# Computational Course for Geology Majors - Seismology Component Outline

Initial Publication Date: October 12, 2015 | Reviewed: November 19, 2018

## Summary

Lecture and programming assignment topics for a new lower division computation course for Geology majors. Proposed seismology component, to last several weeks in a semester-long course.

## Learning Goals

Concepts: seismic wave speeds and governing physical properties; how to go from formulas to graphs in Matlab; Flat earth refraction seismology forward and inverse methods; writing good Matlab script and function files; least squares; basic ideas of randomness and uncertainty; how to conduct simple Monte Carlo experiments in Matlab. Skills: will use all physics, calculus, and physical geology principles encountered in the pre-requisites. The course may include both written and oral presentations.

## Context for Use

Second year, second semester Geology Majors with 1 year of calculus, physical geology, and 1 semester of physics as pre-requisites. 3 or 4 weeks of 2 lecture hours and 2 lab hours each week. Goal is to teach Matlab as a programming language, and related computer science topics. Physical geology course background is essential to understand the problems and their context. Seismology will likely be the first of several topics (gravity, heat flow, climate time series analysis...). No prior Matlab experience needed for the course.

## Description and Teaching Materials

This is an outline of a course still in development, to be taught at UT Austin for the first time Spring 2016. Seismology topics listed below will take up about 25-30% of the semester. Other geophysics topics to be covered: gravity, heat flow, climate time series.

1. Rock properties and seismic waves

Lecture: elastic properties of rocks and seismic waves, wave types

Computational work: Give the students formulas that relate P, S, and Rayleigh wave speeds to rock and fluid physical parameters. Make plots to see how speeds these vary for sedimentary rocks and the whole earth. Students write functions and scripts that compute plots from given formulas. Discuss inferences about rock composition, fluids, etc. that can be made if wave speeds are accurately measured.

2. Seismic experiments

Lecture: flat earth seismology and travel time curves, using the following figure as an example, which includes a Moho refraction event

Computational work: Give students formulas relating refracted arrival slopes / intercept times to layer thicknesses. Students write a function to compute layer thicknesses from slopes and intercept times, and use a test data set to confirm it works. Every student picks offset / time values for refracted arrivals from the figure for later analysis

3. Least Squares

Lecture: basic statistics and random variables, theory and practice of least squares and set up in Matlab

Computational work: Use least squares to find slope and intercept times from the time- offset picks. Use these in the function developed previously to find layer thicknesses associated with the figure above.

4. Assessing uncertainty with Monte Carlo experiments

Lecture: some basic probability and statistics topics and Monte Carlo experiments, including use of histograms, scatter plots...

Computation: Use a Monte Carlo experiment to assess uncertainty in layer thicknesses

1. Rock properties and seismic waves

Lecture: elastic properties of rocks and seismic waves, wave types

Computational work: Give the students formulas that relate P, S, and Rayleigh wave speeds to rock and fluid physical parameters. Make plots to see how speeds these vary for sedimentary rocks and the whole earth. Students write functions and scripts that compute plots from given formulas. Discuss inferences about rock composition, fluids, etc. that can be made if wave speeds are accurately measured.

2. Seismic experiments

Lecture: flat earth seismology and travel time curves, using the following figure as an example, which includes a Moho refraction event

Computational work: Give students formulas relating refracted arrival slopes / intercept times to layer thicknesses. Students write a function to compute layer thicknesses from slopes and intercept times, and use a test data set to confirm it works. Every student picks offset / time values for refracted arrivals from the figure for later analysis

3. Least Squares

Lecture: basic statistics and random variables, theory and practice of least squares and set up in Matlab

Computational work: Use least squares to find slope and intercept times from the time- offset picks. Use these in the function developed previously to find layer thicknesses associated with the figure above.

4. Assessing uncertainty with Monte Carlo experiments

Lecture: some basic probability and statistics topics and Monte Carlo experiments, including use of histograms, scatter plots...

Computation: Use a Monte Carlo experiment to assess uncertainty in layer thicknesses