Full Wavefield Research Articles

Recovery of the complete data set from ultrasound sequences with arbitrary transmit delays

Ultrasound beamforming relies on particular models of propagation to convert samples of the backscattered field through time into spatial samples of an image. The most common model used is straight-line propagation of a focused wave, assuming a narrow steered and focused beam that propagates radially along a selected direction. This model describes the main propagating pulse but fails to capture the true spatial extent of the wave. The reconstructed image suffers from defocusing, reduced signal-to-noise ratio (SNR), and contrast loss. A method is proposed to model transmission as the superposition of individual transmit elements on the transducer array and to efficiently recover the “complete data set,” individual element transmit and receive responses, from an arbitrary scan sequence. Standard diverging wave focusing is applied to the complete data set to produce an image independent of the applied transmit focusing. For a sequence with a fixed transmit focus, the result is a high-SNR, two-way focused image. The proposed method also improves upon other synthetic transmit aperture methods such as plane wave imaging in that it captures the full diffracting wave field rather than relying on approximate field models, maximizing SNR at depth. Phantom and in vivo images are used to demonstrate improvement.

Impact induced damage assessment by means of Lamb wave image processing

Abstract The aim of this research is an analysis of full wavefield Lamb wave interaction with impact-induced damage at various impact energies in order to find out the limitation of the wavenumber adaptive image filtering method. In other words, the relation between impact energy and damage detectability will be shown. A numerical model based on the time domain spectral element method is used for modeling of Lamb wave propagation and interaction with barely visible impact damage in a carbon-epoxy laminate. Numerical studies are followed by experimental research on the same material with an impact damage induced by various energy and also a Teflon insert simulating delamination. Wavenumber adaptive image filtering and signal processing are used for damage visualization and assessment for both numerical and experimental full wavefield data. It is shown that it is possible to visualize and assess the impact damage location, size and to some extent severity by using the proposed technique.

Mesh Interpolated Krylov Recycling Method to Expedite 3-D Full-Wave MoM Solution for Design Variants

Today’s 3-D full-wave electromagnetic (EM) solvers follow the conventional model-mesh-solve workflow to analyze any EM structure. These solvers treat each model independently regardless of any similarity with a previously solved model and, therefore, sacrifice the possibility of accelerating a model solution from information harnessed from a prior solution of a similar model. This is a missed opportunity particularly in the solution of design variants, which involve multiple models with near-identical geometrical features. A Krylov recycling (KR) technique has been proposed in the past for the incremental solution of electrostatic problems. However, the technique is limited by the requirement of an unchanged mesh for the unmodified section of the model, which is difficult to achieve for a conformal mesh of a practical geometry. In this paper, a mesh-interpolated Krylov recycling (MIKR) technique is proposed to expedite the solution of 3-D full-wave surface-volume electric field integral equation-based system by reusing the Krylov subspace from the base design. The mesh interpolation mechanism is proposed to be able to handle mesh changes in the unmodified section of the model. The method is independent of the choice of fast solver compression methodology and the preconditioning strategy, and can be applied in unison with them. Numerical results demonstrate up to $5\times $ speedup in convergence over a cutting-edge preconditioned linear complexity fast solver methodology.

Axial multi-image phase retrieval under tilt illumination

As a coherent diffractive imaging technique, axial multi-image phase retrieval utilizes a series of diffraction patterns on the basis of axial movement diversity to reconstruct full object wave field. Theoretically, fast convergence and high-accuracy of axial multi-image phase retrieval are demonstrated. In experiment, its retrieval suffers from the tilt illumination, in which diffraction patterns will shift in the lateral direction as the receiver traverses along the axis. In this case, the reconstructed result will be blurry or even mistaken. To solve this problem, we introduce cross-correlation calibration to derive the oblique angle and employ tilt diffraction into axial phase retrieval to recover a target, which is successfully demonstrated in simulation and experiment. Also, our method could provide a useful guidance for measuring how obliquely the incident light illuminates in an optical system.

High-Frequency Electrical Modeling and Characterization of Differential TSVs for 3-D Integration Applications

This letter makes a fast and efficient analysis of the scalable differential through-silicon via (TSV) configuration in 3-D integrated circuits. The equivalent-circuit model of a differential TSV pair is described. The critical differential characteristics are analyzed and calculated in terms of a lumped-circuit model and the effective loop parameters of multi-TSVs. The calculated results are validated by the 3-D full-wave field solver high frequency simulator structure (HFSS) over a wide frequency range.

Tomoelastography of the prostate using multifrequency MR elastography and externally placed pressurized-air drivers.

To demonstrate the feasibility of in vivo multifrequency magnetic resonance elastography (MRE) of the prostate using externally placed drivers. Three pressurized-air drivers were used to excite shear waves within the prostate at vibration frequencies of 60, 70, and 80 Hz. Full 3D wave fields were acquired by multislice spin-echo echo-planar imaging in conjunction with tomoelastography wave speed recovery for generating full field-of-view stiffness maps. Twelve healthy volunteers were repeatedly scanned to analyze test-retest reproducibility. Five patients with suspected prostate cancer were investigated to demonstrate the clinical feasibility of the method. In healthy volunteers, the shear wave speed of the entire prostate was 2.24 ± 0.20 m/s with a repeatability coefficient of 0.14 m/s and 88% intraclass correlation coefficient. No significant difference between the peripheral zone (2.27 ± 0.20 m/s) and the central gland (2.22 ± 0.23 m/s) was observed. In patients, wave-speed maps displayed stiff regions consistent with the localization of suspicious masses detected by other imaging markers. The proposed method provides reproducible quantitative maps of tissue stiffness throughout the pelvic region and can easily be integrated into clinical imaging protocols. Clinical stiffness maps display many details of potential interest for cancer diagnosis. Magn Reson Med 79:1325-1333, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

A New Stable Full-Wave Maxwell Solver for All Frequencies

Magnetic vector potential (MVP) formulations are widely used in the electromagnetic (EM) field computation. For problems with both inductive and capacitive effects, existing full-wave MVP formulations are mostly nonuniquely solvable, and sophisticated preconditioners are indispensable when solving these resultant linear matrix equations. To find a stable formulation with a unique solution, it is important to incorporate the necessary physics equations and the gauge condition properly. Traditional Coulomb-gauged formulation using the penalty technique does not work for edge elements, since the divergence of the edge element basis function is zero within each element. In this paper, a novel MVP formulation with Coulomb gauge for full-wave Maxwell equations using edge elements is proposed in the frequency domain. Extensive numerical examples are computed to show that the proposed formulation is stable even for tiny frequencies, which is very useful in full-wave engineering EM field computation.

Comparison of Full Wavefield Synthetics with Frequency-Dependent Traveltimes Calculated Using Wavelength-Dependent Velocity Smoothing

Ray theory-based traveltime calculation that assumes infinitely high frequency wave propagation is likely to be invalid in the near-surface (upper tens of meters) due to the relatively large seismic wavelength compared with the total travel path lengths and the scale of the near-surface velocity heterogeneities. The wavelength-dependent velocity smoothing (WDVS) algorithm calculates a frequency-dependent, first-arrival traveltime by assuming that using a wavelength-smoothed velocity model and conventional ray theory is equivalent to using the original unsmoothed model and a frequency-dependent calculation. This paper presents comparisons of WDVS-calculated traveltimes with band-limited full wavefield synthetics including the results from 1) different velocity models, 2) different frequency spectra, 3) different values of a free parameter in the WDVS algorithm, and 4) different levels of added noise to the synthetics. The results show that WDVS calculates frequency-dependent traveltimes that are generally consistent with the first arrivals from band-limited full wavefield synthetics. Compared to infinite-frequency traveltimes calculated using conventional ray theory, the WDVS frequency-dependent traveltimes are more consistent with the first arrivals picked from full wavefield synthetics in terms of absolute time and trace-to-trace variation. The results support the use of WDVS as the forward modeling component of a tomographic inversion method, or any seismic method that involves modeling first-arrival traveltimes.

Full wavefield decomposition of high‐frequency secondary microseisms reveals distinct arrival azimuths for Rayleigh and Love waves

AbstractIn the secondary microseism band (0.1–1.0 Hz) the theoretical excitation of Rayleigh waves (Rg/LR), through oceanic wave‐wave interaction, is well understood. For Love waves (LQ), the excitation mechanism in the secondary microseism band is less clear. We explore high‐frequency secondary microseism excitation between 0.35 and 1 Hz by analyzing a full year (2013) of records from a three‐component seismic array in Pilbara (PSAR), Australia. Our recently developed three‐component waveform decomposition algorithm (CLEAN‐3C) fully decomposes the beam power in slowness space into multiple point sources. This method allows for a directionally dependent power estimation for all separable wave phases. In this contribution, we compare quantitatively microseismic energy recorded on vertical and transverse components. We find the mean power representation of Rayleigh and Love waves to have differing azimuthal distributions, which are likely a result of their respective generation mechanisms. Rayleigh waves show correlation with convex coastlines, while Love waves correlate with seafloor sedimentary basins. The observations are compared to the WAVEWATCH III ocean model, implemented at the Institut Français de Recherche pour l'Exploitation de la Mer (IFREMER), which describes the spatial and temporal characteristics of microseismic source excitation. We find Love wave energy to originate from raypaths coinciding with seafloor sedimentary basins where strong Rayleigh wave excitation is predicted by the ocean model. The total power of Rg waves is found to dominate at 0.35–0.6 Hz, and the Rayleigh/Love wave power ratio strongly varies with direction and frequency.

Damage detection on composite structures with standing wave excitation and wavenumber analysis

This paper describes the use of wavenumber filtering for damage detection with a signal-frequency standing wave excitation on composite structures. Using a single, fixed frequency excitation from a mounted piezoelectric transducer, the full steady-state wavefield could be obtained using a Laser Doppler Vibrometer with a mirror-tilting device. After completing the scanning, a wavenumber filtering is applied to determine dominant wavenumber components of the measured wavefield, which could be used for indicative of structural damage. Mapping processes based on local wavenumber filtering is then carried out for damaged area visualization. Also introduced are the comparison of two methods for damage identification and visualization: the local wavenumber mapping and acoustic wavenumber spectroscopy. To demonstrate the proposed techniques, several experiments are performed on composite structures with different types of damage, including debonding and delamination on composite plates. The results demonstrate that the techniques are very effective in localizing damage with the potential for the quick inspection of a variety of composite structural components.

Seismic resonances of spherical acoustic cavities

ABSTRACTWe study the interaction of a seismic wavefield with a spherical acoustic gas‐ or fluid‐filled cavity. The intention of this study is to clarify whether seismic resonances can be expected, a characteristic feature that may help in detecting cavities in the subsurface. This is important for many applications, in particular the detection of underground nuclear explosions, which are to be prohibited by the Comprehensive Test Ban Treaty. To calculate the full seismic wavefield from an incident plane wave that interacts with the cavity, we considered an analytic formulation of the problem. The wavefield interaction consists of elastic scattering and the wavefield interaction between the acoustic and elastic media. Acoustic resonant modes caused by internal reflections in the acoustic cavity show up as spectral peaks in the frequency domain. The resonant peaks coincide with the eigenfrequencies of the un‐damped system described by the particular acoustic medium bounded in a sphere with stiff walls. The filling of the cavity could thus be determined by the observation of spectral peaks from acoustic resonances. By energy transmission from the internal oscillations back into the elastic domain, the oscillations experience damping, resulting in a frequency shift and a limitation of the resonance amplitudes. In case of a gas‐filled cavity, the impedance contrast is still high, which means low damping of the internal oscillations resulting in very narrow resonances of high amplitude. In synthetic seismograms calculated in the surrounding elastic domain, the acoustic resonances of gas‐filled cavities show up as persisting oscillations. However, due to the weak acoustic–elastic coupling in this case, the amplitudes of the oscillations are very low. Due to a lower impedance contrast, a fluid‐filled cavity has a stronger acoustic–elastic coupling, which results in wide spectral peaks of lower amplitudes. In the synthetic seismograms derived in the surrounding medium of fluid‐filled cavities, acoustic resonances show up as strong but fast decaying reverberations.

High-Fidelity, High-Performance Computational Algorithms for Intrasystem Electromagnetic Interference Analysis of IC and Electronics

Ever-increasing complexity in high-speed electronic devices and systems presents significant computational challenges in the numerical analysis in terms of desired accuracy, efficiency, and scalable parallelism. The objective of this paper is to investigate high-resolution, high-performance full-wave field solvers for scalable electromagnetic simulations of product-level integrated circuits (ICs) and electronics. The emphasis is placed on advancing parallel algorithms that are provably scalable facilitating a design-through-analysis paradigm, and enabling concurrent multiscale modeling and computation. The capability and the benefits of the algorithms are validated and illustrated through complex 3-D IC and electronics applications.

Theoretical Study of the Self-Assembly and Optical Properties of 1D Chains of Magnetic–Plasmonic Nanoparticles

A study is presented of the self-assembly and optical behavior of one-dimensional (1D) chains of colloidal magnetic–plasmonic core–shell Fe3O4@Au nanoparticles. The superparamagnetic core enables adaptive magnetophoretic control of the particles and provides interparticle coupling that drives the assembly process. The plasmonic shell provides unique optical and photothermal properties of assembled structures. Monte Carlo analysis and full-wave field theory are combined to investigate the self-assembly and optical properties of 1D chains, respectfully. The Monte Carlo simulations demonstrate that the particle volume fraction and surface charge can be tailored to control the formation, aggregation, and spacing of chains. The optical analysis shows that as a chain forms its absorption spectrum red shifts and asymptotically converges to that of an infinite chain. In addition, strong field enhancement occurs in the gaps between neighboring particles at plasmon resonance, while photothermal transduction is focused and enhanced within the center of the chain. The ability to adaptively control the magnetic and optical behavior of colloidal plasmonic particles using an external field opens up a host of opportunities for novel imaging, sensing, theranostic, and optofluidic applications. Moreover, while the theory is demonstrated for the analysis of 1D particle chains, the numerical methods readily extend to 2D and 3D assemblies of multilayered core–shell nanoparticles that have magnetic and plasmonic layers. As such, this approach is useful for the rational design of optically functional colloids and the bottom-up fabrication of nanostructured interfaces and media with novel magnetic and photonic functionality.

Wave propagation of laminated composite plates via GPU-based wavelet finite element method

This paper presents a novel parallel implementation technology for wave-based structural health monitoring (SHM) in laminated composite plates. The wavelet-based B-spline wavelet on the interval (BSWI) element is constructed according to Hamilton’s principle, and the element by element algorithm is parallelly executed on graphics processing unit (GPU) using compute unified device architecture (CUDA) to get the responses in full wave field accurately. By means of the Fourier spectral analysis method, the Mindlin plate theory is selected for wave modeling of laminated composite plates while the Kirchhoff plate theory predicts unreasonably phase and group velocities. Numerical examples involving wave propagation in laminated composite plates without and with crack are performed and discussed in detail. The parallel implementation on GPU is accelerated 146 times comparing with the same wave motion problem executed on central processing unit (CPU). The validity and accuracy of the proposed parallel implementation are also demonstrated by comparing with conventional finite element method (FEM) and the computation time has been reduced from hours to minutes. The damage size and location have been successfully determined according to wave propagation results based on delay-and-sum (DAS). The results show that the proposed parallel implementation of wavelet finite element method (WFEM) is very appropriate and efficient for wave-based SHM in laminated composite plates.

Tremor-rich shallow dyke formation followed by silent magma flow at Bárðarbunga in Iceland

The Barðarbunga eruption in Iceland in 2014 and 2015 produced about 1.6 km3 of lava. Magma propagated away from Barðarbunga to a distance of 48 km in the subsurface beneath Vatnajokull glacier, emerging a few kilometres beyond the glacier’s northern rim. A puzzling observation is the lack of shallow (<3 km deep), high-frequency earthquakes associated with shallow dyke formation near the subaerial and subglacial eruptive sites, suggesting that near-surface dyke formation is seismically quiet. However, seismic array observations and seismic full wavefield simulations reveal the presence and nature of shallow, pre-eruptive, long-duration seismic tremor activity. Here we use analyses of seismic data to constrain the relationships between seismicity, tremor, dyke propagation and magma flow during the Barðarbunga eruption. We show that although tremor is usually associated with magma flow in volcanic settings, pre-eruptive tremor at Barðarbunga was probably caused by swarms of microseismic events during dyke formation, and hence is directly associated with fracturing of the upper 2–3 km of the crust. Subsequent magma flow in the newly formed shallow dyke was seismically silent, with almost a complete absence of seismicity or tremor. Hence, we suggest that the transition from temporarily isolated, large, deep earthquakes to many smaller, shallower, temporally overlapping earthquakes (<magnitude 2) that appear as continuous tremor announces the arrival of a dyke opening in the shallow crust, forming a pathway for silent magma flow to the Earth’s surface. Magma movement is thought to trigger volcanic tremor. However, analysis of seismic data suggests that tremor prior to the Barðarbunga eruption in Iceland instead marked the crust cracking open, whereas subsequent magma flow was seismically silent.

Optical Measurement of In-plane Waves in Mechanical Metamaterials Through Digital Image Correlation

We report on a Digital Image Correlation-based technique for the detection of in-plane elastic waves propagating in structural lattices. The experimental characterization of wave motion in lattice structures is currently of great interest due its relevance to the design of novel mechanical metamaterials with unique/unusual properties such as strongly directional behaviour, negative refractive indexes and topologically protected wave motion. Assessment of these functionalities often requires the detection of highly spatially resolved in-plane wavefields, which for reticulated or porous structural assemblies is an open challenge. A Digital Image Correlation approach is implemented that tracks small displacements of the lattice nodes by centring image subsets about the lattice intersections. A high speed camera records the motion of the points by properly interleaving subse- quent frames thus artificially enhancing the available sampling rate. This, along with an imaging stitching procedure, enables the capturing of a field of view that is sufficiently large for subsequent processing. The transient response is recorded in the form of the full wavefields, which are processed to unveil features of wave motion in a hexagonal lattice. Time snapshots and frequency contours in the spatial Fourier domain are compared with numerical predictions to illustrate the accuracy of the recorded wavefields.

Compressive Sensing Approaches for Condition Monitoring and Laser-scanning Based Damage Visualization

Condition monitoring (CM) and Non-destructive testing (NDT) encounter a big data problem because they require to continuously measure vibration or wave data with a high sampling rate. In this study, compressive-sensing approaches for both condition monitoring and non-destructive testing are proposed to efficiently handle a huge amount of data and to improve the damage-detection capability of the current process. Compressive sensing is a novel sensing/sampling paradigm that takes much fewer samples compared to traditional sampling methods. For CM experiments, a built-in rotating system was used, and all data were compressively sampled to obtain compressed data. Optimal signal features were then extracted without the reconstruction process and were used to detect and classify damage. Also Non-destructive testing was conducted by using compressed scanning with a Laser Doppler Vibrometer (LDV) system equipped with a mirror tilting device. Wave fields were obtained by scanning through a random and compressive pattern in the spatial domain and full wave fields were reconstructed from the compressively measured data. The damage region was then identified and visualized using wavenumber based signal processing. Experimental results showed that the proposed method could effectively improve the data-processing speed and the detection accuracy of condition monitoring and non-destructive testing.

Elastic wave‐vector decomposition in heterogeneous anisotropic media

ABSTRACTThe goal of wave‐mode separation and wave‐vector decomposition is to separate a full elastic wavefield into three wavefields with each corresponding to a different wave mode. This allows elastic reverse‐time migration to handle each wave mode independently. Several of the previously proposed methods to accomplish this task require the knowledge of the polarisation vectors of all three wave modes in a given anisotropic medium. We propose a wave‐vector decomposition method where the wavefield is decomposed in the wavenumber domain via the analytical decomposition operator with improved computational efficiency using low‐rank approximations. The method is applicable for general heterogeneous anisotropic media. To apply the proposed method in low‐symmetry anisotropic media such as orthorhombic, monoclinic, and triclinic, we define the two S modes by sorting them based on their phase velocities (S1 and S2), which are defined everywhere except at the singularities. The singularities can be located using an analytical condition derived from the exact phase‐velocity expressions for S waves. This condition defines a weight function, which can be applied to attenuate the planar artefacts caused by the local discontinuity of polarisation vectors at the singularities. The amplitude information lost because of weighting can be recovered using the technique of local signal–noise orthogonalisation. Numerical examples show that the proposed approach provides an effective decomposition method for all wave modes in heterogeneous, strongly anisotropic media.

Frequency Domain Wave Equation Inversion and Its Application on the Heterogeneous Reservoir Model Data

Seismic full waveform inversion seeks to make use of the full information based on full wave field modeling to extract quantitative information from seismograms. Its serious nonlinearity and high dependence on initial velocity model often results in unsatisfactory inversion results in paleo-karsts carbonate reservoir characterized by strong heterogeneity. The paper presents an improved strategy of multi-scale inversion to establish velocity field model of waveform tomography. the forward wave equation algorithm was derived in frequency domain, and then the Matrix formalism for the iterative inverse methods is derived by gradient methods to speed up calculation and to avoid convergence to local minimum value. After massive amount of frequencies tests, the appropriate bandwidth are extracted, and the velocity field calculated at low frequency is used as the input of the high frequency. After the iteration, the accurate velocity field is inverted. Finally, frequency domain wave equation full waveform inversion in mathematical and physical models is conducted in order to verify the inverse program. The method of selecting the inverse frequencies is proved to be effective.

Numerical simulations of full-wave fields and analysis of channel wave characteristics in 3-D coal mine roadway models

Currently, numerical simulations of seismic channel waves for the advance detection of geological structures in coal mine roadways focus mainly on modeling twodimensional wave fields and therefore cannot accurately simulate three-dimensional (3-D) full-wave fields or seismic records in a full-space observation system. In this study, we use the first-order velocity–stress staggered-grid finite difference algorithm to simulate 3-D full-wave fields with P-wave sources in front of coal mine roadways. We determine the three components of velocity Vx, Vy, and Vz for the same node in 3-D staggered-grid finite difference models by calculating the average value of Vy, and Vz of the nodes around the same node. We ascertain the wave patterns and their propagation characteristics in both symmetrical and asymmetric coal mine roadway models. Our simulation results indicate that the Rayleigh channel wave is stronger than the Love channel wave in front of the roadway face. The reflected Rayleigh waves from the roadway face are concentrated in the coal seam, release less energy to the roof and floor, and propagate for a longer distance. There are surface waves and refraction head waves around the roadway. In the seismic records, the Rayleigh wave energy is stronger than that of the Love channel wave along coal walls of the roadway, and the interference of the head waves and surface waves with the Rayleigh channel wave is weaker than with the Love channel wave. It is thus difficult to identify the Love channel wave in the seismic records. Increasing the depth of the receivers in the coal walls can effectively weaken the interference of surface waves with the Rayleigh channel wave, but cannot weaken the interference of surface waves with the Love channel wave. Our research results also suggest that the Love channel wave, which is often used to detect geological structures in coal mine stopes, is not suitable for detecting geological structures in front of coal mine roadways. Instead, the Rayleigh channel wave can be used for the advance detection of geological structures in coal mine roadways.