Generalized optical theorem in coherent scattering

On seismic interferometry, the generalized optical theorem, and the scattering matrix of a point scatterer

We have analyzed the far-field approximation of the Green’s function representation for seismic interferometry. By writing each of the Green’s functions involved in the correlation process as a superposition of a direct wave and a scattered wave, the Green’s function representation is rewritten as a superposition of four terms. When the scattered waves are modeled with the Born approximation, i...

A Fixed Point Theorem in Generalized D-metric Spaces

GENERALIZED PRINCIPAL IDEAL THEOREM FOR MODULES

The Generalized Principal Ideal Theorem is one of the cornerstones of dimension theory for Noetherian rings. For an R-module M, we identify certain submodules of M that play a role analogous to that of prime ideals in the ring R. Using this definition, we extend the Generalized Principal Ideal Theorem to modules.

Generalized optical theorem for surface waves and layered media.

We present a generalized optical theorem for surface waves. The theorem also applies to body waves since under many circumstances body waves can be written in terms of surface-wave modal summations. This theorem therefore extends the domain of applicability of the optical theorem from homogeneous background media to a general class of body and surface-wave propagation regimes within layered ela...

n seismic interferometry , the generalized optical theorem , and the cattering

We have analyzed the far-field approximation of the Green’s function representation for seismic interferometry. By writing each of the Green’s functions involved in the correlation process as a superposition of a direct wave and a scattered wave, the Green’s function representation is rewritten as a superposition of four terms. When the scattered waves are modeled with the Born approximation, i...