In exploration seismics and non-destructive evaluation, acoustic, elastic and
electro-magnetic waves sensitive to inhomogeneities in the medium under investigation are used to probe its interior. Waves multiply scattered by the inhomogeneities carry significant information but, due to their non-linear relation
with the inhomogeneities, are notoriously dificult to image or invert for subsurface structure. Recently, however, this paradigm may have been broken as it was
shown that high-order multiply scattered acoustic waves can be time-reversed and
focused onto their original source location through arbitrary, unknown, inhomogeneous media using a so-called time-reversal mirror: in a first step, the multiply
scattered waves are recorded on an array of transducers partially surrounding
the medium, in the second step the recorded wavefields are time-reversed and reemitted into the medium (i.e., the time-reversal mirror acts as a linear boundary
condition on the medium injecting the time-reversed, multiply scattered wave-
field). The multiply scattered waves retrace their paths through the medium and
focus on the original source location. In another development the full waveform
Green's function between two (passive) receivers has been observed to emerge
from crosscorrelation of multiply scattered coda waves. This process is called
interferometry. The principal aim of this thesis is to explore the relation between
time-reversal and interferometry and to apply the resulting insights to forward
modelling of wave propagation in the broader context of inversion. A secondary
aim is to see if the seismological receiver function method can be applied to a
reflection setting in ways that are both dynamically and kinematically correct.
These aims are achieved through: (1) Derivation of an integral representation
for the time-reversed wavefield in arbitrary points of an inhomogeneous medium
[first, for the acoustic case, based on the Kirchhoff-Helmholtz integral, then for
the elastic case based on the Betti-Rayleigh reciprocity theorem]. Evaluation of these integral representations for points other than the original source point will
be shown to give rise to the Green's function between the two points. Physically
intuitive explanations will be given as to why this is the case. (2) Application of
ordinary reciprocity to the integral representation for the time-reversed wavefield
to get an expression in terms of sources on the surrounding surface only. This
gives rise to an efficient and flexible forward modeling algorithm. By illuminating
the medium from the surrounding surface and storing full waveforms in as many
points in the interior as possible, full waveform Green's functions between arbitrary points in the volume can be computed by cross correlation and summation
only. (3) Derivation of an exact, interferometric von Neumann type boundary
condition for arbitrary interior perturbed scattering problems. The exact bound-
ary condition correctly accounts for all orders of multiple scattering, both inside
the scattering perturbation(s) and between the perturbations and the background
model and thus includes all so-called higher-order, long-range interactions. (4)
A comprehensive study of the receiver function method in a reflection setting,
both kinematically and dynamically. All presented results are verified and illustrated by numerical (finite-difference) modelling. Overall, the results in this thesis
demonstrate that, while the original instabilities associated with direct inversion
remain, multiply scattered waves can be used in an industrial context { both
in real-life experiments and in forward modelling { in ways that are stable. The
presented advances in forward modelling are argued to have a significant impact
on inversion as well, albeit indirectly
