Full-3D Seismic Waveform Inversion: Theory, Software and Practice

Preface.- Introduction.- Advantages of the seismic ray method.- Drawbacks of the seismic ray method.- Numerical solutions of the seismic wave equation.- A brief history of HPC technology.- Anelastic Wave Propagation (AWP).- Formulation.- Elastic Media.- Viscoelastic Media.- The complex modulus and its approximation.- Physical interpretation of the approximate modulus.- Isotropic viscoelastic media.- Frequency-independent Q.- Discretization.- Free-Surface Boundary.- PML Boundary.- Internal Welded Material Interfaces.- Source Representation.- Software.- Mesh Generation.- Structural Model.- Parameter File.- Sources and Receivers.- File Format.- File Processing.- Recording Grid Points.- Wavefield Simulation.- Synthetic Seismograms.- Half-Space Example Summary.- Application.- SCEC Community Velocity Models (CVMs).- Earthquake Source Models.- Validation of SCEC CVMs.- Green's Functions.- Mathematical Preliminary.- Vector Spaces.- Inner Product.- Linear Transformations.- Hilbert Spaces.- Functions As Vectors.- Dirac Delta Function.- Fourier Transforms.- Operator Algebra.- Fréchet Derivative.- The Adjoint of a Differential Operator.- Ordinary Differential Operators.- Partial Differential Operators.- Scalar Wave Equations.- Gradient, Divergence and Curl.- Viscoelastic Equation of Motion.- Adjoint Initial and Boundary Conditions.- ODE.- Scalar Wave Equations.- Anisotropic Viscoelastic Wave Equation.- Properties of Green's Functions.- Adjoint Green's Functions.- Reciprocity.- Scalar Wave-Equation Operator.- Anisotropic Viscoelastic Wave-Equation Operator.- Inhomogeneous Initial/Boundary Conditions.- General 2nd-Order ODE.- Representation Theorem.- Adjoint Representation Theorem.- Receiver Green Tensor (RGT).- Time-Reversed Adjoint Green's Tensor.- Receiver-Side Strain Green's Tensor (RSGT).- RSGTs in the Half-Space Example.- Born Series.- The Scalar Wave Equation.- Born Kernel.- Born Approximation.- The Anisotropic Viscoelastic Wave Equation.- Data Sensitivity Kernels.- Definition.- Data Functionals.- Data Functionals for u and u.- Filtered RGT.- The Chain Rule.- Time-Domain Waveform Differences.- Frequency-Domain Waveform Differences.- Broadband Cross-Correlation Measurements.- Frequency-Dependent Phase and Amplitude Misfits.- Rytov Approximation.- "Banana-Doughnut" Structure of Rytov Phase Kernels.- Model Parameterization.- Bulk Modulus.- Bulk and Shear Moduli.- Lamé Parameters.- P- and S-wave Velocities.- Love's Elastic Parameters (Hexagonal Symmetry).- Asymptotic Parameters (Triclinic Symmetry).- Anelastic Attenuation Quality Factors.- Finite Moment Tensor (FMT).- Software.- WPK File.- Kernel Calculation.- Kernel Output and Visualization.- More Examples.- S-Wave From a Double-Couple Source.- Rayleigh Wave From a Vertical Body-Force.- Head Waves.- Optimization Algorithms.- The Scattering-Integral (SI) Method.- The Gauss-Newton Algorithm.- F3DT-SI.- Scalable Parallel LSQR (SPLSQR).- Model Covariance.- Annihilator Matrix.- The Adjoint-Wavefield (AW) Method.- The Gradient.- F3DT-AW.- Hessian-Vector Product.- Software.- Adjoint Source Field.- Adjoint Wavefield.- Event Kernel.- CVM-S4.26.- Background.- Convergence Rate.- Data Functionals.- Model Evaluation.- Model Description.- CVM-S4.26 and CVM-S4 Comparison.- CVM-S4.26 and CVM-H11.9 Comparison.- Starting Model Differences.- Data Differences.- Algorithmic Differences.- Earthquake Source Parameter Differences.- Summary.- Southern Walker Lane Belt.- Long Valley Caldera.- Indian Wells Valley - Coso Geothermal Area.- Owens Lake.- Panamint Range.- Southern Sierra Nevada.- SNB Mafic Cumulates.- Tehachapi Anomaly.- Southern San Joaquin Basin.- Basin Geometry.- Great Valley Ophiolite.- Southern Coast Ranges.- Salinian Block.- Nacimiento Block.- Transverse Ranges.- Ventura Basin _ Santa Barbara Channel.- San Bernardino Basin.- Inner Continental Borderland.- Los Angeles Basin.- Offshore Region.- Mojave Desert Region.- Antelope Valley.- POR Schist.- Peninsular Ranges - Salton Trough Region.- Index.