To predict the location of natural resources and reduce the cost of exploration, geophysicists rely on various techniques to map the internal structure of the earth. One common mapping method probes the earth's interior using an acoustic energy source (sound waves). The acoustic waves reflect when they impinge on a location where the acoustic velocity field oscillates rapidly (on the scale of a wavelength). When the waves reflect back to the surface, they carry kinematical information about the location of the oscillatory velocity field. A linearized wave equation models the scattering process and its solution operator is a Fourier integral operator. As such, the scattering operator has a canonical relation $\Lambda$ which describes how the operator maps oscillatory velocity fields to oscillatory wave fields at the surface. The goal of linearized inversion is to obtain an inverse operator (with inverse canonical relation) for the scattering operator. We give a geometrical condition on $\Lambda$ that is equivalent to the existence of a linearized inversion operator. Since the $L\sp2$-adjoint of the scattering operator has inverse canonical relation, geophysicists often apply it to the scattered field to obtain a map of the subsurface. I analyze the scattering operator using high-frequency asymptotics and show that if the geometrical condition fails, the scattering canonical relation is not injective. Therefore, application of the adjoint operator to the scattered wave field can produce artifacts in the resulting map of the subsurface. I demonstrate this effect numerically. I also prove that the scattering operator is continuous between a certain domain and range space iff the geometrical condition on $\Lambda$ holds. Furthermore, I have shown that it is possible to map an experiment where the geometrical condition fails into another experiment where it holds.

The acoustic characterization of six glasses each doped with one of the following dopants: GeO$ sb2$, P$ sb2$O$ sb5$, F, TiO$ sb2$, B$ sb2$O$ sb3$ or Al$ sb2$O$ sb3$ is presented. We have found that a linear variation of acoustic velocities versus dopant concentration for each dopant studied and the addition of Al$ sb2$O$ sb3$ increases the acoustic velocity while all the other dopants decrease this velocity. In addition, the acoustic velocity variation is more sensitive than the optical refractive index to the dopant concentration for the doped silica glasses investigated. Furthermore, the F and GeO$ sb2$ doped silica glasses exhibit higher acoustic loss than pure fused silica does. / These six doped glasses are widely used as core and cladding material for optical fibers. Their acoustic properties can affect the backward stimulated Brillouin scattering since this scattering involves acoustic disturbances of the material. The SBBS threshold is evaluated theoretically taking the Bragg and the nonlinear coupling of the pump and Stokes into account. / Effects of different acoustic profiles of SMOFs on SBBS are experimentally investigated. (Abstract shortened by UMI.)

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A detailed theoretical analysis is presented for calculating the surface acoustic wave (SAW) reflection coefficient of thin metallic layers. Based on this analysis, directions of propagation are classified as symmetric or asymmetric. An augmented scalar transmission line circuit model which contains a new lumped network element that accounts for asymmetry is introduced to describe SAW reflection and transmission through a strip. The resulting network model is used to analyze grating and transducer structures. Computed results based on this new network model are in excellent agreement with measured data, not only on devices oriented along symmetric directions, but also on devices which exhibit directivity due to asymmetric orientations. A simple procedure, based on physical arguments, is outlined for the identification of high directivity orientations. An algebraic construction is given which demonstrates that the coupling-of-modes (COM) modelling of gratings and transducers is derivable from the new network model. Approximate explicit analytical expressions, in terms of the network model, are given for the COM model parameters. The properties of pseudo-surface-waves are re-examined and a new high-velocity pseudo-surface acoustic wave (HVPSAW) is described. It is shown that this mode, not referenced in the SAW device literature, has a low attenuation along certain directions, and is thus very attractive for high-frequency low-loss SAW devices.

Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2006. / Source: Dissertation Abstracts International, Volume: 68-02, Section: B, page: 1018. Adviser: Richard L. Weaver. Includes bibliographical references (leaves ) Available on microfilm from Pro Quest Information and Learning.

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An improved numerical model for calculating the ultrasonic power deposition in layered medium was developed and experimentally verified. The new model takes into account the ultrasound wave reflection and refraction at irregular tissue interfaces thereby providing improved accuracy in ultrasound hyperthermia treatment planning. The model was compared with a simplified model to evaluate when the tissue interfaces could be ignored in the hyperthermia treatment planning and evaluation. The effects of variations in water and tissue temperatures, the fat layer thicknesses, the bone-tissue interface, and the beam entrance angles were also investigated to establish guidelines for treatment execution. It was found that in most cases the effects of the soft tissue interfaces can be ignored. However, in some instances the acoustic focus may be shifted several millimeters off axis in layered medium. This is important when sharply focused transducers are used for ultrasound surgery or under the condition of pulsed, high temperature hyperthermia treatments.

<p> A survey of relevant literature on the topic of wave propagation and scattering in pipes is given first. This review is followed by a theoretical framework which is pertinent to wave propagation in homogeneous, isotropic, pipes. Emphasis is placed on approximate solutions stemming from a computer based, <u>S</u>emi-<u>A</u>nalytical <u> F</u>inite <u>E</u>lement (SAFE) formulation. A modal analysis of the dynamic response of homogeneous, isotropic pipes, when subjected to a transient ultrasonic excitation, demonstrates that dominant features, i.e., singularities in an unblemished pipe&rsquo;s displacement <u> F</u>requency <u>R</u>esponse <u> F</u>unction (FRF) coincide with its cutoff frequencies. This behaviour is confirmed experimentally. A novel technique is developed to deduce such a pipe&rsquo;s wall thickness and elastic properties from three cutoff frequencies. The resulting procedure is simulated numerically and verified experimentally. Agreement between the new ultrasonic procedure and traditional destructive tests is within experimental uncertainty. Then a hybrid-SAFE technique is used to simulate waves scattered by various open rectangular notches. The simulations show, for the first time, that singularities distinct from the unblemished pipe&rsquo;s cutoff frequencies arise in a displacement FRF when an axisymmetric notch is introduced. They also suggest that the new singularities depend on the properties of the parent pipe <i>and</i> the finite element region but effects are local to a notch. It is demonstrated further that the difference between the frequency at which a singularity introduced by a notch occurs and the nearest corresponding unblemished pipe&rsquo;s cutoff frequency is a function of the notch&rsquo;s dimensions. By plotting contours of constant frequency differences, it is shown that it is <i>usually </i> possible to characterize the notch&rsquo;s dimensions by using two modes. However, the frequency difference for a third mode may be also needed occasionally. The more general case of nonaxisymmetric notches is shown to be a straightforward extension of the axisymmetric case.</p>