A unified optical theorem for scalar and vectorial wave fields.

The generalized optical theorem is an integral relation for the angle-dependent scattering amplitude of an inhomogeneous scattering object embedded in a homogeneous background. It has been derived separately for several scalar and vectorial wave phenomena. Here a unified optical theorem is derived that encompasses the separate versions for scalar and vectorial waves.

Extracting the Green's function from measurements of the energy flux.

Existing methods for Green's function extraction give the Green's function from the correlation of field fluctuations recorded at those points. In this work it is shown that the Green's function for acoustic waves can be retrieved from measurements of the integrated energy flux through a closed surface taken from three experiments where two time-harmonic sources first operate separately, and then simultaneously. This makes it possible to infer the Green's function in acoustics from measurements of the energy flux through an arbitrary closed surface surrounding both sources.

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 theorem specializes to the generalized optical theorem when considering a finite-size scatterer embedded in a homogeneous background medium and when utilizing the far-field condition.

Representation theorems and Green's function retrieval for scattering in acoustic media.

Reciprocity theorems for perturbed acoustic media are provided in the form of convolution- and correlation-type theorems. These reciprocity relations are particularly useful in the general treatment of both forward and inverse-scattering problems. Using Green's functions to describe perturbed and unperturbed waves in two distinct wave states, representation theorems for scattered waves are derived from the reciprocity relations.

Coda wave interferometry for estimating nonlinear behavior in seismic velocity.

In coda wave interferometry, one records multiply scattered waves at a limited number of receivers to infer changes in the medium over time. With this technique, we have determined the nonlinear dependence of the seismic velocity in granite on temperature and the associated acoustic emissions. This technique can be used in warning mode, to detect the presence of temporal changes in the medium, or in diagnostic mode, where the temporal change in the medium is quantified.