Seismic 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.