A Friendly Guide to Wave Equation Migration and Inversion

This book provides a systematic introduction to modern seismic imaging and inversion methods based on wave-equation theory. It begins with diffraction-stack migration and the concept of adjoint operators, resolution analysis, and gradually introduces one-way/two-way wave-equation modeling and migration, least-squares migration, angle-domain imaging, and full-waveform inversion. Particular attention is given to the role of the angle-domain Hessian operator in migration and inversion. Advanced topics including elastic and viscoelastic full-waveform inversion, high-order Born inversion, vector-reflectivity inversion, nullspace shuttles, and uncertainty quantification are also presented. Emphasis is placed on physical intuition, mathematical derivations, numerical implementation, and reproducible computational examples. Accompanying Python codes are provided throughout the book to help readers connect theoretical concepts with practical applications. The book is intended for graduate students, researchers, and practicing geophysicists interested in seismic imaging and inversion.