Total Wave Field Research Articles

Imaging of local porosity/voids using a fully non-contact air-coupled transducer and laser Doppler vibrometer system

This study exploits the feasibility of imaging zones of local porosity/voids simulated by introducing microspheres during layup of a unidirectional carbon fiber–reinforced polymer composite panel. A fully non-contact hybrid system primarily composed of an air-coupled transducer and a laser Doppler vibrometer was used for imaging the local porosity/void zones from the guided wave response. To improve image resolution, several preprocessing techniques are performed. The wavefield reconstructed from the laser Doppler vibrometer measurements was first “denoised” using a one-dimensional wavelet transform in the time domain followed by a two-dimensional wavelet transform in the spatial domain. From the total wavefield, the much weaker backscattered waves were separated from the stronger incident wave by frequency–wavenumber domain filtering. In order to further enhance the signal-to-noise ratio and sharpen the image, the attenuation of incident wave propagation to the damage site was compensated through two proposed weight functions. Finally, a zero-lag cross-correlation was performed for imaging the zone where the compensated incident and backscattered waves were in phase. This improved imaging condition, the “denoised” weighted zero-lag cross-correlation, was proposed and tested for defect imaging in the composite panel with eight intentionally introduced zones of high porosity/voids of varying diameters (1.59–6.35 mm) and depths (0.36–1.08 mm). As expected, the sensitivity of the non-contact air-coupled transducer/laser Doppler vibrometer hybrid system was limited by the wavelength of the excitation signal. The system incorporated with the denoised weighted zero-lag cross-correlation imaging condition for guided wave interrogation gave similar image quality in comparison with that by the immersion C-scan.

Surface/interface effects on the effective propagation constants of coherent waves in composites with random parallel nanofibers

The effective propagation constants of elastic waves in an inhomogeneous medium with randomly distributed parallel cylindrical nanofibers are studied. First, the surface energy theory proposed by Huang and Wang (Handbook of Micromechanics and Nanomechanics, 2013) is used to derive the nontraditional boundary conditions on the surfaces of the nanoholes and the interfaces between the nanofibers and the host. Then, the scattering matrix of individual scatterer (cylindrical hole or nanofiber) is derived from the nontraditional boundary condition. The total wave field is obtained by considering the multiple scattering processes among the dispersive scatterers. The configuration average of the total wave field results in the coherent waves or the averaged waves. By using the corrected Linton-Martin formula, the effective propagation constants (effective speed and effective attenuation) of the coherent waves are estimated. The in-plane waves (P and SV waves) and the anti-plane waves (SH wave) are considered, respectively, and the numerical results are shown graphically. Apart from the effects of surface elasticity, the effects of inertia of surface/interface and the effects of residual surface tension (which are often ignored in the previous literature) are also considered. Moreover, the influences of the nonsymmetric parts of in-plane surface stress and the out-of-plane parts of the surface stress are both discussed first based on the numerical examples. These investigations show the underestimation and overestimation of effective propagation constants caused by various simplifications.

Scattering and diffraction of plane SH-waves by periodically distributed canyons

A new method is presented to study the scattering and diffraction of plane SH-waves by periodically distributed canyons in a layered half-space. This method uses the indirect boundary element method combined with Green’s functions of uniformly distributed loads acting on periodically distributed inclined lines. The periodicity feature of the canyons is exploited to limit the discretization effort to a single canyon, which avoids errors induced by the truncation of the infinite boundary, and the computational complexity and the demand on memory can be significantly reduced. Furthermore, the total wave fields are decomposed into the free field and scattered field in the process of calculation, which means that the method has definite physical meaning. The implementation of the method is described in detail and its accuracy is verified. Parametric studies are performed in the frequency domain by taking periodically distributed canyons of semi-circular and semi-elliptic cross-sections as examples. Numerical results show that the dynamic responses of periodically distributed canyons can be quite different from those for a single canyon and significant dynamic interactions exist between the canyons.

Correlation of Wavefield‐Separated Ocean‐Generated Microseisms with North Atlantic Source Regions

Abstract Ocean‐generated microseisms have the potential to be used as a proxy for ocean wave parameters. However, they are often comprised of contributions from multiple, coincidently active source regions. Using a seismic array, it should be possible to separate microseism data consisting of contributions from one or more source areas on the seafloor based on the wavenumber of the signals. Here we investigate the use of frequency–wavenumber filtering on data between 0.1 and 0.25 Hz, corresponding to double‐frequency microseisms, recorded at the Eskdalemuir seismic array in Scotland. As the array is intended for shorter seismic wavelengths than those that occur at microseism frequencies, synthetic and scaled field experiments are performed to establish that the array geometry is suitable. Application is then made to microseism data from the array. Through a comparison with WAVEWATCH3 numerical ocean wave data, we demonstrate that the frequency–wavenumber ( f ‐ k ) filter enables the separation of microseisms into its different geographical source components. This separated microseism data give proxy access to local sea state conditions that are masked in the total microseism wavefield.

Estimation of primaries by sparse inversion with scattering-based multiple predictions for data with large gaps

We have solved the estimation of primaries by sparse inversion problem for a seismic record with large near-offset gaps and other contiguous holes in the acquisition grid without relying on explicit reconstruction of the missing data. Eliminating the unknown data as an explicit inversion variable is desirable because it sidesteps possible issues arising from overfitting the primary model to the estimated data. Instead, we have simulated their multiple contributions by augmenting the forward prediction model for the total wavefield with a scattering series that mimics the action of the free surface reflector within the area of the unobserved trace locations. Each term in this scattering series involves convolution of the total predicted wavefield once more with the current estimated Green’s function for a medium without the free surface at these unobserved locations. It is important to note that our method cannot by itself mitigate regular undersampling issues that result in significant aliases when computing the multiple contributions, such as source-receiver sampling differences or crossline spacing issues in 3D acquisition. We have investigated algorithms that handle the nonlinearity in the modeling operator due to the scattering terms, and we also determined that just a few of the terms can be enough to satisfactorily mitigate the effects of near-offset data gaps during the inversion process. Numerical experiments on synthetic data found that the final derived method can significantly outperform explicit data reconstruction for large near-offset gaps, with a similar computational cost and better memory efficiency. We have also found on real data that our scheme outperforms the unmodified primary estimation method that uses an existing Radon-based interpolation of the near-offset gap.

Simulating propagation of decoupled elastic waves using low-rank approximate mixed-domain integral operators for anisotropic media

In elastic imaging, the extrapolated vector fields are decoupled into pure wave modes, such that the imaging condition produces interpretable images. Conventionally, mode decoupling in anisotropic media is costly because the operators involved are dependent on the velocity, and thus they are not stationary. We have developed an efficient pseudospectral approach to directly extrapolate the decoupled elastic waves using low-rank approximate mixed-domain integral operators on the basis of the elastic displacement wave equation. We have applied [Formula: see text]-space adjustment to the pseudospectral solution to allow for a relatively large extrapolation time step. The low-rank approximation was, thus, applied to the spectral operators that simultaneously extrapolate and decompose the elastic wavefields. Synthetic examples on transversely isotropic and orthorhombic models showed that our approach has the potential to efficiently and accurately simulate the propagations of the decoupled quasi-P and quasi-S modes as well as the total wavefields for elastic wave modeling, imaging, and inversion.

Wave-equation multiple imaging (WeMi) — Swimming between the flags

Deghosting dual-sensor streamer seismic data requires separation of the total recorded wavefield into upgoing and downgoing components during seismic preprocessing. Imaging of multiples exploits the wavefield separation process by using the downgoing wavefield at each receiver location as a virtual source. Multiple imaging has been shown to effectively remove shallow-acquisition-related artifacts commonly seen on wide-tow marine seismic surveys and improve imaging quality of the shallow overburden. Acquisition design factors, imaging condition, and cross-talk noise are the main factors that determine the effectiveness of separated wavefield imaging (SWIM) of dual-sensor streamer data. (SWIM is a common nontrademarked acronym used in the literature to describe multiple imaging of separated wavefields sampled from dual-sensor streamer data.) In a field trial, acquisition design did not allow for proper sampling of the total wavefield, with the result that multiple imaging did not prove to be as robust a technique as examples in the literature might imply. Understanding the effects of acquisition design parameters on image quality is essential to more successfully apply multiple-imaging techniques with greater relevance on the North West Shelf of Australia.

Isolation of ultrasonic scattering by wavefield baseline subtraction

Wavefield imaging generally refers to the measurement of signals over a two-dimensional rectilinear grid that originate from a spatially fixed source. Subtraction of such wavefields is investigated as a means of separating scattered signals from the total wavefield; that is, baseline wavefield data acquired from a defect-free specimen are subtracted from analogous data acquired after introduction of a defect. The wavefields considered here are generated by a 5MHz angle-beam probe and measured over an area of the accessible specimen surface using a laser vibrometer. The primary challenge in isolating the scattered waves is imperfect temporal and spatial alignment of the two wavefields. Two methods for aligning the wavefields in space and time prior to performing baseline subtraction are presented and their efficacy is evaluated using data acquired before and after introducing notches that originate from a through-hole. Although perfect baseline subtraction is not achieved, the improvement in performance after alignment using either method allows for scattered waves from small defects to be separated and visualized, even when their amplitudes are much smaller than those of the incident waves.

Fast least-squares imaging with surface-related multiples: Application to a North Sea data set

In marine seismic acquisition, surface-related multiples constitute a significant portion of the acquired data. Typically, multiples are removed during early-stage data processing because they can lead to phantom reflectors during migration that might result in erroneous geologic interpretations. However, if properly dealt with, multiples can provide valuable extra information and can complement primaries in illuminating the subsurface. Reverse time migration has limitations in imaging multiples. A computationally efficient inversion procedure is proposed which jointly maps primaries and multiples to the true reflectors and estimates the source function on the fly. As a result, high-quality, mostly artifact-free broad-band images are obtained in which the imprint of the source function is partly removed at a computationally affordable expense compared with the combined costs of wave-equation-based surface-related multiple elimination and reverse time migration. All this is achieved by including the total downgoing wavefields as areal sources in least-squares migration in combination with curvelet-domain sparsity promotion. The proposed method is applied to a shallow-water marine data set from the North Sea which contains abundant short-period surface-related multiples, and the efficacy of the method is shown in eliminating coherent imaging artifacts associated with multiples. The benefits of joint imaging of primaries and multiples are demonstrated compared with imaging these signal components separately.

Poststack diffraction imaging using reverse-time migration

We propose a method for imaging small-scale diffraction objects in complex environments in which Kirchhoff-based approaches may fail. The proposed method is based on a separation between the specular reflection and diffraction components of the total wavefield in the migrated surface angle domain. Reverse-time migration was utilized to produce the common image gathers. This approach provides stable and robust results in cases of complex velocity models. The separation is based on the fact that, in surface angle common image gathers, reflection events are focused at positions that correspond to the apparent dip angle of the reflectors, whereas diffracted events are distributed over a wide range of angles. The high-resolution radon-based procedure is used to efficiently separate the reflection and diffraction wavefields. In this study, we consider poststack diffraction imaging. The advantages of working in the poststack domain are its numerical efficiency and the reduced computational time. The numerical results show that the proposed method is able to image diffraction objects in complex environments. The application of the method to a real seismic dataset illustrates the capability of the approach to extract diffractions.

Direct computation of acoustic scattering and difference frequency generation

A simulation of the scattered field at the difference-frequency resulting from the nonlinear interaction of two beams at differing frequencies incident on a fluid scatterer is performed. The total wavefield response is modeled using a finite-difference time-domain approximation and a perfectly matched layer to estimate the spatial scattering features of the medium. A pulsed ultrasonic transducer beam is modeled and its interaction with a fluid scatterer with spatially varying compressibility contrast is visualized. The second-order pressure field is determined as a response to the difference-frequency source field constructed from the first order-response of the scatterer to the two incident beams as well as a spatial distribution of the nonlinear parameter. The performance and accuracy of the numerical simulation is examined.

Wave scattering by nanoheterogeneities embedded in an elastic matrix via BEM

In this work, we study elastic wave scattering and diffraction at the nanoscale by multiple heterogeneities such as cavities and inclusions embedded in an otherwise homogeneous elastic matrix. The dynamic loads are the result of pressure and shear waves propagating through the heterogeneous continuum under two-dimensional conditions. The mathematical model used here combines (a) classical elastodynamic theory for the bulk solid, where the total elastic wave field comprises both incident and scattered wave fields, with (b) non-classical boundary conditions and a localized constitutive equation for the matrix–inclusion interfaces within the framework of the Gurtin–Murdoch surface elasticity theory. The computational platform used is the boundary element method (BEM) defined in terms of the frequency-dependent fundamental solution of the governing equations of motion for the bulk solid under time-harmonic conditions. Following development of the BEM for this category of problems, a verification study is conducted to establish its accuracy with the help of benchmark-type examples. Subsequent numerical simulations for the case of multiple cavities and inclusions embedded in an elastic matrix examine the development of the wave fields in the bulk solid, as well as of the dynamic stress concentration factor (DSCF) at the solid-inclusion interfaces, in terms of the following parameters: (a) nanoheterogeneity shape, which directly influences the surface energy; (b) nanoheterogeneity size; (c) ratio of the bulk material properties of the matrix to those of the inclusion; (d) surface properties such as the interfacial constants and the residual interface tension; (e) dynamic interaction between multiple nanoheterogeneities and (f) direction of propagation and frequency content of the incident wave.

An IBEM solution to the scattering of plane SH-waves by a lined tunnel in elastic wedge space

The indirect boundary element method (IBEM) is developed to solve the scattering of plane SH-waves by a lined tunnel in elastic wedge space. According to the theory of single-layer potential, the scattered-wave field can be constructed by applying virtual uniform loads on the surface of lined tunnel and the nearby wedge surface. The densities of virtual loads can be solved by establishing equations through the continuity conditions on the interface and zero-traction conditions on free surfaces. The total wave field is obtained by the superposition of free field and scattered-wave field in elastic wedge space. Numerical results indicate that the IBEM can solve the diffraction of elastic wave in elastic wedge space accurately and efficiently. The wave motion feature strongly depends on the wedge angle, the angle of incidence, incident frequency, the location of lined tunnel, and material parameters. The waves interference and amplification effect around the tunnel in wedge space is more significant, causing the dynamic stress concentration factor on rigid tunnel and the displacement amplitude of flexible tunnel up to 50.0 and 17.0, respectively, more than double that of the case of half-space. Hence, considerable attention should be paid to seismic resistant or anti-explosion design of the tunnel built on a slope or hillside.

Inverse Shape Reconstruction of Inner Cavities Using Guided SH-Waves in a Plate

The paper proposes an inverse reconstruction method for inner cavities in a 2D plate using guided SH-waves. When a pure incident wave mode is sent toward the flaw area, reflected waves are observed at the far field due to mode conversion. From wave scattering theory, the reflected wave field is expressed by an integral over the unknown flaw surface concerning the total wave field. By the introduction of Born approximation and far-field expressions of Green’s function, it is found that the reflection coefficient for the mode of the same order as that of the incident mode is related to the unknown shape of the cavity by Fourier transform relations. By mathematical deduction, we show that if the basic (0th-order) symmetric and the 1st-order antisymmetric modes are used as incident waves, the locations and shapes of upper and lower boundaries of the cavity can be reconstructed. Numerical examples are illustrated in the paper, and a proper condition for applying this method is discussed. The research can act as a basis of nondestructive inspection for latent flaws within more complicated structures.

Effective dynamic properties of random nanoporous materials with consideration of surface effects

The frequency-dependent dynamic effective properties (velocity, attenuation and elastic modulus) of nanoporous materials with randomly positioned spherical cavities are studied. The surface energy theory proposed by Huang and Wang (Handbook of micromechanics and nanomechanics. Pan Stanford Publishing Pte Ltd., Singapore, pp 303-348, 2013) is used to derive the non-traditional boundary condition on the surface of the nanocavity and further the scattering matrix of a single nanocavity. Then, the total wave field is obtained by considering the multiple scattering processes among the dispersive spherical cavities. The configuration average of the total wave field results in the coherent waves or the averaged waves. The numerical examples of the effective speed, the effective attenuation of the coherent waves and associated effective dynamic modulus of a nanoporous material are given and shown graphically. The effects of surface elasticity and the residual surface tension are both considered. Moreover, the influences of the non-symmetric parts of in-plane surface stress and the out-of-plane parts of the surface stress are also discussed based on the numerical examples.

The scattering properties of a system of structures in water waves

A fixed, rigid structure is said to be cloaked in small amplitude, time-harmonic water waves if it is possible to surround it with other fixed or moving structures or variations in the sea-bed topography in such a way that there are no scattered waves in the far field. The resulting system of structures is said to be transparent to the incident wave field. By finding inequalities which the kinetic and potential energy in the total wave field for such a system must satisfy, it is shown that transparency is impossible for a system of structures which has non-zero volume and satisfies the condition that the free surface is connected and a vertical line drawn from every point on the free surface does not intersect another structure but intersects the sea bed at a point at which the bed is horizontal.

The Scattering of Circular Cylindrical Cavity with Time-Harmonic SH Waves in Infinite Strip Region

The scattering of time harmonic SH waves by arbitrary positions of circular cylindrical cavity is studied in continuous, homogeneous, isotropic, elastic strip region. In this paper, the completely analytical expression of total wave field is explicitly presented and the dynamic stress distribution is symbolically visualized in the strip region. The total wave field is divided into four sub wave fields, incident wave field and scattering wave field by the upper bound, the lower bound and the cylindrical bound, on big arc supposition. Specific wave functions are employed for each wave field expansion in series, such as circular cylindrical functions, respectively. Corresponding infinite linear algebraic equations are constructed by means of solving coefficients of Fourier series expansion on each sub wave field. Coefficients of cylindrical function expansion of each sub wave field are determined by truncated equations, which are reduced number of coefficients on pre-given computational accuracy. Numerical results graphically describe the dynamic stress concentration factor around the circumference of the cavity and the normalized dynamic stress along the cross section directly above the cavity.

Numerical modeling of elastic-wave scattering by near-surface heterogeneities

In land seismic data, scattering from surface and near-surface heterogeneities adds complexity to the recorded signal and masks weak primary reflections. To understand the effects of near-surface heterogeneities on seismic reflections, we simulated seismic-wave scattering from arbitrary-shaped, shallow, subsurface heterogeneities through the use of a perturbation method for elastic waves and finite-difference forward modeling. The near-surface scattered wavefield was modeled by looking at the difference between the calculated incident (i.e., in the absence of scatterers) and the total wavefields. Wave propagation was simulated for several earth models with different near-surface characteristics to isolate and quantify the influence of scattering on the quality of the seismic signal. The results indicated that the direct surface waves and the upgoing reflections were scattered by the near-surface heterogeneities. The scattering took place from body waves to surface waves and from surface waves to body waves. The scattered waves consisted mostly of body waves scattered to surface waves and were, generally, as large as, or larger than, the reflections. They often obscured weak primary reflections and could severely degrade the image quality. The results indicated that the scattered energy depended strongly on the properties of the shallow scatterers and increased with increasing impedance contrast, increasing size of the scatterers relative to the incident wavelength, decreasing depth of the scatterers, and increasing attenuation factor of the background medium. Also, sources deployed at depth generated weak surface waves, whereas deep receivers recorded weak surface and scattered body-to-surface waves. The analysis and quantified results helped in the understanding of the scattering mechanisms and, therefore, could lead to developing new acquisition and processing techniques to reduce the scattered surface wave and enhance the quality of the seismic image.

Inverse Elastic Scattering for Multiscale Rigid Bodies with a Single Far-Field Pattern

We develop three inverse elastic scattering schemes for locating multiple small, extended, and multiscale rigid bodies, respectively. There are some salient and promising features of the proposed methods. The cores of these schemes are certain indicator functions, which are obtained by using only a single far-field pattern of the pressure (longitudinal) wave, or the shear (transversal) wave, or the total wave field. Though the inverse scattering problem is known to be nonlinear and ill-posed, the proposed reconstruction methods are totally “direct, and there are no inversions involved. Hence, the methods are very efficient and robust against noisy data. Both rigorous mathematical justifications and numerical simulations are presented in our study.

On the surface cascade radio emission escape into vacuum through the rough lunar surface

The radio emission escape of an almost horizontal cascade through the rough lunar surface into vacuum is considered. The point approximation is accepted for the shower disk size, taking into account its evolution along the cascade track. The lunar surface is assumed to be flat, but having a single perturbation such as a cylindrical “hill” perpendicular to the shower disk motion direction. The perturbation is not assumed to be small. Diffraction associated with the wave phase progression and variations of the slope of the normal to the rough surface for various rays forming the total wave field in vacuum is taken into account.