Raypath Traveltime Tomography: As discussed in Chapter 1, geophysical traveltime tomography is the procedure for inverting traveltimes of specified body waves for the velocity distribution of the earth. It has been the primary means for earthquake imaging of the Earth’s interior from the early 1970s. Until recently, it was implemented mostly using the high-frequency approximation of ray tracing, but there is a growing tendency to use finite-frequency tomography, in which traveltime residuals are back projected along wavepaths rather than raypaths. Finite-frequency wave-equation tomography, also known as wave-equation tomography or wave-equation traveltime tomography, can be more accurate than raypath tomography. However, it is at least an order of magnitude more costly because the wave equation must be solved numerically for each source. Traveltime tomography also is used in a variety of other fields, such as medical imaging, nondestructive evaluation, and meteorology.
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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.