How Does Surface Deformation at an Active Volcano Relate to Pressure and Volume Change in the Magma Chamber?

Module by Peter LaFemina, Penn State, State College, PA. This cover page by Ali Furmall, University of South Florida, now at University of Oregon.
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This material was originally developed by Spreadsheets Across the Curriculum as part of its collaboration with the SERC Pedagogic Service.


In this Spreadsheets Across the Curriculum activity, students are introduced to the Mogi model of surface deformation and will apply it to volcanic domes. Using Mogi's formulas for horizontal and vertical displacement students can estimate depth to the magma chamber and the pressure conditions within. Using Pearson's chi-squared test, students will compare observed deformation to theoretical values in order to find the most reasonable pressure and depth conditions. This is a self-paced activity in which students follow a PowerPoint presentation to create spreadsheets and graphs using Excel.

Used this activity? Share your experiences and modifications

Learning Goals

Students will:
  • Calculate expected surface deformation for different pressure and depth conditions.
  • Make use of unit conversions involving meters and Pascals.
  • Compare observed deformation to expected deformation to estimate pressure change and depth of magma chamber.
  • Compare observed deformation to expected deformation to estimate volume change and depth of magma chamber.
  • Use Goodness-of-fit (chi-square) to resolve pressure, volume, and depth conditions.
  • Develop a spreadsheet to carry out a calculation.
In the process the students will:
  • Increase their skill at unit conversions.
  • Recognize the relationship between pressure change and volume change within a magma chamber at depth.
  • Consider how surface deformation of a volcano relates to conditions in the associated magma chamber.
  • Learn to value goodness-of-fit for comparing observed data to a model.

Context for Use

Equipment: Each student or pair of students needs a computer with Excel and PowerPoint.

Classes: This module has been used in an Introductory Physical Volcanology course with upper level undergraduates.

In the class, the module was introduced during lab to be completed as homework due the following week. Students turned in hard-copies of the Excel spreadsheets and graphs, as well as their working Excel files. This worked well for junior and senior level students with excellent quantitative skills.

Description and Teaching Materials

PowerPoint SSAC-pv2007.QE522.PL1.1-Student (PowerPoint 1.1MB Dec19 07)

If the embedded spreadsheets are not visible, save the PowerPoint file to disk and open it from there.

This PowerPoint file is the student version of the module.

Teaching Notes and Tips

This module, like the others in this collection, works best if coordinated with lecture and lab material.

If students have difficulty in getting their equations to produce the correct numbers in the orange cells -- especially if their results are off by orders of magnitude -- tell them to check their unit conversions. You cannot ever emphasize unit conversions enough.

Some students jump ahead to the end-of-module assignments without working through the main part of the module carefully. Those students have trouble.


The end-of-module questions can be used for assessment.

The instructor version contains a pre-test

References and Resources

Amelung, F., Jonsson, S., Zebker, H., Segall, P., 2000. Widespread uplift and "trapdoor" faulting on Galapagos volcanoes observed with radar interferometry, Nature, 407, 993-996.

Delaney, P. and McTigue, 1994, Volume of magma accumulation or withdrawal estimated from surface uplift or subsidence, with application to the 1960 collapse of Kilauea volcano, Bull. Volc., 56, 417-424.

Johnson, D., Sigmundsson, F., and Delaney, P., 2000, Comment on "Volume of magma accumulation or withdrawal estimated from surface uplift or subsidence, with application to the 1960 collapse of Kilauea volcano," Bull. Volc., 61, 491-493.

Mogi, K., 1958. Relations between the eruptions of various volcanoes and the deformation of the ground surface around them, Bull. Earthquake Res. Inst., v. 36, 99-134.