Wave Separation Method Research Articles

Hydrodynamic performance of a high-Speed ship in waves using a fully nonlinear wave separation method

ABSTRACT A fully nonlinear time-domain simulation of a ship navigating in waves at high speed is realised by proposing a domain-split wave separation method. In the proposed method, a large distorted area of the free surface near the ship is split, on which the disturbed wave is separated by subtracting the incident wave from the total wave. For the rest of the free surface, the disturbed wave is traced by retaining the higher-order components. The present method is capable to simulate the strongly nonlinear interactions between the ship and waves, and can avoid unnecessary spurious waves. The present results are verified through comparison with experimental data. The steady VBM by navigation reaches its peak when the wavelength of the generated wave equals the ship length at the critical Froude number. The hydrodynamic behaviours of the S175 ship navigating in waves at this critical speed are investigated.

The qP- and qSV-wave separation in 2D vertically transversely isotropic media and their applications in elastic reverse time migration

Compressional and shear wave separation is an important step in anisotropic elastic reverse time migration (ERTM). With separated wavefields, we can generate images between different wave types and reveal more subsurface physical properties, as well as remove unwanted crosstalk and improve image quality. Traditional Helmholtz decomposition based on divergence and curl operations for isotropic media cannot be directly extended to vertically transversely isotropic (VTI) media. Wave-mode separation methods, similar to the nonstationary spatial filter and Poynting vector, cannot preserve the phase and amplitude information of the original coupled wavefield, thus limiting their application in ERTM. Currently, the anisotropic wavefield decomposition methods include the wavenumber-domain approach, the low-rank approximation, and other separation approaches based on different approximations, e.g., weak or elliptical anisotropy. These methods are either computationally intensive or involve large separation errors, especially in models with strong heterogeneities and anisotropy. The VTI wavefield separation operator is essentially defined in a mixed space-wavenumber domain. We introduce scalar operators to transfer operations from this mixed space-wavenumber domain to the space domain. The local wave propagation direction in the scalar operators is estimated using the Poynting vector, which is highly computationally efficient in the space domain. When we apply the wave separation method to ERTM, we not only obtain the vectorized qP and qSV waves but also retrieve the scalar qP wavefield. The scalar and vector wavefields preserve the amplitude and phase information in the original coupled wavefield. For anisotropic ERTM, we suggest using the scalar imaging condition to generate the PP image and the magnitude- and sign-based vector imaging condition to produce the PS image, both having higher image accuracy than the dot-product imaging condition. Numerical examples are used to validate our anisotropic wavefield separation method and the related ERTM workflow.

Global control of propeller-induced aircraft cabin noise using active sound absorbers

A method to attenuate the global acoustic pressure of low-frequency harmonic acoustic disturbances in the interior of a small aircraft cabin mockup is proposed herein. This method is based on the well-known active sound absorption technique, which employs a wave-separation method to separate acoustic waves into incident and reflected waves. The shape identification of the low-frequency acoustic modes, both analytically and via the finite element method (FEM), allows the precise placement of four active sound absorbers in the cabin mockup to achieve global acoustic pressure attenuation. The key advantage of this approach is that acoustic pressure attenuation occurs via the dampening of acoustic modes, thus resulting in a global reduction in the sound pressure level (SPL), instead of creating quiet zones locally. Simulations and experiments for an aircraft cabin mockup show that a SPL attenuation exceeding 9 dB can be achieved in most of the cabin locations. Furthermore, the SPL reduces by up to 20 dB in certain regions. Finally, the surfaces of the active absorbers cover only 2% of the inner surface of the enclosure to achieve these results, thus necessitating only a few transducers.

Study of Shearlet Domain Scale-Angle Adaptive Surface Wave Separation

In the seismic data processing, high energy surface wave overlaps with effective wave, which affects the quality of seismic data imaging. The traditional frequency domain method can effectively remove surface wave, but it will damage the low frequency information of seismic data. In view of this, we proposed a scale-angle adaptive surface wave separation method based on Shearlet sparse transform. The surface wave model obtained by filtering method and the effective wave can decomposed in Shearlet domain, based on the characteristic differences between surface wave and effective wave in frequency, velocity and direction. At different scales and angles, an adaptive surface wave removal operator based on L2 norm of Shearlet coefficient is developed to remove surface wave information from seismic data. The actual seismic data application results show that compared with the traditional surface wave suppression method, the proposed method can thoroughly separate surface wave and effective wave, and obtain high quality denoising seismic data.

Record-based simulation of three-component long-period ground motions: Hybrid of surface wave separation and multivariate empirical mode decomposition

Far-field long-period ground motion (LPGM) records are critical for the performance evaluation of high-rise buildings in the LPGM potential area. However, the typical LPGM records are extremely scarce because of their harsh formation condition (e.g., large magnitude earthquake and basin site). To this end, this study develops a novel record-based approach for simulating three-component LPGMs based on the combination of Hilbert spectra theory, surface wave separation method, and multivariate empirical mode decomposition (MEMD). To be specific, the recorded three-component LPGMs are first divided into surface waves and body waves via the particle polarization-based separation method. Then, MEMD is introduced to decompose these body waves into a set of intrinsic mode functions (IMFs) with a well mode-alignment attribute. Finally, the Hilbert spectra theory is employed to explain the characteristics of the recorded three-component LPGMs, thereby realizing the corresponding simulation. This developed method not only embodies the surface wave polarization feature effectively, but also can well reflect body wave time-frequency characteristics. Numerical examples based on the measured three-component LPGM records demonstrate the effectiveness of the proposed method. Therefore, this method may be an effective way to provide adequate LPGM inputs in the structural performance evaluation.

Assessment and improvement of the wave generation accuracy using a wave separation method

Free-wave contamination is a non-desirable but frequent characteristic in many wave tank experiments. Higher-order wave generation is not widely implemented yet, whereas the effectiveness of active wave absorption systems is frequency-dependent, and usually unknown. The resulting free-wave contamination usually remains unnoticed, but may have important consequences especially at low frequencies. We present a Generation–Separation–Compensation (GSC) procedure to identify, quantify and attenuate the free-wave contamination. The resulting wave field behaves as expected from a higher-order wave generation with no re-reflections at the wave paddle. The attenuation ratio of the unwanted energy content is relatively high (between 60% to 90%).The GSC procedure uses the general framework for wave separation proposed by Padilla and Alsina (2020) with an array of in-line probes. The application of this technique over experimental data is presented with excellent results. The robustness of the qualitative analysis is guaranteed for experimental settings fulfilling a minimum distance between the first and the last probe and a maximum spacing between probes. The stability of the quantitative analysis is guaranteed when P, number of probes forming the array, is above five, and Δxsep/λ, ratio between the spacing of the probes forming the array and the wavelength, is within the recommended range 0.1–0.45.

An underwater discharge shockwave separation method based on minimum-phase cepstrum

Underwater discharge sound sources are widely utilized. The acoustic signals generated by underwater discharge consist of shock waves and bubble pulsations. The shock wave is a major component of underwater discharge sound sources and is worthy of further study. The minimum-phase cepstrum method is selected to separate the shock wave, and a customized experiment is designed to determine the optimal parameters of this method. The mixed shock wave bubble signal and single shock wave signal are simulated and fitted and are transmitted and received in the anechoic pool, respectively. Different parameters are used to process the signals, and the optimal parameters are selected by comparing the separation results. To verify the validity of the method, the shock waves generated with the same electrode and circuit parameters in the anechoic pool and non-anechoic pool are separated and compared. Experimental results show that this shock wave separation method exhibits significant performance. This method of shock wave separation is of service to the research of underwater discharge acoustic sources.

A general framework for wave separation in the frequency domain

A general framework for wave separation in the frequency domain is presented and evaluated with successful results using theoretical examples of nonlinear waves. This framework consists of a qualitative and a quantitative analysis. The qualitative analysis is a novel approach that provides useful information about the existing wave trains within a wave field. This information includes an estimation of the number of wave trains, their direction of propagation (seaward or shoreward), their nature (free or bound) and their relative importance. The quantitative analysis consists in a revisited wave separation method applicable to separate free and bound wave trains travelling seaward and shoreward for both high and low frequencies propagating over uneven bathymetries. This versatility represents an improvement compared to existing methods. The presented separation method is low-sensitive to noise and its robustness is tested for a range of wave separation settings. The potential application of the separation method to random waves is discussed.

Pre-stack separation of PP and split PS waves in HTI media

Separation of PP and split PS waves in transversely isotropic media with a horizontal axis of symmetry is crucial for imaging subsurface targets and for fracture prediction in a multicomponent seismic survey using P-wave sources. In conventional multicomponent processing, when a low velocity zone is present near the surface, it is often assumed that the vertical Z-component mainly records P modes and that the horizontal X- and Y-components record S modes, including split PS waves. However, this assumption does not hold when the ubiquitous presence of azimuthal anisotropy makes near surface velocity structures more complicated. Seismic wavefields recorded in each component therefore generally represent a complex waveform formed by PP and split PS waves, seriously distorting velocity analysis and seismic imaging. Most previous studies on wave separation have tended to separate P and S modes using pre-stack data and to separate split S modes using post-stack sections, under the assumption of orthogonal polarization. However, split S modes can hardly maintain their original orthogonal polarizations during propagation to the surface due to stratigraphic heterogeneity. Here, without assuming orthogonal polarization, we present a method for pre-stack separation of PP, PS1 and PS2 waves using all three components. The core of our method is the rotation of wave vectors from the Cartesian coordinate system established by Z-, R- and T-axes to a coordinate system established by the true PP-, PS1- and PS2-wave vector directions. Further, we propose a three-component superposition approach to obtain base wave vectors for the coordinate system transformation. Synthetic data testing results confirm that the performance of our wave separation method is stable under different noise levels. Application to field data from Southwest China reveals the potential of our proposed method.

Backward wave separation method in a single transmitter and multi-receiver sensor array for improved damage identification of two-dimensional structures

In this paper, a backward wave separation method is proposed. Since the first backward wave can be considered as the damage reflection, the damage reflected wave peaks are artificially amplified by appropriately shifting and summing signals collected from a series of sensing points aligned along the wave propagating direction. This shifting and summing process aims to present the damage reflected wave peaks more distinctively while offsets randomly distributed environmental interferences. Due to the high signal-to-noise ratio of the treated signal, the application of backward wave separation is able to attain baseline-free damage detection. A circular single transmitter and multi-receiver sensor array is then deployed on a metal plate to identify the crack-like damage. Signals collected by the sensor array with and without the treatment of the backward wave separation method are, respectively, imported to the delay-and-sum imaging algorithm to yield individual damage contours. The comparisons between these contours demonstrate that the backward wave separation method is able to significantly improve the damage identification performance of the sensor array with respect to the damage localization accuracy, noise immunity, and damage sensitivity. Both the finite element modeling and laser measurement are conducted to validate the effectiveness of the proposed backward wave separation method.

A Further Study on Wave Propagation Across a Single Joint with Different Roughness

As a key dynamic feature of the rock mass, joint results in wave attenuation when a stress wave propagates across it. An experimental study has obtained the relation between the transmission coefficient and the contact area ratio of joints with different thicknesses (Chen et al. (doi: 10.1007/s00603-015-0716-z)). However, the spatial geometry of the contact surface also determines the dynamic behavior of the discontinuous masses. Thus, the present study is focused on the effects of distribution and dimension of the sawn notches on the contact surface of the joint, which lead to the different spatial geometry. The joint matching coefficient (JMC) was used in this study to define the contact condition. Using a modified SHPB apparatus, all the bars and specimens were aluminum, and the artificial joint formed a rough surface of the specimen contacted to the output bar. Based on the wave separation method, the incident, reflected and transmitted waves across the joint were acquired from the records of the strain gauges on pressure bars. Then the transmission coefficient and specific stiffness of the joint were obtained. Comparisons of them were made on different JMCs, spatial geometries and thicknesses of the joint.

Wave Propagation in the Vicinities of Rock Fractures Under Obliquely Incident Wave

Though obliquely incident plane wave across rock fractures has been extensively investigated by theoretical analysis, the quantitative identification of each wave emerged from fractures has not been achieved either in numerical simulation or laboratory experiment. On the other hand, there are no theoretical results describing the stress/velocity state of the rocks beside a fracture. The superposition of the multiple waves propagating in the media results in the variation of the stress/velocity state. To understand the superposition of the wave components in the adjacent rocks of a facture, based on the geometrical analysis of the wave paths, the lag times among passing waves at an arbitrary point are determined. The normalised critical distances from the fracture to the measuring locations where the corresponding harmonic waves depart from other waves for a certain duration are then derived. Discussion on the correction for an arbitrary incident wave is then carried out considering the changes of the duration of the reflected and transmitted waves. Under the guidance of the analysis, wave superposition is performed for theoretical results and separated waves are obtained from numerical model. They are demonstrated to be consistent with each other. The measurement and the data processing provide an approach for wave separation in a relatively unbounded media. In addition, based on the mechanical analysis on the wave front, an indirect wave separation method is proposed which provides a possibility for laboratory experiments of wave propagation with an arbitrary incident angle.

Variable-order rotated staggered-grid method for elastic-wave forward modeling

Numerical simulations of a seismic wavefield are important to analyze seismic wave propagation. Elastic-wave equations are used in data simulation for modeling migration and imaging. In elastic wavefield numerical modeling, the rotated staggered-grid method (RSM) is a modification of the standard staggered-grid method (SSM). The variable-order method is based on the method of variable-length spatial operators and wavefield propagation, and it calculates the real dispersion error by adapting different finite-difference orders to different velocities. In this study, the variable-order rotated staggered-grid method (VRSM) is developed after applying the variable-order method to RSM to solve the numerical dispersion problem of RSM in low-velocity regions and reduce the computation cost. Moreover, based on theoretical dispersion and the real dispersion error of wave propagation calculated with the wave separation method, the application of the original method is extended from acoustic to shear waves, and the calculation is modified from theoretical to time-varying values. A layered model and an overthrust model are used to demonstrate the applicability of VRSM. We also evaluate the order distribution, wave propagation, and computation time. The results suggest that the VRSM order distribution is reasonable and VRSM produces high-precision results with a minimal computation cost.

Experimental Study on Wave Propagation Across a Rock Joint with Rough Surface

Joints are an important mechanical feature of rock masses. Their effect on wave propagation is significant in characterizing dynamic behaviors of discontinuous rock masses. An experimental study on wave propagation across artificial rock joint was carried out to reveal the relation between the transmission coefficient and the contact situation of the joint surface. The modified split Hopkinson pressure bar apparatus was used in this study while all the bars and specimens were norite cored from the same site. One surface of the specimens with a number of notches was adopted to simulate the artificial rough joint. Two strain gauges were mounted on each pressure bar at a specific spacing. The incident, reflected and transmitted waves across the joints were obtained using a wave separation method. Comparisons of the transmission coefficients were made under two different conditions: with the same joint thickness but different contact area ratios, and with the same contact area ratio but different joint thicknesses. The results show the effects of contact area ratio and thickness of joints on wave transmission.

A near-surface seismic scattered wave separation method

Abstract Considering that near-surface scattered waves could not be suppressed by conventional denoise method, this paper analyzes the characteristics of scattered waves and achieves the near-surface scattered wave separation by the seismic interferometry theory. Seismic data in mountain area is generally characterized by low signal to noise ratio, weak effective wave energy and strong near-surface scattered wave energy, so the near-surface seismic scattered waves must be firstly separated to improve the signal to noise ratio of seismic data during seismic data processing. The events of the near-surface seismic scattered wave in the adjacent common shot gathers are parallel. According to the near-surface scattered wave kinematics, the seismic interferometry method is used to eliminate the influence of seismic wave propagation in the same path, coherently enhance near-surface scattered waves, and then separate them from original seismic records. Taking the seismic data in mountain area in west China as an example, the energy of near-surface scattered wave is enhanced by direct wave field and full wave field seismic interferometry to separate the waves. As a result, the seismic data after processing generally eliminates near-surface scattered waves, verifying the validity and feasibility of the near-surface seismic scattered wave separation method.

Sound wave separation method based on spatial signals resampling with single layer microphone array

In order to reconstruct the sound field of target sources in non-free sound field, a method of sound field separation and reconstruction is presented based on spatial resampling with single layer microphone array. In this method, the spherical harmonics are taken as the basis functions, and the spherical harmonics of different orders are added to describe the mathematical model of the sound field. On the basis of the nearfield acoustic holography, the coefficients of the basis functions can be obtained with two groups' sound pressures resampled from the microphone array, then the sound fields generated by the sound sources on both sides of the microphone array are separated. The mathematical model is validated against the benchmark values. A non-free sound field with a radially oscillating sphere and a transversely oscillating rigid sphere is built, and the impact of various parameters such as the signal to noise ratio, the geometric shape and area of the microphone array, location of target sound source, and frequency of signals on the accuracy of separation is examined. Finally, some suggestions are given for the industrial application of the above method.

Separation Research of Ultrasonic Wave in Transformer Partial Discharge Based on Improved Waveform Matching

The use of direct wave to locate the position of the PD source is of better accuracy in transformer partial discharge ultrasound array positioning. For the signal received by ultrasonic sensor is consisted by direct wave, non-direct wave and a variety of noise, a direct wave separation method based on improved waveform matching is proposed in this paper. It is considered that the direct wave first reaches the ultrasonic sensor. A benchmarks triangle is built and then the attenuation coefficient and the signal frequency are both calculated. In order to search the matching wave, the benchmarks triangle is to pan and zoom. Finally, the best matching waveform is selected from a large number of matching waveforms as a direct wave signal. The result of simulation shows that the method can isolate the ultrasonic direct wave signal from the received signal, which provides some theoretical guidance to improve the position accuracy of the PD source.

Experimental study of stress wave propagation across a filled rock joint

Dynamic properties of rock joints are of great interest to mining engineers, seismologists and geoscientists in characterizing the dynamic mechanical behavior of discontinuous rock mass. An experimental study of stress wave propagation across filled rock joints has been carried out using a modified Split Hopkinson Pressure Bar (SHPB) apparatus. Two granitic bars cored from a rock site were used as the incident and transmitter pressure bars in the SHPB tests, while a sand layer of different widths and water contents sandwiched between the two bars was adopted to simulate the filled joint. Each pressure bar was mounted with two strain gauges with a specific spacing. A wave separation method was used to process the test data. The dynamic stress–strain relation of the filled rock joints was derived from the separated strain waves. Finally, the dynamic stress–strain relations from the tests were curve-fitted by using the least square regression method and compared with a traditional joint model. It was found that the wave separation method is very effective for the SHPB tests using short granitic pressure bars. It was also concluded that the joint width and water content had significant effects on the dynamic stress–strain relation of the filled rock joints. Existing joint models were not able to sufficiently describe such dynamic properties of the filled rock joints.

Wave separation in ambient seismic noise using intrinsic coherence and polarization filtering

This paper deals with passive ambient seismic noise processing. A new wave separation method is proposed when several polarized waves are recorded by a pair of multicomponent sensors. Although it is well known that the information given by the auto-covariance matrix at one sensor is not sufficient for estimating the mixing matrix, it is shown in this paper that with two multicomponent sensors, the identification of the mixing matrix can be completed. In addition to the mathematical proof and synthetic example, an application to a real geophysical data set is also presented. A previous analysis of these data revealed the presence of surface waves. The application of the proposed algorithm leads to the separation of Rayleigh and Love waves.

A modified servo-hydraulic machine for testing at intermediate strain rates

Assessing the mechanical properties of materials at intermediate strain rates (1–200/s) is one of the major concerns in impact engineering. Servo-hydraulic machines are usually used at this range of strain rates. However, detrimental oscillations appear on the measured load for strain rates above 10/s. In this paper, we present a modified servo-hydraulic machine. The load is measured by a Hopkinson bar-like technique. Besides, the BCGO wave separation method is used to overcome the limited test duration problem. Moreover, the strain in the sample is measured using Digital Speckle Photographs (DSP) which is captured via high-speed video camera. This modified machine is an equivalent and alternative solution to the slow bar technique. It is applied to aluminium 2017 T4 alloy at strain rates of approximately 100/s. Compared to the piezoelectric force sensor, the Hopkinson bar-like method gives less-oscillating signals. The sample attaching device is also taken into account. It is considered as a rigid mass. This simple assumption is valid up to strain rates of some hundreds per second.