Reflection Seismology

Theory, Data Processing and Interpretation

Yang Wencai

• Publisher: Elsevier
• Year: 2013
• Print ISBN: 9780124095380
• eBook ISBN: 9780124096004
• Topic: Physical Sciences
• Subtopic: Seismology & Volcanism

Authored by a geophysicist with more than 50 years of experience in research and instruction, Reflection Seismology: Theory, Data Processing and Interpretation provides a single source of foundational knowledge in reflection seismology principles and theory.Reflection seismology has a broad range of applications and is used primarily by the oil and gas industry to provide high-resolution maps and build a coherent geological story from maps of processed seismic reflections. Combined with seismic attribute analysis and other exploration geophysics tools, it aids geologists and geo-engineers in creating geological models of areas of exploration and extraction interest. Yet as important as reflection seismology is to the hydrocarbon industry, it's difficult to find a single source that synthesizes the topic without having to wade through numerous journal articles from a range of different publishers. This book is a one-stop source of reflection seismology theory, helping scientists navigates through the wealth of new data processing techniques that have emerged in recent years.- Provides geoscientists and geo-engineers with a theoretical framework for navigating the rapid emergence of new data processing techniques- Presents a single source of reflection seismology content instead of a scattering of disparate journal articles- Features more than 100 figures, illustrations, and working examples to aid the reader in retaining key concepts- Arms geophysicists and geo-engineers with a solid foundation in seismic wave equation analysis and interpretation

Chapter 1

Introduction to the Wave Theory

Abstract

Physics is the study of the motion of matter. It originates from Newtonian mechanics theory. In classical mechanics, which is established by Newton in the seventeenth century, particle dynamics was first employed to describe the motion of macroscopic objects. However, we must deal with continuously constructed media such as the earth, and the application of particle dynamics has some limitations. Thus, scientists developed continuum mechanics in the early twentieth century, including fluid mechanics and solid mechanics. Quantum mechanics has been developed in the same period to describe the motion of microscopic particles. The theory in this book is based on continuum mechanics and the methods of mathematical physics.

Keywords

Dynamics; Mechanics; Wave theory

Outline

1.1. Wave Motion in Continuous Media

1.2. Vibration

1.3. Propagation and Diffusion

1.4. Acoustic Wave Equation

1.5. Acoustic Wave Equation with Complex Coefficients

1.5.1. Complex Elastic Modulus and the Complex Wave Velocity

1.5.2. Damping Wave Equations in Viscoelastic Media

1.5.3. Viscoelastic Models

1.6. Acoustic Wave Equation with Variant Density or Velocity

1.7. Summary

Physics is the study of the motion of matter. It originates from Newtonian mechanics theory. In classical mechanics, which is established by Newton in the seventeenth century, particle dynamics was first employed to describe the motion of macroscopic objects. However, we must deal with continuously constructed media such as the earth; the application of particle dynamics has some limitations. Thus, scientists developed continuum mechanics in the early twentieth century, including fluid mechanics and solid mechanics. Quantum mechanics has been developed in the same period to describe the motion of microscopic particles. The theory in this book is based on continuum mechanics and the methods of mathematical physics.

The motion of macroscopic objects in general can be divided into three types: The first is displacement, such as linear movement, rotation, flight, and flow. The second is vibration and wave motion, such as periodic motion, water wave, acoustic wave, and seismic wave. The third is chaotic movement, such as intermittent motion, turbulence, and nonlinear wave motion. This book only discusses classical vibration and wave theory. As a kind of physical movement, vibration can be described using an initial value problem of ordinary differential equations for a closed system, in which energy and information do not get exchanged between the system and the outside world. For an open system, in which energy and information get exchanged between the system and the outside world, the initial and boundary value problems of partial differential equations must be applied. This chapter discusses the basic wave theory, focusing on the acoustic wave equation and related wave behaviors.

To make mathematical formulas clear, we use bold English letters for vectors or matrices, and normal Greek letters for scalars in this book.

1.1 Wave Motion in Continuous Media

Wave motion refers to the propagation of vibration in continuous media, which can be described by using the following formulations:

Wave motion = vibration + propagation (in continuous media);

Vibration = periodic motion that an object moves around its equilibrium point;

Propagation = interaction between the vibration and adjoining mass grains and diffusion of the vibration energy.

The above concepts are limited to the situation that the vibration equilibrium point of mass grains is fixed and is stationary during wave propagation; they are accurate for the elastic waves propagating in solid media. Generalized waves involve situations in which the vibration equilibrium point is not fixed and movable. For example, water waves are a kind of generalized waves with moving equilibrium points. We do not discuss generalized waves in this book.

Three assumptions are usually accepted in the study of continuum mechanics and are as follows (Fung, 1977; Spencer, 1980; Du Xun, 1985):

1. Mass motion foll...

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright
• Preface
• Chapter 1. Introduction to the Wave Theory
• Chapter 2. Elastic Waves in a Perfect Elastic Solid
• Chapter 3. From Elastic Waves to Seismic Waves
• Chapter 4. Wave Equation Reduction with Reflection Seismic Data Processing
• Chapter 5. Integral Solutions of the Wave Equation with Boundary and Initial Value Conditions
• Chapter 6. Decomposition and Continuation of Seismic Wave Field
• Chapter 7. Seismic Inversion
• Appendix. Finite Difference Method for Solving the Acoustic Wave Equation with Velocity and Density Variant Media
• References
• Index