Developing a curricular module for introductory geophysics or structural geology courses to quantify crustal strain using EarthScope PBO GPS velocities

A group from several UNAVCO-member institutions that are engaged in EarthScope research is developing resources that introduce geoscience majors to one important use of GPS geodesy: measuring the current infinitesimal strain rate of the crust. These resources will be tested during the 2012-13 academic year, and will be accessible from the Science Education Resource Center (SERC), UNAVCO and EarthScope websites. Location and velocity data (and their associated uncertainties) from the EarthScope Plate Boundary Observatory (PBO) website are used to solve 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 with vector-field maps are used to help students understand reference frames and visualize how GPS velocity vectors can indicate crustal strain. The meanings of "extension" and "stretch" are developed through illustrations showing the simultaneous deformation of a triangle with a circle inscribed within it. A strain primer, intended to supplement textbook material, is provided for students to develop needed background. Supplemental material about 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, insert data into one of three strain calculators (open-source code in MatLab, 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 tensor (and engineering) shear strain, 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: rigid-body translation and rotation, extension, contraction and strike-slip. With more than 1100 PBO stations to choose from, students can pursue their interests by exploring crustal strain between many possible triplets of GPS stations. We provide suggestions to extend this material (e.g., analysis of larger areas using Delaunay triangles) and offer relevant literature references so that students can learn how these techniques are used in research. An important part of the development of this resource is the attention paid to assessment of student learning. We hope the resources provided to teachers in support of this curricular module will be an exemplar for them in developing other topics throughout their courses. Teachers interested in serving as beta testers are encouraged to contact the authors.