Unit 4: GPS and infinitesimal strain analysis
These materials have been reviewed for their alignment with the Next Generation Science Standards as detailed below. Visit InTeGrate and the NGSS to learn more.
OverviewStudents use vectors and vector operations to determine the motion of the crust. Students calculate infinitesimal strain and connect the data to regional earthquakes and discuss the need for possible mitigation solutions.
Science and Engineering Practices
Using Mathematics and Computational Thinking: Use mathematical, computational, and/or algorithmic representations of phenomena or design solutions to describe and/or support claims and/or explanations. HS-P5.2:
Developing and Using Models: Develop and/or use a model (including mathematical and computational) to generate data to support explanations, predict phenomena, analyze systems, and/or solve problems. HS-P2.6:
Constructing Explanations and Designing Solutions: Apply scientific reasoning, theory, and/or models to link evidence to the claims to assess the extent to which the reasoning and data support the explanation or conclusion. HS-P6.4:
Analyzing and Interpreting Data: Consider limitations of data analysis (e.g., measurement error, sample selection) when analyzing and interpreting data HS-P4.3:
Analyzing and Interpreting Data: Analyze data using tools, technologies, and/or models (e.g., computational, mathematical) in order to make valid and reliable scientific claims or determine an optimal design solution. HS-P4.1:
Cross Cutting Concepts
Stability and Change: Change and rates of change can be quantified and modeled over very short or very long periods of time. Some system changes are irreversible. HS-C7.2:
Patterns: Mathematical representations are needed to identify some patterns HS-C1.4:
Earth and Human Activity: Analyze and interpret data on natural hazards to forecast future catastrophic events and inform the development of technologies to mitigate their effects. MS-ESS3-2:
Engineering Design: Analyze a major global challenge to specify qualitative and quantitative criteria and constraints for solutions that account for societal needs and wants. HS-ETS1-1:
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This page first made public: Dec 9, 2016
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).
Unit 4 Learning Outcomes
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
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.
- Unit 4 GPS infinitesimal strain analysis presentation (PowerPoint 2007 (.pptx) 3MB Dec7 16)
- Unit 4 Example interseismic data from Japan (PowerPoint 2007 (.pptx) 11.8MB Dec7 16)
- GPS Strain Calculator Results - example from Tohoku Japan interseismic strain (Excel 2007 (.xlsx) 55kB Nov24 16)
- Instructor answer key files include example output calculations for the three different case study sites based on data from November 2016 (Plate Boundary Observatory)
Includes are variety handouts, exercises, and calculators.
- Exercise files
- Unit 4 GPS infinitesimal strain analysis student exercise (Microsoft Word 2007 (.docx) 5.7MB Jan2 18)
Unit 4 GPS infinitesimal strain analysis student exercise PDF (Acrobat (PDF) 6.1MB Jan2 18)
- Unit 4 GPS infinitesimal strain analysis student exercise vector map worksheets (Acrobat (PDF) 3MB Dec27 17)
(Unit 4 Vector map worksheets editable version (pptx) (PowerPoint 2007 (.pptx) 3.2MB Dec27 17))
- GPS strain calculators and supporting document
- Most classes use Excel: GPS Strain Calculator Excel (Excel 55kB Nov18 16)
- Classes with higher computer science skills may choose to use MatLab: GPS Strain Calculator MatLab (Zip Archive 4kB Sep24 15)
- Explanation of GPS Strain Calculator output (Microsoft Word 2007 (.docx) 1.1MB Dec28 17)
Explanation of GPS Strain Calculator output PDF (Acrobat (PDF) 1.1MB Dec28 17)
- Strain ellipse visualization: There is a simple strain ellipse visualizer within the Excel GPS Strain Calculator. However, if you want your students to interact more with exaggerated ellipses, this viewer can help students gain more intuitive understanding of how the numbers relate to specific examples of strain.
- Have students download the Wolfram CDF Player to use the Visualizer (unless your school has Mathematica licenses).
- Strain ellipse visualization tool (Zip Archive 297kB Sep24 15): Inside the zipped file is the CDF file for the Strain Ellipse Visualizer. Have the Wolfram CDF Player open and then open the Visualizer from inside it. This will prevent your computer getting confused about which software to use. It might default to a text editor.
- Earthquake scenario documents
- Cascadia Magnitude 9.0 Scenario (CREW 2013) (Acrobat (PDF) 3.4MB Sep24 15)
- Wasatch Provo Segment Magnitude 7.2 Scenario (HAZUS 2009) (Acrobat (PDF) 16.1MB Sep24 15)
- San Andreas Fault Magnitude 7.8 Scenario (USGS 2008) (Acrobat (PDF) 9.8MB Sep24 15)
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) 842kB Dec7 16) 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 PBO 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 PBO 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.
- Cascadia: This animation on GPS and earthquake early warning simultaneously overviews the tectonics of Cascadia and introduces students to the very societally important concept of earthquake early warning systems (EEW). EEW systems can warn (tens-of-seconds to over a minute in advance) people and infrastructure of imminent shaking after an earthquake rupture begins.
Youtube: GPS and Earthquake Early Warning
MP4 file: GPS and Earthquake Early Warning (MP4 Video 21.7MB Sep30 15)
- Basin and Range: It can help to show this animation about how extension occurs and how GPS can measure it in order to help students
Youtube: Basin and Range-Measuring Extension
MP4 file: Basin and Range-Measuring Extention (MP4 Video 1.9MB Nov17 16)
- All: Although this focuses on the San Andreas, it actually shows tectonic evolution of all three study areas
MP4 file: Western North American tectonics over the last 38 Ma (EMVC) (MP4 Video 11.2MB Dec5 17)
- 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)
Observation of student activity and conversations, individual questioning, and group discussion are excellent ways to conduct formative assessment as the students complete this exercise.
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
0 point = incorrect answer
References and Resources
- Simkin, T., Tilling, R. I., Vogt, P. R., Kirby, S. H., Kimberly, P., and Stewart, D. B., 2006, This dynamic planet: World map of volcanoes, earthquakes, impact craters, and plate tectonics: U.S. Geological Survey Geologic Investigations Series Map I-2800, 1 two-sided sheet, scale 1:30,000,000.
- U.S. Geological Survey, 2006, Quaternary fault and fold database for the United States.
- Cascadia Example
- Chapman, James S., and Melbourne, T., 2009, Future Cascadia megathrust rupture delineated by episodic tremor and slip: Geophysical Research Letters, v. 36, L22301.
- Johnson, Samuel Y., Potter, Christopher J., and Armentrout, John M., 1994, Origin and evolution of the Seattle fault and Seattle basin, Washington: Geology, v. 22, p. 71–74.
- Lidke, D. J., compiler, 2004, Fault number 550, Calawah fault, in USGS Quaternary fault and fold database for the United States.
- Wasatch Example
- Black, B. D., DuRoss, C. B., Hylland, M. D., McDonald, G. N., and Hecker, S., compilers, 2004, Fault number 2351f, Wasatch fault zone, Salt Lake City section, in USGS Quaternary fault and fold database for the United States.
- Chang, W. L. and Smith, R. B., 2002, Integrated seismic-hazard analysis of the Wasatch Front, Utah: Bulletin of the Seismological Society of America, v. 92, p. 1904–1922.
- Elósegui, P., Davis, J. L., Mitrovica, J. X., Bennett, R. A., and Wernicke, B. P., 2003, Crustal loading near Great Salt Lake, Utah: Geophysical Research Letters, v. 30, 1111 doi:10.1029/2002GL016579.
- Hammond, W. C. and Thatcher, W., 2004, Contemporary tectonic deformation of the Basin and Range province, western United States: 10 years of observation with the global positioning system: Journal of Geophysical Research, v. 109, B08403, doi:10.1029/2003JB002746.
- Parsons, T., and Thatcher, W., 2011, Diffuse Pacific-North American plate boundary: 1000 km of dextral shear inferred from modeling geodetic data: Geology, V. 39, p. 943–946.
- San Andreas Example
- Bryant, W. A., and Lundberg, M., compilers, 2002, Fault number 1g, San Andreas fault zone, Cholame-Carrizo section, in USGS Quaternary fault and fold database for the United States.
- Sieh, K. E., and Jahns, R. H., 1984, Holocene activity of the San Andreas Fault at Wallace Creek, California: Geological Society of America Bulletin, V. 95, p. 883–896.