Multistation Methods for Geotechnical Characterization using Surface Waves

This dissertation deals with soil characterization methods based on surface wave propagation applied to geotechnical engineering purposes. This topic has gained much interest in the last decade because of the appealing possibilities given by non-invasive methods, which are at once very flexible and cost effective. An overview of the properties of Rayleigh waves in layered linear elastic and linear viscoelastic media is presented, together with their applications for site characterization, of whose the SASW (Spectral Analysis of Surface Waves) method is by far the most well-known in geotechnical engineering. The research has been mainly focused on the application of multistation methods, compared with the classical two-station approach typical of the SASW method. Results from both numerical simulations and experimental testing are reported to compare two-station and multistation methods and to clarify the advantages that can be obtained using the latter ones. In particular the research has been developed following two different directions: on the one hand the application of classical geophysical analysis tools (such as domain analysis and slant stack transform) to tests performed with impulsive sources. On the other one the possibility of obtaining from surface wave testing not only a stiffness profile, but also a damping ratio profile for the site. In this respect a new method for simultaneous measurements of Rayleigh dispersion and attenuation curves is proposed. Regarding the first topic, the necessity of a multistation approach to determine the experimental dispersion test is essentially related to the spatial variation of phase velocity. Analyses in the frequency-wavenumber domain and in the frequency-slowness domain are very powerful approaches, still there was a need of studying the effects of the change of scale from geophysical applications to geotechnical ones. Indeed because of the peculiar properties of Rayleigh waves, surface testing is strongly affected by the distance travelled by the analysed wave. The numerical simulations performed in the research show that the phase velocity obtained using multistation methods with a limited number of receivers close to the source is not a modal value as it is for geophysical applications, but an apparent phase velocity arising from modal superposition. The experimental tests showed the good performances of multistation methods when compared to the SASW method. In particular some drawbacks of the latter method, due essentially to its two-station nature, are avoided and the field-testing appears to be very promising for future applications. In particular the application of the frequency-wavenumber domain analysis can lead to much faster and more stable estimates of the experimental dispersion curve and the process is easily automated, with a great saving of time and less requirement for subjective decisions. Another important advantage is given by the stability with respect to a near field effects that lead to a better reconstruction of the dispersion curve for the low frequencies and hence to a deeper characterization. The necessity of a new method for the simultaneous determination of surface wave dispersion and attenuation curves is linked to the strong coupling existing between the two. Such coupling is extremely important for the subsequent inversion process, in a consistent method leading from the field measurements to the stiffness and damping profiles. The proposed method uses a new testing configuration, designed to measure the experimental transfer function. Successively a regression process of the complex quantity with the corresponding expression obtained modelling soil as a linear viscoelastic layered system leads to the experimental dispersion and attenuation curves. Some preliminary results are reported showing very encouraging results, also if a more extensively testing programme is required for the complete validation of the metho

Amplitude and phase sonar calibration and the use of target phase for enhanced acoustic target characterisation

This thesis investigates the incorporation of target phase into sonar signal processing, for enhanced information in the context of acoustical oceanography. A sonar system phase calibration method, which includes both the amplitude and phase response is proposed. The technique is an extension of the widespread standard-target sonar calibration method, based on the use of metallic spheres as standard targets. Frequency domain data processing is used, with target phase measured as a phase angle difference between two frequency components. This approach minimizes the impact of range uncertainties in the calibration process. Calibration accuracy is examined by comparison to theoretical full-wave modal solutions. The system complex response is obtained for an operating frequency of 50 to 150 kHz, and sources of ambiguity are examined. The calibrated broadband sonar system is then used to study the complex scattering of objects important for the modelling of marine organism echoes, such as elastic spheres, fluid-filled shells, cylinders and prolate spheroids. Underlying echo formation mechanisms and their interaction are explored. Phase-sensitive sonar systems could be important for the acquisition of increased levels of information, crucial for the development of automated species identification. Studies of sonar system phase calibration and complex scattering from fundamental shapes are necessary in order to incorporate this type of fully-coherent processing into scientific acoustic instruments

Noise generation in the solid Earth, oceans, and atmosphere, from non-linear interacting surface gravity waves in finite depth

Oceanic pressure measurements, even in very deep water, and atmospheric pressure or seismic records, from anywhere on Earth, contain noise with dominant periods between 3 and 10 seconds, that is believed to be excited by ocean surface gravity waves. Most of this noise is explained by a nonlinear wave-wave interaction mechanism, and takes the form of surface gravity waves, acoustic or seismic waves. Previous theoretical works on seismic noise focused on surface (Rayleigh) waves, and did not consider finite depth effects on the generating wave kinematics. These finite depth effects are introduced here, which requires the consideration of the direct wave-induced pressure at the ocean bottom, a contribution previously overlooked in the context of seismic noise. That contribution can lead to a considerable reduction of the seismic noise source, which is particularly relevant for noise periods larger than 10 s. The theory is applied to acoustic waves in the atmosphere, extending previous theories that were limited to vertical propagation only. Finally, the noise generation theory is also extended beyond the domain of Rayleigh waves, giving the first quantitative expression for sources of seismic body waves. In the limit of slow phase speeds in the ocean wave forcing, the known and well-verified gravity wave result is obtained, which was previously derived for an incompressible ocean. The noise source of acoustic, acoustic-gravity and seismic modes are given by a mode-specific amplification of the same wave-induced pressure field near the zero wavenumber.Comment: Paper accepted for publication in the Journal of Fluid Mechanic

Wave modelling - the state of the art

This paper is the product of the wave modelling community and it tries to make a picture of the present situation in this branch of science, exploring the previous and the most recent results and looking ahead towards the solution of the problems we presently face. Both theory and applications are considered. The many faces of the subject imply separate discussions. This is reflected into the single sections, seven of them, each dealing with a specific topic, the whole providing a broad and solid overview of the present state of the art. After an introduction framing the problem and the approach we followed, we deal in sequence with the following subjects: (Section) 2, generation by wind; 3, nonlinear interactions in deep water; 4, white-capping dissipation; 5, nonlinear interactions in shallow water; 6, dissipation at the sea bottom; 7, wave propagation; 8, numerics. The two final sections, 9 and 10, summarize the present situation from a general point of view and try to look at the future developments

Earthquake-induced rotational ground motions from G-Pisa ring laser gyroscope.

In order to fully characterize the local ground motion induced by earthquakes, one needs to determine three components of translation, six components of strain and three components of rotation (Aki and Richards, 2002). The first two quantities are commonly studied by seismologists with the use of classical seismological instrumentation, like accelerometers/seismometers and strainmeters. Rotational motions in seismology have always been considered negligible, mainly because of the lack of instrumentation of adequate sensitivity. Indeed, the rotation rates which have been observed thus far, range from 10^-1 rad/s close to seismic sources (Nigbor, 1994), to 10^-11 rad/s for large telesismic earthquakes (Igel et al.2005, 2007). It is expected that collocated measurements of translations and rotations may (1) allow the estimate of velocities and propagation directions of the incoming wavefield (2) help to further constrain rupture processes and (3) provide additional hazard-relevant information to earthquake engineers (Igel et al.2007). But as reported just a decade ago by Aki and Richards (2002): “...seismology still awaits a suitable instrument for making such measurements.” Over the last few years ring laser gyroscopes, based on the Sagnac effect, demonstrated a high potential in investigating the rotational ground motion, and they appear to be the most promising instruments to address Aki and Richard's requirements. Theory suggests a general link between rotational and translational motions induced by earthquakes. In the case of horizontally and vertically polarized surface waves (Love and Rayleigh-waves) the relations are particularly simple. Vertical acceleration and rotation rate about a horizontal axis should be in phase and scaled by a factor that corresponds to local Rayleigh-waves phase velocity. By the same token, transverse acceleration and rotation rate about vertical axis should be in phase and scaled by two times Love-waves phase velocity. According to the above relationships, under the plane-wave approximation, collocated measurements of translation and rotation can provide the estimate of phase velocities and propagation directions, otherwise only accessible through seismic array measurements, polarization analysis, or additional strain measurements. This thesis focuses on the data collected by the G-Pisa ring laser gyroscope, developed by the University of Pisa (Department of Physics) and INFN. This instrument has been operating for almost 2 years at the European Gravitational Observatory in Cascina (Pisa), in the framework of the VIRGO project. In particular, I report the very first seismic analysis of the rotational data from a gyrolaser lying in the vertical plane, which is sensitive to rotation about a horizontal axis (tilt). The main part of the thesis is dedicated to the analysis of the Mw=9.0, March 11th, 2011, Japan earthquake; in addition, I also account for recordings from some events occurred at regional distances. The first objective of this work is to characterize the performance of G-Pisa in relation to a collocated accelerometer and to verify the ground-coupling of the instrument. By calculating power spectral density (PSD) of rotation rate and acceleration I first identify the signal to noise ratio as a function of frequency and, by computing time-frequency transforms (spectrograms), I individuate the most energetic frequency bands as a function of time for both the instruments during several selected earthquakes. Then, rotation rates and accelerations are correlated within subsequent frequency bands, in order to quantify similarity between the signals. The second objective of the thesis is to compare the recorded rotation rates with those obtained through an array-based analysis. Applying the seismo-geodetic method by Spudich et al. (2008), I derive the rotation rate from a tripartite array of three-components accelerometers. This method provides an independent estimation of ground rotations that should be in agreement with that directly recorded by the gyrolaser. Results from this analysis show that the two measurements are in general agreement; I attribute the discrepancies to both the geometrical setting of the array and the band limitations of its sensors. The third objective concerns phase velocities estimation and derivation of surface waves dispersion curves from collocated measurements of rotation and translation. Following Igel et al. (2005, 2007) and Kurrle et al. (2010), I address this issue by calculating the zero-lag correlation coefficient between translational and rotational traces. When the correlation coefficient is above an arbitrary threshold, phase velocity is obtained through a linear regression within overlapping sliding time windows. Iterating the procedure after a narrow band-pass filtering of both traces, it is possible to derive a dispersion curve for the selected wave packet. A theoretically equivalent dispersion curve could be derived in frequency domain as showed by Suryanto et al (2006), both for Love- and Rayleigh-waves, simply by calculating the spectral ratios between translation and rotation. I implemented this second procedure using a multitaper method (MTM, Thomson, 1982), in order to reduce variance and bias by averaging periodograms obtained using a properly-designed taper. The dispersion curves calculated in this manner are compared to those obtained with a multi-frequency Plane Wave Fit (PWF) analysis. This method that consists in estimating wavefield slowness for an array of sensors provides independent information about velocities and direction of propagation (azimuth) for plane waves crossing the array. Rayleigh-waves dispersion curves derived from the Japan earthquake, are then compared against the theoretical phase velocities derived from a standard (AK135) Earth Model. Since Rayleigh-waves are fully recorded by the gyrolaser only when their direction of propagation is perpendicular to G-Pisa area vector, I implemented a rotation rate signal correction method that takes into account the different directions of propagation of Rayleigh-waves (as estimated from PWF inversion) with respect to G-Pisa axis of sensitivity. This correction leads to a more reliable result in estimating phase velocities, that otherwise would be overestimated. Collocated measurements of rotation about vertical axis and transverse acceleration for horizontally-polarized seismic waves (SH- and Love-waves) allow estimating direction of propagation and azimuth of the incoming wavefield. Following Igel et al. (2007), and Hadziioannou et al. (2012), I conducted these estimates for Love waves recorded when G-Pisa was configured with area vector oriented vertically. This thesis is organised into five chapters. In the first chapter, I briefly report the general theory behind rotational motions, and present the relationships between rotation and translation in the context of classical elasticity. Here I show that surface-waves phase velocities and thus dispersion curves can be obtained from collocated measurements or rotation and translation. In the second chapter I present the instrumentation and data, with particular reference to G-Pisa and its ability to investigate both Rayleigh-and Love-waves with a sensitivity in the order of a few nrad/s/over the 0.02-1 Hz frequency band. In the third chapter I describe the data analysis methods, and their practical implementation in terms of Matlab scripts. In the fourth chapter I present and critically comment the results from the analysis. This chapter is divided into two sections, dedicated respectively to the Love- and Rayleigh-waves results. The last chapter is dedicated to the general discussion and conclusions

Reducing Uncertainties in the Velocities Determined by Inversion of Phase Velocity Dispersion Curves Using Synthetic Seismograms

Characterizing the near-surface shear-wave velocity structure using Rayleigh-wave phase velocity dispersion curves is widespread in the context of reservoir characterization, exploration seismology, earthquake engineering, and geotechnical engineering. This surface seismic approach provides a feasible and low-cost alternative to the borehole measurements. Phase velocity dispersion curves from Rayleigh surface waves are inverted to yield the vertical shear-wave velocity profile. A significant problem with the surface wave inversion is its intrinsic non-uniqueness, and although this problem is widely recognized, there have not been systematic efforts to develop approaches to reduce the pervasive uncertainty that affects the velocity profiles determined by the inversion. Non-uniqueness cannot be easily studied in a nonlinear inverse problem such as Rayleigh-wave inversion and the only way to understand its nature is by numerical investigation which can get computationally expensive and inevitably time consuming. Regarding the variety of the parameters affecting the surface wave inversion and possible non-uniqueness induced by them, a technique should be established which is not controlled by the non-uniqueness that is already affecting the surface wave inversion. An efficient and repeatable technique is proposed and tested to overcome the non-uniqueness problem; multiple inverted shear-wave velocity profiles are used in a wavenumber integration technique to generate synthetic time series resembling the geophone recordings. The similarity between synthetic and observed time series is used as an additional tool along with the similarity between the theoretical and experimental dispersion curves. The proposed method is proven to be effective through synthetic and real world examples. In these examples, the nature of the non-uniqueness is discussed and its existence is shown. Using the proposed technique, inverted velocity profiles are estimated and effectiveness of this technique is evaluated; in the synthetic example, final inverted velocity profile is compared with the initial target velocity model, and in the real world example, final inverted shear-wave velocity profile is compared with the velocity model from independent measurements in a nearby borehole. Real world example shows that it is possible to overcome the non-uniqueness and distinguish the representative velocity profile for the site that also matches well with the borehole measurements

Electromagnetic interactions in one-dimensional metamaterials

All data created during this research is available in ORE at https://doi.org/10.24378/exe.630Metamaterials offer the freedom to tune the rich electromagnetic coupling between the constituent meta-atoms to tailor their collective electromagnetic response. Therefore, a comprehensive understanding of the nature of electromagnetic interactions between meta-atoms is necessary for novel metamaterial design, which is provided in the first part of this thesis. The subsequent work in the thesis applies the understanding from the first part to design and demonstrate novel one-dimensional metamaterials that overcome the limitations of metamaterials proposed in literature or exhibit electromagnetic responses not previously observed. Split-ring Resonators (SRRs) are a fundamental building block of many electromagnetic metamaterials. In the first part of the work in this thesis, it is shown that bianisotropic SRRs (with magneto-electric cross-polarisation) when in close proximity to each other, exhibit a rich coupling that involves both electric and magnetic interactions. The strength and nature of the coupling between two identical SRRs are studied experimentally and computationally as a function of their separation and relative orientation. The electric and magnetic couplings are characterised and it is found that, when SRRs are close enough to be in each other's near-field, the electric and magnetic couplings may either reinforce each other or act in opposition. At larger separations retardation effects become important. The findings on the electromagnetic interactions between bianisotropic resonators are next applied to developing a one-dimensional ultra-wideband backward-wave metamaterial waveguide. The key concept on which the metamaterial waveguide is built is electro-inductive wave propagation, which has emerged as an attractive solution for designing backward-wave supporting metamaterials. Stacked metasurfaces etched with complementary SRRs (CSRRs) have also been shown to exhibit a broadband negative dispersion. It is demonstrated through experiment and numerical modeling, that the operational bandwidth of a CSRR metamaterial waveguide can be improved by restricting the cross-polarisation effects in the constituent meta-atoms. The metamaterial waveguide constructed using the modified non-bianisotropic CSRRs are found to have a fractional bandwidth of 56.3\% which, based on a thorough search of relevant literature, is the broadest reported value for an electro-inductive metamaterial. A traditional coupled-dipole toy-model is presented as a tool to understand the field interactions in CSRR based metamaterials, and to explain the origin of their negative dispersion response. This metamaterial waveguide should be of assistance in the design of broadband backward-wave metamaterial devices, with enhanced electro-inductive waveguiding effects. In the final part of the thesis, a one-dimensional metamaterial prototype that permits simultaneous forward- and backward-wave propagation is designed. Such a metamaterial waveguide could act as a microwave analogue of nanoparticle chains that support electromagnetic energy transfer with a positive or a negative dispersion due to the excitation of their longitudinal or transverse dipole modes. The symmetry of the designed hybrid meta-atom permits the co-existence of two non-interfering resonances closely separated in frequency. It is experimentally and computationally shown that the metamaterial waveguide supports simultaneous non-interacting forward- and backward-wave propagation in an overlapping frequency band. The proposed metamaterial design should be suitable for realising bidirectional wireless power transfer applications.EPSRC Centre for Doctoral Training in Electromagnetic Metamaterial