Frequency-dependent Elastic Properties Research Articles

Frequency-dependent elastic properties of fracture-induced VTI rocks in a fluid-saturated porous and microcracked background

Fractures are widely distributed underground. The stiffness matrix of fractured rocks has been extensively investigated in a fluid-saturated porous background medium. However, the existing stiffness models only incorporate the attenuation mechanism of wave-induced fluid flow (WIFF). For macroscopic fractures, the elastic scattering (ES) of fractures cannot be ignored. To alleviate this issue, a frequency-dependent stiffness matrix model is developed, including the mesoscopic WIFF between fractures and background (FB-WIFF), the microscopic squirt flow, and the macroscopic ES from the fractures. By combining the far-field scattered wavefields of normal incident P and SV waves with the linear slip theory, the dynamic full-stiffness matrices for fracture-induced effective vertically transversely isotropic rocks in a fluid-saturated porous and microcracked background are derived. Then, the P, SV, and SH-wave velocities and attenuation can be obtained through the Kelvin-Christoffel equation. The results indicate that the FB-WIFF mechanism significantly affects the velocities and attenuation of the P and SV waves but has almost no effect on the SH wave, whereas the squirt flow and ES mechanisms affect the velocities and attenuation of all the P, SV, and SH waves. For validation, the model is compared with existing models and previous experimental ultrasonic data.

On the numerical modeling of poroelastic layers in spring-mass systems

The proper modeling of noise control treatments is a key factor in the robustness of the numerical prediction of the sound transmission under airborne excitation. Typical acoustic treatments applied in the industry include one or more layers of poroelastic materials. These are particularly challenging to model since they exhibit a complex, high-dissipative behavior that is not only dependent on the material properties, but also on the interactions with other components. In this article, three different material formulations derived from the poroelasticity theory are employed to describe the poroelastic middle layer of a spring-mass system. The calculated results are contrasted with data measured in a window test bench. It is observed that for the description of softer materials the full poroelastic formulation provides the most accurate results. Conversely, a description as an elastic solid yields the best results for stiffer poroelastic layers. Moreover, the utilization of frequency-dependent elastic properties improves the match between numerical and experimental results, especially in the high-frequency range.

Vibro-acoustic optimisation of Wood Plastic Composite systems

“Wood Plastic Composite” or WPC is becoming increasingly popular in outdoor applications because of the advantage of a better durability in wet environments compared to natural wood. The possibility of using WPC as a sound barrier, or as façade cladding, is investigated in this paper. The sound transmission loss (TL) of an orthotropic WPC panel, obtained by coupling together several boards, is computed by means of the transfer matrix method. The plate is modelled as a thin orthotropic layer, described by frequency dependent elastic properties. A numerical procedure, based on a finite element simulation, is proposed in order to determine the stiffness properties along the principle direction of the panel. The reliability of this approach is verified by comparing the numerical results with the experimental stiffness measured on a WPC beam. The orthotropic behaviour is approximated by an elliptic interpolation of the flexural stiffness along the two principle directions, based on a simplified assumption which considers the in-plane shear modulus proportional to the orthotropic elastic moduli. The model based within the transfer matrix method framework is validated with the experimental transmission loss measured on a WPC panel in a reverberant room. Finally, the possibility of increasing the acoustic performance of WPC structures by optimising their cross-section is investigated.

Elastic wave manipulation by using a phase-controlling meta-layer

In this work, a high pass meta-layer for elastic waves is proposed. An elastic phase-controlling meta-layer is theoretically realized using parallel and periodically arranged metamaterial sections based on the generalized Snell's law. The elastic meta-layer is composed of periodically repeated supercells, in which the frequency dependent elastic properties of the metamaterial are used to control a phase gradient at the interface between the meta-layer and conventional medium. It is analytically and numerically demonstrated that with a normal incident longitudinal wave, the wave propagation characteristics can be directly manipulated by the periodic length of the meta-layer element at the sub-wavelength scale. It is found that propagation of the incident wave through the interface is dependent on whether the working wavelength is longer or shorter than the periodic length of the meta-layer element. Specifically, a mode conversion of the P-wave to an SV-wave is investigated as the incident wave passes through the meta-layer region. Since the most common and damaging elastic waves in civil and mechanical industries are in the low frequency region, the work in this paper has great potential in the seismic shielding, engine vibration isolation, and other highly dynamic fields.

The attenuation performance of locally resonant acoustic metamaterials based on generalised viscoelastic modelling

Acoustic metamaterials are known as a promising class of materials interacting with acoustic and/or elastic waves. Band gap formation is one of the most spectacular phenomena that they exhibit. Different ways to broaden the attenuated frequency ranges are still being actively explored. It turns out that material damping through intrinsic viscoelastic material behaviour, if accurately tailored, may contribute to the enhancement of the performance of a properly designed acoustic metamaterial. In this study, a locally resonant acoustic metamaterial with periodic multicoated inclusions with viscoelastic layers is investigated. Multiple attenuation regimes obtained with the considered geometry are joined for a certain level of viscosity of the coating layer. The analysis is performed using a generalised Maxwell model, which allows for an accurate description of nonlinear frequency dependent elastic properties, and thus is widely used to model the behaviour of many polymeric materials in a realistic way. The study reveals that variation of the material parameters of the rubber coating with respect to frequency influences not only the position of the band gaps but also the effectiveness of the wave attenuation in the frequency ranges around the band gaps.

An Improved Method for the Modeling of Frequency-Dependent Amplitude-Versus-Offset Variations

A proper description of the frequency-dependent seismic amplitude variation versus offset (AVO) responses should consider the effect of both the layered structure of a reservoir and the dispersive and attenuated property of the media in the reservoir. We propose an improved method to seamlessly link the rock physics modeling and the calculation for frequency-dependent reflection coefficients based on propagator matrix method. The improved AVO modeling method is implemented in frequency-wavenumber domain, and can accurately considers dispersion and attenuation that described by complex and frequency-dependent elastic properties predicted by rock physic models. Therefore, the improved method avoids errors resulting from truncating imaginary parts of the elastic properties as adopted by the conventional Zoeppritz-equation-based method. Moreover, the proposed method considers the intrinsic contribution of the layered structure to frequency-dependence of AVO responses, which has been ignored by current conventional methods. In addition, the method provides an efficient way to calculate seismograms for a dispersive and attenuated layered model. Finally, modeling results show the applicability of the improved method for the interpretation of complex frequency-dependent abnormalities, and indicate the potential for fluid detection in a layered reservoir.

On the influence of frequency-dependent elastic properties in vibro-acoustic modelling of porous materials under structural excitation

The aspects related to modelling the frequency dependence of the elastic properties of air-saturated porous materials have been largely neglected in the past for several reasons. For acoustic excitation of porous materials, the material behaviour can be quite well represented by models where the properties of the solid frame have little influence. Only recently has the importance of the dynamic moduli of the frame come into focus. This is related to a growing interest in the material behaviour due to structural excitation. Two aspects stand out in connection with the elastic-dynamic behaviour. The first is related to methods for the characterisation of the dynamic moduli of porous materials. The second is a perceived lack of numerical methods able to model the complex material behaviour under structural excitation, in particular at higher frequencies. In the current paper, experimental data from a panel under structural excitation, coated with a porous material, are presented. In an attempt to correlate the experimental data to numerical predictions, it is found that the measured quasi-static material parameters do not suffice for an accurate prediction of the measured results. The elastic material parameters are then estimated by correlating the numerical prediction to the experimental data, following the physical behaviour predicted by the augmented Hooke׳s law. The change in material behaviour due to the frequency-dependent properties is illustrated in terms of the propagation of the slow wave and the shear wave in the porous material.

Fine-scale gas distribution in marine sediments assessed from deep-towed seismic data

Abstract In the context of seismic imaging of gas/gas-hydrate systems, the fine-scale structure of subseabed gas-related reflections is assessed by taking advantage of the source signature of the deep-towed high-resolution SYSIF seismic device. We demonstrate the value of an original wavelet-based method and associated multiscale seismic attributes, applied to seismic data recently acquired on the western margin of the Arctic archipelago of Svalbard. From analysis in the wavelet domain, we recognize two types of gas-related reflections associated with submetre-scale distribution of gas. We identify a thin gas-charged layer associated with an apparent normal polarity reflection, and we detect gas patches associated with a reverse-polarity bright spot with frequency-dependent elastic properties at small seismic wavelengths. The results provide valuable information on the scale of features through which gas migrates and resolve ambiguities in the interpretation of the seismic data.