Forward-scattered Waves Research Articles

Damage assessment using the Lamb wave factorization method

The Lamb wave technique has been widely used for damage detection in plate-like structures. However, for two-dimensional (2D) defects like corrosions or one-dimensional (1D) defects like cracks, conventional Lamb wave-based methodology usually selects the detection algorithm in terms of the damage type, which is restricted if the defect remains unknown. To address the issues, this paper proposes a damage assessment approach based on the Lamb wave factorization method, which is a general method that can adapt to the detection of both 2D and 1D defects. In the process, both the forward-scattered wave across the inspection area and the wave back-scattered from the defect are used for detection, so that the enclosed rich information can be fully exploited. To measure the wave field of defect, a transducer array is firstly set around the inspection area, whose transducers would take turns to excite the Lamb wave while others remain listeners. On the basis, the scattered waves of all directions are then extracted and transformed from the time domain to frequency domain. Under a certain frequency, the inspection area is next visualized by sampling the area and solving the inverse scattering problem using the spectral data at each sampling point. By fusing the results of different frequency together, the final image can be eventually obtained. The method is then numerically investigated and also validated through experiments. The results demonstrate that it can give out the outline description of 2D defect and the size evaluation of 1D defect accurately, thus being an effective tool for damage assessment.

Research on an Urban Low-Altitude Target Detection Method Based on Image Classification

With the expansion of the civil UAV (Unmanned Aerial Vehicle) market, UAVs are also increasingly being used in illegal activities such as espionage and snooping on privacy. Therefore, how to effectively control the activities of UAVs in cities has become an urgent problem to be solved. Considering the urban background and the radar performance of communication signals, a low-altitude target detection scheme based on 5G base stations is proposed in this paper. A 5G signal is used as the external radiation source, the method of transceiver separation is adopted, and the forward-scattered waves are used to complete the detection of UAV. This paper mainly analyzes the principle of forward scattering detection in an urban environment, where the forward-scattered wave of a target is stronger than the backward-reflected wave and contains both height difference and midline height information on the target. Based on the above theory, this paper proposes a forward-scattered wave recognition algorithm based on YOLOv3-FCWImageNet, which transforms the forward-scattered wave recognition problem into a target detection problem and accomplishes the recognition of forward-scattered waves by using the excellent performance of algorithms in the field of image recognition. Simulation results show that FCWImageNet can distinguish two different low-altitude targets effectively, and realize the monitoring and classification of UAVs.

Radon-to-Helmholtz mappings and nonlinear diffraction tomography.

This paper addresses a number of approximate, analytically invertible solutions of the scalar Helmholtz equation. Primary attention is devoted to the Glauber approximation (GA) derived for the far-field pattern. It is shown that the GA has the form of a nonlinear Radon-to-Helmholtz (RtH) mapping, which transforms a sinogram of the scattering potential into an approximate solution of the Helmholtz equation. A proposal of how to construct a position space counterpart of the GA is formulated. Also, it is established that a paraxial version of the Glauber model coincides, up to an inessential constant factor, with a momentum-space representation of the Mazar-Felsen propagator, which describes forward-scattered waves. For weakly scattering objects, these solutions are reduced to the conventional Born/Rytov approximations, which may, however, preserve the parametrization and sampling formats of the original nonlinear models. Since all RtH mappings are analytically invertible, they can be applied to the (nonlinear) diffraction tomography of penetrable objects. In particular, the Glauber model, which has been largely ignored for years, is shown to provide efficient inversion of synthetic data. The resulting tomograms clearly outperform the Born inversions, even for moderately scattering potentials.

Finite-frequency traveltime tomography using the Generalized Rytov approximation

SUMMARY Wave-equation-based traveltime tomography has been extensively applied in both global tomography and seismic exploration. Typically, the traveltime Fréchet derivative is obtained using the first-order Born approximation, which is only satisfied for weak velocity perturbations and small phase shifts (i.e. the weak-scattering assumption). Although the small phase-shift restriction can be handled with the Rytov approximation, the weak velocity-perturbation assumption is still a major limitation. The recently developed generalized Rytov approximation (GRA) method can achieve an improved phase accuracy of the forward-scattered wavefield, in the presence of large-scale and strong velocity perturbations. In this paper, we combine GRA with the classical finite-frequency theory and propose a GRA-based traveltime sensitivity kernel (GRA-TSK), which overcomes the weak-scattering limitation of the conventional finite-frequency methods. Numerical examples demonstrate that the accumulated time delay of forward-scattered waves caused by large-scale smooth perturbations can be correctly handled by the GRA-TSK, regardless of the magnitude of the velocity perturbations. Then, we apply the new sensitivity kernel to solve the traveltime inverse problem, and we propose a matrix-free Gauss–Newton method that has a faster convergence rate compared with the gradient-based method. Numerical tests show that, compared with the conventional adjoint traveltime tomography, the proposed GRA-based traveltime tomography can obtain a more accurate model with a faster convergence rate, making it more suited for recovering the large-intermediate scale of the velocity model, even for strong-perturbation and complex subsurface structures.

A Direct Approach to Separate Forward-Scattered Waves from the Direct Blast in Doppler Domain for Forward-Scattering Detection

Forward-scattered waves are often interfered with and overwhelmed by direct blasts when a submerged target crosses the source–receiver line. The approach named low Doppler analysis and recording gram (LODARGRAM) is developed to separate forward-scattered waves from direct blasts in the Doppler domain. This separation, which is based on the kinetic characteristic of the target and the procedure, is conducted using a sliding Blackman window combined with fast Fourier transform. The concept along with its application is validated using the data collected in a tank experiment. The moving target is recognized and identified by a tilt striation on LODARGRAM. Limitations of the LODARGRAM approach are also discussed.

A Direct Approach to Separate Forward-Scattered Waves from the Direct Blast in Doppler Domain for Forward-Scattering Detection

Forward-scattered waves are often interfered with and overwhelmed by direct blasts when a submerged target crosses the source–receiver line. The approach named low Doppler analysis and recording gram (LODARGRAM) is developed to separate forward-scattered waves from direct blasts in the Doppler domain. This separation, which is based on the kinetic characteristic of the target and the procedure, is conducted using a sliding Blackman window combined with fast Fourier transform. The concept along with its application is validated using the data collected in a tank experiment. The moving target is recognized and identified by a tilt striation on LODARGRAM. Limitations of the LODARGRAM approach are also discussed.

Three-Dimensional Microwave Holographic Imaging Employing Forward-Scattered Waves Only

We propose a three-dimensional microwave holographic imaging method based on the forward-scattered waves only. In the proposed method, one transmitter and multiple receivers perform together a two-dimensional scan on two planar apertures on opposite sides of the inspected domain. The ability to achieve three-dimensional imaging without back-scattered waves enables the imaging of high-loss objects, for example, tissues, where the back-scattered waves may not be available due to low signal-to-noise ratio or nonreciprocal measurement setup. The simulation and experimental results demonstrate the satisfactory performance of the proposed method in providing three-dimensional images. Resolution limits are derived and confirmed with simulation examples.

Forward-scattered wave analysis of an optical Hardy-like setup

We analyze a photon interferometric scenario that is closely similar to that of the gedanken experiment of Hardy, where the annihilation of a particle–antiparticle pair is replaced by the interference of two photons on a beam splitter. We discuss its relation to Hardy's paradox. We calculate the forward-scattered waves of the output beam splitters for this setup and analyze their entanglement-like structure.

Hardy's paradox and the entanglementlike structure of forward-scattered waves

We analyze Hardy's paradox from the point of view of scattering theory. This approach has been useful for the understanding of interaction-free measurement, which is a similar setup. We calculate the forward-scattered waves generated by the beam splitters, which are replaceable in the gedanken experiment. These two-mode waves appear to have an entanglementlike structure.

Measurement of the Doppler shift in forward-scattered waves caused by moderate sea surface motion in shallow waters

A study of the impulse response of the acoustic channel in shallow waters is presented with respect to space, time, and frequency shift over a time window of two hours. A broadband chirp (42–54 kHz) and a narrow band sine wave (58 kHz) are transmitted from a static source located at 51 and 166 m from a vertical line receiver array. In 20 m of water with 0.4 m of wave height, an average Doppler shift of 20 Hz is measured at 51 m range, and 10 Hz at 166 m range, due to the sea-surface motion.

Analysis of sound propagation in a fluid through a screen of scatterers

A multiple scattering analysis in a nonviscous fluid is developed in detail in order to predict the coherent sound motion in the presence of disordered heterogeneities, such as particles, fibers, bubbles, or contrast agents. Scatterers can be homogeneous, layered, shell-like with encapsulated liquids or gas, nonabsorbing, or absorbing, and can take a wide variety of shapes. A priori imposed limitations or physical assumptions are absent in the derivation, whether they concern the expected response of the fluid-scatterer mixture, the scatterer size relative to wavelength, or the scatterer concentration or the screen thickness. However, as in any multiple scattering formulation, a closure assumption is invoked. Closed-form results for the backscattered and forward-scattered wave motions on either side of the screen of scatterers are obtained. The fluid-scatterer mixture is shown to behave as an effective dissipative medium from the standpoint of the coherent motion. It is found that the effective medium is fully described once two parameters are determined: the effective wave number and the reflection coefficient for the associated half-space screen. Remarkably, both parameters depend only on the far-field scattering properties of a single scatterer.

Multimode migration of scattered and converted waves for the structure of the Hikurangi slab interface, New Zealand

Reflectivity imaging of local earthquake seismograms has revealed the structure of the Hikurangi subduction interface at the location of two strong earthquakes that occurred in 1990. The earthquakes originated within the continental plate of the North Island of New Zealand and below in the subducting Pacific slab. We used seismograms from 500 well-located events in two earthquake sequences recorded by a small temporary seismograph deployment to directly image the structure and multiphase reflectivity of the plate interface. Synthetic tests of the imaging method show the effects of the poor 3-d geometric coverage afforded by the seismometer array. Kirchhoff summation image sections computed from synthetics show accurate depth imaging of backscattering interfaces. Phase-converting interfaces imaged with forward-scattered waves are smeared by poor ray coverage to 5-km depth inaccuracy and are only imaged over a small range of their horizontal extent. From the data, we computed image sections for P–P, P–S, S–P and S–S scattering. We mitigated imaging artifacts due to poor ray coverage with an obliquity factor, an antialiasing criterion and enhancement by resampling statistics. Imaging used a sharply layered velocity model. We tested for the effects of imaging with first-arriving headwaves by imaging through smoothly varying velocity models. For our ray geometry, early-arrival headwaves contribute little to the images. The plate interface appears as a 3–5-km thick P–P and possibly S–S backscatterer with 5° NW dip, offset 5 km down-to-the-NW above a normal fault in the slab. When illuminated from below, a wedge of the interface on the downdip side of the slab fault forms a very prominent P–P forward scatterer. The edges of the wedge forward-scatter some S–P and S–S energy, but an order of magnitude less than the P–P forward scattering. The imbalances between forward scattering of P and S energy suggest a wedge of subducted sediment retaining significant porosity but with rigidity close to that of surrounding rocks.

Features in coherent transmittance of a monolayer of particles.

Coherent and incoherent transmittance values of a monolayer of particles are considered. Such a monolayer is a set of particles whose centers are located in the same plane. We set forth the conditions for the effect of coherent-transmittance quenching, which takes place as a result of the interference between incident and forward-scattered waves. Using the single-scattering approximation we determined size parameters and particle refractive indexes for this interference effect in the case of identical isotropic spherical particles. The influence of polydispersity and the fine structure of light-scattering characteristics on the quenching effect has been estimated. It is shown that the polydispersity destroys this interference effect only at large widths of particle-size distribution functions. The influence of multiple scattering on this effect is considered in the quasi-crystalline approximation. Multiple scattering results in increasing size parameters and decreasing particle concentration at which coherent transmittance quenching takes place in comparison with the case of single scattering. Our theoretical results for suspensions of latex particles in water are in fairly good agreement with the experimental results.

A turbulence spectral model for sound propagation in the atmosphere that incorporates shear and buoyancy forcings

A three-dimensional model for turbulent velocity fluctuations in the atmospheric boundary layer is developed and used to calculate scattering of sound. The model, which is based on von Karman's spectrum, incorporates separate contributions from shear- and buoyancy-forced turbulence. New equations are derived from the model that predict the strength and diffraction parameters for scattering of sound as a function of height from the ground and atmospheric conditions. The need is demonstrated for retaining two distinct scattering length scales, one associated with scattering strength and the other with diffraction. These length scales are height dependent and vary substantially with the relative proportions of shear and buoyancy forcing. The turbulence model predicts that for forward-scattered waves the phase variance is much larger than the log-amplitude variance, a behavior borne out by experimental data. A new method for synthesizing random fields, based on empirical orthogonal functions, is developed to accommodate the height dependence of the turbulence model. The method is applied to numerical calculations of scattering into an acoustic shadow zone, yielding good agreement with previous measurements.

Interaction-free measurement and forward scattering

Interaction-free measurement is shown to arise from the forward-scattered wave accompanying absorption: a "quantum silhouette" of the absorber. Accordingly, the process is not free of interaction. For a perfect absorber the forward-scattered wave is locked both in amplitude and in phase. For an imperfect one it has a nontrivial phase of dynamical origin (``colored silhouette"), measurable by interferometry. Other examples of quantum silhouettes, all controlled by unitarity, are briefly discussed.

Scattering-matrix propagation algorithm in full-vectorial optics of multilayer grating structures

The scattering of an electromagnetic plane wave incident upon an inhomogeneous multilayer structure is considered in symbolic form. In this framework a scattering-matrix propagation algorithm that decouples recurrences for backward- and forward-scattered wave amplitudes is developed. By construction the scattering-matrix solution procedure is stable against increase of truncation order and depths and number of layers, irrespective of numerical implementation. For grating structures a numerical study using Fouriertransform discretization is performed. In this implementation the convergence issue for TM polarization is recapitulated.

Oblique scattering of an elastic wave from a multilayered cylinder in a solid. Transfer matrix approach

The scattering of an elastic wave obliquely incident on a multilayered cylinder in a solid is studied using a transfer matrix approach. Scattering of longitudinal and shear waves with arbitrary polarizations are considered. To facilitate the derivation of the solutions for scattering in the multilayered cylindrical system, a 6×6 transfer matrix is introduced for each cylindrical layer to relate the stresses and displacements on the inner and outer boundaries of that layer. A total transfer matrix relating the elastic field in the surrounding matrix to that in the cylinder core is obtained as a product of individual transfer matrices of intermediate layers. Numerical examples are given for a coated multiphase SiC fiber in a titanium matrix. Frequency and angle dependencies of specularly reflected and forward-scattered waves, and of the total scattering cross section, are calculated for different fiber-matrix interphase properties.

Two-dimensional velocity models from wide-angle seismic data by wavefield inversion

Modern wide-angle surveys are often multi-fold and multi-channel, with densely sampled source and receiver spacings. Such closely spaced data are potentially amenable to multi-channel techniques involving wavefield propagation methods, such as those commonly used in reflection data processing. However, the wide-angle configuration requires techniques capable of handling very general wave types, including those not commonly used in reflection seismology. This is a situation analogous to that faced in cross-borehole seismics, where similar wave types are also recorded. In a real cross-borehole example, we compare pre-stack migration, traveltime tomography and wavefield inversion. We find that wavefield inversion produces images that are quantitative in velocity (as are the tomograms) but are of significantly higher resolution; the wavefield inversion results have a resolution comparable to that of the (qualitative) pre-stack migration images. We seek to extend this novel development to the larger-scale problem of crustal imaging. An essential element of the approach we adopt is its formulation entirely within the temporal frequency domain. This has three principal advantages: (1) we can choose to ‘decimate’ the data, by selecting only a limited number of frequency components to invert, thus making inversion of data from large numbers of source positions feasible; (2) we can mitigate the notorious non-linearity of the seismic inverse problem by progressing from low-frequency components in the data to high-frequency components; and (3) we can include in the model any arbitrary frequency dependence of inelastic attenuation factors, Q(ω), and indeed solve for the spatial distribution of Q. An initial synthetic test with an anomaly located within the middle crust yields a velocity image with the correct structural features of the anomaly and the correct magnitude of velocity anomaly. This is related to the fact that the reconstruction is obtained from forward-scattered waves. Under these conditions, the method thus behaves much like tomography. A second test with a deeper, more extensive anomaly yields an image with the correct velocity polarity and the correct location, but with a deficiency in low and high wavenumbers. In this case, this is because the reconstruction is obtained from backscattered waves; under these conditions the method behaves not like tomography, but like migration. A more extensive test, based on a large wide-angle survey in south-eastern California and western Arizona, demonstrates a real potential for high-resolution imaging of crustal structures. Although our results are limited by the acoustic approximation and by the relatively low frequencies that we can model today, the images are sufficiently encouraging to warrant future research. The problem of local minima in the objective function is the most significant practical problem with our method, but we propose that appropriate ‘layer’ stripping methods can handle this problem.

Temporal response comparisons between model results and measurements of forward-scattered waves from the sea surface

The underwater acoustic propagation path for the forward scattering of energy from the sea surface is treated as a linear, time-varying random communications channel in the application of the Helmholtz–Kirchhoff integral formulation of this problem. The model used for data comparisons utilizes the bifrequency system function Γ(ω,ω’) developed by McDaniel [IEEE J. Ocean. Eng. 17, 216–221 (1992)] for the temporal response from a rough surface. The data analyzed for this work were obtained from a shallow-water high-frequency acoustic experiment conducted on the Baltic Sea during May 1993. Acoustic data included measurements of surface forward-scattering, surface reverberation, and direct-path intensities. These were made utilizing two large stationary towers resting on the seafloor. Each tower was equipped with horizontal and vertical receiving arrays anchored 7.6 m above the flat bottom depth of 30 m. Concurrent environmental measurements including wave heights, sound velocity profiles, and sample cores were made. The results presented here are for the surface forward-scattered measurements made at 20, 40, 60, and 90 kHz. [Work supported by the Office of Naval Research, Program Element 61153N, with technical management provided by the Naval Research Laboratory, Stennis Space Center, MS.]

Depth measurement for corner cracks of arbitrary angle using Rayleigh waves

The scattering of ultrasonic Rayleigh waves, incident normally on a corner of any angle containing a crack of any angle, is considered using elastodynamic ray theory. For this general geometry, it is shown that crack depth can be measured simply from the spacing of fringes in the frequency spectra of back- or forward-scattered Rayleigh waves. This spectral technique was demonstrated for the back-scattered Rayleigh waves. These waves were generated thermoelastically by partial focusing of a laser pulse to form a circular or line source, and were detected with a piezoelectric sensor. The specimens studied contained either an artificial slot or a fatigue crack in corners of various angles in aluminium alloy blocks. It is shown theoretically that the sensitivity of the technique is generally greater for the back-scattered than for the forward-scattered wave, and varies markedly with crack angle.