# Lithospheric Density

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• Alignment of Learning Goals, Activities, and Assessments
• Pedagogic Effectiveness
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#### Summary

In this Spreadsheets Across the Curriculum activity, students are introduced to the concept of the weighted average through calculation of the density of the layered lithosphere. The module starts by demonstrating how the weighted average is calculated and interpreted from a table of home prices (by size) and a table of university tuition (by residency). These same principles are then applied to the density of the oceanic lithosphere based on its two components: crust and mantle. Since the thickness of the mantle component increases as the oceanic lithosphere ages, students can then calculate how the average density of the oceanic lithosphere changes and compare this value to the density of the underlying asthenosphere. The difference in density determines whether the oceanic lithosphere can descend into the mantle (i.e., be subducted; "sink") or remain on top ("float"). The final tasks of the module ask the students to apply these same principles to the density of oceanic lithosphere that has undergone the basalt-to-eclogite phase transition, and then to the density of the continental lithosphere.

## Learning Goals

### Students will

• Learn how the weighted average is calculated and what it means.
• Use a spreadsheet to compute the weighted average density of the oceanic lithosphere, and see how it changes as the lithosphere ages and thickens.
• Compare the average density of the oceanic lithosphere with that of the underlying asthenosphere to determine if the lithosphere "sinks" or "floats"
• Use the same method to compute the weighted average density of depressed oceanic lithosphere (in which basalt has transformed into eclogite) and the weighted average density of typical continental lithosphere.

### In the process the students will

• Master an important calculation that arises in many contexts.
• Better understand the relationship between the lithosphere, crust, and mantle.
• Develop a sense of magnitude for the density of earth materials. Confront one of the paradoxes of plate tectonics, that oceanic lithosphere can simultaneously float on the surface and sink while subducted.
• Work with real data to perform a calculation important to plate tectonics.

## Context for Use

This module was designed for use in the Hazards of the Earth's Surface service course at USF. It assumes that students are familiar with basic Excel operations, especially the use of relative and absolute cell references and functions. The topic of lithospheric density would also be appropriate in many other geology courses, both introductory and advanced.

## Description and Teaching Materials

• ### Lithospheric Density (PowerPoint 3.4MB May15 12)

Optimal results are achieved with Microsoft Office 2007 or later; the module will function in earlier versions with slight cosmetic compromises. If the embedded spreadsheets are not visible, save the PowerPoint file to disk and open it from there.

The above PowerPoint presentation is the student version of the module. The embedded spreadsheet consists of a template for students on which students complete their work and answer the end-of-module questions, and then turn in for grading. Since this module is designed as a stand-alone resource, instructions for extracting and saving the embedded spreadsheet are included in the PowerPoint presentation.

An instructor version is available by request. The instructor version includes a References & Resources slide and the completed spreadsheet embedded on the last slide. (The instructor version is still being prepared.)

This module is offered in two versions: a traditional SSAC version and a new auto-feedback/graded (AFG) version. The AFG version: (a) provides automatic and immediate feedback to incorrect answers, including formulas; (b) requires students to complete tasks sequentially by not allowing them to advance until they've completed a task perfectly; and (c) automatically computes a grade and encrypts it into a code the students submit to verify successful completion. The files needed for this version can be accessed here .

## Teaching Notes and Tips

This module is constructed to be a stand-alone resource. It can be used as a homework assignment, lab activity, or as the basis of an interactive classroom activity. It has been used as the third module in Hazards of the Earth's Surface, an online service course at USF designed for non-majors, for the last two years. The module assumes that students are familiar with the terms crust, mantle, lithosphere, asthenosphere, basalt, mafic, and ultramafic. The module is a little more difficult than others because it requires students to perform a weighted mean calculation on data arranged both in columns and rows.

The calculations in this module are simplified greatly to make them tractable to students in introductory classes. The densities of the mantle and crust are assumed to be constant at all depths, without any corrections for changes in temperature, pressure, or composition, and have been tweaked slightly to ensure that the oceanic lithosphere "floats" under nearly all conditions (the result obtained from a more rigorous analysis; e.g., Afonso et al., 2007).

## Assessment

There is a slide at the end of the presentation that contains end-of-module questions. The end-of-module questions can be used to examine student understanding and learning gains from the module. The answer key for the end-of-module questions is at the end of the instructor version of the module.

## References and Resources

Afonso, J.C., Ranalli, G., and Fernandez, M., 2007, Density structure and buoyancy of the oceanic lithosphere revisited. Geophysical Research Letters 34 L10302. http://onlinelibrary.wiley.com/doi/10.1029/2007GL029515/full

Ganguly, J., Freed, A.M., and Saxena, S.K., 2009, Density profiles of oceanic slabs and surrounding mantle: integrated thermodynamic and thermal modeling, and implications for the fate of slabs at the 660 km discontinuity. Physics of the Earth and Planetary Interiors 172(3-4), 257-267.

Problem set #3, Isostasy and Ridge Push, by A. Huerta, Central Washington University. http://www.geology.cwu.edu/facstaff/huerta/g456-556/PS/3-isostasy.pdf.