Mathematics for Seismic Data Processing and Interpretation

1 Special Functions.- 1 Functions.- 2 Polynomials and Step Functions.- 3 Trigonometrie Functions.- 4 Power and Exponential Functions.- 5 Inverse Functions.- 6 New Functions from Old.- 7 Numbers.- 2 Calculus: Differentiation.- 1 Introduction.- 2 Higher Derivatives.- 3 Maxima and Minima.- 4 Taylor Series and Approximations.- 5 Partial Derivatives.- 6 Higher Order Partial Derivatives.- 7 Optimisation.- 3 Integration.- 1 Introduction and Definition.- 2 The Relationship between Integration and Differentiation.- 3 Numerical Integration (Quadrature).- 4 Double Integration.- 5 Line Integrals.- 6 Differential Equations.- 4 Complex Numbers.- 1 Introduction.- 2 The Beginning.- 3 Functions of Complex Variables.- 4 Differentiation and Integration.- 5 Matrices.- 1 Introduction.- 2 Definitions and Elementary Properties.- 3 Matrices.- 4 Multiplication of Matrices.- 5 Special Types of Matrices.- 6 Matrices as Functions.- 7 Linear Equations.- 8 Eigenvalues and Quadratic Forms.- 6 Stochastic Processes, Probability and Statistics.- 1 Introduction.- 2 Probability.- 3 Permutations and Combinations.- 4 Probability Distributions.- 5 Joint Distributions.- 6 Expected Values and Moments.- 7 Real Data Samples.- 8 Two Variables.- 9 Simulation and Monte Carlo Methods.- 10 Confidence Intervals.- 11 Stochastic Processes.- 7 Fourier Analysis.- 1 Introduction.- 2 Fourier Series.- 3 Some Examples of Fourier Analysis.- 4 The Phase, Amplitude and Exponential Formulation.- 5 Fourier Transform.- 6 The z-Transform.- 7 The Discrete Fourier Transform.- 8 Fast Fourier Transform.- 9 Frequency Domain.- 8 Time Series.- 1 Stationary and Related Series.- 2 Aliasing and Sampling.- 3 Filters and Convolutions.- 9 Applications.- 1 Wavelets.- 2 Predictive Deconvolution.- Appendix 1 References To Applications.- Appendix 2 Some Useful Formulae for Ready Reference.- Appendix 3 Programs.