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
Chapter 2 Complex transforms
Chapter 3 The acoustic wave equation
Chapter 4 Wavefield extrapolation in homogeneous media
Chapter 5 Back-propagation and the imaging condition
Chapter 6 Linear imaging in low contrast inhomogeneous media
Chapter 7 Image resolution
Chapter 8 Getting the velocity model from the data
Chapter 9 Quantitative analysis of image amplitudes
Chapter 10 Local 1.5D linear inversion of back-propagated data
Chapter 11 Elimination of surface related multiples
Chapter 12 Scale of inhomogeneity in arbitrarily inhomogeneous media
Chapter 13 Towards 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
Appendix D The Zoeppritz equations