The Principles of Quantitative Acoustical Imaging

image of The Principles of Quantitative Acoustical Imaging
  • By Dries Gisolf and Eric Verschuur
  • Format: EPUB
  • Publication Year: 2010
  • Number of Pages: 267
  • Language: English
  • Ebook ISBN: 9789462820135

This book presents a systematic approach to imaging of acoustic reflection measurements and the extraction of media property information from the image amplitudes, based on wave theory.
Although the approach is valid for a wide range of acoustical frequencies and applications, there is a bias towards seismic imaging, because imaging the earth is one of the most challenging of all acoustical imaging applications.
In addition, in oil and gas exploration and production applications the need to obtain quantitative information on the media properties of the object to be imaged is most strongly felt. However, the methods presented are equally valid for ultra-sonic non-destructive testing, or medical diagnostic applications.
The theory of acoustic wave propagation is presented, from the constituent equations Hooke and Newton, to the acoustic wave equation, to wavefield extrapolation and to extraction of image amplitudes. A feature of this book is the careful analysis of every step in these processes in terms of the linearity of the wavefields in the media property representation they are inverted for. Alternatively, the extrapolated wavefields can be inverted directly for the media properties. Towards the end of the book it is demonstrated that significantly higher resolution quantitative information can be obtained if the non-linearity is taken into account

Table of Contents

Chapter 1 Introduction

1.1 Why acoustical imaging?
1.2 Acoustic vs. elastic media
1.3 Imaging vs. inversion
1.4 Linear vs. non-linear
1.5 Wave theory vs. ray theory
1.6 The outline of this book

Chapter 2 Complex transforms
2.1 Fourier transform
2.2 Properties of Fourier transforms
2.3 Discrete Fourier transform
2.4 Laplace transform
2.5 Wave-number/frequency Fourier domain
2.6 Linear Radon transform
Chapter 3 The acoustic wave equation
3.1 Acoustic media
3.2 Hooke’s law and the bulk-modulus
3.3 Newton’s law
3.4 The inhomogeneous acoustic wave equation
3.5 The homogeneous medium acoustic wave equation
3.6 Plane wave solutions
3.7 The wavefield of a point-source
3.8 Near-field particle velocity
3.9 The evanescent field
3.10 One-way wave propagation
Chapter 4 Wavefield extrapolation in homogeneous media
4.1 Forward and backward extrapolation
4.2 The Kirchhoff integral
4.3 Causality of the Kirchhoff integral
4.4 The Rayleigh integrals
4.5 The Rayleigh integral in 2D space
4.6 The Rayleigh integral in the plane wave domain

Chapter 5 Back-propagation and the imaging condition
5.1 Anti-causal form of the Kirchhoff and Rayleigh integrals
5.2 The imaging condition
5.3 Analytical illustration of the imaging condition
5.4 Numerical example

Chapter 6 Linear imaging in low contrast inhomogeneous media
6.1 The Kirchhoff integral in inhomogeneous media
6.2 Linearity
6.3 The Green’s functions in smooth inhomogeneous media
6.4 The Rayleigh integral in a low contrast medium
6.5 The method of the stationary phase
6.6 Ray-theoretical interpretation of the Rayleigh integral
6.7 Numerical example of the stationary phase principle
6.8 The imaging condition in inhomogeneous media
6.9 Multi source imaging
6.10 Back-propagation of receivers and sources
6.11 Numerical illustration of double back-propagation
6.12 Reverse time migration

Chapter 7 Image resolution
7.1 The source wavelet
7.2 The tuning wedge
7.3 Resolution of a point-diffractor for single source illumination
7.4 Resolution of a point-diffractor for multi-source illumination
7.5 The evanescent field under imaging
7.6 Imaging with finite aperture
7.7 Numerical example of imaging with finite aperture
7.8 Imaging of sparsely sampled data

Chapter 8 Getting the velocity model from the data
8.1 Definition of the problem
8.2 Migration Velocity Analysis
8.3 Extracting one-way travel times from the data
8.4 One-way travel time extraction from sparsely sampled 3D data
8.5 Shear travel time extraction from mode-converted data
8.6 Real data example of P and S one-way travel time extraction
8.7 Tomographic inversion of one-way travel times

Chapter 9 Quantitative analysis of image amplitudes
9.1 Acoustic properties, image amplitudes and reflection coefficients
9.2 Plane wave reflection and transmission coefficients
9.3 Dual back-propagation of sources and receivers
9.4 coinciding source/receiver image amplitudes
9.5 Image amplitude vs. horizontal slowness (AVP)
9.6 Synthetic example of image amplitude vs. horizontal slowness
9.7 Image amplitudes of PS converted data
9.8 Real data example of PP and PS image amplitudes

Chapter 10 Local 1.5D linear inversion of back-propagated data
10.1 Introduction
10.2 The role of the smoothly varying background models in inversion
10.3 Damped least squares linear inversion
10.4 Synthetic examples of damped linear inversion
10.5 Discussion of damped linear inversion results

Chapter 11 Elimination of surface related multiples
11.1 Multiples in reflection measurements
11.2 Traditional multiple removal techniques
11.3 Multiple prediction by wavefield extrapolation
11.4 Data-driven multiple prediction
11.5 Surface-related multiple elimination in the 1D case
11.6 Examples of 2D surface-related multiple elimination
11.7 Full 3D implementation of surface-related multiple elimination

Chapter 12 Scale of inhomogeneity in arbitrarily inhomogeneous media
12.1 Arbitrarily inhomogeneous 1D media
12.2 The reflectivity method for total elastic wavefield calculation
12.3 Internal multiple scattering in a two-interface acoustic system
12.4 Absorption and anisotropy through multiple scattering
12.5 Non-linearity in reflection amplitudes as multiple scattering
12.6 Thin layer detectability
Chapter 13 Towards non-linear inversion
13.1 Arbitrarily inhomogeneous media
13.2 Single parameter scattering theory
13.3 Integral representation of the Helmholtz equation
13.4 The background medium
13.5 Solution methods for integral equations
13.6 Imaging by full non-linear inversion
13.7 Iterative non-linear inversion
13.8 Outlook for non-linear inversion

Appendix A The wavefield of a point-source

Appendix B The 2D stationary phase

Appendix C The Green's function amplitude in smooth inhomogeneous media

Appendix D The Zoeppritz equations Bibliography Index




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