Frequency-wavenumber Analysis Research Articles

A seismic ambient noise data classification method based on waveform and frequency-wavenumber analysis: Application to reliable geological interpretation adjacent to Well Songke-2, Northeast China

Passive seismic interferometry techniques enable the retrieval of virtual shot gathers at receiver locations. However, it is difficult to distinguish body waves from surface waves in seismic ambient noise data, which leads to failed dispersion measurements, artificial deep reflections, and misleading geologic interpretations. We develop a new method that uses the waveforms and their corresponding f- k spectra to identify body waves and surface waves. Our technique functions as a data classification procedure before wavefield retrieval and subsequent imaging. A field data example is conducted to test the feasibility of this technique. The field data results demonstrate that our technique can reconstruct satisfactory high signal-to-noise-ratio wavefields for reliable imaging and interpretation purposes. The method can also serve as a validation tool for identifying surface wave-related artificial events in the obtained virtual source reflection image. The marker boundaries of the Songliao Basin in Northeast China are interpreted in the obtained profile and are in agreement with the well-logging data. In addition, two normal faults are detected, which correspond to the extensional rift environment during the early Cretaceous.

Pipe wall thickness estimation by frequency–wavenumber analysis of circumferential guided waves

Ultrasonic guided waves in pipes propagating in the circumferential direction carry information about the thickness of the pipe wall. This study proposes a method for estimating the pipe wall thickness based on measurements from circumferentially distributed sensors and a set of pre-computed theoretical dispersion curves. The recorded data are Fourier transformed into a frequency–wavenumber representation. The wall thickness is obtained by identifying the best fitting dispersion curve to the frequency–wavenumber data by determining the maximum stacking power. The thickness estimation method has demonstrated robustness against noise. Given the presence of significant noise (0.0dB signal-to-noise ratio) and simulations where the thickness ranges from 6.0 to 10.0mm, using eight sensors or more attain a mean absolute percentage error of less than 1%. The method is also supported by real laboratory measurements using eight sensor positions, where the error is less than 0.7%. Experimental measurements near the pipe end demonstrate that with appropriate positioning, end-reflections should not have a detrimental effect on the accuracy. The method estimates the mean thickness in cases where the pipe wall has near-uniform thickness but may not be as reliable when there are large shallow defects caused by metal loss, which is typically the case when the inner wall has suffered from erosion. In this case, monitoring of the stacking power curves could detect regional metal loss due to erosion and analysis of the local maxima could uncover information about individual thickness segments around the pipe circumference.

Monitoring ocean currents during the passage of Typhoon Muifa using optical-fiber distributed acoustic sensing

In situ observations under typhoon conditions are sparse and limited. Distributed acoustic sensing (DAS) is an emerging technology that uses submarine optical-fiber (OF) cables to monitor the sea state. Here, we present DAS-based ocean current observations when a super typhoon passed overhead. The microseismic noise induced by ocean surface gravity waves (OSGWs) during Typhoon Muifa (2022) is observed in the ~0.08–0.38 Hz frequency band, with high-frequency (>0.3 Hz) component being tidally modulated. The OSGW propagation along the entire cable is successfully revealed via frequency–wavenumber analysis. Further, a method based on the current-induced Doppler shifts of DAS-recorded OSGW dispersions is proposed to calculate both speeds and directions of horizontal ocean currents. The measured current is consistent with the tidally induced sea-level fluctuations and sea-surface winds observed at a nearby ocean buoy. These observations demonstrate the feasibility of monitoring the ocean current under typhoon conditions using DAS-instrumented cables.

High-frequency source localization based on steered frequency-wavenumber analysis using sparse array

In this study, we address the problem of estimating the position of a nearby target emitting a high-frequency signal using sparse array. One of the representative localization techniques, Matched Field Processing (MFP), is known to demonstrate reliable performance below 1 kHz. However, at frequencies higher than the design frequency of the array sensor, the localization becomes challenging due to spatial aliasing. Nevertheless, Frequency-Difference Matched Field Processing (FDMFP) is a technique that successfully estimates the position of the target even in the presence of spatial aliasing. It performs signal processing in the low-frequency band using low-frequency components obtained from two high-frequency components. To ensure reliability, we compared and validated the results of this study with the results of FDMFP. In this research, we completed the algorithm by controlling the phenomenon of striation shifting caused by spatial aliasing in the conventional frequency-wavenumber(f-k) analysis through beam steering. We steered the received signal to the location of signal reception and identified the target's position using the f-k spectrum of the steered signal. The data used in the study is the sound of snapping shrimp from SAVEX15, with a frequency range of 5–24 kHz wideband impulse signals.

Identification of guided Lamb wave modes in thin metal plates using water path corrected frequency – wavenumber [f-k] analysis

Acoustic microscopy is widely used for the material characterization of thin plates having thicknesses <100μm. For thin plate material characterization, the acoustic microscopy-based approach utilizes the guided Lamb wave modes generated in the plates by defocusing a single high-frequency focused transducer. Identification of the guided wave modes is vital in material characterization. Frequency-wavenumber analysis using 2D-FFT is commonly used to identify guided wave modes. In PVDF-based focused transducers used in acoustic microscopy, edge waves originating from the transducer rim influence the generation of guided waves, making the conventional frequency-wavenumber analysis erroneous. This study proposes a new water path corrected frequency-wavenumber (f-k) analysis using 2D-FFT to overcome the challenges imparted by the edge waves. In this approach, the water path of the Lamb wave modes is calculated and removed from the waveforms before performing 2D-FFT. The proposed approach has been demonstrated on thin metal plates of Aluminum, Copper and Brass having thicknesses of 45μm, 52μm and 52μm, respectively. A good correlation is obtained between theoretical and experimental results.

Automatized localization of induced geothermal seismicity using robust time-domain array processing

The surveillance of geothermal seismicity is typically conducted using seismic networks, deployed around the power plants and subject to noise conditions in often highly urbanized areas. In contrast, seismic arrays can be situated at greater distances and allow monitoring of different power plants from one central location, less affected by noise interference. However, the effectiveness of arrays to monitor geothermal reservoirs is not well investigated and the increased distance to the source coincides with a decreased accuracy of the earthquake localizations. It is therefore essential to establish robust data processing and to obtain precise estimates of the location uncertainties. Here, we use time-domain array data processing and solve for the full 3-D slowness vector using robust linear regression. The approach implements a Biweight M-estimator, which yields stable parameter estimates and is well suited for real-time applications. We compare its performance to conventional least squares regression and frequency wavenumber analysis. Additionally, we implement a statistical approach based on changepoint analysis to automatically identify P- and S-wave arrivals within the recorded waveforms. The method can be seen as a simplification of autoregressive prediction. The estimated onsets facilitate reliable calculations of epicentral distances. We assess the performance of our methodology by comparison to network localizations for 77 induced earthquakes from the Landau and Insheim deep-geothermal reservoirs, situated in Rhineland-Palatinate, Germany. Our results demonstrate that we can differentiate earthquakes originating from both reservoirs and successfully localize the majority of events within the magnitude range of ML -0.2 to ML 1.3. The discrepancy between the two localization methods is mostly less than 1 km, which falls within the statistical errors. However, a few localizations deviate significantly, which can be attributed to poor observations during the winter of 2021/2022.

Source localization based on steered frequency-wavenumber analysis for sparse array.

When using a sparse array, locating the target signal of a high-frequency component is difficult. Although forecasting the direction in a sparse situation is challenging, the frequency-wavenumber (f-k) spectrum can simultaneously determine the direction and frequency of the analyzed signal. The striation of the f-k spectrum shifts along the wavenumber axis in a sparse situation, which reduces the spatial resolution required to determine the target's direction using the f-k spectrum. In this study, f-k spectra of a high-frequency signal were used for near-field source localization. Snapping shrimp sounds (5-24 kHz) from SAVEX15 (a shallow-water acoustic variability experiment conducted in May 2015) were used as the data source, and a simulation was used to evaluate the proposed method. Beam steering was performed before creating the f-k spectrum to improve spatial resolution. We found that the spatial resolution was improved, and the location of the sound source could be determined when a signal with beam steering was utilized. The shrimp sound from SAVEX15, a near-field broadband signal, was used to determine the shrimp's location (range, 38 m; depth, 100 m) and the tilt of the vertical line array. These results suggest that the proposed analysis helps to accurately estimate the location of sound source.

Parametric evaluation of Kelvin-Voigt dispersion curve fitting

Ultrasound shear wave elastography (SWE) is a useful technique for non-invasive tissue assessment. For effective quantitative analysis the employment of physical models is necessary for rheological parameter estimation, such as the Kelvin-Voigt (KV) model. From SWE data, the frequency response can be calculated, and the shear wave velocity dispersion can be fit, yielding the shear elasticity and shear viscosity, μ1 and μ2, respectively. In this study, a parametric evaluation is performed using staggered-grid finite-difference simulations of materials with μ1 = 1–25 kPa (increment: 1 kPa) and μ2 = 0–10 Pa s (increment: 0.5 Pa s), with an acoustic radiation force push of f-number equal to 2. The novel Stockwell transform combined with a slant frequency-wavenumber analysis (GST-SFK) was compared with the two-dimensional Fourier transform for dispersion curve estimation over a variety of frequency ranges. Regardless of dispersion curve estimation technique, the accuracy of estimating μ1 is confounded for μ2 values above 5 Pa s. It was found that KV fitting benefits from wider frequency ranges (up to 1kHz), with lower μ1 and μ2 estimation errors. The GST-SFK was the best dispersion curve calculation technique, yet the KV fitting process was found to be unreliable for parameter estimation in highly viscous media.

Disbond detection of honeycomb sandwich structure through laser ultrasonics using signal energy map and local cross-correlation

Detecting disbonds in honeycomb sandwich structures using ultrasonics is challenging due to the complex wave propagation. This paper investigates the method for disbond quantification in honeycomb sandwich structures using laser ultrasonics. In the experiments on an aluminum specimen, the detection frequency range was determined by the local defect resonance (LDR) in the disbond regions. The energy maps of bandpass wavefields identified the locations of disbonds. To improve the results, a frequency-wavenumber analysis of the wavefields was performed. The wavenumber spectra were reconstructed by wavenumber filtering to strengthen the outline components for quantifying disbonds. Local cross-correlation (LCC) was proposed to show the outlines of disbonds and honeycomb cells, whose results agreed well with the X-ray imaging. Moreover, LCC could also quantify a disbond in the composite honeycomb sandwich structure. Consequently, combining energy maps and LCC results can effectively detect the locations and sizes of disbonds in honeycomb sandwich structures.

Pipe Wall Thickness Estimation by Frequency-Wavenumber Analysis of Circumferential Guided Waves

Pipe Wall Thickness Estimation by Frequency-Wavenumber Analysis of Circumferential Guided Waves

Direction-of-Arrival Estimation Based on Frequency Difference-Wavenumber Analysis for Sparse Vertical Array Configuration.

Frequency-wavenumber (f-k) analysis can estimate the direction of arrival (DOA) of broadband signals received on a vertical array. When the vertical array configuration is sparse, it results in an aliasing error due to spatial sampling; thus, several striation patterns can emerge in the f-k domain. This paper extends the f-k analysis to a sparse receiver-array, wherein a multitude of sidelobes prevent resolving the DOA estimates due to spatial aliasing. The frequency difference-wavenumber (Δf-k) analysis is developed by adopting the concept of frequency difference, and demonstrated its performance of DOA estimation to a sparse receiver array. Experimental results verify the robustness of the proposed Δf-k analysis in the estimation of the DOA of cracking sounds generated by the snapping shrimps, which were recorded by a sparse vertical array configuration during the shallow water experiment.

On the potential of offshore sensors and array processing for improving seismic event detection and locations in the North Sea

SUMMARY The capability to detect and locate seismicity in the North Sea is necessary to ensure the safety of future CO2 storage operations. Currently, the event location capabilities are hampered by a one-sided network configuration, as only sensors deployed on the Norwegian mainland are providing good signal-to-noise ratios. However, applying array processing techniques to groups of offshore sensors deployed at oil and gas reservoirs can improve the signal-to-noise ratio at such sites, which generally suffer from high noise contamination originating from platforms or seismic shooting. In this study we test the feasibility of array processing to sensors deployed at the Grane oil field to improve earthquake event locations. Out of the 3400 nodes installed, we have access to two data subsets: (i) continuous data from 10 sensors spread out over the whole field and (ii) short segments of data from 30 sensors selected with the purpose to apply array methods. As the average interstation distance between the 10 sensors is 6 km, the recorded wavefield is not coherent and traditional array processing methods are not applicable. To optimize the usage of the 10-sensor offshore data for event location purposes, we develop a new method for incoherent array processing. We compute a characteristic function based on the kurtosis of the seismic traces prior to a frequency–wavenumber analysis. This method successfully determines slowness and backazimuth for almost all the evaluated earthquakes in this study. Using common coherent array processing, the 30 sensors show superior detection capabilities over the 10 sensors and will therefore decrease the detection threshold for seismic events in the region significantly if continuous data are available. We conclude that offshore sensors at Grane can be included as a part of a system for passive seismic monitoring in the North Sea. We recommend using the 30-sensors data for this purpose. However, as we only have access to continuous data from the 10 sensors in this study, we found that they are a good substitute when the 30-sensor data are not available.

Subsurface characterization using passive seismic in the urban area of Dublin City, Ireland

AbstractWe investigate the shallow geological features and previously unknown depths of the main geological interfaces in the highly urbanized Dublin City area by using a set of complementary ambient noise seismic methods. A sparse seismic array, composed of 19 broadband sensors, was installed in a 5 × 5 km area across the city centre. The dataset was acquired over a 5‐month‐long deployment and used to perform horizontal/vertical spectral ratios and frequency–wave number analysis cross‐correlation interferometry. From the horizontal/vertical high‐frequency resonance peaks, we estimate the depth to bedrock. Then we use a subset of six seismic stations to obtain the frequency–wavenumber Rayleigh wave fundamental mode in the 0.8–3 Hz frequency band. Next, the ambient noise dataset is cross‐correlated in order to extract the empirical Green's functions before measuring surface‐wave phase velocities by undertaking a dispersion analysis in the 0.5–9 Hz frequency band. Then, a Monte Carlo global optimization algorithm is used to invert the phase velocity dispersion measurements. We generate a reference one‐dimensional depth S velocity profile along with a set of localized one‐dimensional S velocity profiles. Finally, a smooth three‐dimensional shear wave velocity model is derived for the top 1000 m in the sedimentary Dublin Basin. From the one‐dimensional velocity profiles and three‐dimensional shear velocity model, with some sensitivity down to approximately 1.2 km, we observe velocity changes with depth that highlight the presence of three consistent interfaces. We discuss interpretative scenarios that correlate the velocity features to potential stratigraphic boundaries occurring within the sedimentary Dublin Basin, suggesting that basement rocks could be located at a depth significantly greater than the top kilometre. The results of this study may indicate that future geothermal studies should be directed at structures deeper than 1 km, towards the bottom of the sedimentary basin beneath the city.

Estimation of Shear-Wave Velocity Structures in Taichung, Taiwan, Using Array Measurements of Microtremors

Near-surface S-wave velocity structures (VS) are crucial in site-effect studies and ground-motion simulations or predictions. We explored S-wave velocity structures in Taichung, the second-largest city in Taiwan by population, by employing array measurements of microtremors at a total of 53 sites. First, the fundamental-mode dispersion curves of Rayleigh waves were estimated by adopting the frequency–wavenumber analysis method. Second, the surface-wave inversion technique was used to calculate the S-wave velocity structures of the area. At many sites, observed phase velocities were almost flat, with a phase velocity of approximately 800–1300 m/s in the frequency range of 0.6–2 Hz. A high-velocity zone (VS of 900–1500 m/s) with a convex shape was observed at the shallow S-wave structures of these sites (depths of 50–500 m). On the basis of the inversion results, we constructed two-dimensional and three-dimensional contour maps to elucidate the variations of VS structures in Taichung. According to VS-contour maps at different depths, lowest S-wave velocities are found at the western coastal plain, whereas highest S-wave velocities appear on the eastern side. The S-wave velocity gradually decreases from east to west. Moreover, the S-wave velocity of the Tertiary bedrock is assumed to be 1500 m/s in the area. According to the depth-contour map (VS = 1500 m/s), the depths of the bedrock range from 250 m (the eastern part) to 1550 m (the western part). The thicknesses of the alluvium gradually decrease from west to east. Our results are consistent with the geology of the Taichung area.

A metamaterial ultrasound mode convertor for complete transformation of Lamb waves into shear horizontal waves

This article reports a new mechanism involving a non-perforated resonant elastic metamaterial to achieve the complete conversion of Lamb waves (A0 and S0) into the fundamental shear horizontal (SH0) wave. The proposed metamaterial ultrasound mode convertor is studied via the observation of the special resonant shear motion of its unit cells, initiating with a conventional additive stub design. Thereafter, such a stubbed structure is further modified to fully couple the Lamb modes with the shear horizontal stub motion. By investigating the band structure of the metamaterial unit cell through modal analysis and tuning the shear resonant motions, a complete SH0 mode generation band within the simultaneous Lamb modes bandgap can be established in a wide frequency range. Such a special bandgap situation enables the complete mode conversion from Lamb waves into shear horizontal waves. The transformation capability of the proposed ultrasound mode convertor is further substantiated via the harmonic analysis of metamaterial chain model, showcasing the frequency spectrum of the transmitted wave modes. The optimal configuration is determined by conducting a parametric study to identify the most effective mode conversion performance. Finally, a coupled-field transient finite element simulation is carried out to acquire the dynamic response of the structure. The frequency-wavenumber analysis of the transmitted wave field illuminates the successful realization of the mode conversion behavior. Experimental demonstrations are presented to validate the numerical predictions. The proposed complete mode conversion capability may possess great potential for wave control and manipulation.

An algorithm based on logarithm of wavenumber amplitude for detection of delamination in carbon fiber composite

Delamination is one of the most common types of damage/defect in carbon/glass fiber reinforced composites and many researchers use frequency-wavenumber analysis to detect delamination. There are large fluctuations in amplitudes when Lamb wave propagates in composite plate, so that it is hard to precisely identify the boundary of delamination simply from the change of wavenumber. This paper has presented an algorithm based on logarithm of wavenumber amplitude to detect the delamination in carbon fiber plate with high precision. In wavenumber spectra after logarithm processing, the wavenumber amplitudes at delamination boundary can be significantly amplified and the resulting curve of sum of amplitudes can be used to effectively identify the boundary. In this paper, the principle of the logarithm of amplitude algorithm has been introduced and the effectiveness of the algorithm in delamination identification has been validated by finite element simulations and physical experiments. Compared with conventional algorithms, the proposed algorithm can effectively identify the boundary with better accuracy (less than 5%) and has decent identification stability under different depths of delamination. Our research has great potential for solving the challenge in precise identification of delamination boundary.

Debonding detection in rebar-reinforced concrete structures using second harmonic generation of longitudinal guided wave

Nonlinear features of ultrasonic guided waves (GWs) is studied for debonding detection and location estimation in rebar reinforced concrete structure. The study shows that the presence of debonding between steel rebar and concrete surface produces breathing phenomenon causing contact acoustic nonlinearity (CAN), which generates second harmonics. Time-frequency analysis is used to estimate the location of debonding in this study. At a particular frequency, embedded rebar has much greater number of wave modes in bare rebar. To avoid unnecessary complexity, only longitudinal GW modes for bare and embedded rebar are excited and received to detect and locate debonding. To precisely determine the wave mode at excited frequency and frequency of second harmonics, frequency-wavenumber analysis is performed using 2D-Fast Fourier Transform of time-space data. Three-dimensional explicit finite element simulations are performed for various case studies and the model is validated by experimentally measured data. The results of this study show that the proposed method is practically viable and beneficial for debonding detection and location estimation in reinforced concrete structures.

Phase Velocity Estimation With Expanded Bandwidth in Viscoelastic Phantoms and Tissues.

Ultrasound shear wave elastography (SWE) is a technique used to measure mechanical properties to evaluate healthy and pathological soft tissues. SWE typically employs an acoustic radiation force (ARF) to generate laterally propagating shear waves that are tracked in the spatiotemporal domains, and algorithms are used to estimate the wave velocity. The tissue viscoelasticity is often examined through analyzing the shear wave phase velocity dispersion curves, which is the variation of phase velocity with frequency or wavelength. A number of available methods to estimate dispersion exist, which can differ in resolution and variance. Moreover, most of these techniques reconstruct dispersion curves for a limited frequency band. In this work, we propose a novel method used for dispersion curve calculation. Our unique approach uses a generalized Stockwell transformation combined with a slant frequency-wavenumber analysis (GST-SFK). We tested the GST-SFK method on numerical phantom data generated using a finite-difference-based method in tissue-mimicking viscoelastic media. In addition, we evaluated the method on numerical shear wave motion data with different amounts of white Gaussian noise added. Additionally, we performed tests on data from custom-made tissue-mimicking viscoelastic phantom experiments, ex vivo porcine liver measurements, and in vivo liver tissue experiments. We compared results from our method with two other techniques used for estimating shear wave phase velocity: the two-dimensional Fourier transform (2D-FT) and the eigenvector (EV) method. Tests carried out revealed that the GST-SFK method provides dispersion curve estimates with lower errors over a wider frequency band in comparison to the 2D-FT and EV methods. In addition, the GST-SFK provides expanded bandwidth by a factor of two or more to be used for phase velocity estimation, which is meaningful for a tissue dispersion analysis in vivo.

Low-Frequency Distributed Acoustic Sensing for Early Gas Detection in a Wellbore

An unexpected and unwanted influx of gas or “kick” into the wellbore during hydrocarbon drilling can cause catastrophic blowout incidents, resulting in human casualties, ecological damage, and asset losses. The ability of the oil and gas industry to control gas kick depends on our ability to accurately detect and monitor gas migration in a borehole in real-time. This study demonstrates the application of optical fiber-based Distributed Acoustic Sensors (DAS) for early detection and monitoring of gas in wellbore. Multiphase flow experiments conducted in a 5000 ft. deep test-well are analyzed for different injection, circulation, and pressure conditions. In each case, the low-frequency component of DAS demonstrates a superior capability to detect gas signatures both inside the tubing and the annulus of the well, even at small gas volumes. In comparison, the high-frequency DAS data seems limited in detail. The gas influx velocity was calculated using the frequency-wavenumber analysis of the gradient of the low-frequency DAS phase with respect to time, which shows good agreement with theoretical velocity estimates using flow models and surface gauge measurements. This study demonstrates a novel workflow to analyze low-frequency DAS to qualitatively and quantitatively map gas influx in a wellbore.

Seismic monitoring and high-frequency noise using arrays in the Arabian Peninsula

Seismic arrays provide useful tools for regional seismic monitoring. Two small-aperture, regionally-oriented arrays, QWAR and HQAR, were deployed in Saudi Arabia and Oman in 2012 and 2016. We utilize a time-domain beampacking method, similar to frequency-wavenumber analysis, to examine the performance of the arrays in terms of slowness and azimuthal bias and event detection capabilities. Additionally, we investigate persistent ambient noise sources recorded by the arrays. We find that the arrays provide slowness vectors with biases comparable with similar-sized arrays of the International Monitoring System in other locations around the world. At QWAR, regional events of magnitude 3.0 and above are detected a majority of the time, and as magnitudes increase to 4.0 and above, the detection rate is greater than 82%. Strong noise generation, primarily with slownesses characteristic of Lg waves, is found in the directions of the northern Arabian/Persian Gulf and southern Red Sea and may be a factor in event detection capabilities.