GG691 Geological Data
Analysis II
Spring 2003
Room: POST 702
MWF 10:3011:30
Instructor: Cecily Wolfe
Office: POST
819A
Phone: X
66347
Email: cecily@soest.hawaii.edu
¥Probability
and Statistics
¥Analysis
of Sequences
¥ Spectral
Analysis and Fourier Series
¥
Filtering of 2D and 3D Data Sets
¥ Fractals
in the Geosciences
¥ Gridding
and Interpolation
¥ Map
Analysis
Quantitative
skills are becoming more and more important in the Earth Sciences. With the rapid development of remote
sensing from satellites and remotely operated vehicles, the amount of data an
Earth scientist must process and interpret is overwhelming; being able to
analyze data on a computer becomes a necessity and often a job
requirement. This course is a graduate
level class on how to quantitatively analyze data in the geosciences. Topics to be covered include the
probability and statistics, regression, analysis of sequences, time series and
spectral (Fourier) analysis, filtering of 2D and 3D data sets in the time and
frequency domains, fractals and their use in geology and geophysics,
triangulation, gridding, and interpolation of 3D data sets, and map
analysis. Computer applications of
the various techniques will be presented and will include typical data sets in
the geosciences. Homework will be assigned,
covering both theoretical material and practical, computeroriented
assignments. The homeworks will be
designed so that students will gain proficiency with using Matlab programming
and numerical analysis. There will
be one open book oral exam at the end of the semester. A class project, in which students
analyze a data set of their choice using the techniques discussed in class,
will be due at the end of the semester.
¥ Grading
Policy: Every effort should be
made to complete assignments by the due date (Exceptions can be made if
reasonable excuses are presented ahead of due dates). Final grade will be a weighted average of grades for
homework (30%), class project (30%), oral exam (20%), and in class
participation (20%).
¥ Class
Project: Write a report, with illustrations, presenting an analysis of data
of your choice, using some of the methods taught in this class.
¥ Text:
Davis: "Statistics and Data Analysis in Geology", + the instructor's
handouts.
Syllabus
Dates 
Topics 
Events 
1/15 
Class introduction: students fill out questionnaire on
past experience with various mathematical and programming methods 

1/171/22 (1/20 Holiday) 
probability
and statistics: coin
tossing, binomial distribution, negative binomial, cumulative probability, Bayes
theorem, discrete vs. continuous distributions, normal distribution, mean and
variance, joint distribution, covariance, correlation, logratio
transformation, comparing normal populations, zscore, central limit theorem,
tests of significance, pvalues 
Matlab demonstration 
1/24 
PROBABILITY AND STATISTICS: significance, confidence interval,
the tdistribution, degrees of freedom, ttests (one sided and two sided) 

1/24 
PROBABILITY AND STATISTICS: confidence intervals of the mean,
tests of equality of two sample means, t test of correlation, F distribution
and testing equality of variances, example from seismic tomography 
Homework #1; Discuss Matlab statistical toolbox 
1/261/29 
PROBABILITY AND STATISTICS: analysis of variance (ANOVA), one way
ANOVA, two way ANOVA, nested ANOVA 

1/291/31 
PROBABILITY AND STATISTICS: c^{2}
distribution, confidence interval for the variance, c^{2} test, non parametric statistical methods 

2/3 
MATRIX ALGEBRA: matrix addition, multiplication,
inversion, determinant 
Handout on matrix manipulations using Matlab 
2/5 
MATRIX ALGEBRA: eigenvalues and eigenvectors,
covariance matrix, principal components, singular value decomposition (SVD) 
Homework #2; 
2/7 
ANALYSIS OF SEQUENCES OF DATA: linear interpolation, Markov chains,
historical record of eruptions at Aso volcano and analyses of Aso data using
cumulative plots, empirical survivor function, first order autocorrelation,
test for trend, KS test for Poisson distribution 

2/102/14 (2/17 Holiday) 
ANALYSIS OF SEQUENCES OF DATA: setting up and solving linear
regression as a matrix inversion, goodness of fit, ANOVA for linear
regression, ANOVA for regression with replicates 

2/192/21 
ANALYSIS OF SEQUENCES OF DATA: confidence belts around regression,
curvilinear regression, ANOVA tests of significance for quadratic fit, tests
of significance of increase of quadratic over linear fit 

2/262/28 
ANALYSIS OF SEQUENCES OF DATA: ANOVA tests, reduced major axis
regression, major axis regression, regression through origin, log transformations
in regression, weighted regression 
Homework #3 
3/33/5 
SPATIAL ANALYSIS: splines, zonation, autocorrelation,
cross correlation, semivariogram 

3/73/12 
SPECTRAL ANALYSIS: introduction to the Fourier series,
cosines, sines, fundamental period, amplitude and phase, harmonics,
orthogonality of sines and cosines, Fourier series representation of a time
series, power and amplitude spectrum 
Matlab examples of Fourier decomposition 
3/143/18 
SPECTRAL ANALYSIS: convolution in the time and spectral
domain, sampling theorem 
Homework #4; Discuss student final projects 
3/24/3/28 
SPRING BREAK 

3/31 
SPECTRAL ANALYSIS: Aliasing and leakage 

4/24/7 
SPECTRAL ANALYSIS: filtering, low pass and high pass
filters, zero phase, linear phase, and nonlinear phase filters, causality 
Homework #5; Handout of example filtering of earthquake
seismograms 
4/9 
SPATIAL ANALYSIS: contouring and gridding, Delaunay
triangularization 
Examples from GMT 
4/114/14 
SPATIAL ANALYSIS: kriging, minimum curvature surface
fitting, trend surface analysis 
Homework #6 
4/164/18 (4/18 Holiday) 
2D SPECTRAL ANALYSIS: introduction, examples from linear
image analyses 
Handout of examples of image analysis 
4/234/28 
FRACTALS: What are fractals, fractal dimension, self affinity, measuring
fractal dimension 

4/305/2 
Oral examination 

5/55/7 
Presentations of student projects 
Students turn in papers on final projects 