Directional acoustic beams are used in diverse sonar systems. For efficient transmission of a sonar signal, the sound energy is projected in a narrow beam . For reduced interference in reception, the sound signal is received from a narrow spatial sector. Typically, such beams have associated sidelobes which adversely affect sonar performance. The goal of this thesis is to propose several novel acoustic arrays which are capable of generating desired search-light-type and fan-type beams with greatly reduced sidelobes. These novel acoustic arrays have fewer elements than conventional arrays of similar performance. The design of such novel arrays is inherently more difficult, however, since it involves nonlinear optimization. Such an optimization is normally computationally intensive and may not be globally convergent. This difficulty has been overcome by newly developed concepts and associated array pattern synthesis methods. A new concept called the equivalent linear array is introduced; a design method based on this concept benefits from existing design techniques developed for linear arrays. The equivalent linear array concept is further developed to lead to a new and effective method for array radiation pattern synthesis. A second new concept called the scale-invariance radiation pattern is introduced, and the subsequent relation between two novel arrays is discovered. Using this concept an angle mapping approach is developed which transforms a radiation pattern generated by a circular ring array to that of an elliptic ring array. This approach takes advantage of methodologies developed for the design of circular ring arrays. A third concept, constraint directions, is introduced; a subsequent new iterative method for array pattern synthesis is developed to meet the need in compact receiving/transmitting array design. With the help of these new concepts, the proposed synthesis methods avoid the use of nonlinear optimization techniques and merely require simple matrix operations. The methods can be applied to the problems of synthesizing radiation patterns of arrays with arbitrary sidelobe envelopes, with nonisotropic elements, and with nonuniform spacing between elements. The usefulness of the developed methodologies is demonstrated in various design examples. The methods developed provide powerfuI tools not only to design novel acoustic arrays but also to design antenna arrays. / Graduate

Research on the propagation of acoustic waves in ocean bottom sediment is of interest for active sonar applications such as target detection and remote sensing. Currently, all seabed scattering models available in the literature are based on the full solution of the wave equation, which sometimes leads to mathematically intractable problems. In the electromagnetics community, an alternative formulation that overcomes some of this complexity is radiative transfer theory, which has established itself as an important technique for remote sensing. In this work, radiative transfer (RT) theory is proposed for the first time as a tool for the study of seabed acoustic scattering. The focus of this work is the development of a complete model for the interaction of acoustic energy with water-saturated sediments. The general geometry considered in this study consists of multiple elastic layers containing random distributions of inhomogeneities. The accuracy of the proposed model is assessed by rigorous experimental work, with data collected from random media in which acoustic properties such as the concentration and size of scatterers, background material, and the presence of elastic boundaries are controlled parameters. First, the ultrasound RT model is implemented for layers of finite thickness. The range of applicability of the proposed model is then illustrated using scaled experiments conducted at the Northwest Electromagnetics and Acoustics Research Laboratory (NEAR-Lab). Next, the model is applied to field data collected in a region with gassy sediments and compared to the formulation originally used to explain these data. Finally, insight into the emerging area of study of the time-dependent RT formulation is presented, and its role in the representation of finite broadband pulses is discussed.

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A one-dimensional refractive, randomly-layered medium is considered in an acoustic context. A time harmonic plane wave emitted by a source is incident upon it and generates totally reflected fields which consist of "signal" and "noise". The statistical properties, i.e., mean and correlation functions, of these fields are to be obtained. The variations of the medium structure are assumed to have two spatial scales; microscopic random fluctuations are superposed upon slowly varying macroscopic variations. With an intermediate scale of the wavelength, the interplay of total internal reflection (geometrical acoustics) and random multiple scattering (localization phenomena) is analyzed for the turning point problem. The problem, in particular, above the turning point is formulated in terms of a transition scale. Two limit theorems for stochastic differential equations with multiple spatial scales, called Theorem 1 and Theorem 2, are derived. They are applied to the stochastic initial value problems for reflection coefficients in the regions above and below the turning point, respectively. Theorem 1 is an extension of a limit theorem on O( 1) scaled interval to infinite scale and provides uniformly-valid approximate statistics for random multiple scattering in the region above the turning point (transition as well as outer regions). Theorem 2 deals with stochastic problems with a rapidly varying deterministic component and approximates the reflection process in the region below the turning point which is characterized by the random noise. Finally, the evolution of the reflection coefficient statistics in the whole region is described by combining the two results as a product of a transformation at the turning point and two evolution operators corresponding to the two regions. / Ph. D.

Identification of the resonances and the local determination of the radius of curvature of an acoustically rigid sphere from simulated transient input-output data is presented. The scattering from the sphere is formulated using three techniques: the classic Mie-Lorenz series, the singularity expansion method (SEM), and the asymptotic series approximation. The Mie-Lorenz series is used to provide synthetic data. The SEM and the asymptotic series are used to develop two parametric inverse models. The scattered velocity potential is separated into three components: the reflection, the first creeping wave, and the second creeping wave. The effect of removing various components of the scattered potential on the resonance identification is shown, along with the effect of adding small amounts of noise. We find that the identification of a few resonances requires a relatively high order autoregressive, moving-average model. In addition, we show that removing the reflection from the synthetic output has only a small effect on the single or multiple output identified resonances. However, we find that changing the time origin, removing the second creeping wave, or adding small amounts of noise results in large errors in the identified resonances. We find that the radius of curvature can be accurately determined from synthetic data using the asymptotic series based identification. In addition, the identification is robust in the presence of noise, and requires only a low order asymptotic series model.