Numerical analysis for the geological sciences

목차 (Table of Contents)

• CONTENTS
• Introduction = xix
• About This Book = xx
• General Features of the Text = xxi
• A Note for Instructors = xxiii
• A Note on the Software = xxiii
• RIDGES: A Problem Solving Strategy = xxiii
• Chapter Summary = xxiv
• Suggested Readings = xxv
• 1 A Review of Calculus = 1
• 1.1 History = 1
• 1.1.1 The Derivative = 3
• 1.1.2 The Fundamental Theorem of Integral Calculus = 6
• 1.2 Applications of Calculus = 9
• 1.3 An Ironic Aspect of the Twentieth Century = 14
• Chapter Summary = 15
• Exercises = 15
• References and Suggested Readings = 16
• 2 Carl Friedrich Gauss = 17
• 2.1 A Mathematical Prodigy = 17
• 2.2 Theory of Errors = 18
• 2.2.1 Application of Error Theory: Gaussian Quadrature = 19
• 2.2.2 The General Form for Gaussian Quadrature for m＝I and m＝2 = 24
• 2.2.3 A Table of Gaussian Quadrature Locations t and Weights a = 26
• 2.2.4 Application of Error Theory: Linear Least-Squares Regression = 27
• 2.3 Gaussian Elimination: Solving Simultaneous Equations = 31
• 2.3.1 Advanced Topic: Iterative Improvement for Gaussian Elimination = 34
• Chapter Summary = 35
• Exercises = 36
• References and Suggested Readings = 37
• 3 Concepts in Matrix Algebra = 44
• 3.1 The Concept of a Matrix = 44
• 3.2 Linear, Least-Squares Regression Revisited = 47
• 3.3 Eigendecomposition of a Matrix = 50
• 3.3.1 Roots of an Algebraic Expression = 51
• 3.3.2 Eigenvectors = 52
• 3.3.3 Comments = 55
• 3.3.4 Iterative Solution for Eigendecomposition = 56
• 3.3.5 Computer Example = 56
• Chapter Summary = 57
• Exercises = 57
• References and Suggested Readings = 59
• 4 An Overview of Probability and Statistics = 64
• 4.1 The Need for Statistics = 64
• 4.2 Statistical Parameters = 65
• 4.3 Probability = 67
• 4.3.1 Conditional Probability = 67
• 4.3.2 Bayes' Theorem = 68
• 4.3.3 Continuous Random Variables = 68
• 4.3.4 Probability Density Function for Continuous Random Variables = 69
• 4.3.5 Expected (Mean) Value of a Continuous Random Variable = 69
• 4.3.6 The Normal or Gaussian Distribution = 70
• 4.3.7 Poisson Probability Distribution = 71
• 4.3.8 Graphical Display of a Sample: The Histogram = 71
• 4.3.9 Examining Models for Cumulative Distribution Functions = 72
• 4.4 Asymmetrical Data Distributions: Skew = 74
• 4.5 Nonparametric Statistics = 76
• 4.6 Statistical Correlation: Intervariable Relationships = 77
• 4.7 Statistical Correlation: Intravariable Relationships = 77
• 4.8 Additional Numerical Examples = 78
• 4.8.1 Arithmetic Mean and Median = 78
• 4.8.2 Variance = 78
• 4.8.3 Correlation Coefficient = 79
• 4.8.4 Autocorrelation = 79
• 4.8.5 Histogram = 81
• 4.8.6 Bayes' Theorem = 83
• 4.9 Computer Exercise = 84
• 4.9.1 Histograms = 84
• Chapter Summary = 85
• Exercises = 85
• References and Suggested Readings = 87
• 5 Multivariate Data Analysis = 91
• 5.1 Introduction = 92
• 5.2 An Overview of Multivariate Analytical Methods = 92
• 5.2.1 Principal Components Analysis = 96
• 5.2.2 Representing the PCA Results Graphically = 98
• 5.2.3 Factor Analysis = 99
• 5.3 Correspondence Analysis = 102
• 5.3.1 Eckart-Young Theorem = 106
• 5.3.2 Solutions for Factors in Correspondence Analysis = 109
• 5.3.3 Example Calculations = 109
• 5.4 Advanced Topic: Accounting for Missing Data in Correspondence Analysis = 111
• 5.5 CORSPOND: A Portable FORTRAN-77 Program for Correspondence Analysis = 114
• 5.6 Applications of CORSPOND = 115
• 5.6.1 Analysis of Data from Greenacre (1984) = 115
• 5.6.2 The Stillwater Lakes, Nevada, Environmental Problem Revisited = 115
• 5.6.3 Advanced Application: Accommodating Missing Data in CORSPOND = 125
• 5.7 Discriminant Analysis = 125
• 5.7.1 Application = 128
• Chapter Summary = 130
• Exercises = 131
• References and Suggested Readings = 137
• 6 Geostatigtics: The Art of Spatial Analysis = 150
• 6.1 A Brief History = 151
• 6.2 The Unique Terminology of Geostatistics = 152
• 6.3 Kriging: Gauss' Theory of Errors Revisited = 152
• 6.3.1 Deriving the Solution for Kriging Weights = 154
• 6.4 Determining Spatial Autocovariance = 160
• 6.4.1 Obtaining Autocovariance from the Semivariogram = 161
• 6.5 Calculating the Sennvariogram = 162
• 6.6 FGAM: A Portable FORTRAN-77 Program for Semivariogram Calculation and Plotting = 167
• 6.6.1 Samples = 168
• 6.7 Models of Semivariograms Used for Computing Kriging Weights = 180
• 6.7.1 Equations for the Semivariogram Models = 181
• 6.7.2 The Negative Semidefiniteness of Semivariogram Models = 183
• 6.7.3 Nested Semivariogram Models = 183
• 6.8 Example Calculation to Demonstrate the Use of Kriging = 184
• 6.8.1 The Exact Interpolation Characteristics of Kriging = 187
• 6.8.2 A Note on Kriging Variance = 187
• 6.9 Sample Support = 188
• 6.9.1 Block Kriging Versus Punctual Kriging = 188
• 6.10 JCBLOK: A Portable FORTRAN-77 Program for Punctual and Block Kriging = 191
• 6.10.1 Using JCBLOK with the Lognormal and Indicator Transforms = 192
• 6.11 Case Studies = 193
• 6.11.1 An Application of JCBLOK to the NVSIM.DAT Data Set for Gridding = 193
• 6.11.2 An Application of JCBLOK to the Block Estimation of Lognormal Data = 194
• 6.11.3 Estimation of Indicator Functions Using JCBLOK = 201
• Chapter Summary = 204
• Exercises = 205
• References and Suggested Readings = 206
• 7 Computer Graphics: Visualizing Quantitative Information = 228
• 7.1 Computer Graphics and Hardware = 229
• 7.1.1 VGA Computer Graphics Environment = 229
• 7.2 Viewing and Windowing = 232
• 7.3 Vector Generation = 235
• 7.3.1 Computer-Aided Drawing of Two-Dimensional Graphs = 237
• 7.3.2 GRAPH2D: An Interactive Program for Plotting Two-Dimensional Graphical Images = 239
• 7.4 Two-Dimensional Coordinate Rotations = 245
• 7.5 Three-Dimensional Graphical Images = 247
• 7.5.1 The Forgetting Transform = 247
• 7.5.2 Three-Dimensional Coordinate Rotations = 248
• 7.5.3 Vanishing Points = 250
• 7.5.4 Plotting Three-Dimensional Grids: Hidden Line Removal and Shading Algorithms = 250
• 7.6 Mapping Using Color Density Slicing = 255
• 7.6.1 Color Density Mapping Using the Program COLORDEN = 256
• 7.7 Contour Mapping = 258
• 7.7.1 Algorithm = 258
• 7.7.2 CTOUR: A Computer Algorithm for Contour Mapping = 259
• Chapter Summary = 260
• Exercises = 262
• References and Suggested Readings = 263
• 8 Finite Element Analysis = 294
• 8.1 Hooke's Law = 295
• 8.2 Strain and Stress = 295
• 8.3 Poisson's Ratio = 297
• 8.4 Truss Systems: Finite Element Analysis in Its Most Simple Form = 298
• 8.4.1 Element Stiffness Matrix: Bar Elements = 300
• 8.4.2 Computing the System Stiffness Matrix = 303
• 8.5 A Rayleigh-Ritz Derivation of the Element Stiffness Matrix for Bar Elements = 306
• 8.5.1 An Overview = 306
• 8.5.2 Use of Assumed Displacement Fields in the Rayleigh-Ritz Method = 308
• 8.6 TRUSS: A FORTRAN-77 Program for Two-Dimensional Finite Element Analysis of Truss Systems = 311
• 8.6.1 Error Trapping = 313
• 8.6.2 Finite Element Analysis of a Truss System = 315
• 8.6.3 A Simple Test Problem = 318
• 8.7 Two-Dimensional, Solid, Isoparametric, Four-Node Elements: An Advanced Application of Gaussian Quadrature for Deriving the Element Stiffness Matrix = 319
• 8.7.1 Introduction to Isoparametric, Solid, Four-Node Elements = 321
• 8.7.2 Rayleigh-Ritz Derivation of Element Stiffness = 321
• 8.7.3 The Material Constitutive Matrix [E] = 328
• 8.7.4 An Example of Element Stiffness Matrix Calculation = 329
• 8.7.5 Computing Strain and Stress for Quadrilateral Elements = 334
• 8.8 Nonlinear, Elastic Finite Element Analysis: An Application for the Analysis of Fractured Rock Systems = 335
• 8.8.1 A Summary of the Continuum Analysis of Nonlinear, Elastic Behavior of Fractured Rock Masses = 336
• 8.9 QUAD: A FORTRAN-77 Program for Linear, Elastic and Nonlinear, Elastic Finite Element Analysis Using Four-Node, Isoparametric Elements = 338
• 8.10 Applications of QUAD for Finite Element Analysis Using the Two-Dimensional, Solid, Four-Node, Isoparametric Element = 339
• 8.10.1 Analysis of Displacement Beneath a Spread Footing on Soil = 339
• 8.10.2 Analysis of a Rectangular Opening = 343
• 8.10.3 Analysis of Stress Around an Elliptical Tunnel = 346
• 8.10.4 Analysis of Vertical Fractures for the Tunnel of Example 8.10.3 = 349
• 8.11 A Note on Boundary Conditions = 352
• 8.12 Finite Difference Analysis for Assessing Regional Groundwater Flow = 354
• 8.12.1 Darcy's Law = 354
• 8.12.2 Laplace's Equation = 355
• 8.12.3 Finite Difference Approximation of Laplace's Equation for Steady-State Flow = 355
• 8.12.4 Example Application = 355
• 8.13 Finite Element Method in Comparison to the Finite Difference Method = 360
• Chapter Summary = 360
• Exercises = 361
• References and Suggested Readings = 363
• 9 Fourier Analysis = 394
• 9.1 Sinusoidal Waveforms = 395
• 9.1.1 Cosine Function = 395
• 9.2 The Periodogram = 395
• 9.3 Fourier Transform = 404
• 9.4 Justifying the Use of the Fourier Transform = 407
• 9.5 The Power Spectrum: Spectral Analysis = 408
• 9.6 Examples of Fourier Analysis = 408
• 9.6.1 Sunspot Cycles = 408
• 9.6.2 Analysis of Seismic Data = 411
• 9.7 Fast Fourier Transform (FFT) = 414
• 9.8 A Final Example = 415
• Chapter Summary = 416
• Exercises = 417
• References and Suggested Readings = 418
• 10 Numerical Processing of Digital Images = 427
• 10.1 Digital Imagery = 427
• 10.2 Remote Sensing = 429
• 10.2.1 The Electromagnetic (EM) Spectrum = 429
• 10.2.2 Satellite Technology = 431
• 10.2.3 Spatial, Spectral, Temporal, and Radiometric Resolution = 433
• 10.3 Image Processing = 434
• 10.3.1 The Display of Digital Images Using VGA Hardware = 435
• 10.3.2 Contrast Enhancement of Digital Images = 437
• 10.3.3 Using Look-up Tables for Improved Computation Efficiency = 445
• 10.3.4 CTRAST: A Computer Algorithm for Contrast Enhancement = 447
• 10.3.5 Filtering Digital images = 448
• 10.3.6 Fourier (Frequency) Filtering of Digital Images = 453
• 10.3.7 Classification of Digital Images = 457
• 10.4 Magellan Radar Images of Venus = 461
• 10.5 Examples of Airborne-Sensor-Acquired Digital Imagery = 463
• Chapter Summary = 464
• Exercises = 465
• References and Suggested Readings = 467
• Selected Articles Describing Magellan Images = 468
• 11 Fractals = 489
• 11.1 Nineteenth-Century Discoveries = 490
• 11.1.1 Poincar$$\acute e$$ = 490
• 11.1.2 Fricke and Klein = 491
• 11.1.3 Weierstrass and duBois Reymond = 491
• 11.1.4 Other Nineteenth-Century Discoveries = 491
• 11.2 Fractals in the Twentieth Century = 492
• 11.2.1 Fatou and Julia = 492
• 11.2.2 Richardson = 492
• 11.2.3 The Sketches of M.C. Escher: A Notion of Infinite Smallness = 495
• 11.2.4 Hausdorff and Besicovitch = 495
• 11.2.5 Mandelbrot = 496
• 11.3 Fractals: A Summary of Definitions = 498
• 11.4 A Spectral Notion for Fractal Dimension = 500
• 11.4.1 The Random Fractal = 500
• 11.4.2 Background = 501
• 11.5 Use of the Semivariogram for Fractal Studies = 509
• 11.6 Estimating the Fractal Dimension in Practice = 511
• 11.7 Simulation of Fractal Topography and Clouds = 514
• 11.7.1 Clouds = 516
• 11.7.2 Why Are These Simulations Useful? = 516
• 11.8 Selected Applications of the Fractal Dimension = 518
• 11.8.1 Analysis of Rock Surfaces = 518
• 11.8.2 The Shape and Texture of Concrete Aggregate = 519
• 11.8.3 Chaos? Characteristics of Rainfall for a Storm = 521
• 11.9 Visualizing Periodicities and Fractal Behavior in One-Dimensional Time Series: The Wavelet Transform = 523
• 11.9.1 Specific Information for the Program WAVELET = 527
• Chapter Summary = 527
• Exercises = 528
• References and Suggested Readings = 529
• Appendix A = 539
• Appendix B = 582
• Index = 585