Elastic and Viscoelastic Full-Waveform Inversion
Elastic and Viscoelastic Full-Waveform Inversion: This chapter presents the theory of elastic and viscoelastic full-waveform inversion (FWI), which, in principle, reconstructs both the P- and S-wave velocities from the seismic data. Instead of modeling the acoustic wave equation, the modeling and back projection of the data use numerical solutions to either the elastic or viscoelastic wave equations. To account for attenuation, the viscoelastic wave equation is used both to forward propagate and back propagate the wavefields. This means that estimates of the P-wave attenuation QP and S-wave attenuation QS distributions are needed as input information into the viscoelastic modeling code. These distributions can be estimated by a ray-based inversion scheme or a wave-equation inversion scheme.
Figures & Tables
This book describes the theory and practice of inverting seismic data for the subsurface rock properties of the earth. The primary application is for inverting reflection and/or transmission data from engineering or exploration surveys, but the methods described also can be used for earthquake studies. I have written this book with the hope that it will be largely comprehensible to scientists and advanced students in engineering, earth sciences, and physics. It is desirable that the reader has some familiarity with certain aspects of numerical computation, such as finite-difference solutions to partial differential equations, numerical linear algebra, and the basic physics of wave propagation (e.g., Snell’s law and ray tracing). For those not familiar with the terminology and methods of seismic exploration, a brief introduction is provided in the Appendix of Chapter 1. Computational labs are provided for most of the chapters, and some field data labs are given as well. Matlab and Fortran labs at the end of some chapters are used to deepen the reader’s understanding of the concepts and their implementation. Such exercises are introduced early and geophysical applications are presented in every chapter. For the non-geophysicist, geophysical concepts are introduced with intuitive arguments, and their description by rigorous theory is deferred to later chapters.