Generalized Image-Domain Inversion
Generalized Image-Domain Inversion: The gradient formula is derived for the generalized image objective function and the h-offset moveout curve in the extended image domain; in practice the objective function has an extra summation over all model points in the subsurface. The summation is over the subsurface offset indices. The result shows that Y(y) is a summation of three gradients: a low-wavenumber generalized semblance optimization (H-DSO) gradient, the intermediate-wavenumber gradient associated with differential semblance optimization (DSO), and a high-wavenumber gradient associated with full-waveform inversion (FWI). This image-domain gradient has multi-scale features similar to those of wave-equation-traveltime waveform inversion in the data domain, and it can be used to partly overcome the cycle-skipping problem with FWI.
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.