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Title: Time-reversal and interferometry, with applications to forward modeling of wave propagation and a chapter on receiver functions
Author: van Manen, Dirk-Jan
Awarding Body: University of Edinburgh
Current Institution: University of Edinburgh
Date of Award: 2006
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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.
Supervisor: Robertsson, Johan. ; Curtis, Andrew. Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Geophysics