# ErSE Program Courses

*Core Courses (choose at least 4, one AMCS course is mandatory):*

**ErSE 204/304 -**Geophysical Continuum Mechanics

**ErSE 211 -**Global Geophysics

**ErSE 213/313 -**Inverse Problems

**ErSE 253**- Data Analysis in Geosciences

**AMCS 206 -**Applied Numerical Methods

or

**AMCS 231**- Applied Partial Differential Equations Ior

**AMCS 251 -**Numerical Linear Algebraor

**AMCS 252 -**Numerical Analysis of Differential Equations*Fluid Earth Systems Courses*

**ErSE 201 -**Geophysical Fluid Dynamics I

**ErSE 202 -**Computational Groundwater Hydrology

**ErSE 209/309 -**Thermodynamics of Subsurface Reservoirs

**ErSE 301 -**Geophysical Fluid Dynamics II

**ErSE 303 -**Numerical Methods of Geophysics

**ErSE 305 -**Multiphase Flows in Porous Media

**ErSE 306 -**Ocean Physics and Modeling

**ErSE 307 -**Atmospheric Chemistry and Transport

**ErSE 308 -**Atmospheric Physics and Modeling

**ErSE 324 -**Parallel Scientific Computing in Earth Sciences

**ErSE 353 -**Data Assimilation

**ErSE 390 -**Special Topics in Earth Science

**ErSE 395 -**Internship

**CBE 202 -**Transport Phenomena

**ME 200a -**Fluid Mechanics

**ME 305 -**Computational Fluid Dynamics

*Solid Earth Systems Courses*

**ErSE 210 -**Seismology I

**ErSE 212 -**Geophysical Geodesy and Geodynamics

**ErSE 214 -**Seismic Exploration

**ErSE 215 -**Geomechanics I

**ErSE 217 -**Seismotectonics

**ErSE 218 -**Geophysical Field Methods

**ErSE 225 -**Physical Fields Methods in Geophysics l

**ErSE 260 -**Seismic Imaging

**ErSE 310 -**Seismology II

**ErSE 315 -**Geomechanics II

**ErSE 324 -**Parallel Scientific Computing in Earth Sciences

**ErSE 325 -**Physical Fields Methods in Geophysics ll

**ErSE 328 -**Advanced Seismic Inversion I

**ErSE 329 -**Advanced Seismic Inversion II

**ErSE 345 -**Seismic Interferometry

**ErSE 360 -**Mathematical methods for seismic imaging

**ErSE 390 -**Special Topics in Earth Science

**ErSE 395 -**Internship

#### Course Descriptions

**ErSE 201**

**Geophysical Fluid Dynamics I (3‐0-3)**

**Prerequisite**

*ErSE 204 or consent of instructor*

Introductory description of the Erath’s climate system, governing equations of mass and momentum conservation, equation of state, thermodynamic equation, wave kinematics, dispersion, group velocity, sound waves, gravity waves, effect of rotation, equations of motion in spherical coordinates, primitive equations, Bussiness approximation, changing vertical coordinate, asymptotic analysis and scaling, geostrophic balance, thermal wind, static instability, boundary layers in atmosphere and ocean.

**ErSE 202**

**Computational Groundwater Hydrology (3-0‐3)**

**Prerequisite**

*Basic programming skill in MATLAB or consent of instructor.*

**Co-requisites**

*ErSE 204*

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.

**ErSE 204/304**

**Geophysical Continuum Mechanics (3-0‐3)**

**Prerequisite**

*AMCS 231 or consent of Instructor*

The course provides physical background foundation and overview of mathematical continuum models of geophysics. The goal of the course is to allow students to learn modeling ideas and utilize them in simulation. The course will include a basic introduction to finite difference and finite element methods and their application to continuum modeling and simulation. Topics discussed include: brief introduction to Cartesian tensors, their calculus and algebra; deformations and strain measures; balance laws and equations of motion; thermodynamical relations and constraints; mixture theory and phase change (200‐level for Master students, 300‐level for Ph.D. students with more home and project work).

**ErSE 209/309**

**Thermodynamics of Subsurface Reservoirs (3-0-3)**

This course covers the fundamental laws of thermodynamics and their applications to subsurface reservoirs especially to hydrocarbon reservoirs. Bulk‐phase equilibrium thermodynamics is a focus of this course, which prepares students the required thermodynamic skill for compositional petroleum reservoir simulation. Cubic equations of state and their strengths are discussed for pure components and mixtures. In particular, Peng-Robinson equation of state and its modeling parameters are addressed. Detailed calculation procedures are given to predict volumetric properties, gas and liquid phase compositions, thermal properties and sonic velocities of reservoir fluids. Algorithms on flash calculation and stability analysis are considered. We study bisection and successive substitution techniques based on the Rachford-Rice equation as well as Newton's method. Optional advanced topics in this course include 1) statistical thermodynamics and molecular simulation for phase behaviors of fluids, 2) nonequilibrium and irreversible thermodynamics, especially as applied to reservoir grading, and 3) interfacial thermodynamics and its application to micro-‐pores and nano-particles for oil reservoirs.

**ErSE 210**

**Seismology I (3‐0‐3)**

**Prerequisite**

*ErSE 204 or consent of instructor*

Introductory and advanced concepts of seismic wave propagation. Vectors and tensors, Hooke’s law, elastic coefficient tensors, Christoffel equation, group and phase velocities, and Green's theorem. The following concepts will also be covered: reflection and transmission coefficient formulas for a layered medium, attenuation, Snell's law, Hooke's law, Fermat's principles, Fresnel zone, finite‐difference solutions to the wave equation and eikonal equation, transport equation, and traveltime tomography.

**ErSE 211**

**Global Geophysics (3‐0‐3)**

**Prerequisite**

*ErSE 204 or consent of instructor*

The course provides introductory descriptions of the Earth solid and fluid natural systems and their interaction. It discusses Earth early geological history, plate motions, magnetism and sea floor spreading, earthquakes and earth structure, gravity, geochronology, heat flow, mantle convection and earth’s magnetic field; history of earth climate, formation of oceans and atmosphere, biological history, energy balance climate model, general circulation of ocean and atmosphere, climate change, coupled ocean‐atmosphere‐biosphere climate models.

**ErSE 212**

**Geophysical Geodesy and Geodynamics (3‐0‐3)**

**Prerequisite**

*ErSE 211 or consent of instructor*

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.

**ErSE 213/313**

**Inverse Problems (3‐0‐3)**

**Prerequisite**

*Background in linear algebra, multivariable calculus (gradients, hessians, ...), probability theory, and programming in Matlab*

This course will introduce the principles of Inverse theory and data assimilation with applications to geophysics and other sciences. Both deterministic and stochastic viewpoints will be covered. Subjects studied will include topics such as least squares, generalized inverses, regularization, Kalman filter, adjoint method, etc. Techniques for solving nonlinear inverse and data assimilation problems will be also covered (200-level for Master students, 300-level for Ph.D. students with more home and project work).

**ErSE 214**

**Seismic Exploration (2‐1‐3)**

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.

**ErSE 215**

**Geomechanics I (3-0‐3)**

Concepts of linear elastic fracture mechanics as applied to the classification, origin and evolution of all types of rock fractures; continuum theory in rock mechanics; rock strength and failure criteria; rock mechanics testing; stress tensors; elastic theory; poroelasticity and thermoelasticity; inelastic behaviour; stress regimes; geological applications.

**ErSE 217**

**Seismotectonics (3‐0‐3)**

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.

**ErSE 218**

**Geophysical Field Methods (3‐0‐3)**

**Prerequisite**

*knowledge of basic physics, linear algebra, advanced calculus, and a programming language such as MATLAB, and it is recommended that students have taken a basic seismology course or that they are currently enrolled in one, or consent of instructor*

Theory and practice of seismic refraction, gravity, electromagnetic, and resistivity surveys will be presented. Lectures will overview both geophysical theory and field method procedures, accompanied by either a geophysical field exercise or data processing lab almost every week. Final grade is based on homework grades and a project report + presentation. Field projects cover applications in environmental engineering, exploration, and earthquake hazards. Instruments to be used include the 64-node Syscal multi-node resisitvity system, the Geonics EM-34 frequency domain loop antennae system, the Geonics microgravimeter, and the Geometrics 624-channel seismic recording system. Commercial codes will be used for processing the data.

**ErSE 225**

**Physical Fields Methods in Geophysics l (2-1‐3)**

**Prerequisite**

*PDEs and course in basic EM physics*

Measurement and theory of gravity and magnetic fields of the earth; small to large scale gravity and magnetic anomalies in exploration and global geophysics; reduction of gravity and magnetic data and forward modeling; applications to exploration, tectonics, and environmental problems. Thermal properties, temperatures, and heat transfer within the context of global geological and geophysical processes, such as plate tectonics and sedimentary basin evolution.

**ErSE 253**

**Data Analysis in Geosciences (3‐0‐3)**

**Prerequisite**

*Background in linear algebra, probability theory, statistics, and programming in*

*Matlab*

Time Series (filtering, correlation, deconvolution, spectral analysis, regression), processing of multidimensional data, spatial statistics including variogram, covariance analysis and modeling, multipoint estimation, spatial interpolation including statistical methods (kriging) and dynamical methods (Kalman filter), uncertainty assessment, cross validation, multivariate analysis including principal component analysis and canonical analysis.

**ErSE 260**

**Seismic Imaging (3‐0‐3)**

**Prerequisite**

*ErSE 210 or ErSE 213 or consent of instructor*

This course is devoted to the concept of seismic imaging for exploration purposes. We introduce seismic imaging in the framework of Green’s functions and wavefield extrapolation and discuss the various imaging conditions. We look at the various migration methods including Kirchhoff, phase-shift migration, Downward continuation methods, reverse time migration, and others. We discuss the role that velocity plays in the seismic imaging process.

**ErSE 296**

**Special Seminar (0 credits, Pass/Fail)**

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

**ErSE 297**

**MS Thesis Research (Variable Credit, Pass/Fail)**

**Prerequisite**

*Approval of Advisor*

Master-level Thesis Research.

**ErSE 298**

**Graduate Seminar (0 Credit, Pass/Fail)**

Master-level ErSE program seminar.

**ErSE 299**

**Directed Research (Variable Credit, Pass/Fail)**

**Prerequisite**

*Approval of Advisor*

Master-level supervised research.

**ErSE 301**

**Geophysical Fluid Dynamics II (3-0-3)**

**Prerequisite**

*ErSE 201 or consent of instructor*

Climate and climate change, large-scale atmospheric and oceanic motions, fine-scale processes, shallow water equations, conservation properties of shallow water equations, geostrophic adjustment, vorticity and circulation, circulation theorems, potential vorticity conservation, quasi-geostrophic equations, energetics of quasi-geostrophic equations, Rossby waves, barotropic and baroclinic instabilities.

**ErSE 303**

**Numerical Methods of Geophysics (3-0‐3)**

**Prerequisite**

*ErSE 204 or consent of instructor*

Built on the modeling and simulation foundation developed in ErSE 204, this specialized course will discuss advanced ideas of multi-scale modeling, linear and non-linear finite element methods, investigate modern approaches to numerical simulations of hydrodynamic and geophysical turbulence, problems of theoretical glaciology and material science of ice for the prediction of ice sheet evolution, and wave propagation in linear and non-linear media.

**ErSE 305**

**Multiphase Flows in Porous Media (3‐0-3)**

**Prerequisite**

*One of AMCS 206 or 231 or consent of instructor*

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 Physics and Modeling (3‐0-3)**

**Prerequisite**

*ErSE 201, ErSE 204 or consent of instructor*

This course will introduce the theory and numerical modeling of ocean circulation. This includes the theory of steady and time‐dependent large‐scale circulation, effects of earth's curvature, wind-driven Sverdrup circulation, western boundary currents, eastern boundary upwelling, effects of buoyancy forcing, wind and buoyancy-forced circulation in the thermocline. The course will also review the theoretical models of ocean circulation, including shallow water, barotropic, quasigeostrophic, and primitive equation models; adjustment times, internal length and time scales; the role of advection, bathymetry and coastlines; global models, basin models, regional models.

**ErSE 307**

**Atmospheric Chemistry and Transport (3‐0‐3)**

**Prerequisite**

*ErSE 201, ErSE 204 or consent of instructor*

The course provides an introduction in atmospheric chemical processes and their role in climate system. It covers fundamentals of reactions kinetics, photochemical processes, chemistry of troposphere and stratosphere, tropospheric ozone and air-‐pollution, stratospheric ozone and ozone hole, atmospheric aerosols, chemistry of clouds, atmospheric transport, chemistry transport models, chemistry climate models.

**ErSE 308**

**Atmospheric Physics and Modeling (3‐0-3)**

**Prerequisite**

*ErSE 201, ErSE 204, AMCS 252 or consent of instructor*

The course discusses main physical processes in the Earth's atmosphere and their role in the formation of weather and climate including atmospheric dynamics and general circulation, sub-grid fine-scale processes and their parameterizations, atmospheric convection, cloud and precipitation formation, atmospheric turbulence and the planetary boundary layer, air‐sea interaction, energy balance, radiative-convective equilibrium, general circulation models, coupled ocean-atmosphere models.

**ErSE 310**

**Seismology II (3-0‐3)**

**Prerequisite**

*ErSE 253 and any of ErSE 210, ErSE 211, ErSE 213*

Part I: Whole Earth wave propagation (body waves, surface waves, normal modes); imaging Earth 3D structure with ray-based methods; introduction to methods beyond ray-theory; attenuation and scattering of seismic waves. Part II: Earthquake source mechanics; earthquake kinematics and scaling laws; earthquake dynamics, fracture modes and crack propagation; introduction to probabilistic seismic hazard assessment.

**ErSE 315**

**Geomechanics ll (3‐0-3)**

**Prerequisite**

*ErSE 215, ErSE 204 or consent of instructor*

Application of Geomechanics I to reservoir characterization; borehole imaging and borehole stresses;

borehole failure analysis; pore pressure prediction and effective stress concepts; sand production and sand failure modeling; effects of water on sand production; wellbore stability; drilling practice.

**ErSE 324**

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

**Prerequisite**

*AMCS 252, ErSE 204 or consent of instructor*

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.

**ErSE 325**

**Physical Fields Methods in Geophysics ll (3‐0‐3)**

**Prerequisite**

*PDEs and course in basic EM physics*

General concepts of electromagnetic field behavior. Electromagnetic properties of rocks. Direct current methods, natural-field electromagnetic methods, magnetotelluric field, numerical modeling, magnetotelluric survey methods. Controlled source electromagnetic methods, electromagnetic sounding and profiling. Computer simulation and interpretation of electromagnetic geophysical data.

**ErSE 328**

**Advanced Seismic Inversion I (3-0-3)**

**Prerequisite**

*Include courses in linear algebra and partial differential equations. Knowledge*

*of linear inversion and exploration seismology is helpful. Consent of instructor is*

*required*

Overview of non-linear seismic inversion methods that invert for earth parameters from seismic data. The inversion procedure is a multiscale iterative method (typically, non‐linear conjugate gradient) that employs preconditioning and regularization. Solution sensitivity is analyzed by model covariance matrices, the slice-projection theorem, and the generalized Radon transform. Methods for waveform inversion, wave path traveltime tomography, and least squares migration are presented.

**ErSE 329**

**Advanced Seismic Inversion II (3-0-3)**

**Prerequisite**

*ErSE 328*

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.

**ErSE 345**

**Seismic Interferometry (3-0-3)**

Main objective is to present the key ideas of seismic interferometry and illustrate them with seismic examples from marine data, land data, and synthetic data. MATLAB exercises will be presented that educate the user about the benefits and pitfalls of interferometric imaging. Examples will be presented that use interferometry for 2D deconvolution, data extrapolation, data interpolation, super-‐stacking, passive seismology, surface-wave interferometry, and super-illumination.

**ErSE 353**

**Data Assimilation (3-0-3)**

**Prerequisite**

*ErSE 253*

Data assimilation (DA) is the process of optimally combining observations with the predictions of numerical models to make the best possible estimate of the time-varying state of the phenomenon under study. In particular, DA forms a basis for the forecast of the future and re‐analysis of the past. In the last 20 years, DA has gained center stage in many computational disciplines at both universities and research centers starting with geoscience applications. DA is a subject that requires a balanced understanding of statistics and applied mathematics as well as the relevant geophysical systems. This course introduces the concepts of data assimilation derived in the context of the statistical estimation theory and the deterministic inverse theory. The course covers a variety of assimilation methods for numerical weather prediction, ocean forecasting, reservoir history matching, 4D seismic inversion, and hydrology assimilation. These include, but not limited to, optimal interpolation and three‐dimentional variational (3D‐VAR) methods, Kalman‐filtering, smoothing and four‐dimensional variational (4D‐VAR) methods, low‐rank Kalman filtering, ensemble Kalman filtering and ensemble square-root filters. Advanced topics based on the fully nonlinear Bayesian estimation theory, such as the particle filter and the Gaussian‐Mixture filters, and the state‐of‐art data assimilation systems will also be discussed.

**ErSE 360**

**Mathematical methods for seismic imaging (3-0-3)**

**Prerequisite**

*ErSE260*

This course will be devoted to mathematical algorithms and methods for seismic imaging. We will learn how to extrapolate wavefields efficiently and accurately. This includes looking at finite‐difference, spectral, pseudo‐spectral methods among other methods. We will look into the stable and accurate implementation of the imaging condition and its variations for velocity analysis. We will also look at numerical methods for inverting for the velocity model using seismic imaging.

**ErSE 390**

**Special Topics in Earth Science (3‐0‐3)**

Computational Science and Engineering 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.

**ErSE 395**

**Internship (Variable Credit, Pass/Fail)**

**Prerequisite**

*Approval of Advisor*

**ErSE 396**

**Special Seminar (0 Credit, Pass/Fail)**

Doctoral‐level seminar focusing on special topics within the field.

**ErSE 397**

**Ph.D. Dissertation Research (Variable Credit, Pass/Fail)**

**Prerequisite**

*Approval of Advisor*

Doctoral‐level Dissertation Research

**ErSE 398**

**Graduate Seminar (0 Credit, Pass/Fail)**

Doctoral‐level ErSE program seminar.

**ErSE 399**

**Directed Research (Variable Credit, Pass/Fail)**

**Prerequisite**

*Approval of Advisor*

Doctoral-level supervised research.