same mass-the pressure at some arbitrary level beneath them, such as 40 km, would be the same. They are in hydrostatic equilibrium." -Harry Hess, History of Ocean Basins, 1962

Mohorovičić discontinuity

"Seismic evidence shows that the so-called crustal thickness-depth to the M discontinuity-is 6 km under oceans and 34 km under continents on the average. Gravity data prove that these two types of crustal columns have the same mass-the pressure at some arbitrary level beneath them, such as 40 km, would be the same. They are in hydrostatic equilibrium." -Harry Hess, History of Ocean Basins, 1962

Mohorovičić discontinuity

"Seismic evidence shows that the so-called crustal thickness-depth to the M discontinuity-is 6 km under oceans and 34 km under continents on the average. Gravity data prove that these two types of crustal columns have the same mass-the pressure at some arbitrary level beneath them, such as 40 km, would be the same. They are in hydrostatic equilibrium." -Harry Hess, History of Ocean Basins, 1962



How can we test this assumption?

Testing isostatic equilibrium

"Seismic evidence shows that the so-called crustal thickness-depth to the M discontinuity-is 6 km under oceans and 34 km under continents on the average. Gravity data prove that these two types of crustal columns have the same mass-the pressure at some arbitrary level beneath them, such as 40 km, would be the same. They are in hydrostatic equilibrium." -Harry Hess, History of Ocean Basins, 1962

• Continental crust:
• Mean elevation: 797 m
• Mean thickness: 34 km
• Andesite with density: 2.8 g/cm³

• Density of water: 1 g/cm³

• Oceanic crust:
• Mean elevation: -3686 m
• Mean thickness: 6 km
• Basalt with density: 2.9 g/cm³

What is the density of the mantle in g/cm³?

Testing isostatic equilibrium

The calculation is simplest if we assume compensation depth is the base of the continental crust (instead of the 40 km hypothetical posed by Hess). You should get 3.46 g/cm³ (density of peridotite: 3.1–3.4 g/cm³) using the following mass balance:

$$ \mathrm{ \Delta H_{cc}\rho_{cc} = \Delta H_{w}\rho_{w} + \Delta H_{oc}\rho_{oc} + \Delta H_m\rho_m \\ ~\\ \Delta H_{cc}\rho_{cc} - \Delta H_{w}\rho_{w} - \Delta H_{oc}\rho_{oc} = \Delta H_m\rho_m \\ ~\\ \frac{\Delta H_{cc}\rho_{cc} - \Delta H_{w}\rho_{w} - \Delta H_{oc}\rho_{oc}}{\Delta H_m} = \rho_m \\ ~\\ \Delta H_m = \Delta H_{cc} - \Delta H_{oc} - E_{cc} - E_{oc}\\} $$

where $\Delta H$ is thickness, $E$ is elevation, $\rho$ is density, and the subscripts $w$, $cc$, $oc$, and $m$ correspond to the water in the ocean, the continental crust, the oceanic crust, and the mantle, respectively.

crust_thickness = 34
crust_elevation = 0.797
crust_density = 2.8  # kg/m^3
ocean_thickness = 6
ocean_elevation = -3.686
ocean_density = 2.9  # kg/m^3
water_density = 1
water_thickness = 3.686
mantle_root = crust_thickness - ocean_thickness - (crust_elevation - ocean_elevation)

# crust_thickness*crust_density = water_thickness*water_density + ocean_thickness*ocean_density + 
#                                                                           mantle_density*mantle_root
mantle_density = (
    water_thickness * water_density
    + crust_thickness * crust_density
    - ocean_thickness * ocean_density
) / mantle_root
mantle_density

3.4649827784156138

The topography of the sea-floor

The topography of the sea-floor

The topography of the sea-floor

Consider at least two ways that the topography of the sea-floor (mid-ocean ridges and the increase in depth away from ridges) can be in isostatic equilibrium. Draw a sketch for both.

The topography of the sea-floor

Consider at least two ways that the topography of the sea-floor (mid-ocean ridges and the increase in depth away from ridges) can be in isostatic equilibrium. Draw a sketch for both.

Which model is better at explaining sea-floor topography? Why?

• Heat flow highest at ridge (unlikely to be thicker crust)
• lowest density under the ridge somehow (thermal?)
  • how to make density go up with distance? cooling + transport (convection)

The topography of the sea-floor

"Nevertheless, mantle convection is considered a radical hypothesis not widely accepted by geologists and geophysicists. If it were accepted, a rather reasonable story could be constructed to describe the evolution of ocean basins and the waters within them. Whole realms of previously unrelated facts fall into a regular pattern, which suggests that close approach to satisfactory theory is being attained." -Harry Hess, History of Ocean Basins, 1962

What observations supported this radical hypothesis?

The lithosphere

We can image the crust pretty well, but not the base of the lithosphere

Temperature profile of Earth's lithosphere and upper asthenosphere (sketch first)

Temperature profile of Earth's lithosphere and upper asthenosphere (sketch first)

Temperature profile of Earth's lithosphere and upper asthenosphere (sketch first)

Heat flux (Fourier's law)

The differential form of Fourier's law of thermal conduction shows that the local heat flux density, $q$, is equal to the product of thermal conductivity, $k$, and the negative local temperature gradient, ${\partial T}/{\partial x}$. The heat flux density is the amount of energy that flows through a unit area per unit time.

$$ q = -k \frac{\partial T}{\partial x} $$

How does temperature change over time through conduction?

The diffusion equation: $$ \frac{\partial T}{\partial t} = \frac{\partial q}{\partial x} $$

$$ \frac{\partial T}{\partial t} = -k \frac{\partial^2 T}{\partial x^2} $$

• draw box with flux in and out
• show discrete form where dh/dt = (q1-q2)
• show heat equation (diffusion)

Heat flux (Fourier's law)

• Using your intuition of diffusion, draw some sketches showing:
  • Temperature profile of asthenosphere (1400 $^\circ$C) instantly brought to the surface (0 $^\circ$C)
  • Temperature profile of this asthenosphere after an intermediate time
  • Temperature profile of this asthenosphere after a long time

How does heat flux, $q$, change at the surface in each instance?

• Draw a sketch of a mid ocean ridge, annotating the crust, the lithosphere-asthenosphere boundary, and a few isotherms (temperature contours)

Heat flux observations

Dashed line represents a simple conductive cooling model. What patterns to the misfit do you see?

Younger sea-floor has hydrothermal cooling (lower heat flux than expected). We'll take a closer look at the old sea-floor problem soon!

Under what conditions do you get a steady state solution to the heat equation? What does this solution look like? (draw a profile)

Heat flux observations

Dashed line represents a simple conductive cooling model. What patterns to the misfit do you see?

Younger sea-floor has hydrothermal cooling (lower heat flux than expected). We'll take a closer look at the old sea-floor problem soon!

Under what conditions do you get a steady state solution to the heat equation? What does this solution look like? (draw a profile)

Heat flux observations

Dashed line represents a simple conductive cooling model. What patterns to the misfit do you see?

Younger sea-floor has hydrothermal cooling (lower heat flux than expected). We'll take a closer look at the old sea-floor problem soon!

Under what conditions do you get a steady state solution to the heat equation? What does this solution look like? (draw a profile)

Boundary Layer Model (cooling of an infinite half-space)