Tomography, Adjoint Methods, Time-Reversal, and Banana-Doughnut Kernels

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Forward and adjoint simulations of seismic wave propagation on fully unstructured hexahedral meshes (2011, methodology): “In terms of a parametrization involving compressional wave speed α, shear wave speed β and density ρ, the corresponding kernels are given by a linear combination of these primary kernels (Tromp et al. 2005, eq.”
Hessian kernels of seismic data functionals based upon adjoint techniques (2011, background): “This observation is closely related to the characteristics of Rayleigh scattering from density perturbations (e.g. Wu & Aki 1985; Tarantola 1986).”
Deep-Learning Inversion of Seismic Data (2019, methodology): “to update the model parameters, and the gradient is normally calculated through backward wavefield propagation of data residuals based on adjoint-state methods [13]–[15].”
Time‐reversal imaging of seismic sources and application to the great Sumatra earthquake (2006, background): “Finally, we recall the strong connections between tomographic techniques and time-reversal field [Tarantola, 1988; Tromp et al., 2005].”
Whole-mantle radially anisotropic shear velocity structure from spectral-element waveform tomography (2014, methodology): “One of the primary benefits of the hybrid approach over fully SEM-based techniques using first-order adjoint-state methods (e.g. Tarantola 1984; Tromp et al. 2005) is convergence rate.”