Generalized Differential Semblance Optimization
Generalized Differential Semblance Optimization: Wave-equation traveltime and waveform tomography first inverts the smoothly varying traveltimes of selected events to obtain the low-wavenumber estimate of the velocity model. Then, the rapidly varying waveforms are inverted during the later iterations to estimate the high-wavenumber portion of the velocity model. This physics-based multiscale procedure can mitigate the tendency for iterative waveform inversion to get stuck in a local minimum. Multiscale physics can be adapted to differential semblance optimization (DSO) in the image domain. That is, the space-lag offset can be identified in the subsurface-offset domain as an implicit function of velocity. It describes the smoothly varying moveout of the migration image in the subsurface-offset domain, which is analogous to the smoothly varying travel-time residual of a reflection event in a shot gather.
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.