Inverse Methods in Geophysics (CERI 7260/8260, CIVL 7128/8128) – S2020, 2021, 2022, S2023, S2024, S2025;

This course provides the basic knowledge behind inverse theory applied to geophysics. We learn to combine observations (data) with linear and non-linear inverse methods to estimate model parameters and assess their quality. To do that, we will derive and discuss the fundamental mathematical expressions and, at the same time, learn how to solve an inverse problem using MATLAB® numerically. Topics discussed in class include implicit and explicit linear forms, random variables and probabilities, probability density functions, variance-covariance matrix, measures of length (norms), least squares solution, minimum length solution, weighted damped least squares solution, Lagrange multipliers and linear constraints, model and data resolution matrices, Singular Value Decomposition (SVD), factor analysis, linearization of non-linear problems, non-linear problems, Grid Search, Newton method, Gradient method, Monte Carlo, Simulated Annealing, Genetic Algorithm, and other topics.

Seismotectonics – F2020; F2022;

Synthesis of earthquakes, geophysics, seismic, geodetic, and geologic data to deduce the tectonic framework of both seismically active plate boundaries and intraplate seismic zones. Evolution of plate boundaries over time. Seismic and space-based geodetic techniques will be emphasized. During the course, we will examine the integration of geologic and geophysical data, focused on seismology and geodesy, into the paradigm of Plate Tectonics. At the end of the course, students will be able to describe the three principal types of earthquakes, their relationship to the tectonic forces that cause them, and their geological consequences; describe the three types of plate boundaries and the types of forces, earthquakes, and tectonic systems associated with each;  analyze seismic, geodetic, and geologic data to build a coherent model for the observed data and tectonic structures across those scales.

Geodynamics Applications – F2021; F2023

The course focuses on applications of the finite element method in modeling earthquake-related processes (e.g., coseismic deformation) and the numerical representation of the corresponding tectonic environments (e.g., subduction zones). We will learn how to implement complex boundaries (e.g., irregular fault interfaces and topographic surface), material heterogeneities (e.g., tomographic data), and different rheologic models (e.g., viscoelastic relaxation) in the modeling of active fault systems. We will use advanced finite element meshing tools (e.g., Trelis) and open-source finite element codes (e.g., Defmod) available to numerical modelers and the academic community. The class includes lectures and a computer lab, where the students build their models. Each student will develop a final project using the methods learned in class.

Exploring Geology/Earthquakes via Virtual Reality (HH Honors College) – F2022; F2024

Visualizing objects and physical processes in 3D is a difficult task. In the specific case of geosciences, most people are probably familiar with regular two-dimensional maps, but have difficulties in visualizing 3D objects on two-dimensional media such as a computer screen or paper. Virtual Reality (VR) and 3D Printing are the ideal tools to fill that gap and improve communication between the public and geoscientists. In this forum we are discussing how to use Virtual Reality and 3D printing to represent scientific data with primary focus to geologic processes and earthquakes. The VR experience will also include the visualization of time-dependent tectonic processes, like earthquake ruptures and historic seismicity. Furthermore, students will be encouraged to select a topic and build their own project. State of the art VR systems (laptops + goggles) will be made available during class to forum participants.