Education Help with Education Geodesy Teaching & Learning Resources Data for Educators Educational Resources GETSI Education Resources Map Tools Web Links DLESE Search

Infinitesimal strain analysis using GPS data:
Module for structural geology or geophysics course

  • Developed by:
    Vince Cronin (Baylor University),
    Shelley Olds (UNAVCO),
    Beth Pratt-Sitaula (UNAVCO),
    Phil Resor (Wesleyan University),
    and Nancy West (UNAVCO) with technical input provided by William Hammond and Corne Kreemer (University of Nevada Reno).
  • Contact: eceunavco.org



Students are able to access and analyze GPS data in order to calculate and interpret ongoing strain in the region between three neighboring GPS stations.



This module was designed for and tested in structural geology courses. However elements of it can also be successfully used in geophysics or tectonics courses or possibly even a physics course seeking practical applications.

Skills and concepts that students must have mastered

Students should be familiar with using Excel or Matlab and should already have had an introduction to the concept of strain.

How the module is
situated in the course

Elements from the module can be used as a single lab activity or extend over several weeks of a course and culminate in research projects/presentations by the students.


Understanding how the Earth's crust deforms is crucial in a variety of geoscience disciplines, including structural geology, tectonics, and hazards assessment (earthquake, volcano, landslide). With the installation of numerous high precision Global Positioning System (GPS) stations, our ability to measure how this deformation (strain) occurs has increased dramatically. Despite its importance to cutting edge geoscience research, GPS data is only rarely investigated in undergraduate courses. Most structural geology courses only cover finite strain (generally through the analysis of deformed fossils), missing the rich opportunity to investigate ongoing strain (infinitesimal strain) now measurable through methods such as GPS. This module introduces geoscience majors to using Plate Boundary Observatory (PBO) GPS data in order to study infinitesimal strain and connect it to broader tectonic settings and hazards.

The premise of the module is to have students work with GPS velocity data from three stations in the same region that form an acute triangle. By investigating how the ellipse inscribed within this triangle deforms, students learn about strain, strain ellipses, GPS, and how to tie these to regional geology and ongoing hazards. The calculations can be done as a "black box" using provided Excel or Matlab calculators (most typical) or students can be asked to do the calculations or coding themselves (see extension section).

Download Materials

Basic module

About one week including lab period and some lecture/class time.

All files bundled

42 MB • v: May 9, 2013

Individual files:

Presentation: Intro to GPS

14 MB • v: Dec 22, 2012

This PowerPoint provides a basic introduction to what GPS is, how it works, and how to start reading and interpreting data output from GPS stations in EarthScope's Plate Boundary Observatory (PBO).

Document: Strain Introduction for instructors

Document: Strain Introduction for students

2 MB • v: May 9, 2013

These documents give a more intuitive introduction to strain than is offered in some structural geology text books and is designed to dovetail with other documents in this module.

Activity: Finding location and velocity data for PBO GPS stations

1 MB • v: May 9, 2013

This short exercise can be done as a homework after a short introduction. The explanation walks students through finding and accessing GPS location and velocity data through the PBO site and plotting the net horizontal velocities. The final pages of the document are data recording sheets.

Presentation: Using triangle of GPS velocities to determine strain

4 MB • v: Mar 20, 2013

This PowerPoint provides a basic introduction to how a triangle of velocities from GPS stations can be used to determine the different components of infinitesimal strain that are occurring in the region between the sites.

Activity: GPS strain analysis

1 MB • v: Jan 11, 2013

Students use a strain calculator to determine the different components of strain at three example sites (Coastal Cascadia, Wasatch Fault, and San Andreas) in the PBO network. Can be done individually or in teams as a class-wide "jig-saw" activity. Site-specific instructor's notes included.

Excel Calculator: Strain within triangle of GPS sites

25 KB • v: Dec 22, 2012

Matlab version

These simple calculators intake GPS station location and velocity data and output components of infinitesimal strain (translation, rotation, extension, etc). Excel version is more "black box" whereas Matlab is better for courses intending to investigate the underlying mathematics and coding process.

Document: Explanation of calculator output

0.5 MB • v: May 9, 2013

This document helps students walk through interpreting the meaning of the calculator output.

One Day Option

One lab period only, emphasizing San Andreas

Activity: GPS and strain on the San Andreas

44 KB • v: Nov 15, 2012

This version was modified from the Basic Module by Anne Egger (Central Washington University) to use in the strike-slip portion of her structural geology course. She reports that the students finished relatively quickly. Next time she will probably integrate a similar use of GPS data into each of the three course sections related to: compressional, extensional, and strike-slip settings or do a "jig-saw" activity similar to the "GPS Strain Analysis Activity" above—either using sites from a variety of different tectonic settings or by having different student groups look at different triangles around the San Andreas. She pulled slides from "Introduction to GPS" and "Using triangle of GPS velocities" presentations to orient the students and then produced this activity document.

Extension Options

Activity: Physical models

0.5 Mb • v: Mar 20, 2013

Students gain an intuitive understanding of a variety of strain and structural geology processes and features. They use simple materials such as stretchy fabric and silly putty to investigate different types of strain and consider the relationship between velocity vectors and strain. When testing the module in his own class, Vince had the students do this activity early in the semester prior the rest of the Basic Module above.

Research Project: Calculating and interpreting strain at student-selected site

33 KB • v: Oct 2012

Students select their own triangle of GPS stations, use the calculator to determine the different components of strain occurring in that location, tie their findings to known regional geology, and present findings in 5-minute presentation. This project is an in-depth summative evaluation that opens the opportunity for class conversations about challenges and benefits of using multiple data sets (ex. GPS data and quaternary fault index). Includes detailed evaluation rubric.

Background Documentation

The following files allow much greater exploration of the back ground theory, math, and computer programing involved in the strain calculations.

Infinitesimal Strain Primer

1.3 MB • v: Sept 2012

This document is intended for a faculty member, graduate student, or advanced undergraduate. It walks the reader through the theory and math behind 1-, 2-, and 3-D analysis of infinitesimal strain.

Algorithm for computing infinitesimal strain

890 KB • v: Sept 2012

Explains the steps needed to generate one's own infinitesimal strain calculator – would be particularly useful if one wants students in an advanced geophysics course to learn the inner workings of the otherwise "black box."

Mathematical review

807 KB • v: Sept 2012

Series of handouts that review the math relevant to strain calculations and GPS data: vectors, matrices, dot product, eigenvalues, and eigenvectors.

Module Development

Funding for this module came from the Plate Boundary Observatory and UNAVCO. Authors are Vince Cronin (Baylor University), Shelley Olds (UNAVCO), Beth Pratt-Sitaula (UNAVCO), Phil Resor (Wesleyan University), and Nancy West (UNAVCO) with technical input provided by William Hammond and Corne Kreemer (University of Nevada Reno).

Last modified: Tuesday, 13-May-2014 02:44:50 UTC


Sponsored by

National Science Foundation Logo National Aeronautics and Space Administration Logo