Extraction Of Dispersion Curves Research Articles

Enhancing the Frequency–Bessel Spectrogram of Ambient Noise Cross-Correlation Functions

ABSTRACT The frequency–Bessel (F–J) spectrogram has been used for the extraction of multimodal dispersion curves to constrain the fine crustal shear-wave velocity structure. The original F–J spectrogram was contaminated with curved as well as straight crossed artifacts, which hindered obtaining the dispersion curves, while introducing a considerable error in the inversion result. Curved crossed artifacts in the multicomponent F–J spectrogram are typically removed using the modified F–J transform formulas; to remove straight crossed artifacts, we used the so-called k-filtering method. Based on a synthetic test and field data from the central Asian orogenic belt, we show that our proposed methods can enhance the multicomponent F–J spectrograms by efficiently removing the two types of crossed artifacts, while identifying more higher modes dispersion curves, and the accuracy of picking can also be improved.

Theoretical dispersion curves for borehole real-valued wave modes in vertically transverse isotropic formations

The dispersion curves of real-valued modes in a fluid-filled borehole are widely used in acoustic well logging. The accurate dispersion curves are the precondition of theoretical analysis and inversion process. Generally, these curves can be obtained by solving the conventional dispersion equation for isotropic formations and most vertically transverse isotropy (VTI) formations. However, if the real-valued solutions exist when the radial wavenumbers for the formation quasi-P and quasi-S equals to each other, the existed methods based on the conventional dispersion equation could lead to incorrect results for some VTI formations. Few studies have focused on the influence of these real-valued solutions on dispersion curve extraction. To remove these real-valued solutions, we have proposed a modified dispersion equation and its corresponding solving process. When solving the dispersion equation, the Scholte wave velocity of VTI formation at high frequency is used as the initial guess. The two synthetic examples including fast and slow VTI formations validate that these real-valued solutions do not contribute to the wavefield, and the new dispersion curve extraction method is suitable for all kinds of VTI formations. Consequently, the method can provide reliable dispersion curves for both theoretical analysis and anisotropic parameters inversion in VTI formations.

A physics-informed machine learning based dispersion curve estimation for non-homogeneous media

Modern machine learning has been on the rise in many scientific domains, such as acoustics. Many scientific problems face challenges with limited data, which prevent the use of the many powerful machine learning strategies. In response, the physics of wave-propagation can be exploited to reduce the amount of data necessary and improve performance of machine learning techniques. Based on this need, we present a physics-informed machine learning framework, known as wave-informed regression, to extract dispersion curves from a guided wave wavefield data from non-homogeneous media. Wave-informed regression blends matrix factorization with known wave-physics by borrowing results from optimization theory. We briefly derive the algorithm and discuss a signal processing-based interpretability aspect of it, which aids in extracting dispersion curves for non-homogenous media. We show our results on a non-homogeneous media, where the dispersion curves change as a function of space. We demonstrate our ability to use wave-informed regression to extract spatially local dispersion curves.

Recent advances in phase-array based wideband multimodal dispersion curves extraction and plate-waveguide parameter inversion

Multimodal ultrasonic guided waves with rich dispersion information have been widely applied for waveguide evaluation. However, there are still some challenges to extract multimode dispersion curves using the traditional pitch-catch method, including lack of spatial information and poor signal-to-noise ratio. Phase array has been recently developed for measuring ultrasonic guided waves, which brings many advantages for wideband multimodal dispersion curves extraction and parameter inversion. In the last years, basing on a multi-emitter and multi-receiver measurement, we proposed some array dispersive signal processing strategies for analyzing guided waves in long cortical bone, including the sparse singular vector decomposition (sparse-SVD) method for enhancing wavenumber estimation resolution and the low-amplitude mode extraction, Radon transform and dispersive Radon transform (DRT) with the capability to project temporal array dispersive signals on the space of parameters of interest for solving the inverse problem, and our recent work of deep neural networks for solving the intractable multiparameter inverse problem from the array signals to the waveguide elasticity. In the talk, we present (1) recent advances in array signal processing for extracting wideband multimodal dispersion curves; (2) some new perspectives to retrieve the waveguide parameters; (3) some pilot clinical results of long cortical bone evaluation using ultrasonic guided waves.

SDCnet: An Unet with residual blocks for extracting dispersion curves from seismic data

The ambient noise cross-correlation technique has been widely used to obtain the S-wave velocity structure. Accurate and efficient extraction of dispersion curve from the spectrum energy diagram is extremely important. In this study, a data-driven deep learning network, SDCnet, is proposed for dispersion curve extraction. SDCnet is an improved Unet with a residual block structure. It automatically and intelligently identifies the peak values at different frequencies as a case segmentation task. A trainable upper and lower sampling strategy was introduced into the residual block to improve the ability of feature extraction and avoid network degeneration. Training set from real and synthetic data widely improves the SDCnet's generalization ability. In our study, SDCnet has demonstrated its high accuracy and efficiency in applications of real data from USArray in the western USA. Compared with the traditional model-driven methods, SDCnet can accurately extract dispersion curves without prior information. The network has the advantage of saving labor and time for extracting massive dispersion curves.

Finite Element Modeling Approaches, Experimentally Assessed, for the Simulation of Guided Wave Propagation in Composites

Today, structural health monitoring (SHM) systems based on guided wave (GW) propagation represent an effective methodology for understating the structural integrity of primary and secondary structures, also made of composite materials. However, the sensitivity to damage detection promoted by these systems can be altered by such factors as the geometry of the monitored parts, as well as the environmental and operational conditions (EOCs). Experimental investigations are fundamental but require a long time period and are costly, especially for tests in real-life scenarios. Experimentally validated simulations can help designers to improve SHM effectiveness due to the possibility of further broadening study on the different geometries, load cases, and material types with less effort. From this point of view, this paper presents two finite element (FE) modeling approaches for the simulation of GW propagation in composite panels. The case study consists of a flat and a curved composite panel. The two approaches herein investigated are based on implicit and explicit finite element analysis (FEA) formulations. The comparison of the predicted measures against the experimental dataset allowed the assessment of the levels of accuracy provided by both modeling approaches with respect to the dispersion curves. Furthermore, to assess the different curvature sensitivities of the proposed numerical and experimental approaches, the extracted dispersion curves for both flat and curved panels were compared.

Identification of Material Properties of Elastic Plate Using Guided Waves Based on the Matrix Pencil Method and Laser Doppler Vibrometry

Ultrasonic based inspection of thin-walled structures often requires prior knowledge of their mechanical properties. Their accurate estimation could be achieved in a non-destructive manner employing, e.g., elastic guided waves. Such procedures require efficient approaches for experimental data extraction and processing, which is still a challenging task. An advanced automated technique for material properties identification of an elastic waveguide is proposed in this investigation. It relies on the information on dispersion characteristics of guided waves, which are extracted by applying the matrix pencil method to the measurements obtained via laser Doppler vibrometry. Two objective functions have been successfully tested, and the advantages of both approaches are discussed (accuracy vs. computational costs). The numerical analysis employing the synthetic data generated via the mathematical model as well as experimental data shows that both approaches are stable and accurate. The influence of the presence of various modes in the extracted data is investigated. One can conclude that the influence of the corruptions related to the extraction of dispersion curves is not critical if the majority of guided waves propagating in the considered frequency range are presented. Possible extensions of the proposed technique for damaged and multi-layered structures are also discussed.

Estimating State of Charge of Lithium-ion Batteries by Using Ultrasonic Guided Waves Detection Technology

As a light weight and high power density energy, Lithium-ion batteries have become widely used in electric vehicles, energy storage systems, etc. Thus, accurately capturing the internal battery dynamics and properly estimating the state of charge of a lithium-ion battery attract academic research interest. A reliable battery detection method is particularly important. The mechanical properties (elastic modulus and density) can be affected by the level of lithiation of the electrodes and the volume expansion during charge and discharge cycling. In this work, a theoretical model of ultrasonic guided wave detection for cylindrical lithium-ion battery is established to purchase the guidance of the in-situ monitoring of the battery status. Several numerical cases about cylindrical Lithium cobalt oxide battery are studied, and the effect of the circumferential wave number and state of charge (SOC) on the dispersion characteristics are illustrated. Based on the extracted dispersion curves at different SOC, the relationship between the wave propagation characteristics of the ultrasonic guided waves and the SOC of the lithiumion battery is analyzed. The effective capture of the mapping relationship between SOC and acoustic behaviors can provide new ideas and solutions for the effective evaluation of the reliability and safety of power batteries.

Imaging an Underwater Basin and Its Resonance Modes Using Optical Fiber Distributed Acoustic Sensing

Abstract Distributed acoustic sensing (DAS) is an ideal tool for ambient noise tomography owing to the dense spatial measurements and the ability to continuously record in harsh environments, such as underwater. Although the fine spatial sampling of DAS facilitates the imaging of small-scale lateral velocity heterogeneities, efforts relying on dispersion-based ambient noise tomography are hampered by the underlying premise of negligible lateral variations across the segment used for dispersion curve extraction. To image small-scale structures, this method should be augmented with objective and independent approaches that are not scale limited. Here, we show that power spectral densities (PSDs) and autocorrelations (ACs) of DAS data reveal extremely detailed frequency-dependent resonance and wave propagation characteristics. These observations contain crucial information on lateral and vertical wave propagation. We use these methods to demonstrate the ability to image a complex underwater basin using ambient noise recorded on a fiber deployed offshore Greece. A 2D shear-wave velocity model was derived by analyzing Scholte-wave dispersion. The PSD and AC reveal significant lateral variations across the short 2.5 km long fiber segment, including basin edge effects and scattered waves. These were used to further constrain and modify the velocity model. The modified model is supported by waveform simulations that qualitatively reproduce the PSD and AC observations. Our results demonstrate the advantages of incorporating PSD and AC observations into ambient noise-based imaging. The spatially continuous observation of resonance modes across the basin highlights the benefit of DAS acquisitions for ground-motion estimation.

Modal dispersion curve extraction from shipping noise at two synchronized vertical arrays

The results of modal dispersion analysis, using low-frequency (20 to 250 Hz) shipping noise in shallow water with a soft bottom is presented. Experiments were carried out in the Sea of Galilee (Lake Kinneret, Israel) having a maximum depth of ∼40 m and a gassy upper sedimentary layer. A receiving system combined two synchronized, 10-hydrophone vertical line arrays (VLAs) located at the center of the lake with distance Dr = 40 m between them. The noise source, R/V “Hermona,” was moving along the straight line joining VLAs, up to 1 km from VLAs. A method of obtaining modal dispersion curves from shipping noise is proposed. For each frequency ω and variable horizontal wavenumber q = ω/cph the noise is spatially filtered at each VLA using calculated solution of the wave equation with the measured sound speed profile in water and the pressure-release condition imposed at the water surface. Then, the ratio of complex modal amplitudes at VLAs is calculated and multiplied by a factor of . The real part of the resulting 2-D structure exhibits the modal dispersion curves, which are used for acoustic characterization of the seabed. [Work supported by ISF, grant 946/20, and RFBR, grant 20-05-00119.]

Automatically Extracting Surface-Wave Group and Phase Velocity Dispersion Curves from Dispersion Spectrograms Using a Convolutional Neural Network

Abstract To image high-resolution crustal and upper-mantle structures, ambient noise tomography (ANT) has been widely used on local and regional dense seismic arrays. One of the key steps in ANT is to extract surface-wave group and phase velocity dispersion curves from cross-correlation functions of continuous ambient noise recordings. One traditional way is to manually pick the dispersion curves from dispersion spectrograms in the period-velocity domains, which is very labor intensive and time consuming. Another way is to automatically pick the dispersion curves using some predefined criteria, which are not reliable in many cases especially for phase velocity data. In this study, we propose a novel method named DisperPicker to automatically extract fundamental mode group and phase velocity dispersion curves using a convolutional neural network (CNN). The inputs to CNN include paired group and phase velocity dispersion spectrograms in the period-velocity domains, which are calculated from empirical surface-wave Green’s functions. In this way, group velocity dispersion curves can implicitly guide the extraction of phase velocity dispersion curves, which have large ambiguities to pick on the dispersion spectrograms. The labels or outputs of the network are the probability images converted from dispersion curves. The U-net architecture is adopted because it is powerful for image processing. We have assembled short-period surface-wave data from three different dense seismic arrays to train the network. The trained network is further tested and validated by two datasets close to Chao Lake, China. The tests show that DisperPicker has the generalization ability to efficiently and accurately extract dispersion curves of large datasets without new training.

Study of an Automatic Picking Method for Multimode Dispersion Curves of Surface Waves Based on an Improved U-Net

Surface wave exploration has been increasingly used in near-surface geophysical investigations. However, the accuracy and efficiency of picking dispersion curves are key to surface wave inversion. Traditional dispersion curve extraction requires manual picking, and the extraction accuracy and efficiency depend on the experience and knowledge of the interpreters. Therefore, developing a fast, high-precision and intelligent dispersion curve extraction method is urgent. This paper improves the structure and output of the U-Net neural network and regards the picking process of dispersion curves as an image classification problem, which quickly and accurately extracts dispersion curves from dispersion energy images. After combining the dispersion energy images of synthetic seismic data with the manually extracted dispersion curve and the theoretical dispersion curve obtained by the Schwab-Knopoff algorithm, the ICM (energy image and dispersion curve extracted manually) training set and the ICS (energy image and dispersion curve calculated by Schwab-Knopoff algorithm) training set are created. The synthetic data tests verify the feasibility of the improved U-Net neural network for automatically picking multimode dispersion curves. The dispersion curve picking results corresponding to two different training sets reveal that the U-Net network model obtained from the ICS training sets exhibits better extraction accuracy. Additionally, we analyze the influence of the sample number of the training set on the dispersion curve picking effect of the improved U-Net and conclude that the improved U-Net network has the advantages of a low training set size requirement and a high dispersion curve extraction accuracy. Finally, the trained network extracts the dispersion curves of two groups of measured surface wave data and obtains plausible extraction results, further proving the proposed method’s effectiveness.

Geoacoustic inversion using explosive air gun signals received by a single hydrophone in the East Siberian Sea, Arctic Ocean

Goacoustic inversions using low-frequency impulsive sources in shallow water have been recently performed to estimate geoacoustic parameters of sediments. In this talk, we present the geoacoustic inversion results estimated using explosive air gun data received by a single hydrophone in the East Siberian Sea in September 2019. The single hydrophone was deployed by the Korean icebreaker R/V Araon operated by Korea Polar Research Institute. The geoacoustic inversion is carried out by extracting modal dispersion curves from air gun data received from tens of km. A signal processing method called warping is applied to separate normal mode components and then the extracted dispersion curves are compared to the replicas predicted by the KRAKEN normal mode program. Although it was not possible to compare to in situ measurements of sediment, our inversion results are valuable in that they provide indirect information about geoacoustic parameters of the Arctic Ocean. [This research was a part of the project titled ‘Korea-Arctic Ocean Warming and Response of Ecosystem (K-AWARE, KOPRI, 1525011760)’, funded by the Ministry of Oceans and Fisheries, Korea and supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (2020R1A2C2007772).]

DisperNet: An Effective Method of Extracting and Classifying the Dispersion Curves in the Frequency–Bessel Dispersion Spectrum

ABSTRACTThe subsurface shear-wave structure primarily determines the characteristics of the surface-wave dispersion curve theoretically and observationally. Therefore, surface-wave dispersion curve inversion is extensively applied in imaging subsurface shear-wave velocity structures. The frequency–Bessel transform method can effectively extract dispersion spectra of high quality from both ambient seismic noise data and earthquake events data. However, manual picking and semiautomatic methods for dispersion curves lack a unified criterion, which impacts the results of inversion and imaging. In addition, conventional methods are insufficiently efficient; more precisely, a large amount of time is required for curve extraction from vast dispersion spectra, especially in practical applications. Thus, we propose DisperNet, a neural network system, to extract and discriminate the different modes of the dispersion curve. DisperNet consists of two parts: a supervised network for dispersion curve extraction and an unsupervised method for dispersion curve classification. Dispersion spectra from ambient noise and earthquake events are applied in training and validation. A field data test and transfer learning test show that DisperNet can stably and efficiently extract dispersion curves. The results indicate that DisperNet can significantly improve multimode surface-wave imaging.

Extraction of Multimodal Dispersion Curves From Ambient Noise With Compressed Sensing

AbstractWe propose a compressed sensing (CS) method for extracting multimodes from ambient noise. We solve the CS inverse problem by using two methods: an l1‐based optimization algorithm and a Bayesian method. Synthetic and field data examples are conducted to validate our method. The dispersion curves extracted by our method are consistent with those extracted by the widely used frequency‐Bessel transform (F‐J) method, but our method is more efficient and can extract higher‐resolution spectrograms than the F‐J method. Our method can quickly and reliably extract multimodes from ambient noise, thereby facilitating studies of ambient noise tomography.

A Fast GUI-Based Tool for Group-Velocity Analysis of Surface Waves

AbstractWe present an interactive graphical tool for extraction of group-velocity dispersion curves of seismic traces for rapid manual picking of large amounts of data: a task commonly encountered in ambient-noise tomography. The program can be used for group-velocity analysis of surface waves from earthquakes and controlled source data as well as of Green’s functions from cross-correlated ambient-noise data. The presented tool is especially suited to datasets in which automatic picking algorithms fail and so dispersion analysis is only possible by visual inspection. Such situations can occur in highly heterogeneous regions with complex surface-wave dispersion or where surface-wave arrivals are poorly emerged (as can often be the case with ambient-noise-derived Green’s functions from temporary seismic deployments). In these datasets, the poor signal-to-noise ratio, spectral holes, or limited bandwidth may therefore mean that manual analysis is the only choice. However, without an efficient workflow the feasibility of this can be seriously constrained by the analysis time for the potentially vast number of traces to be analyzed. We tackled this problem by implementing well-known techniques of dispersion curve analysis (traditional frequency–time analysis) in a fast and interactive graphical environment. It is specifically developed for high user processing speed, prioritizing fast computation, and high display responsiveness. This solution retains the benefits of manual dispersion picking for complex datasets, while maintaining good user processing efficiency. An experienced analyst can measure upward of 200 traces per hour. xdcpick stands for an X-window-based picking of dispersion curves.

Spatial autocorrelation method for reliable measurements of two-station dispersion curves in heterogeneous ambient noise wavefields

SUMMARYThe microtremor survey method (MSM) is used to estimate S-wave velocity profiles from microtremors or ambient noise. Although array-based MSM analyses are usually used for shallow exploration purposes because of their robustness, the extraction of numerous phase-velocity dispersion curves by two-station microtremor analysis is attractive because those dispersion curves can be used to construct high-resolution phase-velocity maps by solving a least-squares problem. However, in exploration studies (>1 Hz), the reliability of two-station microtremor analysis can be affected by short data acquisition times and heterogeneous noise distributions mainly caused by anthropogenic noises. In this study, we propose a new approach to estimate surface wave dispersion curves between station pairs considering a heterogeneous ambient noise distribution based on the spatial autocorrelation method. We first estimated azimuthal variations of noise energy from the complex coherencies between all station pairs in a receiver array, and then estimated dispersion curves between station pairs. Our field example demonstrates that modelling the azimuthal noise energy distribution allows us to use not only the real parts of complex coherencies, but also the imaginary parts, which are usually neglected when assuming a homogeneous noise field. The simultaneous use of the real and imaginary parts of complex coherencies improves the reliability and continuity of phase-velocity estimations between station pairs. Because the stability of phase-velocity estimations depends on the azimuths between station pairs, we carefully selected between-station azimuths that produce stable phase velocities. Selected phase velocities at 8 Hz can be used to construct high-resolution phase-velocity maps with least-squares inversion. Because our approach does not require a regular receiver interval for two-station analysis, it allows for more flexible seismic array geometries. This is particularly important for MSM analyses in urban areas, where limited space is available to install seismic stations. We conclude that our proposed approach is effective in reconstructing high-resolution shallow structures in heterogeneous ambient noise fields.

High-resolution Lamb waves dispersion curves estimation and elastic property inversion

Ultrasonic Lamb waves have been widely used for non-destructive evaluation and testing. However, the inversion from the measured guided signals to the material properties is still a challenging task in terms of multimodal dispersive signal processing and parameter estimation. This paper presents a robust strategy including the high-resolution extraction of the multimodal dispersion curves and model-based elastic property estimation. First, the estimation of signal parameters via rotation invariant technique (ESPRIT) is employed to extract the dispersion curves of the Lamb waves in the plates. Then, the particle swarm optimization (PSO) algorithm is used to retrieve the optimal model parameters by maximizing the objective function built from the dispersion equations. The elastic properties (i.e., two independent constants for the isotropic plate and four constants for the transversely isotropic plate) can thus be determined. Results of the steel, aluminum and composite plates demonstrate that the estimates are in agreement with the references. The root mean squared errors (RMSEs) between the estimated and theoretical dispersion curves calculated by the inversed model parameters for simulation, steel, aluminum and composite experiments are 0.027 rad/mm, 0.032 rad/mm, 0.033 rad/mm and 0.102 rad/mm respectively. The estimated error of thickness is less than 1%. The proposed model-based inversion strategy offers several advantages: (1) the high-resolution estimation of dispersion curves allows the objective function built for the parameter inversion without a peak-finding process. (2) The ESPRIT based dispersion curves extraction strategy offers a sharp objective function in the parameter space. (3) The inverse problem for ultrasonic waveguide characterization is solved using the PSO optimizer which can be implemented with ease and few parameters need to be tuned.

Extracting Dispersion Curves From Ambient Noise Correlations Using Deep Learning

We present a machine-learning approach to classifying the phases of surface wave dispersion curves. Standard FTAN analysis of surfaces observed on an array of receivers is converted to an image, of which, each pixel is classified as fundamental mode, first overtone, or noise. We use a convolutional neural network (U-net) architecture with a supervised learning objective and incorporate transfer learning. The training is initially performed with synthetic data to learn coarse structure, followed by fine-tuning of the network using approximately 10% of the real data based on human classification. The results show that the machine classification is nearly identical to the human picked phases. Expanding the method to process multiple images at once did not improve the performance. The developed technique will faciliate automated processing of large dispersion curve datasets.

Ambient noise wavefield decomposition and shear-wave velocity retrieval in the south of Tehran, Iran and in the Colfiorito basin, Italy

Knowledge about ambient noise wavefield, through decomposition into different participant waves and determination of precise singularities in ellipticity curves, could be very beneficial to improve the obtained subsurface velocity structures. In this paper, two array processing methods; WaveDec and high-resolution Rayleigh three-component beamforming (RTBF) and four single-station methods; Horizontal-to-Vertical Spectral Ratio (HVSR) or H/V, HVTFA (H/V using time frequency analysis), RayDec (Random Decrement Technique) and DOP-E (Degree Of Polarization) are applied to decompose ambient noise wavefield and to extract dispersion and ellipticity curves of surface waves. Two sites with different geological and geophysical conditions are chosen to examine the results of the measurements. The first selected site is in the south of Tehran, Iran, as a site with a low impedance contrast structure. The second one is in the Colfiorito basin, Italy, as a major impedance contrast structure site. Wavefield decomposition resulted in Rayleigh and Love wave separation and also mode distinction. The decomposed modes of surface waves and ellipticity curves of Rayleigh waves are used in a joint inversion process. The retrieved shear-wave velocity profiles are in close agreement with previous studies in the mentioned sites.