GG691 Geological Data Analysis II

Spring 2003


Room: POST 702

MWF 10:30-11:30


Instructor: Cecily Wolfe

Office:            POST 819A

Phone:             X 66347




•Probability and Statistics

•Analysis of Sequences

• Spectral Analysis and Fourier Series

• Filtering of 2-D and 3-D 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 2-D and 3-D data sets in the time and frequency domains, fractals and their use in geology and geophysics, triangulation, gridding, and interpolation of 3-D 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, computer-oriented 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.








Class introduction:  students fill out questionnaire on past experience with various mathematical and programming methods



(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, z-score, central limit theorem, tests of significance, p-values

Matlab demonstration


PROBABILITY AND STATISTICS:  significance, confidence interval, the t-distribution, degrees of freedom, t-tests (one sided and two sided)



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


PROBABILITY AND STATISTICS:  analysis of variance (ANOVA), one way ANOVA, two way ANOVA, nested ANOVA



PROBABILITY AND STATISTICS:  c2 distribution, confidence interval for the variance, c2 test, non parametric statistical methods



MATRIX ALGEBRA:  matrix addition, multiplication, inversion, determinant

Handout on matrix manipulations using Matlab


MATRIX ALGEBRA:  eigenvalues and eigenvectors, covariance matrix, principal components, singular value decomposition (SVD)

Homework #2;


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, K-S test for Poisson distribution



(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



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



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


SPATIAL ANALYSIS:  splines, zonation, autocorrelation, cross correlation, semivariogram



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


SPECTRAL ANALYSIS:  convolution in the time and spectral domain, sampling theorem

Homework #4;

Discuss student final projects





SPECTRAL ANALYSIS:  Aliasing and leakage



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


SPATIAL ANALYSIS:  contouring and gridding, Delaunay triangularization

Examples from GMT



SPATIAL ANALYSIS:  kriging, minimum curvature surface fitting, trend surface analysis

Homework #6


(4/18 Holiday)

2-D SPECTRAL ANALYSIS:  introduction, examples from linear image analyses

Handout of examples of image analysis


FRACTALS:  What are fractals, fractal dimension, self affinity, measuring fractal dimension



Oral examination



Presentations of student projects

Students turn in papers on final projects