Mathematics for Seismic Data Processing and Interpretation

ISBN-13: 9780860105763 / Angielski / Miękka / 1984 / 255 str.

A. R. Camina; J. Janacek

Opis

With the growth of modern computing power it has become possible to apply far more mathematics to real problems. This has led to the difficulty that many people who have been working in various jobs suddenly find themselves not understanding the modern processing which is being applied to their own professional field. It also means that the people presently being trained in these subjects need to understand a much wider range of mathe matics than in the past. It is to both of these groups that this book is addressed. The major objective is to present the reader with the basic mathematical understanding to follow the new developments in their own field. The mathematics in this book is based on the need to understand signal process ing. The modern work in this area is mathematically very sophisticated and our purpose is not to train professional mathematicians but to make far more of the literature accessible. Since this book is based on courses devised for Racal Geophysics there is clearly going to be a bias towards the applications in that area, as the title implies. It is also true that the bibliogra phy has been chosen in order to aid the reader in that field by pointing them in the direction of recent applications in geophysics."

Spis treści

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.