# Thermal Evolution of the Oceanic Lithosphere

#### Summary

The goal of this problem set is to evaluate the thermal evolution of the oceanic lithosphere. As discussed in class, temperature in the oceanic upper mantle is well described by a half-space cooling model, in which a thermal boundary layer grows with time as the oceanic plate drifts away from the ridge axis. This results in systematic changes in seafloor bathymetry and heat flow as the oceanic lithosphere thickens away from the ridge axis. In this exercise the students will determine how well the half-space cooling model predicts seafloor bathymetry in the Atlantic ocean basin.

## Learning Goals

The goal of the exercise is for students to gain experience comparing models with data. Specifically, the students take an simple analytic model for half-space cooling and plot its predictions for mantle temperature and seafloor subsidence. They then take real seafloor bathymetry data and determine how well it compares to this simple model. The later step also exposes students to the challenges of handling real datasets. Matlab is advantageous for this exercise because of the Mapping Toolbox, which is extremely useful for manipulating and visualizing geographical datasets.

## Context for Use

This is a problem set for an introductory graduate-level course on Geologic Oceanography that is taught at Woods Hole Oceanographic Institution. Class size is typically 5-10 students. Before the problem set is assigned, the half-space cooling model will have been covered in class — so all necessary equations will be available from their class notes. Most of our students have used Matlab to some degree before taking the course, though others may be learning it for the first time.

## Description and Teaching Materials

Problem Set: Thermal Evolution of the Oceanic Lithosphere

The goal of this problem set is to evaluate the thermal evolution of the oceanic lithosphere. As discussed in class, temperature in the oceanic upper mantle is well described by a half-space cooling model, in which a thermal boundary layer grows with time as the oceanic plate drifts away from the ridge axis. This results in systematic changes in seafloor bathymetry and heat flow as the oceanic lithosphere thickens away from the ridge axis.

Use the half-space cooling model to calculate temperature in the upper 100 km of the oceanic upper mantle as a function of plate age. Assume a mantle potential temperature of 1350ºC, a surface temperature of 0ºC, and a thermal diffusivity of 1 mm2/s. Make a plot showing mantle temperature contoured in 100ºC intervals from 0–100 km depth and for plate ages of 0–150 Myr.

Plot the predicted seafloor bathymetry from the half-space cooling model as a function of distance from the ridge axis assuming a spreading half-rate of 1.25 cm/yr (appropriate for the Mid-Atlantic Ridge).

Next, compare this predicted bathymetry with actual seafloor bathymetry data. Using Matlab's etopo.m function load the global ETOPO5 bathymetric dataset. This will create a 2160 x 4320 size array containing an elevation value located every 5" globally. Extract a bathymetric profile across the Mid-Atlantic Ridge from the ETOPO dataset. This can be accomplished by first creating an array of latitude and longitude pairs along a great circle path from the Mid-Atlantic Ridge axis to eastern margin of North America using track2.m and then interpolating the bathymetry along this track using interp2.m. Finally, calculate the distance between these points in kilometers (using deg2km.m) and plot the data as a function of distance from the ridge axis. Note that it will be necessary to remove the depth of the ridge axis in order to facilitate comparison with the predictions from the half-space cooling model.

Comparing the model predictions to the seafloor bathymetry data determine where the half-space cooling model is a good fit to the observed bathymetry. Where is the model not such a good fit. Discuss the possible causes for these discrepancies.

The goal of this problem set is to evaluate the thermal evolution of the oceanic lithosphere. As discussed in class, temperature in the oceanic upper mantle is well described by a half-space cooling model, in which a thermal boundary layer grows with time as the oceanic plate drifts away from the ridge axis. This results in systematic changes in seafloor bathymetry and heat flow as the oceanic lithosphere thickens away from the ridge axis.

Use the half-space cooling model to calculate temperature in the upper 100 km of the oceanic upper mantle as a function of plate age. Assume a mantle potential temperature of 1350ºC, a surface temperature of 0ºC, and a thermal diffusivity of 1 mm2/s. Make a plot showing mantle temperature contoured in 100ºC intervals from 0–100 km depth and for plate ages of 0–150 Myr.

Plot the predicted seafloor bathymetry from the half-space cooling model as a function of distance from the ridge axis assuming a spreading half-rate of 1.25 cm/yr (appropriate for the Mid-Atlantic Ridge).

Next, compare this predicted bathymetry with actual seafloor bathymetry data. Using Matlab's etopo.m function load the global ETOPO5 bathymetric dataset. This will create a 2160 x 4320 size array containing an elevation value located every 5" globally. Extract a bathymetric profile across the Mid-Atlantic Ridge from the ETOPO dataset. This can be accomplished by first creating an array of latitude and longitude pairs along a great circle path from the Mid-Atlantic Ridge axis to eastern margin of North America using track2.m and then interpolating the bathymetry along this track using interp2.m. Finally, calculate the distance between these points in kilometers (using deg2km.m) and plot the data as a function of distance from the ridge axis. Note that it will be necessary to remove the depth of the ridge axis in order to facilitate comparison with the predictions from the half-space cooling model.

Comparing the model predictions to the seafloor bathymetry data determine where the half-space cooling model is a good fit to the observed bathymetry. Where is the model not such a good fit. Discuss the possible causes for these discrepancies.

## Teaching Notes and Tips

## Assessment

The problem set is a graded assignment.