Survey of Numerical Tools for Spatial Analysis


Abstract: This class will introduce data sources and use of computer algorithms to capture, visualize, analyze, and support dynamic modeling of a wide variety of terrestrial features and processes. A significant difference from other scientific computing classes will be the amount of attention devoted to demonstrating the capabilities of raster and TIN data structures to describe the characteristics and dynamics of surfaces that are important to the earth science community (e.g. topography). The motivation for this focus stems from the fact that historically earth sciences professionals have used these spatial representations to help resolve a wide range of complex challenges. A few examples include: erosion modeling, exploiting remote sensing imagery, analyzing thin sections, landslide prediction, , geophysical mapping of all kinds modeling glacier dynamics, ground water modeling, seismic modeling, visualizing changing engineering properties of the superficial deposits, fossil distributions, fault planes, capturing variability in physical properties of different rock types including density, thermal attributes, seismic velocity, magnetic susceptibility and other electromagnetic parameters. The class will also be designed to complement other quantitative classes on campus and will provide explicit links to other to other math, applied math, computer science and ESS classes that can provide additional numerical tools (e.g. AMATH 301) or data sources (e.g. ESS 421)

Target Audience: New graduate students.

Customization: In order to provide the students with the widest range of topics the material will be presented with two different approaches.  The first half of the course material will be presented with ‘classic’ lectures to explain core critical concepts that all students need to some extent. In the second half of the course the students will have a number of lectures (which in total cover much more information than could be covered in a typical class) made available to them in videos. The students can then select the best subset of these videos to customize the class to best support their particular research goals.   

Prerequisites: While most mathematical deployment will emphasize intuitive graphics and geological examples, with only ‘pointers’ to formal mathematical proofs, a common level of mathematical maturity indicated by a familiarity with topics found in ESS 310-Mathematical Methods in the Earth Sciences is required. Confidence with the Windows operating system is also necessary.

Text book: While “Mathematical Methods in the Physical Sciences”, by Mary L. Boas will be the main mathematical reference, and the source of all mathematical symbols, no single text covers the material from an earth science perspective. Thus the class will use a combination of: dynamic web pages (both current and customized pages), copies from sections from selected text books (subject to resolving copyright issues) and reserve readings. Ideally some of this material would be useful in other ESS classes.

Programing Language: The Python 2.7 programing language and several scientific libraries (including Sage, Scipy/Numpy, Matplotlib, and VPython) will be the backbone of this class. Major motivations of using Python is that it is: