| Summary: | Many recent methods of seismic wave field processing and inversion concern themselves with the fine detail
of the amplitude and phase characteristics of measured events. Processes of absorption and dispersion have a
strong impact on both; the impact is particularly deleterious to the effective resolution of images created from
the data. There is a need to understand the dissipation of seismic wave energy as it affects such methods. I
identify: algorithms based on the inverse scattering series, algorithms based on multiresolution analysis, and
algorithms based on the estimation of the order of the singularities of seismic data, as requiring this kind of
study. As it turns out, these approaches may be cast such that they deal directly with issues of attenuation,
to the point where they can be seen as tools for viscoacoustic forward modelling, Q estimation, viscoacoustic
inversion, and/or Q compensation.
In this thesis I demonstrate these ideas in turn. The forward scattering series is formulated such that
a viscoacoustic wave field is represented as an expansion about an acoustic reference; analysis of the convergence
properties and scattering diagrams are carried out, and it is shown that (i) the attenuated wave
field may be generated by the nonlinear interplay of acoustic reference fields, and (ii) the cumulative effect
of certain scattering types is responsible for macroscopic wave field properties; also, the basic form of the
absorptive/dispersive inversion problem is predicted. Following this, the impact of Q on measurements of the
local regularity of a seismic trace, via Lipschitz exponents, is discussed, with the aim of using these exponents
as a means to estimate local Q values. The problem of inverse scattering based imaging and inversion is
treated next: I present a simple, computable form for the simultaneous imaging and wavespeed inversion of
ID acoustic wave field data. This method is applied to ID, normal incidence synthetic data; its sensitivity
with respect to contrast, complexity, noise and bandlimited data are concurrently surveyed. I next develop
and test a Born inversion for simultaneous contrasts in wavespeed and Q, distinguishing between the results of
a pure Born inversion and a further, bootstrap, approach that improves the quality of the linear results. The
nonlinear inversion subseries of the inverse scattering series is then cast for simplified viscoacoustic media, to
understand the behaviour and implied capabilities of the series/subseries to handle Q. The "communication
between events" of the inversion subseries is developed in theory and with numeric examples; it is shown
that terms which contain cumulative information from all portions of the data dominate over local terms in
determining correct, local, model amplitudes. Finally, I consider the use of a wavelet-based regularization of
the operator for viscoacoustic downward continuation.
The inclusion of absorption and dispersion in the theory that underlies many seismic methods leads to
processing and inversion methods that estimate attenuation parameters and compensate for unwanted effects.
These methods are sensitive to amplitude and phase information (by design) and so require low noise, often
broadband data; however the methods have responded very favourably to synthetic data tests, and tend to
be forgiving to bandlimited data with small amounts of error.
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