Frequency-dependent Attenuation Research Articles

Inversion of shear wave slowness and attenuation from dipole acoustic logging data based on an equivalent tool theory

The presence of a sonic logging tool affects the propagation characteristics of dipole-flexural wave in a fluid-filled borehole. As a result, the tool effect should be considered during the processing and inversion of the dipole-flexural wave for acoustic properties of shear wave. We show that the presence of the tool not only changes the slowness dispersion of the flexural wave but also results in a shift of its frequency-dependent attenuation toward lower frequencies. Equivalent tool theory (ETT) can realistically model the effect of an acoustic tool on guided wave propagation. With the ETT framework, we develop a unified workflow for estimating both the shear wave slowness and attenuation from dipole array acoustic waveforms. The workflow is an extension of the model-based dispersive processing of dipole logging data. The proposed workflow involves two inversion procedures. By matching the actual dispersion data with the theoretical dispersion predicted by the ETT, we can invert the shear wave slowness and tool parameters. With the estimated shear wave slowness and other borehole parameters, we further calculate the partition coefficients of flexural waves using the ETT. Based on the concept of energy partitioning, we formulate a linear optimization problem and invert for the shear wave attenuation from the frequency-dependent dipole attenuation. We use synthetic and field data to demonstrate the effectiveness and applicability of the developed method. The results show that it is important to incorporate the tool effect when processing dipole acoustic logging data for shear wave slowness and attenuation, especially in a fast formation.

Comparison of Near-Surface Attenuation from Surface Array-Based Seismic Noise Data and Borehole Weak-Motion Recordings at the STIN Test Site in Northeastern Italy

Abstract Seismic wave attenuation and the related shear-wave quality factor (QS) in the near surface are crucial parameters for ground motion simulations and seismic hazard assessments. Although recent approaches developed to calculate QS from seismic noise acquired by surface arrays have been accepted for practice, additional testing and comparison of results estimated using various geophysical methods are still necessary to verify the reliability of such techniques. This work presents the results of an experiment conducted at the STIN site in northeastern Italy, which is equipped with a 100 m deep instrumented borehole. A seismic noise campaign was implemented by installing a temporary independent local surface array of seismological stations. The gathered data were used to initially estimate the shear-wave velocity (VS) profile and frequency-dependent Rayleigh-wave attenuation, and subsequently determine the QS factor via a linearized inversion method. The study compares these findings with the VS and QS values derived from analyzing weak-motion events recorded by two permanent seismic sensors positioned at the top and bottom of the well. The results confirm the potential of the inversion procedure used to obtain QS from local-scale seismic noise arrays as a promising approach for conducting attenuation studies at the local level in less geologically complex sites.

Unveiling attenuation structures in the northern Taiwan volcanic zone.

This cutting-edge study delves into regional magmatism in northern Taiwan through advanced 3-D P- and S-wave frequency-dependent attenuation tomography. Positioned at the dynamic convergence boundary between the Philippine Sea Plate and the Eurasian Plate, Taiwan experiences moderate earthquakes and intriguing volcanic activity, with a focus on the Tatun volcano group. Employing the Formosa seismic array for high-resolution results, our research identifies high-attenuation anomalies (low Q) beneath the northern Taiwan volcanic zone (NTVZ) and offshore submarine volcanoes, indicative of potential hydrothermal activities and magma reservoirs at varying depths. Additionally, we explore low-attenuation anomalies (high Q) in the forearc region of the Ryukyu subduction zone, suggestive of partial saturation linked to serpentinization processes resulting from seawater infiltration or forearc mantle hydration. These findings shed light on the complex geological features and provide essential insights into the crustal properties of northern Taiwan, contributing to a deeper understanding of its magmatic evolution and tectonic processes.

Measurement of frequency-dependent shear wave attenuation coefficients using an oblique incidence pulse-echo ultrasonic method

A pulse-echo oblique incidence technique for determining the frequency-dependent attenuation of ultrasonic shear waves in metallic materials is considered and improved. To measure the attenuation coefficient, the wave signals are measured when the waveform-converted shear waves propagate over different distances. A diffraction correction is introduced to minimize the beam-spreading loss of the wave, and narrowband signals are used to minimize the effects of a downward shift in frequency. The attenuation coefficient is measured at a certain frequency, and experiments are performed over a broad bandwidth range of frequencies; a curve fitting method is then applied to these attenuation values to ensure an accurate estimate of the frequency-dependent shear wave attenuation. Experiments are performed to evaluate the effectiveness of the proposed method, and the frequency-dependent shear attenuation curves for some commonly used metallic materials are obtained. One of the most significant findings from the results is that the shear wave attenuation follows a power law dependence on frequency with exponents between 2 and 3, which lie between the theoretical values of the exponents from the classical stochastic and Rayleigh scattering theories. The effects of grain size on shear wave attenuation are investigated, and a quantitative comparison is drawn between the experimentally observed attenuation and that predicted by the classical theory. The proposed measurement method and the experimental results presented here are expected to provide good references for researchers interested in frequency-dependent shear wave attenuation behavior.

Attenuation characteristics of concrete using smart aggregate transducers: Experiments and numerical simulations of P-wave propagation

Concrete is a highly heterogeneous construction material. Waves that propagate through concrete face significant reflection, scattering, and attenuation issues. Understanding the behavior of waves as they propagate through concrete and arrive at a sensor has generated much attention, especially for developing real-world field applications. In this study, a predictive model of attenuated P-wave propagation using Rayleigh damping is presented. The method used frequency excitations ranging from 20 to 200 kHz and smart aggregates (SAs) were embedded in a concrete specimen to excite and receive P-waves. Moreover, 10 distances were marked opposite the exciter at two propagation paths. In the simulations and experiments, signal processing methods were utilized to extract the first arrival packet for calculating amplitude attenuation. The P-wave damping coefficient was modeled using the multi-physical finite element method, and the results of the predictive model were compared with the experimental results. A discussion on the utilization of frequency-dependent attenuation coefficients was conducted to explore potential P-wave attenuation factors and their respective contributions to the overall attenuation. Numerical studies have demonstrated a strong correlation with the experiments when an appropriate level of material damping coefficient was considered. By enhancing the overall comprehension of the P-wave damping coefficient and attenuation characteristics within concrete, damage detection techniques based on P-waves can be improved.

Dispersive Elastic Moduli and Frequency-Dependent Attenuation due to Wave-Induced Fluid Flow in Metapelite

Dispersive Elastic Moduli and Frequency-Dependent Attenuation due to Wave-Induced Fluid Flow in Metapelite

Enhancing Structural Health Monitoring with Acoustic Emission Sensors: A Case Study on Composites under Cyclic Loading.

This study conducts an in-depth analysis of the failure behavior of woven GFRP under cyclic loading, leveraging AE sensors for monitoring damage progression. Utilizing destructive testing and AE methods, we observed the GFRP's response to varied stress conditions. Key findings include identifying distinct failure modes of GFRP and the effectiveness of AE sensors in detecting broadband frequency signals indicative of crack initiation and growth. Notably, the Felicity effect was observed in AE signal patterns, marking a significant characteristic of composite materials. This study introduces the Ibe-value, based on statistical parameters, to effectively track crack development from inception to growth. The Ibe-values potential for assessing structural integrity in composite materials is highlighted, with a particular focus on its variation with propagation distance and frequency-dependent attenuation. Our research reveals challenges in measuring different damage modes across frequency ranges and distances. The effectiveness of Ibe-values, combined with the challenges of propagation distance, underscores the need for further investigation. Future research aims to refine assessment metrics and improve crack evaluation methods in composite materials, contributing to the field's advancement.

Frequency-dependent velocities and attenuations in fluid-saturated rocks: Fractures aligned in isotropic medium with random pore shape

The modeling of seismic wave velocity and attenuation is crucial for the interpretation of seismic data. In fluid-saturated rocks, the presence of fractures causes dispersion and attenuation of seismic waves due to fluid flow between cracks and pores. Meanwhile, the parallel distribution of cracks is an important reason for the anisotropy of rocks. Combined with poroelasticity theory, we extend Chapman’s model to media with penny-shaped fractures and an isotropic porous matrix, for which no restrictions are placed on the pore shape of the matrix. We conduct simulations at different frequencies to indicate the predicted anisotropy of velocity and attenuation. The variation of velocities and attenuations with orientation angle is consistent with Chapman’s model. Because a typical porous matrix is used in the new model, predicted velocities are lower than those under assumption of spherical matrix pores. Then, we analyze the effect of pore compressibility of the matrix on the velocity and attenuation. We also conduct discussions about the effect of different porosities on velocity and attenuation. The analysis indicates that the predictions of the new model are more closely related to the modulus of the porous matrix than Chapman’s model. The strength of fluid flow in the new model also will change with the matrix pores. The comparison of the new model and Chapman’s model with experimental data indicates that the new model is in better agreement with the experimental results.

Filter-based solutions for finite and infinite edge diffraction

Sound diffraction occurs at (building) corners, objects and openings, prominently affecting occluded and reflected sounds. Here, a physically-based, parametric filter model for diffraction at arbitrary wedges is presented. The model connects existing high-frequency asymptotic and exact solutions in geometrical acoustics using up to four half-order low-pass filters. Compact expressions for the transfer function and impulse response of the singly diffracted field are derived, with errors below 0.1 dB. A filter modification is suggested to account for the exact solution at low frequencies. The filter solution is further simplified to approximate the spectral effects of diffraction from finite wedges and objects composed thereof, referred to as universal diffraction filter approximation (UDFA). A computationally highly-efficient recursive filter implementation is presented and it is demonstrated that diffraction from flat finite objects like plates or apertures can be closely approximated. To account for effects of higher-order diffraction at the object, a heuristic filter extension is suggested. The presented filter-based diffraction solution is suited for the prediction and simulation of sound propagation including non-specular reflections in architectural acoustics. For virtual acoustics, UDFA provides an efficient and accurate approximation of edge diffraction to account for perceptually relevant frequency-dependent attenuation, extendable to arbitrary objects.

Evaluation of ultrasound sensors for transcranial photoacoustic sensing and imaging

Photoacoustic imaging through skull bone causes strong attenuation and distortion of the acoustic wavefront, which diminishes image contrast and resolution. As a result, transcranial photoacoustic measurements in humans have been challenging to demonstrate. In this study, we investigated the acoustic transmission through the human skull to design an ultrasound sensor suitable for transcranial PA imaging and sensing. We measured the frequency dependent losses of human cranial bones ex vivo, compared the performance of a range of piezoelectric and optical ultrasound sensors, and imaged skull phantoms using a PA tomograph based on a planar Fabry–Perot sensor. All transcranial photoacoustic measurements show the typical effects of frequency and thickness dependent attenuation and aberration associated with acoustic propagation through bone. The performance of plano-concave optical resonator ultrasound sensors was found to be highly suitable for transcranial photoacoustic measurements.

The dynamics of unstable waves in sea ice

Wave and sea ice properties in the Arctic and Southern Oceans are linked by feedback mechanisms, therefore the understanding of wave propagation in these regions is essential to model this key component of the Earth climate system. The most striking effect of sea ice is the attenuation of waves at a rate proportional to their frequency. The nonlinear Schrödinger equation (NLS), a fundamental model for ocean waves, describes the full growth-decay cycles of unstable modes, also known as modulational instability (MI). Here, a dissipative NLS (d-NLS) with characteristic sea ice attenuation is used to model the evolution of unstable waves. The MI in sea ice is preserved, however, in its phase-shifted form. The frequency-dependent dissipation breaks the symmetry between the dominant left and right sideband. We anticipate that this work may motivate analogous studies and experiments in wave systems subject to frequency-dependent energy attenuation.

Snow Attenuation of Infrasound Signals and Wind Noise

Abstract Infrasound monitoring of geophysical and human-sourced activity, such as explosions, eruptions, earthquakes, and avalanches, may be impacted by burial of sensors in a snowpack. We studied the frequency-dependent attenuation of sound, vertical sound speed, and wind noise reduction in a natural snowpack using earthquakes as a natural source of infrasound. Our experiment used a 2 m vertical distribution of sensors deployed during the 2021–2022 winter in the Sawtooth mountains of Idaho. We recorded 38 earthquakes and their primary infrasound propagating vertically upward through the snow. For these events, average attenuation appeared negligible between 0 and 8 Hz, rose to 0.1 dB/cm at ∼12 Hz, and remained at this level for higher frequencies. Using timing lags across the vertical profile the speed of infrasound in the snow was measured at 160 ± 51 m/s, significantly subsonic and indicative of pore-space waves. Finally, we quantified the significant reduction in the amount of background noise measured for snow-buried compared with free-air sensors. The 24 dB of reduction of noise observed for high wind speed conditions was evident with only 20 cm of snow burial and demonstrates the powerful capability of snowpack as a noise reduction filter. This study provides a clearer understanding of how snow burial filters infrasound and minimizes noise levels and has implications for monitoring of both natural and human-made hazards.

Machine learning regression implementation for high-frequency seismic wave attenuation estimation in the Aswan Reservoir area, Egypt

Attenuation characteristics have been estimated to understand the effect of the heterogeneity in the tectonically active Aswan Reservoir, the southern part of Egypt using data collected by a ten-station local seismological network operating across the reservoir. The quality factor was estimated from 350 waveform spectra of P- and S-waves from 50 earthquakes. By applying a spectral ratio technique to bandpass-filtered seismograms, obtained results show variations in both P-waves attenuation (Q_alpha) and corresponding S-waves (Q_beta) as a function of frequency, according to the power law Q=Q_0 times f^n, with n ranging between 0.85 and 1.19 for P-waves and between 0.92 and 1.18 for S-waves. A supervised machine learning algorithm known as Orthogonal distance regression was utilized to fit the attenuation power law functions. Estimates of Q_alpha and Q_beta show a clear dependence on frequency. The frequency-dependent attenuation is found to be Q_alpha = (11.22 pm 2.2) times f^{(1.09 pm 0.07)} and Q_beta = (9.89 pm 1.89) times f^{(1.14 pm 0.07)} for P- and S-waves, respectively. The average ratio Q_alpha /Q_beta is higher than unity, which is commonly observed in tectonically active regions characterized by a high degree of heterogeneity of the crustal structure of the area. Final results indicate that seismic wave attenuation in the AHDR region is highly frequency-dependent. Moreover, estimated low values of Q_0 clearly highlight the heterogeneity of the AHDR with considerably high seismic activity. These findings will be useful in any future assessment of seismic hazards and the damage pattern of earthquakes.

Acoustic Wave Reflection in Water Affects Underwater Wireless Sensor Networks.

The phenomenon of acoustic wave reflection off fluid-solid surfaces is the focus of this research. This research aims to measure the effect of material physical qualities on oblique incidence acoustic attenuation across a large frequency range. To construct the extensive comparison shown in the supporting documentation, reflection coefficient curves were generated by carefully adjusting the porousness and permeability of the poroelastic solid. The next stage in determining its acoustic response is to determine the pseudo-Brewster angle shift and the reflection coefficient minimum dip for the previously indicated attenuation permutations. This circumstance is made possible by modeling and studying the reflection and absorption of acoustic plane waves encountering half-space and two-layer surfaces. For this purpose, both viscous and thermal losses are taken into account. According to the research findings, the propagation medium has a significant impact on the form of the curve that represents the reflection coefficient, whereas the effects of permeability, porosity, and driving frequency are relatively less significant to the pseudo-Brewster angle and curve minima, respectively. This research additionally found that as permeability and porosity increase, the pseudo-Brewster angle shifts to the left (proportionally to porosity increase) until it reaches a limiting value of 73.4 degrees, and that the reflection coefficient curves for each level of porosity exhibit a greater angular dependence, with an overall decrease in magnitude at all incident angles. These findings are given within the framework of the investigation (in proportion to the increase in porosity). The study concluded that when permeability declined, the angular dependence of frequency-dependent attenuation reduced, resulting in iso-porous curves. The study also discovered that the matrix porosity largely affected the angular dependency of the viscous losses in the range of 1.4 × 10-14 m2 permeability.

A Correction Method for the Measurement of Frequency-Dependent Attenuation Coefficient With Curved Surface Specimens Using Normal Contact Transducer

The ultrasonic pulse-echo technique has been widely employed for the measurement of the frequency-dependent attenuation coefficient in polycrystalline metals. However, the nonuniform thickness of the coupling layer between the transducer piston and the curved surface is inevitable for curved specimens, resulting in a significant overestimation. In addition, the curved surface also affects the diffraction loss caused by the divergence and convergence of ultrasonic beams during the propagation path. In this study, a correction method is proposed for the experimental calculation of the frequency-dependent attenuation with the curved surface components using a contact transducer. First, with the analysis of the nonuniform coupling layer created by the curved surface and transducer piston, the integral over the effective cross-sectional area is introduced to determine the reflection coefficient. Second, an equivalent rectangular transducer sound field model is proposed to calculate the diffraction loss for different curvatures and propagation distances based on the multi-Gaussian beam (MGB) theory. Then, a correction model is established to compensate for the deviation caused by the curved surfaces. To verify the feasibility of the proposed method, two cylindrical bars and five blanks with different curvatures were designed. The experimental results show that the proposed correction method can effectively eliminate the deviation caused by the curved surface and improve the stability of measurement. With the correction, the variation of the attenuation spectrum for the curved specimens is reduced by approximately 5%. This facilitates researchers to better develop and use frequency-dependent attenuation coefficients of materials for further applications.

Fault Damage Zone Effects on Ground Motions during the 2019 Mw 7.1 Ridgecrest, California, Earthquake

ABSTRACT We have simulated 0–3 Hz deterministic wave propagation in the Southern California Earthquake Center Community Velocity Model (CVM) version CVM-S4.26-M01 for the 2019 Mw 7.1 Ridgecrest earthquake. A data-constrained high-resolution fault zone model (Zhou et al., 2022) is incorporated into the CVM to investigate the effects of the near-fault low-velocity zone (LVZ) on the resulting ground motions, constrained by strong-motion data recorded at 161 stations. The finite-fault source used for the simulation of the Ridgecrest event was obtained from the Liu et al. (2019) kinematic inversion, enriched by noise following a von Karman correlation function above ∼1 Hz with a f−2 high-frequency decay. Our results show that the heterogeneous near-fault LVZ inherent to the fault zone structure significantly perturbs the predicted wave field in the near-source region, in particular by more accurately generating Love waves at its boundaries. The fault zone decreases the 0.1–0.5 Hz mean absolute Fourier amplitude spectrum bias to seismic recordings for all sites in the model and in the Los Angeles basin area (∼200 km from the source) by 16% and 26%, respectively. The fault zone structure generally improves modeling of the long-period features in the data and lengthens the coda-wave trains, in better agreement with observations. The favorable fit to data was obtained with a model including high-resolution surface topography, a 700-m-thick geotechnical layer and frequency-dependent anelastic attenuation in the model domain, with QS=0.1VS and QS(f)=0.1VSf0.5 (VS in m/s) for frequencies lower and higher than 1 Hz, respectively. We recommend that a data-constrained fault zone velocity structure, where available, be included in ground-motion modeling to obtain the least-biased fit to observed seismic data.

Phase analysis of signals using frequency-dependent attenuation for measurements of seismic waves

Attenuation refers to any decrease in the power of a propagated signal through a medium. Attenuation measurement techniques include ultrasonic, resonance bar, and stress-strain methods. The stress-strain method measures elastic and viscoelastic properties in the seismic frequency range. The signals received via attenuation measurement systems using the stress-strain method can be considerably weak. Moreover, the noise in these signals causes errors when estimating the signal phase-angle difference between the sample signal and probe signal, thereby reducing system precision and measurement accuracy. Accurate measurements of such phase differences are essential to the measurement of attenuation. A seismic-wave attenuation with frequency-dependent measurement based on the stress-strain method and digital signal processing techniques has been performed. The system estimates the attenuation of a rock by measuring the phase shift in the stress-strain cycle. As a preprocessing method, the finite impulse response band-pass filters are designed to eliminate the influence of noise and direct current offset while ensuring that the phase difference of the measured signal remains unchanged. Three methods for phase difference estimation, i.e., crosscorrelation, fast Fourier transform (FFT), and Hilbert transform are compared, for different signal-to-noise ratios, sampling frequencies, data sample lengths, and true phase differences. The results find that the phase difference estimation based on FFT is the best among all three methods and can effectively improve the precision of the experimental results. Simulation and measurement results further indicate that the attenuation measurement system achieves stable and reliable attenuation measurements in the range of 3–2000 Hz.

Lateral Variations of Attenuation in the Crust of Alaska Using Lg Q Tomography

ABSTRACT We have conducted a crustal seismic (QLg) attenuation tomography study across Alaska using recordings from the EarthScope USArray from 2014 to 2019. The resolving power of the inversion is 150 × 150 km for most of Alaska, and it is 75 × 75 km in central and southern Alaska. Numerous fault systems and high mountain ranges are present across Alaska and accommodate compression in the north–south direction and shearing of southern Alaska toward the west. These mountain ranges include the Brooks range in the north, the Alaska range in central Alaska, and the Aleutian range in the southwest. The average LgQ for all of Alaska is significantly higher than in the western United States and Canada. This lower average attenuation impacts seismic hazard estimates for the region. According to the tomographic results, we see a significant variation of the QLg values from low to high across the southern part of the Brooks range. Also, we found higher attenuation in the southeast region of Alaska, where the Wrangell volcanoes are located. Moreover, we see an area of lower attenuation associated with weak frequency dependence in the south-central region of Alaska next to Anchorage. Another anomaly with lower attenuation can be seen extending from central Alaska to southeast Alaska, possibly associated with the Yukon–Tanana terrane. There are a few areas like southwest Alaska associated with the Togiak terrane and an area next to Fairbanks in Alaska’s interior that shows lower attenuation with lower frequency dependence and higher attenuation with higher frequency dependence, respectively, for low frequencies up to 3 Hz. Our model’s highest η zones (η≳95) are mostly confined to major tectonic terranes and other major tectonic elements such as faults and fractures. Regional variations in crustal attenuation can impact local seismic hazard estimates if incorporated into the hazard analysis.

A Comparison of the Performance of Four Acoustic Modulation Techniques for Robot Communication in Pipes

Autonomous robotics is an emerging technology for the inspection of a vast network of underground pipes. Communication between autonomous robots is essential to optimise their efficiency and network coverage. However, sending a message acoustically is not a well-researched topic because most of the existing literature is devoted to the study of the acoustic properties of the pipe for the purpose of sensing rather than communication. In particular, the influence of multi-modal propagation and background noise on the quality of acoustic communication in pipes has not been well understood. This paper studies the performance of four standard acoustic communication techniques in a dry drainage pipe to fill this knowledge gap. The noise resistance, communication range and data rate of these techniques are estimated through numerical simulations and laboratory experiments. It has been found that the techniques based on shift keying requires at least 5--10 dB signal to noise ratio (SNR) to function properly while the chirp linear frequency modulation technique can operate reliably with SNR = 0 dB or event lower SNR. The results also suggest that the multi-modal propagation in the pipe has significant effects on the package error rate. The frequency dependent sound attenuation in the pipe also affects the communication range and data rate. In particular, for a 150 mm diameter dry pipe the maximum robot operation distance is likely to be limited to 50--100 m with the highest carrier frequency of around 10 kHz and data rates below 6300 bps. The results of this work pave the way to the development of acoustic communication modules to be deployed on tetheless robots designed to inspect a buried pipe network autonomously and collaboratively.

Lamb waves in thermoplastic polymer plates: An application to monitoring

Thin thermoplastic polymer components are widely used in different fields of engineering, including high-technology industries such as automotive or energy. Due to the rapid technological development in these industries, there is an increased demand for polymer components to achieve advanced functionalities, such as the continuous monitoring of their structural health. In this work, we propose to take advantage of elastic guided waves, which are both emitted and measured using arrays of transducers integrated within the structure. This application requires first investigating the Lamb waves in these attenuating and heterogeneous materials. To that end, we estimate the dispersion curves of Lamb waves using a laser vibrometer. A transversely isotropic material model and a fitting algorithm allow for estimating the elastic parameters of the specimens. Then, for each mode, the frequency-dependent attenuation is evaluated. Finally using both theoretical models and experimental analysis, we evaluate the sensitivity of the guided waves to asses various structural changes in the thermoplastic polymer components such as temperature or the presence of contaminants.