GETSI Teaching Materials >GPS, Strain, and Earthquakes > Unit 4: GPS and infinitesimal strain analysis
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# Unit 4: GPS and infinitesimal strain analysis

## Summary

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. This unit contains the primary infinitesimal strain analysis for the module. After the instructor demonstrates the method using data from Japan, students investigate three different GPS station triangles in three difference tectonic regimes: convergent (U.S. Pacific Northwest), extensional (Wasatch fault, Utah), and strike-slip (San Andreas Fault, California).

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## Learning Goals

### Unit 4 Learning Outcomes × Horizontal velocities of three neighboring GPS stations in the Oregon Coast Range allow for calculation of infinitesimal strain in the region between them.

• Students will be able to use the GPS Strain Calculator to compute how a three-station triangle of GPS stations has rotated, translated, and or strained in relation to a stable reference frame (i.e., in relation to stable North America).
• Students will be able to analyze the tectonic and geological implications of the calculated strain, connect to regional earthquake risks, and develop mitigation strategy proposals.

### Unit 4 Teaching Objectives

• Behavioral: Provide an opportunity for students to learn to use the GPS Strain Calculator and Strain Ellipse Visualization tool.
• Cognitive: Facilitate students' ability to interpret the GPS Strain Calculator output for geologic and tectonic implications.
• Affective: Encourage reflection and analysis of societal impacts of earthquakes.

## Context for Use

This module was designed for structural geology courses but can also be successfully used in geophysics, tectonics, or geohazards courses or possibly even a physics or engineering course seeking practical applications. It can be done at almost any point during the term. The module assumes that students have had a basic physical geology introduction to plate tectonics, faults, and earthquakes. Unit 4 assumes that students know how the use the software for the chosen GPS strain calculator (Excel or MatLab). Unit 4 is the heart of the module—where students actually analyze GPS data to determine infinitesimal strain. Unit 3: Getting started with GPS data is a necessary precursor to Unit 4 so that students know how what GPS data is an how to access it. Unit 6: Applying strain and earthquake hazard analyses to different regions is the summative assessment for the module and gives the students a chance to test their analysis skills on a site of their own choosing.

## Description and Teaching Materials

This unit presents several examples of GPS station triplets for different tectonic environments. These examples are provided as possible "unknown" triplets for students to use in solving the instantaneous strain problem. Three sites are in the United States in different tectonic regimes. Interseismic data from Japan prior to the 2011 Tohoku earthquake is also included so the instructor can walk the students through the analysis process and simultaneously refer back to Unit 1 learning about the Tohoku event and societal impact. There are several ways these example sites can be used: (1) the examples can be approached as a "jigsaw" where students are assigned to work on one or two of the examples and then share their results with teammates and then the class as part of their introduction to strain, (2) all students can do all three sites in the same lab exercise, or (3) the exercise can be done over a longer interval of the course (probably a structural geology course) in association with study of specific tectonic environments (compressional, extensional, strike-slip). More detailed instructor notes are below.

### Student exercise

Includes are variety handouts, exercises, and calculators.

## Teaching Notes and Tips

### More Technical/Quantitative Extensions

• We also provide supporting math materials in Unit 2 for instructors interested in having student take the quantitative analysis to a deeper level. These include vector, matrices, and infinitesimal strain analysis background.
• If an instructor wishes to have the students actually develop and code their own GPS Strain Calculator, GPS Strain Triangle Algorithm (Microsoft Word 2007 (.docx) 745kB Oct3 23) walks through the necessary steps need to complete the algorithm. The coding could be done in a variety of software (for example, MatLab or Mathematica).

### Tips and Notes

• Olympic Peninsula station P401 is co-located with two other newer stations (P815 and P816) because NOTA is testing the stability of different GPS monuments. You can use any of the three stations for the exercise, but because P401 has the longest record, it is recommended. Sometimes it can be challenging to "see" P401 using the map function because P816 appears on top of it. Students can use the search function on the main NOTA network page to directly search for P401.
• Similarly, San Andreas station P541 is located near borehole strainmeters B900 and B905, so one needs to zoom in fairly fair to see all three instruments separately on the map if you are using the map that shows more instruments than just the GPS stations.
• Students often need some review (or introduction for the first time) to the geology of the case study sites. Generally, they are familiar with the San Andreas Fault, but knowledge of Cascadia and Basin and Range is more spotty. Some existing videos can help.
• It can also help to bring out the stretchy fabric from Unit 2 to give students a chance to tangibly see the types of strain being calculated.
• If you are ever interested in having students generate vector maps for other GPS stations besides the ones featured in this module, you can use this Adobe Illustrator file as a starting point. GPS Triangle Vector Map (Adobe Illustrator) (Zip Archive 2.2MB Nov18 16)

## Assessment

### Formative Assessment:

Observation of student activity and conversations, individual questioning, and group discussion are excellent ways to conduct formative assessment as the students complete this exercise.

### Summative Assessment:

The student exercise is the summative assessment for this unit. Many of the questions have definite right or wrong answers. To receive full credit, students must show their work, where appropriate. Where an open-ended answer is required, students are assessed based on a simple 2-point system.
2 points = correct answer with thorough supporting evidence and/or complete description
1 point = answer not completely correct or lacking thorough supporting evidence or description