Resolution Limits for Wave Equation Imaging*
Resolution Limits for Wave Equation Imaging: In 2014, I coauthored the following reprinted paper with Yunsong Huang on deriving resolution limits for imaging wave equations, based on our work together at King Abdullah University of Science and Technology (KAUST), in Thuwal, Saudi Arabia. As noted in the opening paragraphs, “To optimize the use of wave equation imaging one must understand its limits of spatial resolution. Without this understanding, models can be over parameterized and lead to solutions that honor the data but violate the wavelength-based resolution limits of wave propagation. Such models should be avoided in our attempts to understand the earth.” Resolution limits for wave equation imaging, published in the Journal of Applied Geophysics, builds on developments over the past 30 years in mathematically defining resolution limits. It begins by showing how wavepaths can estimate resolution for traveltime tomography and migration. Spatial resolution is defined intuitively as the minimum width and height of the intersection of Fresnel zones at the trial image point. Then, that definition is proved by deriving the resolution limits for each variety of wavepath, showing their relationship to the acquisition geometry. This work gives a comprehensive asymptotic analysis of the model resolution function for least-squares migration, with resulting formulae that allow the geoscientist to optimize resolution characteristics in full-waveform inversion, least-squares migration, and reverse time migration.
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.