Wave-scattering Effects Research Articles

Inertial interaction in pile-groups: A study of the influence of coupling via an iterative wave-scattering approach

The increasing urban population is leading to the exploitation of building sites close to sources of ground-borne vibration, such as railways and busy roads. Piled foundations can provide a significant vibration transmission path into a building, which can then cause disturbance to occupants and sensitive equipment. There is a strong need to develop numerical models that can capture the essential dynamics of a piled foundation, over the frequency range associated with ground-borne vibration, to help practising engineers decide on appropriate countermeasures. In this paper, a piled foundation is modelled as a pile-group embedded in a homogeneous half-space. Previous research has explored the dynamics of pile-groups to inertial loading at relatively low frequencies, over the seismic range. Here, an iterative approach is developed using a source-receiver boundary-element model to account for the wave-scattering effect that becomes more significant at higher frequencies. Predictions of the dynamic interaction factors, which describe the pile-soil-pile interaction, show very good agreement with a standard boundary-element model for a range of geometric and material parameters. The results show that using uncoupled source-receiver models can account effectively for the interaction between piles without resorting to fully coupled models, even at frequencies well above those of previously published results.

Borehole elastic wave anisotropic scattering and application to hydraulic fracturing

Anisotropy is an important property of inhomogeneous underground rocks and a central topic for geophysical exploration. Detecting the inhomogeneous anisotropy of rocks is key for rational oil and gas reservoir utilization and well placement optimization. Conventional cross dipole measurements can only evaluate the anisotropy of formation rocks near the borehole wall, and are therefore unable to evaluate the rock anisotropy at a distance from the borehole. This study investigates the anisotropic distribution of rock heterogeneity and the resulting azimuthal variation of the acoustic scattering intensity. The results show that this azimuthal scattering intensity variation of the dipole shear-wave acoustic logging data can be used to evaluate the anisotropic distribution of the rock heterogeneity. A borehole model with a three-dimensional heterogeneous and anisotropic elastic formation was established first, and the dipole acoustic logging along the borehole model was simulated using a finite difference technique. The wave-scattering effect in the borehole dipole wave data, measured in terms of a coda wave attenuation, was analyzed. The scattering attenuations of coda waves measured in different azimuthal directions exhibit significant variations, which are related to the azimuthal variation of the formation inhomogeneity. Based on the results of theoretical modeling, a method for the evaluation of the anisotropic variation of formation inhomogeneity (via azimuthal pattern of the scattering attenuations) was proposed. The method was applied to dipole acoustic logging data, acquired before and after hydraulically fracturing a tight reservoir. The field data results show that the scattered dipole-shear coda wave attenuation of the after-fracturing data exhibits an elongated, anisotropic variation pattern, where the direction of elongation coincides with the fracture extension direction. This indicates good potential for using the proposed method for hydraulic fracture evaluation. Because wave scattering occurs in a large volume around the borehole, application of this method and analysis can significantly enhance the measurement volume of the cross-dipole logging technology. This extends its effectiveness toward the evaluation of hydraulic fracturing results for unconventional reservoirs (e.g., shale gas).

Nanostructured PMMA-coated Love wave device as a platform for protein adsorption studies

The development of nanostructured surfaces can enhance molecular interaction with sensors by increasing the available surface area. The associated potential for increased sensitivity towards analytes is of significance to the analytical and biophysical sector. In this work we explore the effect of nanostructures created on the surface of an acoustic wave device based on a Love wave geometry. Nanopillars with a diameter of 35nm and a height range of 60–280nm were created on top of a PMMA waveguide film by oxygen plasma etching. The effect of the pillar height on the acoustic response was tested by measuring the adsorption of BSA; increasing the pillar height up to 155nm led to an increase in the acoustic phase response associated with wave velocity. At higher surface roughness, wave-scattering effects dominated: at nanopillar heights larger than 200nm these effects were so severe that the sensors could not be used for protein sensing. In addition to phase, amplitude measurements were used to derive information on the structure of the adsorbed protein film and its dependency on the nanopillar height. This work demonstrates the importance of controlling the roughness of the waveguiding layer of a Love wave device, since the nanostructure-dependent response has considerable effects on designing sensitive biochip platforms for clinical and diagnostic applications.

High-Q cross-plate phononic crystal resonator for enhanced acoustic wave localization and energy harvesting

A high-Q cross-plate phononic crystal resonator (Cr-PCR) coupled with an electromechanical Helmholtz resonator (EMHR) is proposed to improve acoustic wave localization and energy harvesting. Owing to the strongly directional wave-scattering effect of the cross-plate corners, strong confinement of acoustic waves emerges. Consequently, the proposed Cr-PCR structure exhibits ∼353.5 times higher Q value and ∼6.1 times greater maximum pressure amplification than the phononic crystal resonator (Cy-PCR) (consisting of cylindrical scatterers) of the same size. Furthermore, the harvester using the proposed Cr-PCR and the EMHR has ∼22 times greater maximum output-power volume density than the previous harvester using Cy-PCR and EMHR structures.

Reflection and transmission of ocean wave spectra by a band of randomly distributed ice floes

AbstractA new ocean wave/sea-ice interaction model is proposed that simulates how a directional wave spectrum evolves as it travels through an arbitrary finite array of circular ice floes, where wave/ ice dynamics are entirely governed by wave-scattering effects. The model is applied to characterize the wave reflection and transmission properties of a strip of ice floes, such as an ice edge band. A method is devised to extract the reflected and transmitted directional wave spectra produced by the array. The method builds upon an integral mapping from polar to Cartesian coordinates of the scattered wave components. Sensitivity tests are conducted for a row of floes randomly perturbed from a regular arrangement. Results for random arrays are generated using ensemble averaging. A realistic ice edge band is then reconstructed from field experiment data. Simulations show good qualitative agreement with the data in terms of transmitted wave energy and directional spreading. In particular, it is observed that short waves become isotropic quickly after penetrating the ice field.

Site Amplification, Scattering, and Intrinsic Attenuation in the Mississippi Embayment from Coda Waves

We estimate site amplification, intrinsic Q ( Q I ) and scattering Q ( Q S ) values from three-component coda of broadband data recorded by Cooperative New Madrid Sesimic Network stations for center frequencies 0.2, 0.5, 1.0, 2.0, and 5.0 Hz. Near 0.5 and 1.0 Hz, site amplification factors for the transverse component recorded by stations in the Mississippi embayment are between 1.7 and 18, compared with stations outside the embayment. The amplification factor becomes smaller at frequencies lower than 0.5 Hz and higher at those greater than 1.0 Hz. The radial component shows a similar amplification; however, the vertical component shows relatively less amplification. Q I and Q S are estimated from coda using an energy flux model for two time windows after the direct S wave and at 0.5 and 1.0 Hz center frequencies. The two time windows include coda up to and after twice the S -wave travel time at each station. Coda parameters change with the time window and are attributed to a mixture of incoherent coda with coherent S-wave reverberations directly after the S wave. Q I and Q S inferred from stations outside of the embayment have higher values than those from stations within the embayment. A plane wave model qualitatively explains the lack of coda amplification at high frequencies compared with a low frequency without recourse to anelastic attenuation arguments. However, the plane wave model cannot explain the very large observed coda amplifications at 1 and 0.5 Hz seen in the data, suggesting that other wave-scattering effects must be occurring in the embayment velocity structure. This is consistent with the relatively low Q S values inferred from the energy flux model for stations within the embayment. In addition to coda amplification, we performed a synoptic noise study that revealed that pre-event ambient background noise behaves in a similar manner to the coda for stations within and outside of the embayment. The presence of large lateral velocity heterogeneities in the embayment may cause Q S values to be low there.

Accuracy and efficiency considerations for wide-angle wavefield extrapolators and scattering operators

SUMMARY Several observations are made concerning the numerical implementation of wide-angle one-way wave equations, using for illustration scalar waves obeying the Helmholtz equation in two space dimensions. This simple case permits clear identification of a sequence of physically motivated approximations of use when the mathematically exact pseudo-differential operator (PSDO) one-way method is applied. As intuition suggests, these approximations largely depend on the medium gradients in the direction transverse to the main propagation direction. A key point is that narrow-angle approximations are to be avoided in the interests of accuracy. Another key consideration stems from the fact that the so-called ‘standard-ordering’ PSDO indicates how lateral interpolation of the velocity structure can significantly reduce computational costs associated with the Fourier or plane-wave synthesis lying at the heart of the calculations. A third important point is that the PSDO theory shows what approximations are necessary in order to generate an exponential one-way propagator for the laterally varying case, representing the intuitive extension of classical integral-transform solutions for a laterally homogeneous medium. This exponential propagator permits larger forward stepsizes. Numerical comparisons with Helmholtz (i.e. full) wave-equation finite-difference solutions are presented for various canonical problems. These include propagation along an interfacial gradient, the effects of a compact inclusion and the formation of extended transmitted and backscattered wave trains by model roughness. The ideas extend to the 3-D, generally anisotropic case and to multiple scattering by invariant embedding. It is concluded that the method is very competitive, striking a new balance between simplifying approximations and computational labour. Complicated wave-scattering effects are retained without the need for expensive global solutions, providing a robust and flexible modelling tool.

Modification of Weak Turbulence Theory Due to Perturbed Orbit Effects. I. General Formulation

A new formulation is presented to derive a wave-kinetic equation for the spectral function of the fluctuation potential in a weakly turbulent plasma. The theory takes into account both the orbit-modification effect due to strong wave-particle resonant interactions and the wave-scattering effect usually considered in the weak turbulence theory. The effect of a uniform external electric field is also taken into consideration. The method consists in a systematic use of a diagram technique in order to collect secular term contributions. The modified propagator generalized over the previous version by Dupree and Weinstock and the wave-kinetic equation consistent with the usual weak turbulence theory are obtained.