This book introduces a methodology for solving the seismic inverse problem using purely numerical solutions built on 3D wave equations and which is free of the approximations or simplifications that are common in classical seismic inversion methodologies and therefore applicable to arbitrary 3D geological media and seismic source models. Source codes provided allow readers to experiment with the calculations demonstrated and also explore their own applications.Table of Contents: Preface.- Introduction.- An elastic Wave Propagation (AWP).- Green's Functions.- Data Sensitivity Kernels.- Optimization Algorithms.- CVM-S4.26.- Index.