This thesis studies the target identified by analyzed scattering signal which is from active sonar impinged under water. In general, the specular reflected waves and corner waves provide the information of target profile in scattering signal. The resonance scattering waves and surface waves submit the material properties of target by analysis signal. The Rayleigh wave is a candidate for target identified in surface wave analysis. Since then, the theorem focuses on Rayleigh wave propagation on solid sphere and cylinder in this thesis. To analyze the problem of scattering wave, if the normal mode methed is applied to solve it, the character of reflected surface wave can not appear on the solution. So the Sommerfeld-Watson transform(SWT) method is used to solve it. This method can convege the infinite partial-wave series rapidly and the physical property of acoustic wave can be elucidated easily. In experiment, the reduced scale experiment is setup for Rayleigh wave measurement using ultrasonic wave. For Rayleigh wave discussion, the individual profile, sizes and material of target is applied respectively in this experiment. The beam pattern is also measured in the Rayleigh wave filed. The result appears the target identified by analytical Rayleigh wave obviously.

The presence of subsurface anomalies, such as cavities, faults, unknown tunnels, etc., either natural or man-made, can cause public safety hazards. The detection of these features requires the development of new methods. Seismic Rayleigh surface wave imaging is a relatively new non-destructive testing technique (NDT) which generates subsurface images without drilling boreholes into the ground, and in recent years has been widely used for soil characterization in geotechnical investigations. In the last decade, some researchers have applied the technique to near-surface imaging and showed the possibility and potential for engineering applications. This research presents the development of a technique to process seismic Rayleigh waves to detect and image subsurface anomalies. This study conducted investigations of Rayleigh wave behaviors and developed a new strategy for Rayleigh wave isolation from raw field data. The strategy applies wavelet transforms, instead of the conventional spectral analysis of surface waves (SASW) method, or popular multichannel analysis of surface waves (MASW) techniques, to pair-channel analysis of the isolated Rayleigh wave data for dispersion calculation. Finally, a simple steady inversion technique was applied to yield shear velocity as a function of both depth and distance, and shear velocity field images (SVF), for near surface section display. This research consists of development, computer programming, field tests, data processing and interpretation. Three sites in different scenarios were used for seismic investigations: old mining tunnels in medium dipping coal seams in Stellarton coalfield, mining cavities in steeply dipping gold-bearing veins in West Waverley Gold District and an anomaly in nearly horizontal strata in Liverpool. All these sites are in the province of Nova Scotia, Canada. The results from seismic surface wave technique introduced in this research can be evaluated by field observations, documents and borehole logs. The satisfactory interpretations and success of this investigation shows that this technique is suitable for engineering application for subsurface investigations.

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The asymptotic behaviour of an elastically supported infinite string and an elastic isotropic half plane (in frames of specific asymptotic model) under a moving point load are studied. The main results of this work are uniform asymptotic formulae and the asymptotic profile for the string and the exact solution and uniform asymptotic formulae for a half plane. The crucial assumption for both structures is that the acceleration is sufficiently small. In order to describe asymptotically the oscillations of an infinite string auxiliary canonical functions are introduced, asymptotically analyzed and tabulated. Using these functions uniform asymptotic formulae for the string under constant accelerating and decelerating point loads are obtained. Approximate formulae for the displacement in the vicinity of the point load and the singularity area behind the shock wave using the steady speed asymptotic expansion with additional contributions from stationary points where appropriate are derived. It is shown how to generalise uniform asymptotic results to the arbitrary acceleration case. As an example these results are applied for the case of sinusoidal load speed. It is shown that the canonical functions can successfully be used in the arbitrary acceleration case as well. The graphical comparative analysis of numerical solu- tion and approximations is provided for different moving load speed intervals and values of the parameters. Vibrations of an elastic half plane are studied within the framework of the asymp- totic model suggested by J. Kaplunov et al. in 2006. Boundary conditions for the main problem are obtained as a solution for the problem of a string on the surface of a half plane subject to uniformly accelerated moving load. The exact solution over the interior of the half plane is derived with respect to boundary conditions. Steady speed and Rayleigh wave speed asymptotic expansions are obtained. In the neighborhood of the Rayleigh speed the uniform asymptotic formulae are derived. Some of their interesting properties are discovered and briefly studied. The graphical comparative analysis of the exact solution and approximations is provided for different moving load speed intervals and values of the parameters.

High-resolution seismic images of lithospheric structures allow us to infer the tectonics that modified the lithosphere. We apply such methods to understand Cenozoic modification of the lithosphere by tectonic and magmatic processes in the tectonically active western United States. Using USArray Transportable and Flexible Array data, we present high-resolution images for three regions in this thesis. (1) In the Mendocino triple junction, we use a joint inversion of Rayleigh-wave dispersion data and receiver functions to obtain a new crust and upper Vs model to ~150km depth. The model shows four distinct, young lithosphere-asthenosphere boundary systems. A low-Vs anomaly beneath the Great Valley-Sierra Nevada reconciles existing slab window models with the mantle-wedge geochemical signatures in Coast Range volcanics, and explains the ~3 Myr delay of the onset of volcanism after slab removal. Uppermost mantle low velocities provide evidence for forearc mantle serpentinization extending along the Cascadia margin. (2) In the Colorado Plateau, a Rayleigh wave tomography model sheds light on the volcanism along the margins and plateau uplift. Strong upper mantle heterogeneity across the plateau edge results from the combined effect of a ~200-400 K temperature difference and ~1% partial melt. A ring of low velocities under the plateau periphery suggests that the rehydrated Proterozoic lithosphere is progressively removed by convective processes. Particularly, a high-Vs anomaly imaged beneath the western plateau adds evidence for a downwelling/delamination hypothesis [Levander et al., 2011]. Thermo-chemical edge-driven convection causing localized lithospheric downwelling provides uplift along the margins and magmatic encroachment into the plateau center. (3) In the final study, we developed a 3-D teleseismic scattering wave imaging technique based on the Kirchhoff approximation and 3-D inverse Generalized Radon Transform. Synthetic tests demonstrate higher resolution imaging for continuous, irregular interfaces or localized scatterers, in comparison to conventional methods. Applied to the High Lava Plains dataset, the transmission coefficient structure shows a deepening Moho near 117.6°W and three negative events that correlate well with the Rayleigh wave low-Vs zones. Images made with the Mendocino data clearly show rapidly decreasing lithosphere-asthenosphere boundary depths from the subduction to transform regime.

Basic diffusion analytical solutions of one-dimensional consolidation are presented for the case of a semi-infinite domain. Typical tractions considered include instantaneous loads of the medium with a free boundary pressure, as well as the case of a permeable membrane located at the forced boundary. <br /><br /> Two-dimensional boundary value problems for a porous half-space, described by the widely recognized Biot's equations of poroelasticity, including inertia effects is discussed. In this poroelastic version of Lamb's problem in the classical theory of linear elastic waves, the surface of a porous half-space is subjected to a prescribed line traction. The following two broadly applicable cases are considered: 1) A steady state harmonic load, 2) An impulsive load (Dirac delta function time dependence). A general analytical solution of the problem in the Fourier -- Laplace space was obtained by the application of the standard Helmholtz potential decomposition, which reduces the problem to a system of wave equations for three unknown potentials, which correspond to three types of motion: P1, slow P2 wave, and the shear wave S. The possibilities of, and procedure for, obtaining analytic solutions in the physical space subsequently are discussed in detail. When viscous dissipation effects are taken into account, a steady-state harmonic line traction solution can be represented in the form of well convergent integrals, while for the case when viscous dissipation is ignored, closed form analytic solutions can be obtained for impulsive forcing with the application of the Cagniard -- de Hoop inversion technique. Numerical studies of the dispersion relation of the Rayleigh, or surface, wave for cases in which the dissipation is not negligible are presented.

Basic diffusion analytical solutions of one-dimensional consolidation are presented for the case of a semi-infinite domain. Typical tractions considered include instantaneous loads of the medium with a free boundary pressure, as well as the case of a permeable membrane located at the forced boundary. <br /><br /> Two-dimensional boundary value problems for a porous half-space, described by the widely recognized Biot's equations of poroelasticity, including inertia effects is discussed. In this poroelastic version of Lamb's problem in the classical theory of linear elastic waves, the surface of a porous half-space is subjected to a prescribed line traction. The following two broadly applicable cases are considered: 1) A steady state harmonic load, 2) An impulsive load (Dirac delta function time dependence). A general analytical solution of the problem in the Fourier -- Laplace space was obtained by the application of the standard Helmholtz potential decomposition, which reduces the problem to a system of wave equations for three unknown potentials, which correspond to three types of motion: P1, slow P2 wave, and the shear wave S. The possibilities of, and procedure for, obtaining analytic solutions in the physical space subsequently are discussed in detail. When viscous dissipation effects are taken into account, a steady-state harmonic line traction solution can be represented in the form of well convergent integrals, while for the case when viscous dissipation is ignored, closed form analytic solutions can be obtained for impulsive forcing with the application of the Cagniard -- de Hoop inversion technique. Numerical studies of the dispersion relation of the Rayleigh, or surface, wave for cases in which the dissipation is not negligible are presented.

Nonlinear mixing of two collinear, initially monochromatic, Rayleigh waves propagating in the same direction in an isotropic, nonlinear elastic solid is investigated: analytically, by finite element method simulations and experimentally. In the analytical part, it is shown that only collinear mixing in the same direction fulfills the phase matching condition based on Jones and Kobett 1963 for the resonant generation of the second harmonics, as well as the sum and difference frequency components caused by the interaction of the two fundamental waves. Next, a coupled system of ordinary differential equations is derived based on the Lagrange equations of the second kind for the varying amplitudes of the higher harmonic and combination frequency components of the fundamentals waves. Numerical results of the evolution of the amplitudes of these frequency components over the propagation distance are provided for different ratios of the fundamental wave frequencies. It is shown that the energy transfer is larger for higher frequencies, and that the oscillation of the energy between the different frequency components depends on the amplitudes and frequencies of the fundamental waves. Furthermore, it is illustrated that the horizontal velocity component forms a shock wave while the vertical velocity component forms a pulse in the case of low attenuation. This behavior is independent of the two fundamental frequencies and amplitudes that are mixed. The analytical model is then extended by implementing diffraction effects in the parabolic approximation. To be able to quantify the acoustic nonlinearity parameter, β, general relations based on the plane wave assumption are derived. With these relations a β is expressed, that is analog to the β for longitudinal waves, in terms of the second harmonics and the sum and the difference frequencies. As a next step, frequency and amplitude ratios of the fundamental frequencies are identified, which provide a maximum amplitude of one of the second harmonics as well as the sum or difference frequency components to enhance experimental results. Subsequently, the results of the analytical model are compared to those of finite element method simulations. Two dimensional simulations for small propagation distances gave similar results for analytical and finite element simulations. Consquently. this shows the validity of the analytical model for this setup. In order to demonstrate the feasibility of the mixing technique and of the models, experiments were conducted using a wedge transducer to excite mixed Rayleigh waves and an air-coupled transducer to detect the fundamentals, second harmonics and the sum frequency. Thus, these experiments yield more physical information compared to the case of using a single fundamental wave. Further experiments were conducted that confirm the modeled dependence on the amplitudes of the generated waves. In conclusion, the results of this research show that it is possible to measure the acoustic nonlinearity parameter β to quantify material damage by mixing Rayleigh waves on up to four ways.

A method for numerical simulation of train induced track vibration and wave propagation in subgrade has been proposed. The method uses a mass to simulate the bogie of a train and considers the effect of rail roughness. For this method, rail roughness is considered as a randomly generated signal and a filter is used to block the undesired components. The method predicts the particle velocity around the track and can be applied to many kinds of railroad trackbeds including traditional ballast trackbed and modern Hot mix asphalt (HMA) trackbed. Results from ballast and HMA trackbeds are compared and effects of HMA layer on damping track vibration and dissipating wave propagation are presented. To verify the credibility of the method, in-track measurements were also conducted. Site measurements included performing geophysical tests such as spectral analysis of surface wave test and seismic refraction test to determine the subsurface conditions at the test site. Ballast and HMA samples were tested in the laboratory by resonant column test to obtain the material properties. Particle velocities were measured and analyzed in the frequency domain. Results from in-track tests confirm the applicability of the numerical method. The findings and conclusions are summarized and future research topics are suggested.

Traditional methods of imaging the Earth’s subsurface using seismic waves require an identifiable, impulsive source of seismic energy, for example an earthquake or explosive source. Naturally occurring, ambient seismic waves form an ever-present source of energy that is conventionally regarded as unusable since it is not impulsive. As such it is generally removed from seismic data and subsequent analysis. A new method known as seismic interferometry can be used to extract useful information about the Earth’s subsurface from the ambient noise wavefield. Consequently, seismic interferometry is an important new tool for exploring areas which are otherwise seismically quiet, such as the British Isles in which there are relatively few strong earthquakes. One of the possible applications of seismic interferometry is the ambient noise tomography method (ANT). ANT is a way of using interferometry to image subsurface seismic velocity variations using seismic (surface) waves extracted from the background ambient vibrations of the Earth. To date, ANT has been used to successfully image the Earth’s crust and upper-mantle on regional and continental scales in many locations and has the power to resolve major geological features such as sedimentary basins and igneous and metamorphic cores. In this thesis I provide a review of seismic interferometry and ANT and apply these methods to image the subsurface of north-west Scotland and the British Isles. I show that the seismic interferometry method works well within the British Isles and illustrate the usefulness of the method in seismically quiet areas by presenting the first surface wave group velocity maps of the Scottish Highlands and across the British Isles using only ambient seismic noise. In the Scottish Highlands, these maps show low velocity anomalies in sedimentary basins such as the Moray Firth and high velocity anomalies in igneous and metamorphic centres such as the Lewisian complex. They also suggest that the Moho shallows from south to north across Scotland, which agrees with previous geophysical studies in the region. Rayleigh wave velocity maps from ambient seismic noise across the British Isles for the upper and mid-crust show low velocities in sedimentary basins such as the Midland Valley, the Irish Sea and the Wessex Basin. High velocity anomalies occur predominantly in areas of igneous and metamorphic rock such as the Scottish Highlands, the Southern Uplands, North-West Wales and Cornwall. In the lower crust/upper mantle, the Rayleigh wave maps show higher velocities in the west and lower velocities in the east, suggesting that the Moho shallows generally from east to west across Britain. The extent of the region of higher velocity correlates well with the locations of British earthquakes, agreeing with previous studies that suggest British seismicity might be influenced by a mantle upwelling beneath the west of the British Isles. Until the work described in Chapter 6 of this thesis was undertaken in 2009, seismic interferometry was concerned with cross-correlating recordings at two receivers due to a surrounding boundary of sources, then stacking the cross-correlations to construct the inter-receiver Green’s function. A key element of seismic wave propagation is that of source-receiver reciprocity i.e. the same wavefield will be recorded if its source and receiver locations and component orientations are reversed. By taking the reciprocal of its usual form, in this thesis I show that the impulsive-source form of interferometry can also be used in the opposite sense: to turn any energy source into a virtual sensor. This new method is demonstrated by turning earthquakes in Alaska and south-west USA into virtual seismometers located beneath the Earth’s surface.