
Mathematical Aspects of Seismology
Developments in Solid Earth Geophysics
Free Global Shipping
No minimum orderDescription
Developments in Solid Earth Geophysics, 4: Mathematical Aspects of Seismology introduces studies of the more advanced parts of theoretical seismology. The manuscript first ponders on contour integration and conformal transformation, methods of stationary phase and steepest descent, and series integration. Discussions focus on Love waves in heterogeneous isotropic media, Laguerre's differential equation, Hermite's differential equation, method of steepest descent, method of stationary phase, contour integration in the complex plane, and conformal transformation. The text then examines series integration, Bessel functions, Legendre functions, and wave equations. Topics include general considerations of the wave equation, expansion of a spherical wave into plane waves, common features of special functions and special differential equations, applications of Legendre functions, Legendre polynomials, Bessel's differential equation, and properties of Bessel coefficients. The book explores the influence of gravity on wave propagation, matrix calculus, wave propagation in liquid media, integral equations, calculus of variations, and integral transforms. The text is a valuable source of data for researchers wanting to study the mathematical aspects of seismology.
Table of Contents
Preface
Chapter 1. Introduction
1.1 Differential Equations of Mathematical Physics
1.2 Coordinate Transformations
1.3 The Gamma and Beta Functions
Part I. Integration Methods
Chapter 2. Contour Integration and Conformal Transformation
2.1 Contour Integration in the Complex Plane
2.2 Conformal Transformation
Chapter 3. Methods of Stationary Phase and of Steepest Descent
3.1 Method of Stationary Phase (or Principle of Stationary Phase)
3.2 Method of Steepest Descent
3.3 The Airy Integral
Chapter 4. Series Integration
4.1 Fundamental Concepts
4.2 Legendre's Differential Equation
4.3 Bessel's Differential Equation
4.4 Hermite's Differential Equation
4.5 Laguerre's Differential Equation
4.6 Gauss' (Hypergeometric) Differential Equation—Whittaker's Functions
4.7 Love Waves in Heterogeneous Isotropic Media
Part II. Special Functions
Chapter 5. Bessel Functions
5.1 Origin of Bessel Functions
5.2 Properties of Bessel Coefficients
5.3 Related Bessel Functions
5.4 Applications of Bessel and Hankel Functions
Chapter 6. Legendre Functions
6.1 Legendre Polynomials
6.2 Legendre Functions
6.3 Applications of Legendre Functions
Chapter 7. The Wave Equation
7.1 General Considerations of the Wave Equation
7.2 Solution of the Space Form of the Wave Equation
7.3 Expansion of a Spherical Wave into Plane Waves: Sommerfeld's Integral
7.4 Kirchhoff's Solution of the Wave Equation
7.5 Common Features of Special Functions and of Special Differential Equations
Part III. Selected Mathematical Methods
Chapter 8. Integral Transforms
8.1 Introduction to Laplace and Fourier Transforms
8.2 Use of the Laplace Transform for the Solution of Differential Equations
8.3 Impulsive Functions
8.4 Cagniard's Method
Chapter 9. Matrix Calculus
9.1 Introduction
9.2 Haskell's Matrix Method for Rayleigh Waves
9.3 Love Waves
9.4 Body-Wave Propagation through a Many-Layered Medium
Chapter 10. Calculus of Variations
10.1 Fundamentals of the Calculus of Variations
10.2 Applications of the Calculus of Variations
Chapter 11. Integral Equations
11.1 Definitions and Solutions of Integral Equations
11.2 Application to Seismic Ray Theory
Part IV. Selected Seismological Applications
Chapter 12. Lamb's Problem
12.1 Two-Dimensional Problem in an Isotropic Elastic Solid (Area Souce, Line Source)
12.2 Three-Dimensional Problem in an Isotropic Elastic Solid (Volume Source, Point Source)
12.3 Aibitrary Time Variation in the Three-Dimensional Case
Chapter 13. Wave Propagation in Liquid Media
13.1 Wave Propagation in a Two-Layered Liquid Half-Space
13.2 Wave Propagation in a Liquid Half-Space with Velocity Varying with Depth
Chapter 14. Influence of Gravity on Wave Propagation
14.1 Mathematical Introduction
14.2 Body Waves
14.3 Surface Waves
References
Author Index
Subject Index
Product details
- No. of pages: 428
- Language: English
- Copyright: © Elsevier 1968
- Published: January 1, 1968
- Imprint: Elsevier
- eBook ISBN: 9781483274973
About the Author
Markus Båth
Ratings and Reviews
There are currently no reviews for "Mathematical Aspects of Seismology"