Geophysical Data Analysis - part 1
Winter 2020, Tues/Thurs 9-10:20am
IGPP Munk, 303
This web page documents the progress of SIOG223A,
Geophysical Data Analysis, Part I, Winter 2020. It contains class notes,
assignments, and datasets to be used for analysis. Click on the links below to
download a pdf file of the notes.
SIOG223A is the first part of a 2- quarter course: Part 2 will be taught
in Spring 2020. The outline is a reasonably accurate reflection of topics to be
covered, but they may be revised and expanded as we go along. It is also likely
that these topics will be taught in a somewhat different sequence from the
chapter numbers given in the outline.
The goal of this class is to introduce you to fundamental
methods for geophysical data analysis that will be useful in your
research. I expect that taking this
class will require the average student to invest about 10 hours per week: 2 hours and 40 minutes of class time, 3 hours
of reading, and 3-4 hours on homework. Depending on your background you may
require much less or a bit more time.
Grades will be based on homework, typically about 6 or 7
sets distributed through the quarter, and occasional class presentation and
discussions. I encourage you to discuss material with your colleagues, except
for the final problem set which I usually ask students to complete without
consultation. I don’t usually set specific office hours, but you are welcome to
drop by and ask questions (IGPP Munk 329). If everything seems too hard please ask for
help sooner rather than later.
Lecture 1: 01/07/2020 –
Read the Course Outline PDF , and notes by Duncan Agnew entitled Graphical Rhetoric on Communicating Your Results
through Words, Equations, and Visualization.
Outline PDF
Bibliography and suggestions for further
reading throughout the class have also been
posted.
Communicating Your Results through Words, Equations, and
Visualization, aka Chapter 1,
Graphical Rhetoric
Homework # 1 - Find and bring to next class
one example of what you consider a highly informative graphic, along with
your rationale for the choice. Read Chapters 1 and 1.
Slides from
Lecture 1
Lecture 2: 01/09/2020
Discussion of Chapter 1, examples of
data/results you have encountered and how to represent them.
Plus the second chapter 1 on Probability,
Statistics, and Reality
Slides from
Lecture 2
Lecture 3: 01/14/2020
We will discuss geomagnetic reversals and
earthquake times as examples of stochastic processeses
before moving on to Chapter 2 on
Probability and Random Variables
Slides from Lecture 3
Homework#2 – due 1/23/2020
Lecture 4: 01/16/2020
From conditional probabilities to Bayes’
Theorem, Random variables, Density andDistribution Functions
Slides from Lecture 3 & 4
Lecture 5: 01/21/2020
Moving from RVs and PDFs to Conventional Variables
Sums and functions of random variables
Characteristic functions and the central
limit theorem
Slides from Lectures 5&6
Lecture 6: 01/23/2020
Homework#2 – is due
today.
Chapter 3
provides a bestiary of univariate distributions, starting with uniform,
Normal, exponential and Poisson distributions, then moving onto many others.
This chapter also introduces pseudorandom numbers and the idea of using them
to simulate random variables with a specified underlying pdf.
Homework#3 – due
1/30/2020 and uses California
earthquake times
Lecture 7: 01/28/2020
Chapter
4 Multivariate
random variables, correlation, propagating uncertainty, correlation,
conditional and marginal distributions, covariance and correlation
coefficients.
Lecture 8: 01/30/2020
Solutions to Homework #2 are here. Today we will finish up Chapter
4 with a look at linear transformations of random
variables, propagation of errors, revisit regression in the context of curve
fitting. Next week we will move onto the business of parameter estimation
discussed in Chapter 5.
Lectures 9 &10: 02/04/2020 and 02/06/2020
Read Chapter 5, pages 95-110 on estimates
of location and scale, including method of moments, order statistics (median and
interquartile range), and trimmed estimates. Then move on to Monte Carlo
methods and the idea of resampling to provide bootstrap estimates directly
from the data. We finish Lecture 10 with a discussion of confidence limits or
confidence intervals, and an example on how to find the confidence interval
for the mean of normally distributed data when the variance is unknown, an
application of the t-distribution introduced in Chapter 3.
Lectures 11 & 12: 02/11/2020 and 02/13/2020
This week we will complete Chapter 5, pages
110-124. Following a discussion of desirable properties for estimators
(unbiased, efficient, and consistent) we’ll introduce the likelihood function
and the method of maximum likelihood.
Homework#4 is now posted and is due
2/18/2020
As announced on 2/13, the due
date for homework 4 has been revised to 2/20/20
Partial solutions to Homework 3
are here.
Lectures 13& 14: 02/18/2020, 02/20/2020
Statistical hypothesis testing is the topic
of Chapter 6 in the notes.
Lecture 15: 02/25/2020
Least Squares Estimation is the topic of Chapter 7 in the notes.
Lecture 16: 02/27/2020
NLLS,
adding a side constraint, penalized least squares
Supplementary
notes on Optimization by Bob Parker
Lecture 17: 03/03/2020
Total
least squares and robust methods are briefly outlined in Chapter 8.
Lecture 18: 03/05/2020
Today’s lecture will be on non-parametric
density function estimation. For
motivation we’ll start with an example of the application of the robust
M-type methods described last time. A full description is given in this reference. Notes on density estimation are in Chapter 9.
A PDF of lecture slides from
Lectures 15-18 is
available.
solutions to Homework 4 are here.Homework # 5 is here, and due on March 18,
2020. Datasets for jcd.dat, and
old Faithful are available for download.
Lectures 19 & 20: 03/10/2020, 03/12/2020
We will complete the
quarter with a brief introduction to Geophysical Modeling and Inverse Theory
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