Typescript (Photocopy) / viii, 138 leaves : ill ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Depts. of Applied Mathematics and Mechanical Engineering, 1990

The work presented in this thesis consists of two parts: development and application of a novel passive acoustical approach for field measurement of breaking surface waves, and interpretation of the resulting observations in terms of wave field information so as to improve the understanding of wave breaking. The development of the acoustical approach has been motivated by the difficulties inherent in measurement of breaking waves. This approach makes use of an array of four broadband hydrophones which is able to track individual breaking waves by passive detection of the naturally generated sound of wave breaking. The Generalized Cross Correlation method is used to determine time differences of acoustic signals from breaking waves arriving at the array, allowing the breaking waves to be located with the given array geometry. Observations of breaking waves were made by means of this technique during the Surface Wave Processes Program (SWAPP). The spatial and temporal statistics of breaking waves, including breaking wave density, travel velocity, lifetime of breaking and spacing, are obtained from the observations. Statistical models are developed to assess, and where appropriate, correct for any bias resulting from limitations of the measurement approach. The breaking wave statistics provide important information about the physical process of wave breaking and its distribution in different wave fields. It is found that wave breaking in the open ocean occurs at a scale substantially smaller than the scale associated with the dominant wind wave component in the wave spectrum. Numerical simulation of breaking wave statistics and comparison with the observations demonstrates that the scale of breaking can be predicted from the directional wave spectrum by a linear model with a single breaking threshold. These results will provide input to comprehensive models of wave dissipation. Acoustical radiation properties of individual breaking waves are a further aspect of wave breaking that has been observed with the aforementioned technique. Investigation of the sound radiated from breaking waves reveals information both on the nature of the sound generation mechanism by breaking and the dimension of breaking waves. Statistical analysis of the acoustic source intensity associated with wave breaking suggests that the source intensity can be related to the breaking scale and wave energy dissipation, thus implying that surface wave dissipation could be remotely measured by using ambient sound. / Graduate

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Experimental investigations of structurally-dictated surface waves supported by periodically textured metallic substrates with different symmetries, are the primary focus of the work presented in this thesis. The electromagnetic response of three near perfectly conducting substrates perforated with arrays of holes with different geometries,together with a low-profile high-impedance structure are characterised. Experimental measurement techniques are employed to record the transmission, and reflection from the structures under investigation, together with phase-resolved measurements to directly obtain the dispersion of the surface waves supported by these structures. From these measurements information about the nature of the surface modes supported by the structures under investigation can be observed. A study of diffractively coupled surface waves supported by a close-packed array of square cross-section, close-ended holes in the limit where the wavelength of incident radiation and periodicity of the hole array are comparable, is presented. An additional grating, which has a periodicity comparable to the hole array is used to control the strength of diffractive coupling to the mode. Using a free-space measurement technique,information about the dispersion of the modes supported by the structure is obtained by recording the azimuthal-dependent reflection from the structure. It is found that the relative positions of the hole array and `coupling-in' grating is significant, a key issue not addressed in the literature when investigating grating-coupling to surface modes. Good agreement with numerical predictions is demonstrated. Structurally-dictated surface waves on a metallic substrate pierced by a close-packed array of deep, rectangular holes is characterised. In this arrangement, the fundamental resonance in the holes in the orthogonal directions is different and the frequency therefore to which the dispersion of the surface waves supported by the structure is limited, varies with sample orientation. The anisotropic dispersion, resulting from an ellipsoid of limiting frequencies, is directly mapped using a phase-resolved measurement technique. Furthermore by exploiting the anisotropy of the unit cell, a family of higher order surface waves associated with the quantisation of the electromagnetic fields within the holes is explored in this chapter. Once again good agreement with numerical predictions is shown.The `enhanced transmission' recorded through a `zigzag' hole array, attributed to the excitation of diffractively coupled surface waves, is explored. Due to the specific symmetry of the unit cell of the zigzag hole array it is shown that coupling to these surface waves can be achieved with both transverse magnetic and transverse electric polarised incident radiation. Further, incident radiation can directly couple to the surface modes supported by the zigzag hole array, via scattering from its inherent in-plane periodicity. The observed polarisation-selective excitation of individual surface wave bands, agrees well with numerical predictions and is shown to be a direct consequence of the reduced symmetry of the system. Finally, the dispersion of the modes supported by an ultra-thin, high-impedance surface in the form of a Sievenpiper `mushroom' structure, with rectangular geometry is directly recorded. The behaviour of the Sievenpiper structure is rather complex and to aid understanding of the electromagnetic response of the structure, the results are compared with the modes supported by a simpler patch array structure. The anisotropy arising from the rectangular geometry is characterised and an in depth discussion of the origin of the modes presented.

The work presented within this thesis details the experimental investigation of the surface waves supported on metasurfaces. Particular attention has been given to the reflection of these surface waves from planar discontinuities associated with these metasurfaces. Various experimental techniques have been developed throughout this work to characterise surface wave supporting metasurfaces. These include a new technique for measuring the dispersion of surface waves supported on metasurfaces, characterisation of the near-field associated with the surface waves, a device for launching planar phase front surface waves and finally a technique for measuring the surface wave reflection coefficient. The dispersion of surface waves on a square array of square cross-section metal pillars has been fully characterised and compared to FEM modelling. The results show that a family of surface waves may be supported by pillar or crossed slit structures rather than just holes even though there is now no lowest cut-off frequency. A family of TM surface modes have been shown to exist with dispersions which asymptote to frequencies defined by the pillar heights (slit depth) and the refractive index of the material filling the slits. Primarily this work focussed on the surface wave properties associated with a square array of square metal patches on a dielectric coated ground plane and a Sievenpiper `mushroom' metasurface. The amplitude reflection coefficient of these surface waves has been studied for three distinct systems: Firstly for surface waves incident upon the termination of a these metasurfaces to free space, secondly for surface waves incident upon the interface between a dielectric coated and uncoated metasurface and thirdly for surface waves incident on the boundary between two metaurfaces. The reflection coefficient of surface waves incident upon the termination of the metasurface to free space is found to increase significantly with the confinement of the surface mode. This confinement, and therefore the form of the reflection coefficient, is significantly different for the two metasurfaces considered due to their dispersions. This increase in the reflection coefficient is caused by both the momentum mismatch of the surface wave compared to the freely propagating modes and the different field distributions of the two modes. The reflection coefficient of surface waves incident upon the boundary between a coated and uncoated metasurface has been experimentally characterised for the metal patch array and Sievenpiper `mushroom' metasurfaces. It is shown that the addition of a thin, significantly subwavelength, dielectric overlayer onto the metasurface vastly perturbs the surface wave dispersion. The reflection coefficient of the surface waves is found to depend on the dispersion of the mode supported on the coated and uncoated metasurface and the overlayer thickness. Most noticeably the thickness of the overlayer, by comparison to the surface wave decay length, has a significant effect on scattering to free space associated with the surface wave reflection. The final system considered was designed to investigate the impedance approximation, often used to describe metasurfaces, and found it to be an incomplete description of the surface waves supported on the metasurfaces used within this study. In the impedance approximation the two surfaces considered are said to be `impedance matched` at certain frequencies. It is demonstrated that the failure of the impedance approximation to accurately describe this system is due to the behaviour of the electric field within the metasurfaces. These are not analytically described in the impedance approximation and are required for an accurate description of the surface waves supported on these metasurfaces.

published_or_final_version / Physics / Master / Master of Philosophy

In general, the depths of shallow earthquakes are poorly resolved in current catalogues. Variations in depth of ±10 km can significantly alter the tectonic interpretation of such earthquakes. If the depth of a seismic event is in error then moment tensor estimates can also be significantly altered. In the context of nuclear-test-ban monitoring, a seismic event whose depth can be confidently shown to exceed say, 10km, is unlikely to be an explosion. Surface wave excitation is sensitive to source depth, especially at intermediate and short periods, owing to the approximate exponential decay of surface wave displacements with depth. The radiation pattern and amplitude of surface waves are controlled by the depth variations in the six components of the strain tensor associated with the surface wave eigenfunctions. The potential exists, therefore, for improvements to be made to depth and moment tensor estimates by analysing surface wave amplitudes and radiation patterns. A new method is developed to better constrain seismic source parameters by analysing 100-20s period amplitude spectra of fundamental-mode surface waves. Synthetic amplitude spectra are generated for all double-couple sources over a suitable depth range and compared with data in a grid-search algorithm. Best fitting source parameters are calculated and appropriate bounds are placed on these results. This approach is tested and validated using a representative set of globally-distributed events. Source parameters are determined for 14 moderately-sized earthquakes (5.4 ≤ M_w ≤ 6.5), occurring in a variety of tectonic regimes with depths calculated between 4-39km. For very shallow earthquakes the use of surface wave recordings as short as 15s is shown to improve estimates of source parameters, especially depth. Analysis of aftershocks (4.8 ≤ M_w ≤ 6.0) of the 2004 great Sumatra earthquake is performed to study the depth distribution of seismicity in the region. Three distinct tectonic regimes are identified and depth estimates calculated between 3-61km, including the identification of one CMT depth estimate to be in error by some 27km.

Seismology is the study of earthquakes and the Earth’s internal structure using seismic waves. Traditional seismology is constrained by the timing and location of seismic sources, and by the location of seismometers with which energy from the sources are recorded. Improvements in the global seismometer networks have reduced the latter constraint. Furthermore, recent advances into Seismic Interferometry (SI) have enabled detailed information about the Earth’s interior to be obtained using ambient seismic noise, hence even in areas with low natural seismicity. The most common approach to SI is to use the cross-correlation of ambient noise recordings to construct an estimate of the Green’s function between two seismometer locations. The Green’s function estimate is then analysed or inverted for seismic properties of the Earth. This method of noise interferometry is now a popular approach in earthquake seismology as in some situations it renders active seismic sources (earthquakes or synthesised explosions) obsolete, as subsurface information can be obtained even in times of seismic quiescence. This thesis investigates a different method: Source-Receiver Interferometry (SRI). SRI can be used to construct earthquake seismograms on seismometers that were not necessarily deployed when the earthquakes occurred - a form of ‘retrospective seismology’. This might be useful if, for example, we wish to analyse old earthquakes with newly installed seismometers. The application of SRI involves evaluating two interferometric integrals. The first integral is evaluated using ambient noise interferometry: at least 6 months of noise data is cross-correlated to estimate the Green’s functions between pairs of seismometers. These inter-receiver Green’s functions are then used as the “propagators” for SRI. Their role is to project earthquake signals recorded on a backbone array of seismometers to the location of a target sensor at which a new, novel earthquake seismogram is to be constructed - a form of spatial redatuming. To spatially redatum the earthquake data, the second interferometric integral is evaluated using either processes of correlation (resulting in correlation-correlation SRI) or convolution (correlation-convolution SRI). The method used depends on the relative location of the target sensors with respect to both the backbone seismometer array and the earthquake epicentre. The SRI process is completed by integrating (summing) over all projected earthquake signals. To regularise the spatial distribution of the projected earthquake data and to invoke this second interferometric integral more precisely, the backbone seismometers are embedded within 2D spatial Voronoi cells. New seismograms for 87 earthquakes were reconstructed on up to eight target sensors, seven of which were deployed when the earthquakes occurred and are used to test the success of the method by comparing with the SRI results with the directly-recorded seismograms. The seismogram reconstructions on the eighth target sensor are truly novel. The SRI method was developed to operate over two length scales. The first focusses on relatively small length scales in which the inter-station distance between the eight target sensors and the backbone array seismometers is between ~ 210 km and 540 km. Both correlation-correlation SRI and correlation-convolution SRI are used to reconstruct the earthquake seismograms on four of the same target sensors. Applying correlation-convolution SRI is shown to remove spurious signals associated with correlation-correlation SRI. Second, a significantly larger length scale is considered where a second set of target sensors are located up to 2420 km from a second backbone seismometer array. The correlation-correlation and correlation-convolution SRI methods are used in parallel to increase the spatial extent of the study. The quality of the SRI seismograms constructed is shown to depend on the quality of three components: 1) the SRI propagators constructed using ambient noise interferometry, 2) the earthquake signals recorded on the backbone seismometer array, and 3) the correlation (or convolution) functions that are summed in the second interferometric integral to construct the final SRI seismogram. The quality of each component is quantified by its signal-to-noise ratio and root-mean-square value, and criteria are proposed to obtain optimal earthquake seismogram reconstructions using SRI. SRI is most successful when the target sensors are located less than 540 km from the backbone array seismometers. Such SRI seismograms are being used to create a catalogue of new, ‘virtual’ earthquake seismograms that are available to complement real earthquake data for use in future earthquake seismology studies. An alternative approach to noise interferometry is also considered: the recordings from just 15 earthquakes are used to perform multidimensional deconvolution (MDD) to estimate the Green’s functions between pairs of seismometers. This is the first time such data has been used to perform MDD, which is valid in attenuating media and is thus theoretically more valid in earthquake seismology settings than correlational interferometry. The Green’s functions estimated using MDD are compared with those same Green’s functions estimated using ambient noise interferometry and the results are comparable on several occasions, despite using far fewer data for MDD. However, the quality of the results of MDD is significantly affected by the illumination of the receiver array from the earthquake sources. A greater density of earthquakes that sufficiently illuminates all backbone array seismometers is required to obtain accurate Green’s functions by MDD.

M.Sc., Faculty of Science, University of the Witwatersrand, 2011 / Rayleigh wave dispersion curves are used to invert for the group velocity maps of the southwestern block of the Congo craton. The group velocity maps were then inverted to obtain the three dimensional shear-wave velocity of the lithosphere beneath the region. In the process, the adjacent Kalahari craton and Damara mobile belt were also mapped to help constrain the southernmost edge of the Congo craton. To obtain the surface wave group velocity tomography, event-station dispersion curves of Rayleigh waves were measured using the multiple filter analysis method. Then the dispersion curves were inverted using the conjugate gradient least-square (CGLSQR) inversion method. To check the reliability of the result, a checkerboard test was performed. The 2-dimensional group velocities and 3-dimensonal shear-wave velocities were found to be faster beneath the southwestern block of the Congo craton and the Kalahari craton and slower in the Damara mobile belt. The group velocity map at 20s period shows that basins are 0 to 3% slower than PREM model. For longer period (50s to 120s), the Central and East African Rift system are ~ 5 % faster, cratons are 5 to 8% faster, and the adjacent mobile belts are 0 to 4% faster than the PREM model. The Afar depression is the slowest, up to 6% slower than the continental PREM model at all periods. The shear-wave velocity maps reveal that (1) the Afar area is the slowest (up to 8% slower than the IASP91 model), (2) the cratons are faster (up to 6% faster than IASP91) than the surrounding mobile belts (up to 2% faster than IASP91). The East African Rifts system is also slow (up to 5%). The Damara mobile belt constitutes a clear separation terrain between the Congo craton and the Kalahari craton. This result is consistent with previous studies by Pasyanos and Nyblade (2007), and Priestly et al. (2006, 2008), who also found faster shear-wave velocities beneath the Kalahari, Congo and Tanzania cratons. The relatively slow seismic velocities (-1 to 2% compared to IASP91) in the Proterozoic Damara mobile belt between the southwestern block of the Congo craton and the Kalahari craton are explained by the view that the Proterozoic lithosphere has hotter rock materials than the SW block of the Congo craton and the Kalahari craton. Our model of faster lithosphere beneath the SW block of the Congo and the Kalahari craton is also consistent with the model of strongly depleted (in basaltic components) lithosphere beneath these craton; compared to less depleted lithosphere beneath the DMB.