Frequency-wavenumber Filtering Research Articles

Near-surface defect detection in additively manufactured components using laser induced phased arrays with surface acoustic wave crosstalk suppression

In-process inspection of the additive manufacturing process requires a technique that can provide reliable measurements given the extreme operating environments, the small size of the defects and the cyclic melting and heating of the material, caused by subsequently deposited layers. A remote and couplant-free ultrasonic inspection technique using bulk waves that can image near-surface defects could address these in-process inspection requirements. Laser induced phased arrays (LIPA) generate and detect ultrasound based on laser ultrasonics principles, while the array is synthesised in post-processing. However, when using LIPAs for inspection, the surface acoustic waves (SAWs) interfere with the bulk wave modes giving rise to crosstalk and artefacts, which makes near-surface defect imaging difficult. This work experimentally validates and compares five techniques for SAW suppression: amplitude thresholding, mean waveform subtraction, principal component subtraction, frequency-wavenumber filtering, and phase coherence imaging. SAW suppression is demonstrated in ultrasonic images of transverse waves based on 71-element LIPA data synthesised on a Ti-6Al-4V directed energy deposition-arc (DED-Arc/Ti6Al4V) sample with a ∼1 mm diameter side drilled hole, located at ∼4 mm below the inspected surface. The reported results show that the principal component subtraction approach achieved the highest ‘signal-to-crosstalk ratio’ improvement of 16 dB, while successfully suppressing the SAW.

Near-surface characterization using distributed acoustic sensing in an urban area: Granada, Spain

SUMMARY The Granada Basin in southeast Spain is an area of moderate seismicity. Yet, it hosts some of the highest seismic hazards in the Iberian Peninsula due to the presence of shallow soft sediments amplifying local ground motion. In urban areas, seismic measurements often suffer from sparse instrumentation. An enticing alternative to conventional seismometers is the distributed acoustic sensing (DAS) technology that can convert fibre-optic telecommunication cables into dense arrays of seismic sensors. In this study, we perform a shallow structure analysis using the ambient seismic field interferometry method. We conduct a DAS array field test in the city of Granada on the 26 and 27 August 2020, using a telecommunication fibre. In addition to the existing limitations of using DAS with unknown fibre-ground coupling conditions, the complex geometry of the fibre and limited data recording duration further challenge the extraction of surface-wave information from the ambient seismic field in such an urban environment. Therefore, we develop a processing scheme that incorporates a frequency–wavenumber (f−k) filter to enhance the quality of the virtual shot gathers and related multimode dispersion images. We are able to use this data set to generate several shear-wave velocity (VS) profiles for different sections of the cable. The shallow VS structure shows a good agreement with different geological conditions of soil deposits. This study demonstrates that DAS could provide insights into soil characterization and seismic microzonation in urban areas. In addition, the results contribute to a better understanding of local site response to ground motion.

De-noising distributed acoustic sensing data using an adaptive frequency–wavenumber filter

Summary Data recorded by distributed acoustic sensing (DAS) along an optical fibre sample the spatial and temporal properties of seismic wavefields at high spatial density. Often leading to massive amount of data when collected for seismic monitoring along many kilometre long cables. The spatially coherent signals from weak seismic arrivals within the data are often obscured by incoherent noise. We present a flexible and computationally efficient filtering technique, which makes use of the dense spatial and temporal sampling of the data and that can handle the large amount of data. The presented adaptive frequency–wavenumber filter suppresses the incoherent seismic noise while amplifying the coherent wavefield. We analyse the response of the filter in time and spectral domain, and we demonstrate its performance on a noisy data set that was recorded in a vertical borehole observatory showing active and passive seismic phase arrivals. Lastly, we present a performant open-source software implementation enabling real-time filtering of large DAS data sets.

Application of Noise Attenuation on 2D Shallow Offshore Seismic Reflection Data: A Case Study from the Baltic Sea

Noise is always present in offshore seismic data, as there isn't a single method that could eliminate all the forms of noise. In this study, noise removal techniques were applied to attenuate different noises in 2D shallow-marine seismic data from the Baltic Sea area. Amplitude recovery should be applied before the noise attenuation stage as a preconditioning process for showing all noises in the deeper part of the seismic data. Frequency filters (notch filter and low-cut filter), frequency-wavenumber (FK) filter, and swell noise attenuation (Deswell) were applied as robust noise attenuation techniques. The method of directly modifying the amplitude spectrum of the seismic data is known as frequency filtering. A notch filter can be used to remove the harmonic noise of the power line harmonic noise (mono-frequency noise). A low-cut filter can be used to remove the low-frequency noises due to the influence of hydrostatic pressure variations. The linearly correlated events, such as tail-buoy and operational noise, were removed using the FK filter. Incoherent noise, such as swell noise, can be attenuated by swell noise attenuation (Deswell). The seismic results are displayed before and after the applied noise attenuation techniques to prove the validity of the applied filters. This study aimed to show the importance of shallow offshore seismic data processing in removing different types of noise, as it increases the value of data for seismic data interpretation and marine geohazard assessment.

Thin-Plate Imaging Inspection Using Scattered Waves Cross-Correlation Algorithm and Non-Contact Air-Coupled Transducer

Abstract This paper presents a non-contact air-coupled Lamb wave imaging technique using a two-dimensional (2D) cross-correlation method that not only detects the damage but also precisely quantifies for orientations and sizes. The air-coupled transducers (ACT) is used together with a scanning laser Doppler vibrometer (SLDV) for sensing, making a fully non-contact Lamb wave system used for this study. We first show that single-mode Lamb wave actuation can be achieved by the ACT-based on Snell's law. Detailed study and characterization of the directional ACT Lamb waves are conducted. For damage detection, a 2D cross-correlation imaging technique that uses the damage introduced scattered waves of all directions is proposed for correlating with the incident waves. The frequency-wavenumber filtering technique is used to implement the acquisition of the scatted waves and incident waves, respectively. In the end application to notches with various orientations and various sizes in terms of depth and length is given. The results show the proposed technique can precisely imaging the damages and can quantitatively evaluate the damage size in terms of length and depth.

Lamb wave imaging with actuator network for damage quantification in aluminum plate structures

Lamb waves have been widely used for damage detection on plate-like structures. However, there are still considerable interests on quantifying damage with complex profile. In this article, quantification of complex damage in plate-like structures using a network of actuators and time-space Lamb wavefield is investigated. The actuator network inspection system is implemented with multiple PZT transducers for Lamb wave actuation in round robin pattern and scanning laser Doppler vibrometer for wavefield sensing. The PZT network is arranged in a way that the target area is fully enclosed and Lamb waves come to the damage from all directions. Waves induced by the damage are subsequently obtained through frequency-wavenumber filtering, using the experimentally acquired dispersion curves presented in the paper. The filtered waves from all wave actuators are then used to generate a synthetic image of the damage being inspected. Two cases of complex damage are evaluated on aluminum plates, mass loss with triangular profile and mass addition with a three-letter cluster profile. Our results show that the damages are not only detected but also their profiles are clearly outlined in the images. We believe the subject methods provide improved evaluation of damage profile for Lamb wavefield based damage quantification.

Quality Assessment of Friction Stir Welded Joints – Using the Fundamental Anti-Symmetric Lamb Wave Mode

Having a robust non-destructive evaluation (NDE) technique for friction stir welded (FSWed) joints is of interest to the processing community. Such a technique has to be sensitive to the different types and shapes of internal weld defects and has to be applicable for both similar and dissimilar material FSW joints. Investigated was the ability of ultrasonic guided waves to detect and assess the quality of FSW joints. The fundamental anti-symmetric (A0) mode was selected to detect the flaws in FSW joints. Guided waves were excited (using PZT wafers) and received (using a laser Doppler vibrometer, LDV). Implemented was the frequency-wavenumber filtering technique to separate forward propagating wave from any back propagating reflected wave due to the welded joint. Identified was the reflection of the A0 mode caused by the presence of the interface and/or defects within the joint. The findings indicate little sensitivity to the presence of material interface suggesting this technique to have a promising potential among guided-wave-based techniques in the qualitative and quantitative assessment of FSW joints.

Robust dual‐sensor data sea‐surface ghost attenuation for quality control purposes

ABSTRACTThree‐dimensional receiver ghost attenuation (deghosting) of dual‐sensor towed‐streamer data is straightforward, in principle. In its simplest form, it requires applying a three‐dimensional frequency–wavenumber filter to the vertical component of the particle motion data to correct for the amplitude reduction on the vertical component of non‐normal incidence plane waves before combining with the pressure data. More elaborate techniques use three‐dimensional filters to both components before summation, for example, for ghost wavelet dephasing and mitigation of noise of different strengths on the individual components in optimum deghosting. The problem with all these techniques is, of course, that it is usually impossible to transform the data into the crossline wavenumber domain because of aliasing. Hence, usually, a two‐dimensional version of deghosting is applied to the data in the frequency–inline wavenumber domain. We investigate going down the “dimensionality ladder” one more step to a one‐dimensional weighted summation of the records of the collocated sensors to create an approximate deghosting procedure. We specifically consider amplitude‐balancing weights computed via a standard automatic gain control before summation, reminiscent of a diversity stack of the dual‐sensor recordings. This technique is independent of the actual streamer depth and insensitive to variations in the sea‐surface reflection coefficient. The automatic gain control weights serve two purposes: (i) to approximately correct for the geometric amplitude loss of the Z data and (ii) to mitigate noise strength variations on the two components. Here, Z denotes the vertical component of the velocity of particle motion scaled by the seismic impedance of the near‐sensor water volume. The weights are time‐varying and can also be made frequency‐band dependent, adapting better to frequency variations of the noise. The investigated process is a very robust, almost fully hands‐off, approximate three‐dimensional deghosting step for dual‐sensor data, requiring no spatial filtering and no explicit estimates of noise power. We argue that this technique performs well in terms of ghost attenuation (albeit, not exact ghost removal) and balancing the signal‐to‐noise ratio in the output data. For instances where full three‐dimensional receiver deghosting is the final product, the proposed technique is appropriate for efficient quality control of the data acquired and in aiding the parameterisation of the subsequent deghosting processing.

Exploiting the control of phase in marine vibrators

Marine seismic vibrators are considered to be more environmentally friendly than air guns and this has prompted a resurgence of interest in their use. However, these devices have novel features that are potentially of great benefit to seismic imaging and that have not yet been exploited - in particular, we can control the phase. With marine vibrators, the emitted waveform can be chosen freely, provided that it lies within the envelope of what the device can emit. Typically, the waveform is a swept-frequency sinusoid. In this paper, we show how the sweep phase can be used to suppress the residual shot noise (RSN) and to separate simultaneous sources of high multiplicity. This work is also described by Laws and Halliday (2013) and is closely related to that of Laws (2012). The control of phase is a benefit of marine vibrators that can be exploited to great effect. First, we look at the RSN situation. The conventional wisdom is that roughly a 10s shot-time interval is required in marine seismic data acquisition so that the RSN is acceptably small relative to the signal. Because both signal and RSN originate from the seismic source, the ratio of signal/RSN is not improved by using a larger source (pace Landro, 2008). We show a simple case of RSN attenuation using alternating sine and cosine sweeps. That is to say, the sequence of source phases goes, for successive shots, [0° 90° 0° 90° 0° 90° 0° 90°... and so on]. We show schematically how this ‘phase sequencing’ leads to a dramatic attenuation of the RSN. It does so by moving the RSN into parts of the frequency-wavenumber spectrum where there is no signal. We then use frequency-wavenumber filtering to remove the RSN. This can be done with simple filtering up to the limit imposed by spatial aliasing and beyond that limit by using wavefield reconstruction methods, such as generalized matching pursuit (Ozbek et al., 2010; Vassallo et al., 2010). Reconstruction methods decompose the seismic wavefield into a set of basis functions that allow the signal and RSN to be identified and separated. Then, we look at the simultaneous source situation. The RSN removal problem can be considered as a special case of the more general simultaneous source separation problem. As an example, in the case of two simultaneous sources, one source can be swept with consistent phase, while the other source is swept with alternating phase, i.e., the sequence of relative phases is [0° 180° 0° 180° 0° 180° 0° 180°... and so on]. The simultaneous source separation is demonstrated using the same type of reconstruction method as described above for the RSN. See also Moore et al. (2008) and Ji et al. (2012). The use of phase sequencing opens up possibilities for simultaneous source separation using large numbers of sources. By having complete control over the phases of all the sources it is possible, in certain domains, to make simultaneous source data look similar to aliased data from a single source. This opens the door to using many established wavefield interpolation and dealiasing-techniques to perform high-multiplicity simultaneous source separation.

Iterative deblending using shaping regularization with a combined PNMO-MF-FK coherency filter

Simultaneous shooting achieves a much faster acquisition but poses a challenging problem for subsequent processing because of the interference from the neighbor crews. Separation of different sources, also called deblending, becomes important for the overall success of the new acquisition technology. In this paper, we propose a novel deblending approach following the shaping regularization framework. The shaping operator is chosen as an effective filter, combining pseudo normal-moveout, median filtering, and frequency wavenumber filtering (PNMO-MF-FK). We combine the median-filter based deblending approaches and the FK filter based deblending approach within the proposed framework. Instead of simply using the median filter to remove blending noise, we apply a pseudo NMO (PNMO) to prepare a relatively flatter profile in advance, which can make the median filter more effective. It is the first time that the PNMO, median filtering, and FK filtering are combined to form a powerful coherency filter in order to improve the performance of iterative deblending. The proposed deblending approach with the PNMO-MF-FK filter can obtain successful performance within small number of iterations. Compared with the alternative MF-FK filter and FK filter, the PNMO-MF-FK filter can obtain obviously better deblending results. We use both simulated synthetic and field data examples to demonstrate the performance of the proposed approach.

Intermittency of the near pressure field induced by a compressible coaxial jet

A novel method of analysis based on the combined use of the wavelet transform and linear stochastic estimation (LSE) is applied to pressure and velocity signals obtained in a coaxial jet at low subsonic flow conditions. The aim of the analysis is to identify and clarify the role of intermittency in the generation of noise. The wavelet analysis extracts intermittent events from the near field pressure signals and the LSE technique identifies velocity fluctuations which are linearly associated with the selected pressure fluctuations. A frequency–wavenumber filtering procedure is also applied to the near field pressure in order to separate the hydrodynamic and the acoustic components. The results achieved helps to identify and localize fluid dynamic events responsible for the generation of near field hydrodynamic and acoustic intermittent pressure fluctuations.

Seismic noise filtering based on Generalized Regression Neural Networks

This paper deals with the application of Generalized Regression Neural Networks to the seismic data filtering. The proposed system is a class of neural networks widely used for the continuous function mapping. They are based on the well known nonparametric kernel statistical estimators. The main advantages of this neural network include adaptability, simplicity and rapid training. Several synthetic tests are performed in order to highlight the merit of the proposed topology of neural network. In this work, the filtering strategy has been applied to remove random noises as well as source-related noises from real seismic data extracted from a field in the South of Algeria. The obtained results are very promising and indicate the high performance of the proposed filter in comparison to the well known frequency–wavenumber filter.

Educing the source mechanism associated with downstream radiation in subsonic jets

AbstractThis work belongs to the ongoing debate surrounding the mechanism responsible for low-angle sound emission from subsonic jets. The flow, simulated by large eddy simulation (Bogey & Bailly,Comput. Fluids, vol. 35 (10), 2006a, pp. 1344–1358), is a Mach 0.9 jet with Reynolds number, based on the exit diameter, of$4\ensuremath{\times} 1{0}^{5} $. A methodology is implemented to educe, explore and model the flow motions associated with low-angle sound radiation. The eduction procedure, which is based on frequency–wavenumber filtering of the sound field and subsequent conditional analysis of the turbulent jet, provides access to space- and time-dependent (hydrodynamic) pressure and velocity fields. Analysis of these shows the low-angle sound emission to be underpinned by dynamics comprising space and time modulation of axially coherent wavepackets: temporally localized energization of wavepackets is observed to be correlated with the generation of high-amplitude acoustic bursts. Quantitative validation is provided by means of a simplified line-sourceAnsatz(Cavalieriet al. J. Sound Vib., vol. 330, 2011b, pp. 4474–4492). The dynamic nature of the educed field is then assessed using linear stability theory (LST). The educed pressure and velocity fields are found to compare well with LST: the radial structures of these match the corresponding LST eigenfunctions; the axial evolutions of their fluctuation energy are consistent with the LST amplification rates; and the relative amplitudes of the pressure and velocity fluctuations, which are educed independently of one another, are consistent with LST.

An Automatic Framework Using Space-Time Processing and TR-MUSIC for Subsurface and Through-Wall Multitarget Imaging

We present an automatic framework combined space-time signal processing with Time Reversal electromagnetic (EM) inversion for subsurface and through-wall multitarget imaging using electromagnetic waves. This framework is composed of a frequency-wavenumber (FK) filter to suppress direct wave and medium bounce, a FK migration algorithm to automatically estimate the number of targets and identify target regions, which can be used to reduce the computational complexity of the following imaging algorithm, and a EM inversion algorithm using Time Reversal Multiple Signal Classification (TR-MUSIC) to reconstruct hidden objects. The feasibility of the framework is demonstrated with simulated data generated by GPRMAX.

Application of multichannel Wiener filters to the suppression of ambient seismic noise in passive seismic arrays

We are concerned with the detection and location of small seismic events, such as can be encountered in monitoring hydro-fracturing with surface sensors. Ambient seismic noise is the main problem in detection of weak seismic phases from these events, particularly as the sites of interest are often within or near producing fields. Band-pass filtering and stacking are the most widely used techniques for enhancing the signal-to-noise ratio (SNR) in passive seismic experiments, but they are of limited value when noise and signal share the same frequency band. Seismic arrays can be used to reduce the unwanted noise (e.g., traffic noise, pumping noise, scattering ground roll) by delay-and-sum techniques (also called beamforming) or by frequency-wavenumber filtering. Beamforming maximizes the array response for the assumed direction and slowness of the signal. Whereas in some situations it can be highly effective, and the azimuth and slowness of the signal can be determined by a grid search approach, it is vulnerable to contamination by side-lobe energy, particularly for broadband signals and noise (Rost and Thomas, 2002). Frequency-wavenumber filtering can be very effective but requires regularly spaced arrays and implicitly assumes plane-wave propagation. Both methods perform poorly when the waveform changes significantly between stations of the array, as might be caused, for example, by differences in site response. In this article, we present a multichannel Wiener filtering technique, which allows the removal of coherent noise from three-component 2D arrays without making a priori assumptions about the mode of propagation (e.g., no plane-wave assumption is required for the noise field). We test the effectiveness of this filter with two case studies. In the first case, we add synthetic signals of varying strengths to actual noise data recorded with a hexagonal array during hydro-fracturing within a producing oil field in Wyoming, USA. Using this test, we are able to provide estimates of the smallest event detectable with the filtered data, and compare the results with conventional techniques, such as stacking. The second test case is a dense, small-aperture 2D seismic array of 95 stations placed within an area of 130 m x 56 m on a landslide deposit in the Northern Apennines, Italy. Numerous microearthquakes have been recorded with this array, whose faint P-phases serve as an ideal data set for testing filtering techniques.

Local linear coherent noise attenuation based on local polynomial approximation

We propose a new technique for the attenuation of locally coherent noise. We assume that the moveout of the noise is locally linear and approximate its amplitude variations with offset using piecewise (local) polynomial models. Thus, our method consists of three steps: detection of the noise (locally linear coherent noise, LLCN), amplitude estimation by a local polynomial approximation (LPA), and subtraction of the estimated coherent noise from the original data. Applying the proposed method to synthetic data and to a field data set shows that the LPA filter has good ability to model LLCN and is insensitive to the filter parameters. Comparisons of the results obtained by our method with those from the traditional frequency-wavenumber filter and the localized 2D filter in the Fourier projection domain (FPF) show that the new method outperforms both traditional methods in situations with complex coherent noise.

Portable dense geophone array for shallow and very shallow 3D seismic reflection surveying: Part 1—Data acquisition, quality control, and processing

A strategy is presented for 3D seismic reflection imaging of shallow and very shallow targets, utilizing a portable dense geophone array. A dense 2D geophone array identifies faint shallow reflections and suppresses coherent noise. Fixing the receiver locations enables the design of quality control (QC) procedures that improve event identification. The number of shots, shot locations, and their effect on target illumination can be evaluated with various QC tools during acquisition to improve overall data quality. At the same time the portability of the array increases the cost effectiveness. Radially projected supergathers enable the choice of efficient processing parameters. With sufficiently high fold and 3D frequency–wavenumber filtering, the dense geophone array is shown to image reflectors from 8 to 50 ms, along with a dominant 20‐ms water table reflection.

Localized 2-D filter-based linear coherent noise attenuation

A novel localized two-dimensional (2-D) filter is proposed. The proposed filter derived from the frequency-wavenumber filter and Radon transform filter, with the filtering operation applied at the stage of Fourier projection, has good local property and less filtering distortion. An example of the proposed method to attenuate linear coherent noise in a seismic image is given. Comparisons of the results between our method and the conventional 2-D filters (including frequency-wavenumber filter and Radon transform filter) show that the new method outperforms both frequency-wavenumber method and Radon transform method.

Seismic characteristics of an airgun fired over snow

An alternative seismic source was investigated in an experiment conducted near Rothera Station, Antarctic Peninsula. The source was an airgun fired above the snow surface. Comparison shots using explosive and hammer sources were also recorded. A clear reflection was obtained from the ice/bedrock interface 300 m beneath the site on the unprocessed airgun record. On the explosive and hammer records the reflection could only be seen after frequency-wavenumber filtering had attenuated shearwaves and ground roll. The technique has potential use in profiling ice shelf thickness and seabed depth using a single, small airgun.

PSV-wave propagation in a medium with local heterogeneities: a hybrid formulation and its application

SUMMARY Hybrid methods, which combine so-called ‘numerical’ and ‘analytical’ methods, are a successful tool for computing synthetic seismograms for media with localized heterogeneous regions. Each of the two methods is applied in that part of the medium in which it can be employed efficiently. This paper deals with a combination of a finite-difference algorithm, applied in the neighbourhood of the heterogeneity, and a frequency–wavenumber filter for the PSV-wave equation applied outside. This method is an alternative to the use of Green's theorem as a wavefield-continuation method (e.g. van den Berg 1984). In the hybrid method presented here, absorption can be incorporated additionally. For different models with first-and second-order discontinuities the hybrid method was tested successfully against the reflectivity method. The hybrid method was applied to study the effects of a heterogeneous lower crust on the wavefield. This application has been inspired by recent deep seismic reflection profiling, which often reveals a highly reflecting lower crust. The scattering models have been divided into three groups: horizontal, vertical and isotropic scatterers. The comparison of the reflection responses of these models shows that thin horizontal or small isotropic scatterers yield high reflected energy, coherent over a few kilometres, in the time window of lower crustal reflections. Vertical structures, characterized by a small correlation length in horizontal direction, have less energy in this time window, but they can generate a complex Moho reflection with a strong Moho coda. It is also shown that the acoustic approximation is mostly not sufficient to describe the wave propagation in such complex media.