## Accuracy bounds for normal-incidence acoustic structure estimation

dc.contributor.author | Theriault, Kenneth B. | |||

dc.date.accessioned | 2006-12-01T17:44:51Z | |||

dc.date.available | 2006-12-01T17:44:51Z | |||

dc.date.issued | 1977-08 | |||

dc.identifier.uri | http://hdl.handle.net/1912/1358 | |||

dc.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 | en | ||

dc.description.abstract | Determnation of the structure of a medium from normal-incidence 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 noise-corrupted 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 Cramer-Rao 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 two-reflector situations. The bound's ability to predict estimator performance is demonstrated, as is the inadequacy of a particular ad-hoc 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, non-random 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 normal-incidence 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. | en | ||

dc.description.sponsorship | Supported by a variety of sources: a National Science Foundation Graduate Fellowship, a Vinton Hayes Graduate Fellowship, and by the Office of Naval Research. | en | ||

dc.format.extent | 7863374 bytes | |||

dc.format.mimetype | application/pdf | |||

dc.language.iso | en_US | en | ||

dc.publisher | Massachusetts Institute of Technology and Woods Hole Oceanographic Institution | en | ||

dc.relation.ispartofseries | WHOI Theses | en | ||

dc.subject | Acoustic impedance | en | ||

dc.subject | Estimation theory | en | ||

dc.subject | Stochastic processes | en | ||

dc.title | Accuracy bounds for normal-incidence acoustic structure estimation | en | ||

dc.type | Thesis | en | ||

dc.identifier.doi | 10.1575/1912/1358 |