Acoustic Waveform Inversion and its Numerical Implementation: Waveform tomography inverts seismic traces for the earth’s elastic parameters. Unlike traveltime tomography, it utilizes both the amplitude and phase information of all arrivals rather than only the traveltimes of selected events. Although elegant in theory, waveform inversion is not always used in exploration geophysics because it is computationally expensive (often more than an order of magnitude more expensive than migration), it requires an expert user to get it to work well, and sometimes it does not work at all. The most challenging problem is that the iterative nonlinear inversions tend to get stuck in a local minimum. Fortunately, the increasing speed of computers, more effective inversion strategies, and a greater demand for accurate lithology information will increase its use in the future.
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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.