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基本説明
Step-by-step applications of Mathematica to formulate and solve quantitative problems in geology.
Full Description
Computational Geosciences with Mathematica is the only book written by a geologist specifically to show geologists and geoscientists how to use Mathematica to formulate and solve problems. It spans a broad range of geologic and mathematical topics, which are drawn from the author's extensive experience in research, consulting, and teaching. The reference and text leads readers step-by-step through geologic applications such as custom graphics programming, data input and output, linear and differential equations, linear and nonlinear regression, Monte Carlo simulation, time series and image analysis, and the visualization and analysis of geologic surfaces. It is packed with actual Mathematica output and includes boxed Computer Notes with tips and exploration suggestions.
Contents
1 Introduction to Mathematica.- 1.1 What is Mathematica.- 1.2 Getting Help.- 1.3 Installing and Running Mathematica.- 1.4 How the Bookis Organized.- 1.5 A Brief Tour of Mathematica.- 1.6 References and Recommended Reading.- 2 Special Plots for Geoscience Data.- 2.1 Mathematica Packages You Will Need.- 2.2 Overview.- 2.3 Stem Plots.- 2.4 Rose Plots.- 2.5 Ternary Plots.- 2.6 Stereographic Projections.- 2.7 Equal Area Projections.- 2.8 Box and Whisker Plots.- 2.9 Well Logs.- 2.10 References and Recommended Reading.- 3 Manipulating and Solving Equations.- 3.1 Mathematica Packages You Will Need.- 3.2 Basic Symbolic Manipulation.- 3.3 Matrix and Vector Operations.- 3.4 Linear Equation Solving.- 3.5 Ordinary Differential Equations.- 3.6 Partial Differential Equations.- 3.7 References and Recommended Reading.- Random Variables and Univariate Probability Distributions.- 4.1 Mathematica Packages You Will Need.- 4.2 The Concept of Random Variables.- 4.3 Some Continuous Distributions.- 4.4 Some Discrete Distributions.- 4.5 Relating Distributions to Data: Method of Moments.- 4.6 Parametric Hypothesis Testing: t and F tests.- 4.7 Nonparametric Hypothesis Testing: K-S Tests.- 4.8 Generating Random Numbers from Probability Distributions.- 4.9 Care and Feeding of the Random Number Generator.- 4.10 Illustrating the Central Limit Theorem.- 4.11 The Pitfalls of Undersampling.- 4.12 References and Recommended Reading.- Probabilistic Simulation.- 5.1 Mathematica Packages You Will Need.- 5.2 Flood Frequency Modeling.- 5.3 Didn't We Just Have a 100 Year Flood?.- 5.4 Monte Carlo Simulation of a Wetting Front.- 5.5 Monte Carlo Analysis of Infinite Slope Stability.- 5.6 Apparent Clast Size Distributions: The Outcrop Effect.- Interpolation and Regression.- 6.1 Mathematica Packages You WillNeed.- 6.2 Interpolation or Regression: Which is Appropriate?.- 6.3 Interpolation.- 6.4 Linear Regression.- 6.5 Nonlinear Regression.- 6.6 References and Recommended Reading.- Visualizing and Analyzing Surfaces.- 7.1 Mathematica Packages You Will Need.- 7.2 Gridded Data.- 7.3 Irregularly Spaced Data.- 7.4 Trend Surface Mapping.- 7.5 References and Recommended Reading.- 8 Digital Signal and Image Processing.- 8.1 Mathematica Packages You Will Need.- 8.2 The Nature of Periodic Waveforms.- 8.3 Discrete Fourier Tranforms.- 8.4 Autocovariance and Autocorrelation.- 8.5 Filters and Convolution.- 8.6 Image Processing.- 8.7 Recommended Reading.- Appendix A Mathematica Functions in the Computational Geoscience Package.- A.1 Introduction.- A.2 Plotting and Calculations.- A.3 Color Functions.- Appendix B Working with Color.- B.5.1 Hue, Saturation, and Brightness.- B.5.2 Red, Green, and Blue (RGB).- B.5.3 Cyan, Magenta, Yellow, and Black (CMYK).- B.5.4 Other Color Systems.- B.6 Using Color in Plots and Graphics.- B.6.1 Plot and ListPlot.- B.6.2 Contour and Density Plots.- B.6.3 Surface Plots and Graphics.- B.6.4 Graphics3D.
