Differential semblance measures the deviation from flatness or focus of image gathers. The differential semblance objective function posed on the sub-surface offset domain responds smoothly to velocity changes. Therefore gradient descent methods are uniquely attractive for velocity updating by differential semblance optimization. Because of their kinematic fidelity, wave equation (depth extrapolation) migration methods are natural platforms for velocity analysis in complex structures. The gradient of the objective function with respect to velocity is fomulated through the adjoint of differential migration. Limited memory BFGS algorithm is used for the velocity optimization. The method for wave equation velocity analysis developed in this thesis study is applied to both synthetic and real data examples.

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.

Hearing loss effects millions of people of all ages and is commonly treated with hearing aids and prostheses. Bone anchored hearing prostheses use bone conduction to transmit sound through the skull bone to the functioning inner ear and cochlea, bypassing the outer and middle ear. A challenge associated with these prostheses is optimizing the location of the surgical implant. A better understanding of how vibrations travel through the skull bone will be beneficial in the improvement of current prostheses and the development of new bone conduction technologies. Using laser Doppler vibrometry, vibration characteristics of dry human skulls were investigated. Three-dimensional vibration patterns were obtained at several frequencies and the dispersion relationship was determined. A closed-spherical shell model proved to be a good indicator of the frequency response of a dry human skull in the frequency range of normal human hearing.

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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.)

Instrumentation commonly used to measure snowpack stratigraphy, snow density, Snow Water Equivalent (SWE), temperature and liquid water content is usually invasive and requires disruption of the snowpack. Most measurement techniques modify the snow medium and more than one sample cannot be taken at the same location. This does not permit continuous monitoring of these parameters using a single measurement instrument. An acoustic wave sent into the snowpack was used to measure snow. To provide the theory required to make acoustic measurements, the Biot-Stoll model of sound wave propagation in porous media was modified using a mixture theory so that it was applicable to a multiphase porous medium. The combined model is called the Unified Thermoacoustic Model (UTAM) for snow. An acoustic measurement device, the System for the Acoustic Sensing of Snow (SAS2), was designed to send sound waves into snow and to receive the reflected sound waves using a loudspeaker and a microphone array. A stationary version of the SAS2 was deployed on a met station and a portable version of the SAS2 was placed on a roving ski-based platform. The systems were deployed at field sites in the Canadian Rocky Mountains, Alberta. The results showed that the SAS2 was able to measure snow density, temperature, and liquid water content and serve as a replacement technology for snowtube and snowpit measurements. Snow density was estimated more accurately by the SAS2 than from commonly-used snow tube techniques.

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