GENERALIZED OPTICAL THEOREM IN THE TIME DOMAIN

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...

The reciprocity theorem for the scattered field is the progenitor of the generalized optical theorem.

By analyzing correlation-type reciprocity theorems for wavefields in perturbed media, it is shown that the correlation-type reciprocity theorem for the scattered field is the progenitor of the generalized optical theorem. This reciprocity theorem, in contrast to the generalized optical theorem, allows for inhomogeneous background properties and does not make use of a far-field condition. This t...

GENERALIZATION OF TITCHMARSH'S THEOREM FOR THE GENERALIZED FOURIER-BESSEL TRANSFORM

In this paper, using a generalized translation operator, we prove theestimates for the generalized Fourier-Bessel transform in the space L2 on certainclasses of functions.

Field Fluctuations, Imaging with Backscattered Waves, a Generalized Energy Theorem, and the Optical Theorem

We show the connection between four aspects of wave propagation: the autocorrelation of field fluctuations, imaging with backscattered waves, a theorem for energy flow, and the generalized optical theorem. The autocorrelation of field fluctuations can be used to extract the imaginary component of the Green’s function at the source. The Green’s function usually is singular at the source, but the...

A Fixed Point Theorem in Generalized D-metric Spaces