Accuracy bounds for normalincidence acoustic structure estimation
Citable URI
http://hdl.handle.net/1912/1358DOI
10.1575/1912/1358Abstract
Determnation of the structure of a medium from normalincidence
acoustic reflection data is a basic problem in fields
as diverse as medical technology and the earth sciences; this
research examines the accuracy with which quantitative structure
estimates can be made from noisecorrupted measurements
of reflected energy. Two classes of simple physical models,
which exclude geometrical spreading and attenuation, are
developed: one in which the properties of the medium change
continuously with depth, and one in which they change discretely.
Given these reasonable models, estimation accuracy
is studied by computing a statistical lower bound on estimator
performance, the CramerRao bound, for three cases of interest.
(1) The bound is computed for the estimation of unknown, nonrandom
reflection coefficients in a medium containing only
discrete reflectors; special attention is given to the one and
tworeflector situations. The bound's ability to predict
estimator performance is demonstrated, as is the inadequacy of
a particular adhoc estimdtion method based on the Wiener
Levinson algorithm of stochastic filtering theory. (2) The
bound is developed for estimation in a continuous medium whose
structure (acoustic impedance, for exaiple) parametrized by a
set of unknown, nonrandom coefficients, and for which the
reflection response may be computed in closed form. The
problem of estimating the parameters of a single, isogradient
velocity layer of known depth is studied in detail. It is
demonstrated that one can identify the parameters of such a
layer from normalincidence measurements given an appropriate
source and experimenc geometry. (3) A unique extension of
some known results in random process estimation is used to
derive a pointwise bound for estimation in a continuous medium
whose structure (reflection coefficient density) is a random
process. Again we give special consideration to the problem
of identifying a single isolated layer structure. We demonstrate
that for a weakly scattering structure, estimation
accuracy is independent of the mean or nominal structure.
Description
Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution August, 1977
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