Acoustic Impedance Ratio Research Articles

Optimization on Thin Film Bulk Acoustic Resonator (FBAR) by Transmitting Line Method

In this paper, the transmitting line method is applied to analyze the properties of FBAR, and the input impedance equation is obtained, and the series resonance frequency fs and the parallel resonance frequency fp are calculated by this method. Moreover, the elastic effects of the electrode on the effective electromechanical coupling factor, k2eff , and the resonance factor, Qs> , of FBAR are investigated by the transmitting line method. Results indicate that the acoustic impedance ratio of the electrode to the piezo-film dominantly determines the behaviors of the k2eff , the variation of Qs versus the thickness of the electrode crucially depends on the acoustic impedance ratio of electrode to piezoelectric films. The results will be applied in the theoretical optimization of FBAR, which are available to optimize the fabrications of FBARs and similar devices.

Thin-layer effects in glaciological seismic amplitude-versus-angle (AVA) analysis: implications for characterising a subglacial till unit, Russell Glacier, West Greenland

Abstract. Seismic amplitude-versus-angle (AVA) methods are a powerful means of quantifying the physical properties of subglacial material, but serious interpretative errors can arise when AVA is measured over a thinly-layered substrate. A substrate layer with a thickness less than 1/4 of the seismic wavelength, λ, is considered "thin", and reflections from its bounding interfaces superpose and appear in seismic data as a single reflection event. AVA interpretation of subglacial till can be vulnerable to such thin-layer effects, since a lodged (non-deforming) till can be overlain by a thin (metre-scale) cap of dilatant (deforming) till. We assess the potential for misinterpretation by simulating seismic data for a stratified subglacial till unit, with an upper dilatant layer between 0.1–5.0 m thick (λ / 120 to > λ / 4, with λ = 12 m). For dilatant layers less than λ / 6 thick, conventional AVA analysis yields acoustic impedance and Poisson's ratio that indicate contradictory water saturation. A thin-layer interpretation strategy is proposed, that accurately characterises the model properties of the till unit. The method is applied to example seismic AVA data from Russell Glacier, West Greenland, in which characteristics of thin-layer responses are evident. A subglacial till deposit is interpreted, having lodged till (acoustic impedance = 4.26±0.59 × 106 kg m−2 s−1) underlying a water-saturated dilatant till layer (thickness < 2 m, Poisson's ratio ~ 0.5). Since thin-layer considerations offer a greater degree of complexity in an AVA interpretation, and potentially avoid misinterpretations, they are a valuable aspect of quantitative seismic analysis, particularly for characterising till units.

Bandgap calculation of two-dimensional mixed solid–fluid phononic crystals by Dirichlet-to-Neumann maps

A numerical method based on the Dirichlet-to-Neumann (DtN) map is presented to compute the bandgaps of two-dimensional phononic crystals, which are composed of square or triangular lattices of circular solid cylinders in a fluid matrix. The DtN map is constructed using the cylindrical wave expansion in a unit cell. A linear eigenvalue problem, which depends on the Bloch wave vector and involves relatively small matrices, is formulated. Numerical calculations are performed for typical systems with various acoustic impedance ratios of the solid inclusions and the fluid matrix. The results indicate that the DtN-map based method can provide accurate results for various systems efficiently. In particular it takes into account the fluid–solid interface conditions and the transverse wave mode in the solid component, which has been proven to be significant when the acoustic impedance of the solid inclusions is close to or smaller than that of the fluid matrix. For systems with an acoustic impedance of the inclusion much less than that of the matrix, physical flat bands appear in the band structures, which will be missed if the transverse wave mode in the solid inclusions is neglected.

Seismic response of a single and a set of filled joints of viscoelastic deformational behaviour

Rock joints are often filled with weak medium, for example, saturated clay or sand, of viscoelastic nature. Their effects on wave propagation can be modelled as displacement and stress discontinuity conditions. The viscoelastic behaviour of the filled joint can be described by either the Kelvin or the Maxwell models. The analytical solutions for wave propagation across a single joint are derived in this paper by accounting for the incident angle, the non-dimensional joint stiffness, the non-dimensional joint viscosity and the acoustic impedance ratio of the filled joint. It is shown that the viscoelastic behaviour results in dissipation of wave energy and frequency dependence of the reflection and transmission coefficients. Based on curve fitting of the experimental data of P-wave propagation across a single joint filled with saturated sand, both the Kelvin and Maxwell models are found to reproduce the behaviour of the filled joint, in terms of the amplitude and frequency contents. Then, wave transmission across a filled joint set is studied with the virtual wave source method and the scattering matrix method, where multiple wave reflections among joints are taken into account. It is shown that the non-dimensional joint spacing and the number of joints have significant effects on the transmission coefficients.

Removing Reverberation in Ice Sheets from Receiver Functions

Crustal thickness estimation using P receiver function (PRF) for seismometers deployed on ice sheets is difficult because of reverberation in the ice sheet. The strong reverberation in ice sheets is due to the large acoustic impedance ratio of ice-to-crustal rock (about 4.5). Consequently, such reverberation could disturb multiples from the crust-mantle boundary in PRFs and cause unstable inversion of PRFs for velocity model (Dahl-Jensen et al . 2003; Lawrence et al . 2006). Therefore, direct use of PRFs for crustal thickness estimation from stations on the ice sheet could be open to misinterpretation (Lawrence et al . 2006; Hansen et al . 2009). Because of this, alternative approaches have been taken to measure the depth to Moho beneath ice sheets (Winberry and Anandakrishnan 2004; Kumar et al . 2007; Hansen et al . 2009). In this study, I introduce a method to suppress the reverberation in the ice sheet that can approximately retrieve ice sheet–free PRF and lead to the standard PRF inversion for crustal thickness estimation. I test this method with synthetic experiments, the results of which show that application of the proposed method to PRFs from actual seismic stations on ice sheets could be feasible if we have reliable thicknesses of the ice sheet. The idea begins with comparison between the PRF for Model C and convolution of the PRF for Model A and the PRF for Model B (see Figure 1 for Models A, B, C). Model C combines Model A and Model B. If the convolution approximates to the PRF for Model C, the PRF for Model A will be approximated by deconvolution of the PRF for Model C with the PRF for Model B. The convolution is described by multiplication of the PRFs …

Study on Acoustic Characteristics of Lined Duct (Comparison between Experiment and BEM Analysis Using Impedance of Absorbent Measured by Impedance Tube)

Lined ducts are widely used to reduce the noise generated from various equipments such as a large wind tunnel and exhaust pipes of engines. Especially the noise reduction is required in offices and hospitals accompanying with the spread of air conditioning equipments. The noise reduction of non-lined ducts is usually predicted by using the FEM and the BEM techniques. But, there were a few cases that the analytic value was compared with the actual measurement about the lined duct which the noise absorbing material was used for. In this research, the analytic value of BEM was compared with the actual measurement value for the attenuation quantity within a lined duct. Then, a noticeable gap was caused between the both results in specific frequency. So, the cause was probed with a viewpoint of the specific acoustic impedance ratio used for BEM. As a result, it was found that the prediction of sound attenuation of the duct agrees with the experimental result by applying the impedance measured by the impedance tube with φ100 diameter to the BEM analysis.

Acoustic band gaps in finite-sized two-dimensional solid/fluid phononic crystals

Acoustic band gaps in two-dimensional phononic crystal consisting of a finite-sized square array of parallel hollow aluminum cylinders in air are investigated with the finite difference time domain (FDTD) method. Experimental measurements were carried out to validate the theoretical predictions with excellent overall agreement achieved. The numerical method is used subsequently to study the band gap properties of phononic crystals composed of cylinder (both solid and hollow)/fluid systems for two different acoustic impedance ratios. For both types of system, the influence of the transverse size of the phononic crystal on the propagation properties is analyzed, and the minimum size to achieve the largest band gap width for different filling factors is determined.

Effects of Thickness Deviation of Elastic Plates in Multi-Layered Resonance Systems on Frequency Spectra

A model of high-overtone bulk acoustic resonators is used to study the effects of thickness deviation of elastic plates on resonance frequency spectra in planar multi-layered systems. The resonance frequency shifts induced by the thickness deviations of the elastic plates periodically vary with the resonance order, which depends on the acoustic impedance ratios of the elastic plates to piezoelectric patches. Additionally, the center lines of the frequency shift oscillations linearly change with the orders of the resonance modes, and their slopes are sensitive to the thickness deviations of the plates, which can be used to quantitatively evaluate the thickness deviations.

Effects of material parameters on elastic band gaps of two-dimensional solid phononic crystals

In this paper we study the influences of the material parameters on phononic band gaps of two-dimensional solid phononic crystals. The analysis begins with the basic wave equations and derives the material parameters directly determining band gaps. These parameters include the mass density ratio, the shear modulus ratio, and Poisson’s ratios of the scatterer and host materials (or equivalently, the wave velocity ratio, the acoustic impedance ratio, and Poisson’s ratios). The effects of these parameters on phononic band gaps are discussed in details for phononic crystals with different filling fractions and lattice forms for both antiplane and in-plane wave modes. Band gaps are calculated by the plane wave expansion method. The results show that for the antiplane mode, the mass density ratio predominantly determines the band gap, while that for the in-plane mode, both mass density ratio and shear modulus ratio play equally important roles. The maximum band gap will appear at both large density ratio and shear modulus ratio (i.e., large acoustic impedance ratio with small mismatch in wave velocities) for either antiplane or in-plane wave mode; but band gaps may appear in other situations depending on the filling fraction and lattice forms. It is also shown that neither acoustic impedance ratio nor wave velocity ratio can determine the band gap independently. The present analysis can be applied to artificial design of band gaps.

3D inversion of lithological properties in the Gullfaks Brent Group

Gullfaks is a structurally com-plex field with sandstone reservoir units of Cretaceous to Triassic age. The reservoir quality is generally very good, with porosities in the range of 30–35% and per-meability up to several darcies in the most important Brent Group reservoir. The baseline streamer survey was acquired in 1985, one year before the start of production. A simultaneous seismic AVO in-version of the baseline streamer survey was performed in 2006 to obtain acoustic impedance (AI) and Poisson's ratio (PR). AI and PR contain valuable information about rock and fluid properties, and one goal of this project was to create empirical relationships based on well-log data between AI/PR and porosity (φ), differential pressure (Pd), lithology (Vsh), and fluid bulk modulus (Kf). Kf is directly linked to brine saturation. The next step was to estimate rock and fluid properties as functions of AI and PR from the seismic inversion. This approach depends on good agreement between modeled and well-log data and als...

Electromechanical Properties of Piezoelectric Integrated Structures on Porous Substrates

The fabrication of piezoelectric transducers for high resolution medical imaging applications requires a backing material to damp the piezoelectric resonance, resulting in a shorter time response, i.e. improved resolution, but lower sensitivity. Thus, the choice of such a substrate must be made according to its acoustical properties, namely the ratio of acoustic impedance of the backing material and the piezoelectric layer. Moreover, this backing material must have a relatively high attenuation, and provide good surface properties such as a low roughness and diffusion potential. Finally, the substrate material must have a good mechanical behavior at high temperature (around 900°C for the sintering of the piezoelectric thick film). In this context a review of available materials is first given, and the corresponding list is found to be quite limited. Several PZT/PGO piezoelectric thick films deposited by screen-printing have been fabricated on dense alumina [1] and have delivered good electromechanical performance, but the substrate attenuation was too low to be used as a backing for high frequency transducers. In this paper, new porous Al 2 O 3 substrates have been fabricated and used for the fabrication of a batch of piezoelectric films. The effects of a barrier layer and bottom electrode (conductive material type and thickness) are studied and related to the electromechanical performance of the piezoelectric thick film and then to the electro-acoustic properties of the ultrasonic transducer integrating these structures. Finally, these results are compared with previous studies [2] using porous PZT substrate. These comparisons are performed in terms of fabrication facility, electromechanical constants of the thick films (in thickness mode) and electro-acoustic responses of ultrasonic transducers with center frequencies over 20 MHz.

Effects of electrodes on performance figures of thin film bulk acoustic resonators

The effects of mechanical losses and elastic properties of the electrodes on the performance figures of a thin film bulk acoustic resonator (FBAR) are analyzed by numerical simulation. Results indicate that the material loss of the electrode has no visible effect on the characterization of the effective electromechanical coupling factor, k(eff)2. The acoustic impedance ratio of the electrode to the piezo-film dominantly determines the behaviors of the k(eff)2 variation with the electrode thickness. The resonance Q value, Q(s), of the FBAR closely relies on the material Q values of film and of electrodes as expected. Besides, the variation of Q(s) versus the thickness of the electrodes crucially depends on the acoustic impedance ratio as well. Especially, three characteristic parameters, i.e., the maximum value of k(eff)2, the sectional mass ratio of the electrode to the piezo film corresponding to the maximum k(eff)2, and the tolerance range of the ratio to keep k(eff)2 near the maximum, are calculated for some typical samples. These results would be useful for optimizing FBAR designs and performances.

Elastic behaviour of North Sea chalk: A well‐log study

ABSTRACTWe present two different elastic models for, respectively, cemented and uncemented North Sea chalk well‐log data. We find that low Biot coefficients correlate with anomalously low cementation factors from resistivity measurements at low porosity and we interpret this as an indication of cementation. In contrast, higher Biot coefficients and correspondingly higher cementation factors characterize uncemented chalk for the same (low) porosity. Accordingly, the Poisson's ratio–porosity relationship for cemented chalk is different from that of uncemented chalk.We have tested the application of the self‐consistent approximation, which here represents the unrelaxed scenario where the pore spaces of the rock are assumed to be isolated, and the Gassmann theory, which assumes that pore spaces are connected, as tools for predicting the effect of hydrocarbons from the elastic properties of brine‐saturated North Sea reservoir chalk. In the acoustic impedance–Poisson's ratio plane, we forecast variations in porosity and hydrocarbon saturation from their influence on the elastic behaviour of the chalk. The Gassmann model and the self‐consistent approximation give roughly similar predictions of the effect of fluid on acoustic impedance and Poisson's ratio, but we find that the high‐frequency self‐consistent approach gives a somewhat smaller predicted fluid‐saturation effect on Poisson's ratio than the low‐frequency Gassmann model. The Gassmann prediction for the near and potentially invaded zone corresponds more closely to logging data than the Gassmann prediction for the far, virgin zone. We thus conclude that the Gassmann approach predicts hydrocarbons accurately in chalk in the sonic‐frequency domain, but the fluid effects as recorded by the acoustic tool are significantly affected by invasion of mud filtrate.The amplitude‐versus‐angle (AVA) response for the general North Sea sequence of shale overlying chalk is predicted as a function of porosity and pore‐fill. The AVA response of both cemented and uncemented chalk generally shows a declining reflectivity coefficient versus offset and a decreasing normal‐incidence reflectivity with increasing porosity. However, for the uncemented model, a phase reversal will appear at a relatively lower porosity compared to the cemented model.

Specific Features of Excitation and Propagation of Longitudinal and Transverse Subsurface Waves in Solids: II. Effects of Some Boundary Conditions on Formation of Acoustic Fields

Modification of boundary conditions for propagation of transverse and longitudinal subsurface waves by covering a specimen's boundary surface with a layer of liquid may significantly affect amplitude PA and the form and directivity characteristic (DC) of a subsurface wave (SW) source in a near-surface zone even in the case when the ratio of acoustic impedances of coupling media is m12≈0.1. Dependences of the wave amplitude and the DC of probes of transverse and longitudinal SWs on geometric parameters of a rectangular protrusion located on the surface of the inspected solid body and on the wave frequency are established. The DC of a transverse-SW source has two global maxima located in the volume of the raised area and beneath it. These maxima are due to superposition of the fields belonging to the principal ST mode and to an additional mode transformed on the protrusion's edge. The studies performed have shown an increase in the sensitivity to flaws located beneath the extension of the coupling surface's plane in the protrusion's volume or above it.

Electrode effects on frequency spectra and electromechanical coupling factors of HBAR

In this paper, effects of electrodes on the spectra of high-overtone bulk acoustic resonator are analyzed phenomenologically by numerical simulations. Acoustic impedance ratio of the substrate to piezo-film, Zsb/Z0, and acoustic impedance ratio of the electrode to piezo-film, Ze/Z0, are taken as the category parameters for different combinations of three kinds of substrates, three kinds of piezo-films, and seven kinds of electrodes. The numerical simulations for all of the combinations are carried out. The results indicate that the acoustic impedance ratio of the substrate to piezo-film is a key factor for the variations of the space of parallel resonance frequency and the effective coupling factor versus the mode order. The mechanical effects of the electrodes have significant contribution as well. Several approximate formulae are given to evaluate the effective coupling factor for different combinations.

Ultrasonic Studies of Poly(vinyl acetate) Solution in Dimethylformamide

ABSTRACT Acoustical parameters such as adiabatic compressibility, specific acoustic impedance, relaxation strength, space-filling factor, and molecular ratio are evaluated for the solutions of poly(vinyl acetate) in dimethylformamide by measuring viscosity, ultrasonic velocity, refractive index, and density at different temperatures, (30°, 35°, 40°, and 45°C) and for different concentrations of poly(vinyl acetate) in solution. The results are discussed based on the solute and solvent interactions.

Measuring wave dynamics in IC engine intake systems

Wave dynamics in the intake system are known to strongly influence the performance of naturally aspirated internal combustion (IC) engines. Detailed measurements of the wave dynamics are required to optimize the performance of an engine, to validate the results of an engine performance simulation or to better understand the physics of the intake system. Five different methods for making such measurements are discussed in this paper. Four are based on different forms of pressure measurement and one uses hot-wire anemometry. The different methods are investigated by using results obtained on a single cylinder research engine. The different methods are used to produce measurements of fluctuating pressure and velocity as well as the specific acoustic impedance ratio of the intake pipe. Both time and frequency domain results are considered. The conclusion is that no single method is perfect or indeed universally applicable to all situations and in a typical investigation of wave action more than one method is likely to be used. The combined use of two methods, wave decomposition and an unusual bi-directional pitot-static tube, seems to offer a robust reliable and useful strategy for measuring wave dynamics in the intake pipe that should prove successful on most IC engines.

三次元地震探査データのポアソン比と音響インピーダンスによるガス砂岩分布の予測

The purpose of this study is to verify the applicability of the 3D seismic inversiondata for the hydrocarbon determination. The 3D seismic data consisting of two angle stack data (0-22 .5 degree and 22.5-45 degree), were inverted into acoustic impedance and Poisson's ratio data. The target interval is the Upper Cretaceous, Coniacian sand and we tried to discriminate between the gas sand and the water sand by them.The two sets of angle stack data were inverted for angle impedance. Angle impedance is a physical quantity which depends on acoustic impedance, shear impedance and the angle of reflection wave.The match between the angle impedance results from the 3D seismic data and the angle impedance logs is rated from good to very good with respect to both reflector placement and absolute angle impedance value. The near angle stack data results in the better solution than the far angle stack data.Poisson's ratio and acoustic impedance volumes were calculated from the angle impedance inversion results. Comparison of the calculated AVO attributes with the well log data shows that the acoustic impedance volume is of very good quality and tha Poisson's ratio volume is of good to poor quality.A lithology cube was produced on the basis of lithology probability calculated from the cross-plotting of Poisson's ratio versus acoustic impedance. Although an amplitude anomaly of full stack data yields only a sand distribution, a gas sand distribution was interpreted by using this cube.

Optical methods in fault dynamics

The Rayleigh pulse interaction with a pre-stressed, partially contacting interface between similar and dissimilar materials is investigated experimentally as well as numerically. This study is intended to obtain an improved understanding of the interface (fault) dynamics during the earthquake rupture process. Using dynamic photoelasticity in conjunction with high-speed cinematography, snapshots of time-dependent isochromatic fringe patterns associated with Rayleigh pulse–interface interaction are experimentally recorded. It is shown that interface slip (instability) can be triggered dynamically by a pulse which propagates along the interface at the Rayleigh wave speed. For the numerical investigation, the finite difference wave simulator SWIFD is used for solving the problem under different combinations of contacting materials. The effect of acoustic impedance ratio of the two contacting materials on the wave patterns is discussed. The results indicate that upon interface rupture, Mach (head) waves, which carry a relatively large amount of energy in a concentrated form, can be generated and propagated from the interface contact region (asperity) into the acoustically softer material. Such Mach waves can cause severe damage onto a particular region inside an adjacent acoustically softer area. This type of damage concentration might be a possible reason for the generation of the “damage belt” in Kobe, Japan, on the occasion of the 1995 Hyogo-ken Nanbu (Kobe) Earthquake.

Measurement of Rock Fabric in Shallow Refraction Seismology

A three dimensional (3D) seismic refraction survey carried out across a shear zone shows that there is an increase in the depth of weathering and a decrease in seismic velocity in the sub-weathering associated with the shear zone. Although the shear zone is generally considered to be a two dimensional (2D) feature, the significant lateral variations in both depths to, and seismic velocities within the refractor in the cross-line direction, indicate that it is best treated as a 3D target. These variations are not predictable on the basis of a 2D profile recorded earlier. Qualitative measures of azimuthal anisotropy are obtained from the seismic velocities and the time-depths computed from the traveltime data with the generalised reciprocal method (GRM) algorithms and from the head wave amplitudes. These three methods give similar, consistent results, with the direction of the greater seismic velocity being approximately parallel to the direction of the dominant geological strike over most of the survey area. Conversely, all three methods show that the direction of the greater seismic velocity is approximately orthogonal to the direction of the dominant geological strike in a small region adjacent to the shear zone. The amplitudes of the refracted signals are approximately proportional to the ratio of the specific acoustic impedances between the upper layer and the refractor, and they provide a convenient and detailed qualitative measure of azimuthal anisotropy or rock fabric. The amplitudes also contain additional useful geological information, although some of the cross-line amplitudes could not be completely explained. The in-line results show that both accurate refractor depths and seismic velocities can be computed with moderate cross-line offsets, say less than 20 m, of shot points. These results demonstrate that swath shooting with a number of parallel recording lines would be adequate for 3D surveys over targets such as highways, damsites and pipelines. Only a modest increase in the number of shot points over the requirements for the normal 2D program would be required in the cross-line direction to measure azimuthal anisotropy and rock fabric with amplitudes. The results of this study demonstrate that simple and efficient 3D refraction methods using a GRM approach can provide more useful geological interpretations than would be the case with detailed 2D approaches.