Preface

Full-3D seismic waveform inversion (F3DWI) refers to inversions that seek to minimize the discrepancies between the observed and synthetic seismic waveforms, wiggle for wiggle, by solving the three-dimensional acoustic or (visco) elastic wave equations. Its development is important both for the theoretical foundations of modern quantitative seismology and for the practical applications of seismological methods in exploring the Earth’s interior. Driven by the rapid advances in high-performance computing technology and efficient numerical methods for solving 3D wave equations, significant progresses in F3DWI have been made in the past decade, especially in large-scale structural studies that use passive sources. This book is derived from what I have learned in the past 10 years. F3DWI is by its very nature both a theoretical and a practical subject. It requires a certain level of understanding of the underlying mathematical formulation, a collection of parallelized software tools and a certain amount of practice. In this book, I try to give an integrated treatment of all three. In Chap. 1, I give a brief introduction about the subject of this book and some discussions that motivates the development of F3DWI. Throughout this book, a parallelized finite-difference (visco)elastic wave-equation solver is used for demonstration purposes. The mathematical formulation and detailed instructions about how to set up and run this wave-equation solver for F3DWI purposes are summarized in Chap. 2. The theoretical framework for F3DWI developed in Chaps. 3–5 is quite general and encompasses both the adjoint method (F3DT-AW), which back-propagates the misfits from the receivers to image structures, and the scattering-integral method (F3DT-SI), which sets up the Gauss-Newton normal equation by calculating and storing the sensitivity (Fréchet) kernel for each misfit. The derivation of F3DT-SI in our previous publications requires the use of the reciprocity principle and the receiver-side Green’s tensor (RGT). In Chap. 3, I generalize the formulation of F3DT-SI through adjoint analysis and show that the requirement on reciprocity can be removed by replacing the RGT with the timereversed adjoint Green’s tensor. This result may open up the possibility of applying the “scattering-integral-type” methods based on Green’s functions to a larger class of inverse problems, in which the reciprocity principle may not hold. In Chap. 3, I