MATLAB® Recipes for Earth Sciences (eBook)

MATLAB® is used for a wide range of applications in geosciences, such as image processing in remote sensing, the generation and processing of digital elevation models, and the analysis of time series. This book introduces methods of data analysis in geosciences using MATLAB, such as basic statistics for univariate, bivariate and multivariate datasets, jackknife and bootstrap resampling schemes, processing of digital elevation models, gridding and contouring, geostatistics and kriging, processing and georeferencing of satellite images, digitizing from the screen, linear and nonlinear time-series analysis, and the application of linear time-invariant and adaptive filters. The revised and updated Third Edition includes ten new sections and has greatly expanded on most chapters from the previous edition, including a step by step discussion of all methods before demonstrating the methods with MATLAB functions. New sections include: Data Storage and Handling, Data Structures and Classes of Objects, Generating M-Files to Regenerate Graphs, Publishing M-Files, Distribution Fitting, Nonlinear and Weighted Regression, Color-Intensity Transects of Varved Sediments, and Grain Size Analysis from Microscope Images. The text includes numerous examples demonstrating how MATLAB can be used on data sets from earth sciences. All MATLAB recipes can be easily modified in order to analyse the reader's own data sets.

Preface 5
Contents 9
1 Data Analysis in Earth Sciences 12
1.1 Introduction 12
1.2 Data Collection 12
1.3 Types of Data 14
1.4 Methods of Data Analysis 18
Recommended Reading 20
2 Introduction to MATLAB 21
2.1 MATLAB in Earth Sciences 21
2.2 Getting Started 22
2.3 The Syntax 24
2.4 Data Storage and Handling 28
2.5 Data Structures and Classes of Objects 31
2.6 Scripts and Functions 36
2.7 Basic Visualization Tools 39
2.8 Generating M-Files to Regenerate Graphs 42
2.9 Publishing M-Files 45
Recommended Reading 46
3 Univariate Statistics 47
3.1 Introduction 47
3.2 Empirical Distributions 47
Measures of Central Tendency 49
3.3 Example of Empirical Distributions 54
3.4 Theoretical Distributions 61
Binomial or Bernoulli Distribution 63
Poisson Distribution 64
Normal or Gaussian Distribution 65
Logarithmic Normal or Log-Normal Distribution 66
Student’s t Distribution 67
Fisher’s F Distribution 68
? 2 or Chi-Squared Distribution 69
3.5 Example of Theoretical Distributions 69
3.6 The t-Test 71
3.7 The F-Test 76
3.8 The ?2-Test 80
3.9 Distribution Fitting 83
Recommended Reading 87
4 Bivariate Statistics 88
4.1 Introduction 88
4.2 Pearson’s Correlation Coeffi cient 89
4.3 Classical Linear Regression Analysis and Prediction 97
4.4 Analyzing the Residuals 101
4.5 Bootstrap Estimates of the Regression Coeffi cients 103
4.6 Jackknife Estimates of the Regression Coeffi cients 104
4.7 Cross Validation 107
4.8 Reduced Major Axis Regression 108
4.9 Curvilinear Regression 109
4.10 Nonlinear and Weighted Regression 112
Recommended Reading 115
5 Time-Series Analysis 116
5.1 Introduction 116
5.2 Generating Signals 117
5.3 Auto-Spectral and Cross-Spectral Analysis 121
5.4 Examples of Auto-Spectral and Cross-Spectral Analysis 126
5.5 Interpolating and Analyzing Unevenly-Spaced Data 135
5.6 Evolutionary Power Spectrum 140
5.7 Lomb-Scargle Power Spectrum 144
5.8 Wavelet Power Spectrum 148
5.9 Nonlinear Time-Series Analysis (by N. Marwan) 155
Phase Space Portrait 155
Recurrence Plots 161
Recommended Reading 167
6 Signal Processing 169
6.1 Introduction 169
6.2 Generating Signals 170
6.3 Linear Time-Invariant Systems 172
6.4 Convolution and Filtering 174
6.5 Comparing Functions for Filtering Data Series 177
6.6 Recursive and Nonrecursive Filters 180
6.7 Impulse Response 181
6.8 Frequency Response 184
6.9 Filter Design 190
6.10 Adaptive Filtering 193
Recommended Reading 199
7 Spatial Data 201
7.1 Types of Spatial Data 201
7.2 The GSHHS Shoreline Data Set 202
7.3 The 2-Minute Gridded Global Relief Data ETOPO2 204
7.4 The 30-Arc Seconds Elevation Model GTOPO30 207
7.5 The Shuttle Radar Topography Mission SRTM 209
7.6 Gridding and Contouring Background 212
7.7 Gridding Example 215
7.8 Comparison of Methods and Potential Artifacts 219
7.9 Statistics of Point Distributions 224
Test for Uniform Distribution 224
Test for Random Distribution 227
Test for Clustering 229
7.10 Analysis of Digital Elevation Models (by R. Gebbers) 232
7.11 Geostatistics and Kriging (by R. Gebbers) 243
Theorical Background 243
Preceding Analysis 243
Variography with the Classical Variogram 246
Kriging 255
Discussion of Kriging 260
Recommended Reading 261
8 Image Processing 263
8.1 Introduction 263
8.2 Data Storage 264
8.3 Importing, Processing and Exporting Images 269
8.4 Importing, Processing and Exporting Satellite Images 274
8.5 Georeferencing Satellite Images 276
8.6 Digitizing from the Screen 279
8.7 Color-Intensity Transects of Varved Sediments 282
8.8 Grain Size Analysis from Microscope Images 287
8.9 Quantifying Charcoal in Microscope Images 294
Recommended Reading 298
9 Multivariate Statistics 299
9.1 Introduction 299
9.2 Principal Component Analysis 301
9.3 Independent Component Analysis (by N. Marwan) 308
9.4 Cluster Analysis 312
Recommended Reading 317
10 Statistics on Directional Data 318
10.1 Introduction 318
10.2 Graphical Representation 319
10.3 Empirical Distributions 320
10.4 Theoretical Distributions 325
10.5 Test for Randomness of Directional Data 327
10.6 Test for the Signifi cance of a Mean Direction 328
10.7 Test for the Diff erence between Two Sets of Directions 329
Recommended Reading 333
General Index 334