Frequency-dependent Attenuation Research Articles

Evaluation and modeling of velocity dispersion and frequency-dependent attenuation in gas hydrate-bearing sediments

Wave velocity and attenuation of gas hydrate-bearing samples are often extrapolated from ultrasonic to lower seismic/sonic frequencies, but the impact of measurement frequency on these properties is rarely studied. This study evaluates velocity dispersion and frequency-dependent attenuation in gas hydrate-bearing sediments (GHBS) by comparing vertical seismic profile (VSP) and sonic logging data from the Nankai Trough and Mallik field. We also employ rock physics modeling to simulate the velocity dispersion and frequency-dependent attenuation at both sites. The results show strong velocity dispersion and frequency-dependent attenuation in the Nankai Trough, attributed to thin, low-saturation hydrate intervals. In contrast, the Mallik field exhibits weak dispersion and frequency dependence, likely due to thick, highly saturated hydrate layers. A compilation of global hydrate reservoir attenuations indicates frequency dependence, with a peak in the sonic logging range, likely due to pore-scale hydrate effects. These findings emphasize the necessity of considering the effect of measurement frequency when performing time-to-depth conversion for seismic data based on the sonic velocity at higher frequencies, particularly for thin and lowly saturated hydrate layers, thereby improving the accuracy of hydrate reservoir characterization.

Calibration of Frequency-Dependent Wave Speed and Attenuation in Water Pipes Using a Dual-Sensor and Paired-IRF Approach

Calibration of Frequency-Dependent Wave Speed and Attenuation in Water Pipes Using a Dual-Sensor and Paired-IRF Approach

Adaptive-coefficient finite difference frequency domain method for time fractional diffusive-viscous wave equation arising in geophysics

The diffusive-viscous wave (DVW) equation is a widely used model to describe frequency dependent attenuation of seismic wave in fluid-saturated porous medium. In this paper taking power law frequency dependent attenuation into account, we first introduce a modified DVW equation (time fractional DVW equation) in which the first order temporal derivative of viscous term is replaced with a fractional order temporal derivative. In consideration of that most of the existing numerical simulations for seismic wave equations are based on time domain methods and truncation with some specific boundary conditions, we incorporate the absorbing boundary condition as complex-frequency-shifted (CFS) perfectly matched layer (PML) into the time fractional DVW equation, and then develop an adaptive-coefficient (AC) finite difference frequency domain (FDFD) method for numerical simulation. The corresponding analytical solution for homogeneous time fractional DVW equation is provided for model validation, and the effectiveness of the developed AC FDFD method is verified by some numerical examples including the homogeneous model and the layered model. Numerical results show that AC FDFD method is more accurate than the traditional 2nd-order FDFD method for numerical modeling of time fractional DVW equation with CFS PML absorbing boundary condition, while requiring similar computational costs.

Development of a Semi-Autonomous Pulse and Receive Concrete Inspection System

Concrete structures are being subjected to increasing loads and used beyond their intended lifespan. When combined with operators shrinking maintenance budgets it is imperative structures are monitored for damage. Acoustic Emission (AE) and AE Tomography offer a method for damage detection and characterisation. However, they are encumbered by their equipment and setup requirements, and best used on areas where damage is already known to have occurred. An autonomous pulse catch system could be used to identify these areas. To explore the potential of such a system, seven concrete beams differentiated by their aggregate size were tested using an automated pulse and receive system. The effect of aggregate size, and pulse frequency on attenuation and wavespeed are investigated. The pulse regime consisted of narrowband pulses ranging from 30 kHz to 500 kHz. The results show that high frequency pulses experienced greater attenuation than low frequency pulses. Whilst a link appears between the size of the aggregate and the rate of attenuation of high frequency signals. A strong negative correlation between amplitude loss and pulse frequency was observed. For the specimen containing coarse aggregate, pulse velocity was constant between 100 kHz and 500 kHz, whereas specimens containing coarse aggregate experienced frequency dependant attenuation. This testing shows the significant potential for an automated pulse and receive system, which could lead to the development of an autonomous health monitoring system. In addition, the approach can be instrumental in developing large data sets, that can be used in Machine Learning processes, to develop a deeper understanding of AE signal propagation in concrete materials.

Machine learning classification of permeable conducting spheres in air and seawater using electromagnetic pulses

Abstract This paper presents machine learning classification on simulated data of permeable conducting spheres in air and seawater irradiated by low frequency electromagnetic pulses. Classification accuracy greater than 90% was achieved. The simulated data were generated using an analytical model of a magnetic dipole in air and seawater placed 1.5–3.5 m above the center of the sphere in 50 cm increments. The spheres had radii of 40 cm and 50 cm and were of permeable materials, such as steel, and non-permeable materials, such as aluminum. A series RL circuit was analytically modeled as the transmitter coil, and an RLC circuit as the receiver coil. Additive white Gaussian noise was added to the simulated data to test the robustness of the machine learning algorithms to noise. Multiple machine learning algorithms were used for classification including a perceptron and multiclass logistic regression, which are linear models, and a neural network, 1D convolutional neural network (CNN), and 2D CNN, which are nonlinear models. Feature maps are plotted for the CNNs and provide explainability of the salient parts of the time signature and spectrogram data used for classification. The pulses investigated, which expand the literature, include a two-sided decaying exponential, Heaviside step-off, triangular, Gaussian, rectangular, modulated Gaussian, raised cosine, and rectangular down-chirp. Propagation effects, including dispersion and frequency dependent attenuation, are encapsulated by the analytical model, which was verified using finite element modeling. The results in this paper show that machine learning methods are a viable alternative to inversion of electromagnetic induction (EMI) data for metallic sphere classification, with the advantage of real-time classification without the use of a physics-based model. The nonlinear machine learning algorithms used in this work were able to accurately classify metallic spheres in seawater even with significant pulse distortion caused by dispersion and frequency dependent attenuation. This paper presents the first effort towards the use of machine learning to classify metallic objects in seawater based on EMI sensing.

Frequency-dependent shear wave attenuation across the Central Anatolia region, Türkiye

Abstract. The Central Anatolian Plateau with its volcanic provinces represents a broad transition zone between the compressional deformation in the east and the extensional regime in the west. The Central Anatolian Fault Zone separates the Kırşehir Block in the north and the Anatolide–Tauride Block in the south within the plateau. A proper understanding of physical properties such as seismic attenuation in the crustal volume of this region can provide hints toward the possible source for the geodynamic events in the past and present that likely lead to the observed deformation. In order to model intrinsic and scattering attenuation separately, we perform a nonempirical coda-wave modeling approach in which a fitting process between observed and synthetic coda-wave envelopes is performed for each earthquake in multiple frequency bands. Here, the acoustic radiative transfer theory, assuming multiple isotropic scattering, was utilized for the forward modeling of the synthetic coda-wave envelopes of local earthquakes. Our findings generally highlight the prominent nature of intrinsic attenuation over scattering attenuation, implying the presence of thick volcanic rocks with relatively high attenuation values beneath Central Anatolia. Overall, the spatial distribution of the attenuation at varying frequencies marks the Kırşehir Massif distinctively with its considerable high-attenuating character. Our findings, combined with early seismological and geo-electrical models, suggest a possible partial melt beneath most of the Central Anatolian Volcanic Province, and the resultant zones of elevated fluid-rich content exhibit high and dominant intrinsic attenuation. To the southeast, a gradual decrease in the observed attenuation coincides with the Central Taurus Mountains where high altitude is considered to be evolved following the slab break-off and resulting mantle upwelling.

Investigation of Viscoelastic Guided Wave Properties in Anisotropic Laminated Composites Using a Legendre Orthogonal Polynomials Expansion-Assisted Viscoelastodynamic Model.

This study investigates viscoelastic guided wave properties (e.g., complex-wavenumber-, phase-velocity-, and attenuation-frequency relations) for multiple modes, including different orders of antisymmetric, symmetric, and shear horizontal modes in viscoelastic anisotropic laminated composites. To obtain those frequency-dependent relations, a guided wave characteristic equation is formulated based on a Legendre orthogonal polynomials expansion (LOPE)-assisted viscoelastodynamic model, which fuses the hysteretic viscoelastic model-based wave dynamics and the LOPE-based mode shape approximation. Then, the complex-wavenumber-frequency solutions are obtained by solving the characteristic equation using an improved root-finding algorithm, which leverages coefficient matrix determinant ratios and our proposed local tracking windows. To trace the solutions on the dispersion curves of different wave modes and avoid curve-tracing misalignment in regions with phase-velocity curve crossing, we presented a curve-tracing strategy considering wave attenuation. With the LOPE-assisted viscoelastodynamic model, the effects of material viscosity and fiber orientation on different guided wave modes are investigated for unidirectional carbon-fiber-reinforced composites. The results show that the viscosity in the hysteresis model mainly affects the frequency-dependent attenuation of viscoelastic guided waves, while the fiber orientation influences both the phase-velocity and attenuation curves. We expect the theoretical work in this study to facilitate the development of guided wave-based techniques for the NDT and SHM of viscoelastic anisotropic laminated composites.

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 waves in a fluid-filled borehole. As a result, the tool effect should be considered during the processing and inversion of the dipole-flexural waves for the acoustic properties of a shear wave (S 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. The 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 the S-wave slowness and attenuation from dipole array acoustic waveforms. The workflow is an extension of the model-based dispersive processing of dipole logging data. Our workflow involves two inversion procedures. By matching the actual dispersion data with the theoretical dispersion predicted by the ETT, we can invert the S-wave slowness and tool parameters. With the estimated S-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 S-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 S-wave slowness and attenuation, especially in a fast formation.

On the frequency-dependent attenuation in low-frequency mechanical testing of rock samples

On the frequency-dependent attenuation in low-frequency mechanical testing of rock samples

3D attenuation tomography of the Uttarakhand, NW Himalaya: Linkage to fluid or partial melt zones - Seismic hazard

This work proposes the shear-wave attenuation tomography of the Garhwal and Kumaun regions, Uttarakhand Himalaya, to investigate the crustal state. Based on attenuation characteristics, the high attenuated layer identified starts at ∼10 km in the Garhwal region and ∼5 km in the Kumaun region. The obtained model revealed that quality factor (Q) values vary from 16 to 664 and 49 to 866 at 1 Hz frequency for the Kumaun and Garhwal regions, respectively. The high attenuation rate (1/Q) in the Kumaun region compared to the Garhwal region may be due to the high attenuated layer at a shallower depth in the Kumaun region. The comparatively low attenuation rate of the Garhwal characterizes it as a region with high seismic hazard potential. Pioneeringly, layered frequency-dependent attenuation models are proposed up to a depth of 30 km for six different layers with 5 km thickness each, which will provide new insight into seismic hazard evaluation.

Spatial variation of body wave attenuation in Garhwal-Kumaun Himalaya region, India

We have investigated the spatial variation of body wave attenuation in Garhwal-Kumaun Himalaya region from the datasets of 465 well located earthquakes, recorded at 52 broadband stations between 2017 and 2020. The body wave attenuation parameters QP and QS were estimated at each station by applying the extended coda normalization method for five different central frequencies ranging from 1.5 to 18 Hz. Strong frequency-dependent body wave attenuation was observed at each station over the whole region. Also, we found a significant variation of QP and QS from north to south which is consistent with geotectonic diversity beneath the study region. We have also made separate estimations of frequency-dependent relations for Garhwal and Kumaun Himalaya region in order to investigate the lateral variation in attenuation characteristics, and obtained the frequency-dependent relations as follows: QP=30±3f1.05±0.05, QS=143±20f0.88±0.07 for the Garhwal Himalaya region and QP=31±1f1.09±0.02, QS=121±11f1.00±0.04 for the Kuamun Himalaya region. Obtained Q values indicate strong body wave attenuation for both the region with no significant lateral variation. It may suggest the presence of crustal level folding, faulting, aqueous fluids, and metamorphic fluids below both the regions. Also, the ratios of QS/QP are high (>1) for the entire analyzed frequency range, suggesting a significant level of heterogeneity and tectonic complexities in the crust of the study region.

An explicit granular-mechanics approach to marine sediment acoustics.

Here, we theoretically and computationally study the frequency dependence of phase speed and attenuation for marine sediments from the perspective of granular mechanics. We leverage recent theoretical insights from the granular physics community as well as discrete-element method simulations, where the granular material is treated as a packing of discrete objects that interact via pairwise forces. These pairwise forces include both repulsive contact forces as well as dissipative terms, which may include losses from the fluid as well as losses from inelasticity at grain-grain contacts. We show that the structure of disordered granular packings leads to anomalous scaling laws for frequency-dependent phase speed and attenuation that do not follow from a continuum treatment. Our results demonstrate that granular packing structure, which is not explicitly considered in existing models, may play a crucial role in a complete theory of sediment acoustics. While this simple approach does not explicitly treat sound propagation or inertial effects in the interstitial fluid, it provides a starting point for future models that include these and other more complex features.

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.

Influence of the liquid ionic strength on the resonance frequency and estimated shell parameters of lipid-coated microbubbles

Measurement of the resonance frequency and shell properties of coated microbubbles (MBs) is important in understanding and optimizing their response to ultrasound. In many applications MBs are in ionic liquids; however, the influence of the medium charges on the MB behavior is not well investigated. This study aims to measure the medium charge interactions with MBs by measuring the frequency-dependent attenuation of the same size MBs in mediums of varying charge density. In-house lipid-coated MBs were size isolated to a mean size of 2.35 μm using differential centrifugation. MBs were suspended in distilled water (DW), Phosphate-Buffered Saline solution (PBS1×) and PBS10×. The frequency-dependent attenuation of the MBs solutions was measured using a system of two aligned 100% bandwidth transducers with 10 MHz center frequency. The MB shell properties were estimated by fitting the linear equation to experiments. With increasing salinity, the frequency of the peak attenuation decreased (13, 7.5 and 6.25 MHz in DW, PBS1× and PBS-10×, respectively) and attenuation peak increased (∼140%). Estimated MBs shell elasticity decreased by 64% between DW and PBS-1× and 36% between PBS-1x and PBS-10x. The estimated shell viscosity reduced by ∼40% between DW and PBS-1× and 42% between PBS-1× and PBS-10×. The significant reduction in the fitted stiffness and viscosity is possibly due to the formation of a densely charged layer around the shell and requires proper inclusion in the related MB models.

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

Measurement of ultrasonic pulse arrival time by constructing a signal model to determine its propagation velocity

The paper considers several methods of measuring the arrival time of ultrasonic pulses. A method for determining the pulse arrival time based on the construction of a signal model with an adaptive dictionary and the search for the minimum of the target function by the quantum swarm intelligence method is proposed. The results of numerical and modeling experiments on measuring the propagation velocity of ultrasonic waves in various samples are presented. It is shown that the proposed method of determining the time of pulse arrival is more resistant to distortion of the echo waveform arising due to frequency-dependent attenuation in the material of the control object.

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.