Mathematical Inverse Methods in Earth and Environmental Sciences (353-0-01)
Instructors
Suzan van der Lee
847/491-8183
Tech F494
Office Hours: By appointment
Meeting Info
Technological Institute F491: Tues, Thurs 11:00AM - 12:20PM
Overview of class
Data-driven modeling via solving inverse problems and estimating model parameters. Application of linear algebra to the modeling of physical data. Students learn to model large amounts of imperfect data using linear algebra, optimization and regularization techniques, and common physical sense. Via lab exercises and homework, the course emphasizes application over theory. Exercises include but are not restricted to 1) locating events or objects from line-of-sight signal travel times, 2) de-blurring an image, 3) characterizing the subsurface from surface measurements of wave dispersion, 4) locating engineering structures from anomalous gravity data, and 5) tomography: non-destructive characterization of internal structure of materials, human bodies, or the Earth. We will emphasize linear, discrete, ill-posed inverse problems, but will also review time series analysis, including Fourier Transforms and matched filtering, and touch on the principles of solving non-linear inverse problems via directed and random searches in model space.
Registration Requirements
Recommended Background: Linear algebra and differential calculus of multivariable functions.
Teaching Method
Two 80-minute instructor-guided sessions per week and problem-sets to be worked on in class and as homework.
Class Materials (Required)
There are no required class materials.