High frequency wave propagation in the earth: theory and observation

The wave-theoretical analysis of acoustic and elastic waves refracted by a spherical boundary across which both velocity and density increase abruptly and thence either increase or decrease continuously with depth is formulated in terms of the general problem of waves generated at a steady point source and scattered by a radially heterogeneous spherical body. A displacement potential representation is used for the elastic problem that results in high frequency decoupling of P-SV motion in a spherically symmetric, radially heterogeneous medium. Through the application of an earth-flattening transformation on the radial solution and the Watson transform on the sum over eigenfunctions, the solution to the spherical problem for high frequencies is expressed as a Weyl integral for the corresponding half-space problem in which the effect of boundary curvature maps into an effective positive velocity gradient. The results of both analytical and numerical evaluation of this integral can be summarized as follows for body waves in the crust and upper mantle:

1) In the special case of a critical velocity gradient (a gradient equal and opposite to the effective curvature gradient), the critically refracted wave reduces to the classical head wave for flat, homogeneous layers.

2) For gradients more negative than critical, the amplitude of the critically refracted wave decays more rapidly with distance than the classical head wave.

3) For positive, null, and gradients less negative than critical, the amplitude of the critically refracted wave decays less rapidly with distance than the classical head wave, and at sufficiently large distances, the refracted wave can be adequately described in terms of ray-theoretical diving waves. At intermediate distances from the critical point, the spectral amplitude of the refracted wave is scalloped due to multiple diving wave interference.

These theoretical results applied to published amplitude data for P-waves refracted by the major crustal and upper mantle horizons (the Pg, P*, and Pn travel-time branches) suggest that the 'granitic' upper crust, the 'basaltic' lower crust, and the mantle lid all have negative or near-critical velocity gradients in the tectonically active western United States. On the other hand, the corresponding horizons in the stable eastern United States appear to have null or slightly positive velocity gradients. The distribution of negative and positive velocity gradients correlates closely with high heat flow in tectonic regions and normal heat flow in stable regions. The velocity gradients inferred from the amplitude data are generally consistent with those inferred from ultrasonic measurements of the effects of temperature and pressure on crustal and mantle rocks and probable geothermal gradients. A notable exception is the strong positive velocity gradient in the mantle lid beneath the eastern United States (2 x 10^-3 sec^-1), which appears to require a compositional gradient to counter the effect of even a small geothermal gradient.

New seismic-refraction data were recorded along a 800 km profile extending due south from the Canadian border across the Columbia Plateau into eastern Oregon. The source for the seismic waves was a series of 20 high-energy chemical explosions detonated by the Canadian government in Greenbush Lake, British Columbia. The first arrivals recorded along this profile are on the Pn travel-time branch. In northern Washington and central Oregon their travel time is described by T = Δ/8.0 + 7.7 sec, but in the Columbia Plateau the Pn arrivals are as much as 0.9 sec early with respect to this line. An interpretation of these Pn arrivals together with later crustal arrivals suggest that the crust under the Columbia Plateau is thinner by about 10 km and has a higher average P-wave velocity than the 35-km-thick, 62-km/sec crust under the granitic-metamorphic terrain of northern Washington. A tentative interpretation of later arrivals recorded beyond 500 km from the shots suggests that a thin 8.4-km/sec horizon may be present in the upper mantle beneath the Columbia Plateau and that this horizon may form the lid to a pronounced low-velocity zone extending to a depth of about 140 km.

Ultrasonic imaging of 3D displacement vectors using a simulated 2D array and beamsteering.

Most quasi-static ultrasound elastography methods image only the axial strain, derived from displacements measured in the direction of ultrasound propagation. In other directions, the beam lacks high resolution phase information and displacement estimation is therefore less precise. However, these estimates can be improved by steering the ultrasound beam through multiple angles and combining displacements measured along the different beam directions. Previously, beamsteering has only considered the 2D case to improve the lateral displacement estimates. In this paper, we extend this to 3D using a simulated 2D array to steer both laterally and elevationally in order to estimate the full 3D displacement vector over a volume. The method is tested on simulated and phantom data using a simulated 6-10MHz array, and the precision of displacement estimation is measured with and without beamsteering. In simulations, we found a statistically significant improvement in the precision of lateral and elevational displacement estimates: lateral precision 35.69μm unsteered, 3.70μm steered; elevational precision 38.67μm unsteered, 3.64μm steered. Similar results were found in the phantom data: lateral precision 26.51μm unsteered, 5.78μm steered; elevational precision 28.92μm unsteered, 11.87μm steered. We conclude that volumetric 3D beamsteering improves the precision of lateral and elevational displacement estimates.

Ultrasonic imaging of 3D displacement vectors using a simulated 2D array and beamsteering

Most quasi-static ultrasound elastography methods image only the axial strain, derived from displacements measured in the direction of ultrasound propagation. In other directions, the beam lacks high resolution phase information and displacement estimation is therefore less precise. However, these estimates can be improved by steering the ultrasound beam through multiple angles and combining displacements measured along the different beam directions. Previously, beamsteering has only considered the 2D case to improve the lateral displacement estimates. In this paper, we extend this to 3D using a simulated 2D array to steer both laterally and elevationally in order to estimate the full 3D displacement vector over a volume. The method is tested on simulated and phantom data using a simulated 6-10 MHz array, and the precision of displacement estimation is measured with and without beamsteering. In simulations, we found a statistically significant improvement in the precision of lateral and elevational displacement estimates: lateral precision 35.69 μm unsteered, 3.70 μm steered; elevational precision 38.67 μm unsteered, 3.64 μm steered. Similar results were found in the phantom data: lateral precision 26.51 μm unsteered, 5.78 μm steered; elevational precision 28.92 μm unsteered, 11.87 μm steered. We conclude that volumetric 3D beamsteering improves the precision of lateral and elevational displacement estimates. © 2012 Elsevier B.V. All rights reserved.

An Ultrasonic Relaxation Study of 1-Alkyl-3-Methylmidazolium-Based Room Temperature Ionic Liquids: Probing the Role of Alkyl Chain Length in the Cation

Ultrasound absorption spectra of four 1-alkyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide were determined as a function of the alkyl chain length on the cation from 1-propyl- to 1-hexyl- from 293.15 to 323.15 K at ambient pressure. Herein, the ultrasound absorption measurements were carried out using a standard pulse technique within a frequency range from 10 to 300 MHz. Additionally the speed of sound, density and viscosity have been measured. The presence of strong dissipative processes during the ultrasound wave propagation was found experimentally, i.e. relaxation processes in the megahertz range were observed for all compounds over the whole temperature range. The relaxation spectra (both relaxation amplitude and relaxation frequency) were shown to be dependent on the alkyl side chain length of the 1-alkyl-3-methylimidazolium ring. In most cases, a single Debye model described the absorption spectra very well. However, a comparison of the determined spectra with the spectra of a few other imidazolium-based ionic liquids reported in the literature (in part recalculated in this work) shows that the complexity of the spectra increases rapidly with the elongation of the alkyl chain length on the cation. This complexity indicates that both the volume viscosity and the shear viscosity are involved in relaxation processes even in relatively low frequency ranges. As a consequence, the sound velocity dispersion is present at relatively low megahertz frequencies.

Ultrasonic Study Of The Elastic Properties And Phase Transitions In Selected Mixed Sulphate Crystals

The thesis investigated the elastic properties and phase transitions in selected mixed sulphate crystals – Lithium Hydrazinium Sulphate [LiN2H2SO4], Lithium Ammonium Sulphate [LiNH4SO4] and Lithium Potassium Sulphate [LiKSO4] – using ultrasonic technique. The pulse echo overlap technique has been used for measuring ultrasonic velocity and its dependence on temperature along different directions with waves of longitudinal and transverse polarizations. Two major numerical techniques and the corresponding computer programs developed as part of present work are presented in this thesis. All the 9 elastic constants of LHS are determined accurately from ultrasonic measurements and applying misorientation correction refines the constants. Ultrasonic measurements are performed in LAS to determine the elastic constants and to study the low temperature phase transitions. Temperature variation studies of elastic constant of LAS are performed for 6 different modes of propagation for heating and cooling at low temperatures. All the 5 independent elastic constants of LPS is determined using ultrasonic measurements. It is concluded that LPS crystal does not undergo a phase transition near this temperature. A comparison of the three crystals studied shows that LPS has maximum number of phase transitions and LHS has the least number. It is interesting to note that LPS has the simplest formula unit among the three. There is considerable scope for the future work on these crystals and others belonging to the sulphate family.

Ultrasonic measurement of the elastic constants of selected nonlinear optical /semiorganic crystals with orthorhombic symmetry

Ultrasonic is a good tool to investigate the elastic properties of crystals. It enables one to determine all the elastic constants, Poisson’s ratios, volume compressibility and bulk modulus of crystals from velocity measurements. It also enables one to demonstrate the anisotropy of elastic properties by plotting sections of the surfaces of phase velocity, slowness, group velocity, Young’s modulus and linear compressibility along the a-b, b-c and a-c planes. They also help one to understand more about phonon amplification and help to interpret various phenomena associated with ultrasonic wave propagation, thermal conductivity, phonon transport etc. Study of nonlinear optical crystals is very important from an application point of view. Hundreds of new NLO materials are synthesized to meet the requirements for various applications. Inorganic, organic and organometallic or semiorganic classes of compounds have been studied for several reasons. Semiorganic compounds have some advantages over their inorganic and inorganic counterparts with regard to their mechanical properties. High damage resistance, high melting point, good transparency and non-hygroscopy are some of the basic requirements for a material to be suitable for device fabrication. New NLO materials are being synthesized and investigation of the mechanical and elastic properties of these crystals is very important to test the suitability of these materials for technological applications

Ultrasonic measurement of the elastic properties of benzoyl glycine single crystals

Certain organic crystals are found to possess high non- linear optical coefficients,often one to two orders of magnitude higher than those of the well known inorganic non-linear optical materials.Benzoyl glycine is one such crystal whose optical second-harmonic generation efficiency is much higher than that of potassium dihydrogen phosphate. Single crystals of benzoyl glycine are grown by solvent evaporation technique using N,N-dimethyl formamide as the solvent.All the nine second-order elastic stiffness constants of this orthorhombic crystal are determined from ultrasonic wave velocity measurements employing the pulse echo overlap technique.The anisotropy of elastic wave propagation in this crystal is demonstrated by plotting the phase velocity, slowness,Young's modulus and linear compressibility surfaces along symmetry planes.The volume compressibility, bulk modulus and relevant Poisson's ratios are also determined. Variation of the diagonal elastic stiffness constants with temperature over a limited range are measured and reported.

Proposed design for an ultrasonic optical force-feedback microphone

We discuss a novel approach that would lead to the development of an ultrasonic optical force-feedback measurement microphone.

Ultrasonic densitometer using a multiple reflection technique

This work presents recent improvements in a density measurement cell with a double-element transducer that can eliminate diffraction effects. A new mechanical design combined with the use of more appropriate materials has resulted in better parallelism between interfaces, more robust assembly, and chemical resistance. A novel method of signal processing, named energy method, is introduced to obtain the reflection coefficient, reducing sensitivity to noise and improving accuracy. The measurement cell operation is verified both theoretically, using an acoustic wave propagation model, and experimentally, using homogeneous liquids with different densities. The accuracy in the density measurement is 0.2% when compared with the measurements made with a pycnometer.

Thermal characterization of an ultrasonic density-measurement cell

An ultrasonic density-measurement cell is experimentally characterized as a function of temperature. The measurement of propagation velocity and density of several liquids is performed in the 15 degrees C-40 degrees C temperature range. Results are compared to the tabulated values in the case of distilled water, showing an accuracy of 0.07% for the propagation velocity. The cell was tested with distilled water, alcohol, and homogenized milk, and density values are compared to those obtained with a pycnometer, showing 0.2% accuracy in density measurement for stabilized temperature and 0.4% accuracy under thermal gradient conditions.

Energy method to calculate the density of liquids using ultrasonic reflection techniques

In this work it is introduced a new approach to calculate the density of liquids in terms of the energies of the acoustic signals. This method is compared to other methods in the time domain (peak-to-peak amplitudes) and frequency domain magnitudes at a single frequency. It is used a measurement cell based on a multiple reflection technique, and it is developed an acoustic model for the cell. Simulations and experiments using several liquids are presented, showing that the energy method a less sensitive to noise than the other techniques. The relative errors in the density are smaller than 0.2% when compared to the values measured with a pycnometer.

Thermodynamic response of an ultrasonic densitometer

An ultrasonic densitometer is experimentally characterized as a function of temperature. The measurement of propagation velocity and density of several liquids is performed in the 15 to 40°C temperature range. Results are compared to tabulated values in the case of distilled water, showing accuracy of 0.07% for the propagation velocity. Density values are compared to those obtained with a pycnometer, showing 0.2% accuracy in density measurement for stabilized temperature and 0.4% under thermal gradient conditions.

Ultrasonic non-destructive testing of plate-like structures using piezoelectric array transducers

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Theoretical Analysis and Experimental Validation of the Scholte Wave Propagation in Immersed Plates for the Characterization of Viscous Fluids

This work reports the study of an attractive interfacial wave for application in ultrasonic NDE techniques for inspection and fluid characterization. This wave, called quasi-Scholte mode, is a kind of flexural wave in a plate in contact with a fluid which presents a good sensitivity to the fluid properties. In order to explore this feature, the phase velocity curve of quasi-Scholte mode is experimentally measured in a plate in contact with a viscous fluid, showing a good agreement with theory.

Sparse Signal Representation of Ultrasonic Signals for Structural Health Monitoring Applications

Assessment of the integrity of structural components is of great importance for aerospace systems, land and marine transportation, civil infrastructures and other biological and mechanical applications. Guided waves (GWs) based inspections are an attractive mean for structural health monitoring. In this thesis, the study and development of techniques for GW ultrasound signal analysis and compression in the context of non-destructive testing of structures will be presented. In guided wave inspections, it is necessary to address the problem of the dispersion compensation. A signal processing approach based on frequency warping was adopted. Such operator maps the frequencies axis through a function derived by the group velocity of the test material and it is used to remove the dependence on the travelled distance from the acquired signals. Such processing strategy was fruitfully applied for impact location and damage localization tasks in composite and aluminum panels. It has been shown that, basing on this processing tool, low power embedded system for GW structural monitoring can be implemented. Finally, a new procedure based on Compressive Sensing has been developed and applied for data reduction. Such procedure has also a beneficial effect in enhancing the accuracy of structural defects localization. This algorithm uses the convolutive model of the propagation of ultrasonic guided waves which takes advantage of a sparse signal representation in the warped frequency domain. The recovery from the compressed samples is based on an alternating minimization procedure which achieves both an accurate reconstruction of the ultrasonic signal and a precise estimation of waves time of flight. Such information is used to feed hyperbolic or elliptic localization procedures, for accurate impact or damage localization.