The M.S. degree requirement is 30 credit hours (up to 6 credit-hours of directed study included), and the Ph.D. requires a minimum of an additional 18 credit hours of course work and 24 hours of dissertation research. A student seeking a degree in ErSE must specify one track as a major. M.S. students need to complete three core courses of the program; two courses required in each track; and three elective courses. Each course carries 3 credit hours. Ph.D. students need a minimum of 4 courses at the 300 level or above as a part of their degree work.

ErSE 216 – Inverse Problems

ErSE 203 - Continuum Methods for Environmental Physics I

ErSE 303 – Continuum Methods for Environmental Physics II

ErSE 253 – Data Analysis in Geosciences

AMCS 201 – Applied Mathematics I

AMCS 206 – Applied Numerical Methods**Fluid Earth Systems Courses (at least 3 from the list)**

ErSE 201 – Geophysical Fluid Dynamics I

ErSE 301 – Geophysical Fluid Dynamics II

ErSE 224, 305, 306, 308, 307,309 **Solid Earth Systems Courses (at least 3 from the list)**

ErSE 210 – Seismology I

ErSE 211 – Global Geophysics

ErSE 212, 214, 215, 217, 225, 260, 314, 316, 326, 345

In addition to the above, a number of courses from other programs (MarSE, ME, EE, AMCS) may serve as appropriate electives for students in ErSE. Those courses could be taken upon approval by graduate advisor.

Prerequisites: ME 250 and ErSE 120 or consent of instructor. Topics include governing equations of mass and momentum conservation; wave kinematics, dispersion, group velocity; surface and internal gravity waves, shallow water theory; stratified fluids and normal mode analysis; waves in rotating fluids: Kelvin, Poincare and Rossby waves; the Rossby adjustment problem and conservation of potential vorticity; the quasigeostrophic approximation; planetary waves and Charney-Drazin theory; barotropic and baroclinic instability theory.

Prerequisites:, AMCS 201 (or AMCS 199 or ErSE 120) and basic programming skill in MATLAB or consent of instructor. Co-requisite: ErSE 200. Derivation of mathematical models for porous media flow. Development and application of massconservative simulator models of single phase, miscible fluids in porous media. Solution of the pressure equation. Numerical methods for convection diffusion equations.

Prerequisites: ME 260 and ErSE 120 or consent of instructor. Introductory and advanced concepts of seismic wave propagation. Vectors and tensors, Hooke’s law, elastic coefficient tensors, effective media theories, Christoffel equation, group and phase velocities, boundary conditions, representation theorem, seismogram synthesis in layered media, asymptotic methods.

Prerequisites: ME 260 and ErSE 120 or consent of instructor. Co-requisite: ErSE 210. Earth and planets, early history, plate motions, magnetism and sea floor spreading, earthquakes and earth structure, gravity, geochronology, heat flow, mantle convection and earth’s magnetic field.

Prerequisite: ErSE 211. Satellite geodesy, gravimetry, GPS, Interferometric Synthetic Aperture Radar (InSAR), radar altimetry. Plate tectonics and paleomagnetism, plate motions, plate-boundary deformation, seismic cycle, heat flow, basin subsidence, plate-flexure, post-glacial rebound, geoid determination, gravity anomalies, sea-level measurements, tides, earth rotational variations, volcano geodesy.

An introductory course on Seismic exploration covering the basics of seismic waves, seismic data, seismic acquisition, data processing, filters, seismic velocities, and stacking. The course includes an introduction to seismic imaging.

Basic statistics, classical inverse theory, numerical optimization, regularization, global optimization, statistical inverse theory and uncertainty estimation.

Stress and strain, tensor analysis, rheology, brittle vs. ductile deformation, fracture, fault mechanics, friction, stable and unstable sliding, double-couple representation of earthquake sources, moment tensors, coulomb failure stress changes, earthquake triggering, stress drop, Kostrov's summation, comparative seismotectonics

Prerequisites:. Basic Math and statistics, and basic programming skills (Matlab) Time series (filtering, correlation, deconvolution, spectral estimation, regression), processing of two dimensional data, stochastic methods including variogram and covariance analysis and modeling, multipoint estimation, spatial interpolation (kriging), introduction to dynamical interpolation (data assimilation), uncertainty assessment, cross validation.

Prerequisites: Basic Seismology course or consent of instructor. Seismic migration methods are developed. Green's theorem is used to derive Lippmann-Schwinger equation and the following migration methods: phase-shift migration, Fourier Finite Difference migration, Kirchhoff migration, diffraction stack migration, reverse time migration, and F-X migration.

Master-level seminar focusing on special topics within the field.

Master-level supervised research.

Prerequisites: ErSE 201 or consent of instructor. Climate and climate change, large-scale atmospheric and oceanic motions, fine-scale processes. Quasigeostrophic motion of a stratified fluid on a sphere, the equations of motions in spherical coordinates, scaling and asymptotic analysis, potential-vorticity equation. Rossby waves in a stratified fluid, Rossby wave normal modes, vertical structure. Forced stationary waves in the atmosphere, wave-zonal flow interaction. Rossby waves in the two-layer model. Theory of instability, conditions for instability, normal modes, baroclinic instability, barotropic instability, instability of flows with horizontal and vertical shear. Energy and enstrophy, geostrophic turbulence. Numerical models of general circulation of atmosphere, pressure vertical coordinate, linear and nonlinear numerical instabilities.

Prerequisite: ErSE 202. Thermodynamics of pressure, volume, temperature and composition relationships in water, oil or nonaqueous phase liquids and gas mixtures. Modeling compositional and thermal fluids, including streamline flow, fractional flow and both immiscible and miscible flow.

ErSE 306 Ocean Modeling (3-0-3)

ErSE 307 Atmospheric Chemistry (3-0-3)

ErSE 308 Atmospheric Physics (3-0-3)

ErSE 314 Advanced Global Seismology (3-0-3) )

ErSE 316 Geomechanics ll (3-0-3)

**ErSE 324 Parallel Scientific Computing in Earth Sciences (3-0-3)**

Prerequisites: AMCS108 or AMCS206, ErSE 120. Introduction to the basics of modern parallel computing: parallel architectures, message passing, data and domain decomposition, parallel libraries, programming languages, data management and visualization and parallel numerical algorithms. Applications to scientific computing problems in earth sciences and engineering.

Prerequisites:Advanced Seismic Inversion I Codes for waveform tomography, wavepath traveltime tomography, traveltime tomography, least squares migration, and skeletalized inversion are used to help student evaluate limits and benefits of these methods, and extend the frontier of seismic inversion. A term project is required that will be written as a paper, and possibly submitted to a relevant scientific journal.

Programming experience and familiarity with basic discrete and numerical algorithms and experience with one or more computational applications. Case studies of representative and prototype applications in partial differential equations and meshbased methods, particle methods, ray-tracing methods, transactional methods.