Analytical studies in signal theory, wave propagation, anisotropy, seismic migration, tomography and inversion
The notion of structural stability is important in seismic inversion and imaging. Structurable stable systems are robust, and -- to put it simply -- an 'image' is said to be structurally stable if its structure remains qualitatively the same, independent of small changes in some external parameters. The primary images of a parabolic Radon transform and zero-offset migration within the paraxial approximation are structurally unstable. A 3D plot of the parabolic Radon transform (picture) reveals the position of singular points. The analytical studies include signal theory, wave propagation, anisotropy, seismic migration, seismic tomography and seismic inversion.