## Curricular module for introductory geophysics or structural geology courses to quantify crustal strain using EarthScope PBO GPS velocities Abstract

### abstract

• We have developed resources that introduce geoscience majors to an important use of GPS geodesy – measuring the current infinitesimal strain rate of the crust. These resources were developed and tested during the 2012-13 academic year and are posted to the UNAVCO website (http://www.unavco.org/edu_outreach/resources/gps-strain/majors-gps-strain/majors-gps-strain.html) Location and velocity data (and their associated uncertainties) from the EarthScope Plate Boundary Observatory (PBO) website are used as input to a perfectly constrained problem involving the infinitesimal strain of a triangle defined by three PBO GPS sites. Simple physical models made of inexpensive materials are used to build student intuition about homogeneous strain of a continuum. Introductory exercises using vector-field maps are used to help students understand reference frames and visualize how GPS velocities relate to crustal strain. The meanings of "extension" and "stretch" are developed through illustrations showing the simultaneous deformation of a triangle with a circle within it. A strain primer, intended to supplement textbook material, is provided for students and faculty to develop needed background. Supplemental materials on vectors, vector dot products, matrix mathematics, determinants, and computation of the eigensystem of a symmetric square matrix help support students who have gaps in their mathematical background. Students compute site velocities and uncertainties from PBO data, input data into one of three strain calculators (open-source code in MatLab and Mathematica and an Excel spreadsheet), and learn to interpret the output. A complete algorithm and worked example are also provided so that capable students can develop their own code to solve the problem. Strain calculator output includes the mean translation velocity vector, the rotational velocity, the relative magnitudes and directions of the horizontal infinitesimal strain axes, the maximum shear strain (tensor and engineering), the area strain (dilation), the invariants of the strain tensor, and associated uncertainties. We provide several example triplets of GPS stations that illustrate different crustal-strain environments, such as extensional, contractional and strike-slip deformation. With more than 1100 PBO stations to choose from, the possibilities for student exploration of areas that interest them are extensive. We provide suggestions to extend this material (e.g., possible research project in which students research other GPS triangles of interest) and offer relevant literature references for students to learn how these techniques are used in research.

• 2014