Attenuation Layer Research Articles

Discussion of errors in the Green’s function parabolic equation for outdoor sound propagation

As is to be expected of any numerical method, use of the Green’s function parabolic equation (GFPE) does result in small errors that can propagate and increase. The main causes of errors in using the GFPE for outdoor sound propagation with constant sound speeds appear to be inadequate spatial sampling, approximated starting fields, and errors in the numerical integration used to compute the surface wave. The relative significance of these errors as well as a set of appropriate computational parameters for avoiding or minimizing them will be discussed. With the proper parameter selection (for step sizes, attenuation layer depth, etc.), the GFPE produces reliably accurate results for outdoor sound propagation even over finite impedance grounds and beyond barriers or changes in ground height.

Recursive asymptotic stiffness matrix method for analysis of surface acoustic wave devices on layered piezoelectric media

Based on a simple second-order thin layer asymptotic expansion for the transfer matrix, an asymptotic solution for the stiffness matrix for a general anisotropic piezoelectric thin layer is obtained. The total stiffness matrix for thick layers or multilayers is calculated with arbitrary precision by subdividing them into thin sublayers and combining recursively the thin layer stiffness matrices. It is shown that this method converges to the exact solution and is computationally stable, efficient and easy to implement. A semispace substrate is substituted for by a finite thickness layer loaded by a perfectly matched attenuating layer. The effective permittivity and general Green’s functions for a layered system on a substrate are formulated in terms of stiffness and compliance matrices. The advantage of the method is that one does not need to compute the exact wave propagation solution for an anisotropic piezoelectric layer or semispace.

Parietal Pleura and Extrapleural Space in Chronic Tuberculous Empyema: CT–Pathologic Correlation

The purpose of this work was to describe CT findings of the parietal pleura and extrapleural space in patients with chronic tuberculous empyema and to compare them with histopathologic findings following decortication. Chest CT scans obtained from 13 patients with chronic tuberculous empyema who underwent decortication were retrospectively reviewed. All patients were men from 18 to 67 years old (mean 42 years old). CT findings of the parietal pleura and extrapleural space were correlated with histopathologic findings in all patients. Histopathologically, the enhanced parietal pleural peel on CT was fibrous collagenous tissue, and a low attenuated layer with 2 mm thickness within the parietal pleural peel (n = 2) was either a layer of histiocytes or caseation necrosis. The extrapleural space seen as an intermediate attenuation in six patients on CT was the proliferation of vessels, inflammatory cells, and granulomas in loose collagen background. The linear soft tissue attenuation interrupting the extrapleural fat (n = 5) on CT was a collagenous fibrous layer with proliferation of vessels and inflammatory cells. A layer of low attenuation in the parietal pleural peel may be due to different episodes of infection. The extrapleural space with intermediate attenuation may indicate ongoing inflammation. Linear soft tissue attenuation interrupting the extrapleural fat represents a fibrous layer rather than the subcostalis muscle.

Indentification of the 6H-SiC(0001) 3×3 surface reconstruction core-level shifted components

We investigate the 6H-SiC(0001) 3×3 surface reconstruction by Si 2p and C 1s core-level photoemission spectroscopy using synchrotron radiation providing the first identification of surface core-level shifted components. Specific spectral features at the Si 2p core level, including bulk (B) and two surface shifted (SS1 and SS2) components, show a surface reconstruction structure involving several silicon atomic planes. In comparison, the C 1s core level shows no involvement of carbon atoms in the 6H-SiC(0001) 3×3 surface reconstruction structure. These results, obtained by an attenuation layer model, indicate that SS1 is related to the Si adatom and that SS2 is related to the Si adlayer+trimer of the 6H-SiC(0001) 3×3 surface reconstruction.

Vaporization of micrometer size droplets in simulated in vivo environments

Droplets were generated for a range of albumin (bovine) concentrations. Resulting emulsions were examined for size distribution, number density and yield. Albumin concentrations as low as 1 mg per ml were capable to form stablized droplets. Changes in number density and mean size were observed. Reducing the amount of albumin by a factor of 16 resulted in an increase of the number density by a factor of 40 while the mean droplet size decreased by a factor of 2.5. The measured droplet yield was approximately 30%. Droplets were vaporized using short ultrasonic tone bursts for frequencies ranging from 1.5 to 8 MHz. Two 1-cm Zerdine 81 layers of acoustic attenuation of 0.5 dB/MHz/cm were overlaid on the flow tube used. Droplets were phase transitioned in saline and in blood. Pressure thresholds for vaporization were acquired for conditions with and without Zerdine as well as saline or blood as bulk fluid. It has been seen that the threshold in saline increased by approximately 25% by introducing the Zerdine layers (1.5 MHz) and 60% for the Zerdine-blood combination. [Work supported in part by PHS Grant No. R01 HL54201 from the National Heart, Lung and Blood Institute.]

Azimuthal variation inP-wave signatures due to fluid flow

The favored dominant mechanism for attenuation in the upper crust at seismic frequencies is intracrack fluid flow. In cracked media, the azimuthal attenuation of the P-wave amplitudes arising from such flow is predicted to be quite substantial. The consequence of this variation in azimuth is a modification in the amplitude behavior of the base event from a cracked reservoir due to transmission through the attenuative layer. Indeed, the effect is of sufficient strength to exacerbate, diminish, or reverse variations that arise solely due to the reflectivity coefficient. Thus, although this attenuation is always greatest perpendicular to the crack strike, the direction of the dimming or brightening of the base reservoir event will depend upon the exact attenuation law and the crack properties. The combination of these factors contributes to a wave behavior that can provide a more adequate discrimination between conditions of brine and oil fill than an interpretation assuming the reflection coefficient alone. Unfortunately, regions of commonality do remain, and the distinction between fills is still only apparent for particular reservoir and crack conditions. The attenuated amplitudes are large enough to be seen at small offsets and may possibly account for the significant azimuthal variations in the P-wave signatures observed in field data.

Ultrasonic focusing and steering through the skull: Toward brain imaging

The time-reversal method has been experimentally applied to the focusing through the skull bone. This technique needs the knowledge of the Green’s function of a dominant scatterer available in the medium. Moreover, it is shown that the skull induces severe attenuation of ultrasound and reduces the efficiency of the time-reversal approach. Nevertheless, an improvement of time-reversal processing for ultrasonic waves focusing through an aberrating and absorbing layer can be achieved. When the attenuating layer is located close to the array, this method consists of inversing the amplitude modulation before the time-reversal operation. Conversely, when the attenuating layer is located some distance away from the transducer array, numerical backpropagation is used to discriminate between the amplitude modulations resulting, respectively, from interference and absorption. Moreover, although time reversal is only self-adaptative to the artificial source implanted inside the imaging volume, this method is generalized to steer the ultrasonic beam on other points surrounding this acoustic source. This process has already been applied to hyperthermia through the skull bone and it can be applied to noninvasive brain imaging.

Ultrasound for the mediation of a therapeutic agent through the blood–brain barrier

There is a critical need to develop safe, noninvasive, nonchemical methods to enhance the delivery of nonlipophilic neuropharmaceuticals to the brain. A novel method for mediating nonlipophilic drug transport across the blood–brain barrier (BBB) will be presented. Preliminary data were obtained using a unit operating at 1.6 MHz with ultrasound coupled through water and an attenuating layer onto an in vitro cell-culture model of the BBB. The effects of different intensities on permeation rate and cell integrity were investigated. Various microscopic techniques were used to determine cell condition and viability. At low intensities no effects were seen. At intermediate intensities enhanced permeation up to levels of a factor of 3 increase were measured. At the highest intensity substantial cell disruption was observed. Preliminary observations regarding the mechanism for the interaction of ultrasound with the BBB will be presented. Work is in progress to determine the conditions for effective trans-cranial delivery of ultrasound using phantoms constructed to model in vivo brain. By promoting transport of nonlipophilic drugs across the BBB, this approach has the potential to safely and effectively treat a wide range of brain and central nervous system disorders.

Multichannel estimation of frequency -dependent Q from VSP data

A Method of estimating attenauation from the first arrivals of VSP data is presented. The motivation is the desire to investigate the effects of scattering on wave propagation, and particularly the apparent attenuation and associated phase delay due to fine layering (the O'Doherty-Anstey effect). In order to take account of the frequency dependence of the predicted scattering attenuation, and to provide robust statistics for the estimates, a beam-forming method is used to measure the attenuation. This simularaneously estimates the slowness and polarization angle of the different wave modes, and results in attenuation measurements which are largely free of interference from reflected and mode-converted energy. By working in the frequency domain and measuring amplitude decay with depth, the frequency dependence of the attenuation is also accounted for. The beam-forming algorithm works in two passes, the first of which estimates slownesses and polarization angles over a small depth range, while the second uses the information from the first pass over a larger depth range to estimate attenuation. An approximate error analysis of the method shows that the standard variance of the estimated Q values is proportional to Q2 and the data quality (measured by its spectral coherence), and inversely proportional to the square of the analysis depth range and the square of the frequency. Hence the depth resolution is traded against the stability of the results. The method is applied to a zero-offset three-component VSP. The data are of good quality, with a bandwidth ranging from 180 Hz in the shallow part to 100 Hz in the deepest part. Stable results were obtained using a 450 m depth range. Above about 50 Hz, there is little evidence of frequency dependence in the attenuation. There is a clear division in depth into layers of higher and lower attenuation, with values of Q typically between 50 and 200. Below 50 Hz, however, attenuation increases rapidly with decreasing frequency throughout the depth range, with values of Q of less than 10 at 15 Hz. This behaviour appears anomalous since on physical grounds we expect very high values of Q at low frequency, and we have no explanation for these observations.

Multichannel estimation of frequency‐department Q from VSP data1

AbstractA Method of estimating attenauation from the first arrivals of VSP data is presented. The motivation is the desire to investigate the effects of scattering on wave propagation, and particularly the apparent attenuation and associated phase delay due to fine layering (the O'Doherty‐Anstey effect).In order to take account of the frequency dependence of the predicted scattering attenuation, and to provide robust statistics for the estimates, a beam‐forming method is used to measure the attenuation. This simularaneously estimates the slowness and polarization angle of the different wave modes, and results in attenuation measurements which are largely free of interference from reflected and mode‐converted energy. By working in the frequency domain and measuring amplitude decay with depth, the frequency dependence of the attenuation is also accounted for. The beam‐forming algorithm works in two passes, the first of which estimates slownesses and polarization angles over a small depth range, while the second uses the information from the first pass over a larger depth range to estimate attenuation.An approximate error analysis of the method shows that the standard variance of the estimated Q values is proportional to Q2 and the data quality (measured by its spectral coherence), and inversely proportional to the square of the analysis depth range and the square of the frequency. Hence the depth resolution is traded against the stability of the results.The method is applied to a zero‐offset three‐component VSP. The data are of good quality, with a bandwidth ranging from 180 Hz in the shallow part to 100 Hz in the deepest part. Stable results were obtained using a 450 m depth range. Above about 50 Hz, there is little evidence of frequency dependence in the attenuation. There is a clear division in depth into layers of higher and lower attenuation, with values of Q typically between 50 and 200. Below 50 Hz, however, attenuation increases rapidly with decreasing frequency throughout the depth range, with values of Q of less than 10 at 15 Hz. This behaviour appears anomalous since on physical grounds we expect very high values of Q at low frequency, and we have no explanation for these observations.

Ultrasonic beam focusing through tissue inhomogeneities with a time reversal mirror: application to transskull therapy

Time reversal of ultrasonic fields allows a very efficient approach to focus pulsed ultrasonic waves through lossless inhomogeneous media. Time reversal mirrors (TRMs) are made of large transducer arrays, allowing the incident field to be sampled, time reversed, and reemitted. Time reversal method corrects for phase, amplitude, and even shape aberration and thus, is more efficient than time shift compensation techniques. However, this technique needs the knowledge of the Green's function of a dominant scatterer available in the medium. Aberration correction for ultrasonic hyperthermia could be achieved by combining TRM with an artificial acoustic source or sensor implanted inside the treatment volume. In this paper, time reversal method has been experimentally applied to the focusing through the skull bone. It is shown that the skull induces severe attenuation of ultrasound and reduces the efficiency of the time reversal approach. Then, an amplitude correction method is proposed to focus through an attenuating layer located close to the array. This method consists in inversing the amplitude modulation and then time reversing these signals. Finally, this method is combined with numerical backpropagation to compensate for an attenuating layer located some distance away from the transducer array.

Inversion ofQ value structure beneath the Tibet Plateau

A total of 11 earthquakes with 15 Rayleigh wave paths, recorded at 11 broadband digital PASSCAL seismometers installed in the Tibet Plateau by the Sino-U.S. joint research group, were used to determine the phase velocity and attenuation coefficient of surface waves in periods of 10–130 s. The average shear wave velocity and quality factor {ie271-1} structures in the crust and upper mantle were obtained in this region. The result shows the average {ie271-2} is low and there exists a high attenuation ({ie271-3}=93–141) layer in the crust. The depth range of the low {ie271-4} value layer (16–42 km) is consistent with the range of low velocity layer (21–51 km) in the crust. Below 63 km in the lower crust, {ie271-5} decreases with depth from 114 to 34 at depth of 180 km. The low shear wave velocity and low value of {ie271-6} at the same depth range in the crust indicate that the rocks in the range is probably melted or partially melted. According to the shear wave velocity structure, the average thickness of the crust is about 71 km and a clear velocity discontiniuty appears at the depth of 51 km. The low-velocity zone (4. 26 km/s) at depth of 96–180 km may be corresponding to the asthenosphere.

Q β structure of the crust and upper mantle in the eastern Sino-Korean paraplatform

Based on the long period surface wave data recorded by the China Digital Seismograph Network (CDSN), theQ R of fundamental mode Rayleigh wave with periods from 10 s to 146 s is determined for the eastern Sino-Korean paraplatform in this paper. TheQ β models of the crust and upper mantle are respectively obtained for the 4 paths, with the aid of stochastic inverse method. It shows that in the eastern Sino-Korean paraplatform, the average crustalQ β is about 200, and that there exists a weak attenuation layer in the middle crust (about 10–20 km deep) which is possibly related to earthquake-prone layer. A strong attenuation layer (lowQ) of 70 km thick extensively exists in the uppermost mantle, with the buried depth about 80 km. The averageQ R of fundamental mode Rayleigh wave is between the value of stable tectonic region and that of active tectonic region, and much close to the latter.

CT of intussusception in the pediatric patient: diagnosis and pitfalls

Intussusception in the pediatric patient may have a varied clinical presentation depending on its location, presence of lead point, intermittent occurrence, or underlying systemic disease. Computed tomography (CT) may be used at times in the evaluation of children with complicated presentations. The purpose of this investigation was to review the findings of CT images obtained in children with intussusception. Five patients with intussusception were diagnosed by CT at our institution between 1989 and 1994. An intraluminal mass was found in all patients. Intraluminal eccentrically located fat, as well as the target sign of alternating layers of high and low attenuation, was seen in most patients. In patients with a more long-standing process, fluid-distended loops, inflammation, and loss of tissue planes were seen and corresponded with necrosis and areas of nonviable bowel found at surgery. Finally, potential pitfalls with the layered or target appearance are discussed in the form of two patients who were initially felt to have intussusception at CT, but in whom the target appearance was later found to be due to other processes.

A two‐layer attenuation model for the upper mantle at short periods

Estimates of maximum mean P‐wave attenuation (described by the quality factor Qα) are used to make a two‐layer model of Qα in the period range 0.125–1 s for the northwest Pacific subducting region. A shallow highly attenuating layer (Qα ≈ 150) of only 85 km thickness overlays a less attenuating layer to a depth of 450 km (Qα > 1000). The added bandwidth made available by the use of array data yields key information for testing the validity of textbook models predominantly based on extrapolation from longer period data. We find that seismic attenuation at short periods appears to behave differently to long‐period attenuation. This reversal is represented by a modification to the absorption band model obtained from longer period data.

Quartz etching for phase shifting masks

In this paper a technology for dry etching of quartz for the fabrication of Phase Shift Masks (PSMs) and micromechanic applications is presented. Reactive Ion Etching (RIE) with CF 4/SF 6+ O 2 chemistry and a chrome and/or resist/chrome mask is applied to quartz etching. Quartz structures and PSM with high resolution have been fabricated on commercially available chrome-quartz blanks. The chrome layer serves two purposes: first, it is used to define the structures with high resolution and low edge roughness, and second, it is used as an attenuating layer for rim-type PSM after wet etching or as a phase shifter in combination with the residual resist layer.

A method for including lateral waves in normal-mode calculations

A method for including the lateral (or head) wave in a normal-mode propagation model [E. K. Westwood etal., J. Acoust. Soc. Am. 95, 2908(A) (1994)] for acoustoelastic ocean environments has been developed. The method consists of replacing the original lower half-space with a thick layer having a constant sound speed but a small gradient in attenuation. Below the attenuating layer, the new lower half-space is given parameters such that there is no mismatch at the half-space interface. As a result, (1) the branch point corresponding to the critical angle in the half-space is moved upward in the complex k plane (where k is horizontal wave number), (2) the Pekeris branch line integral is also moved upward such that it becomes negligible, and (3) modes appear in the complex k plane between the old and new branch points. The cost of introducing the thick layer is not great because Airy function solutions are used in each layer. Removal of the Pekeris branch line integral, in conjunction with including the leaky modes, makes the mode solution represent the complete acoustic field. [Work supported by the ARL Internal Research and Development Program.]

Sensitivity analysis of the Green’s function parabolic equation model for atmospheric sound propagation

A sensitivity analysis was performed on the Green’s function parabolic equation (GFPE) model to determine parameter bounds which maintain model validity. To determine these bounds, inverse theory was used to determine the ‘‘best’’ combination of input parameters over a two-dimensional domain using a normalized sum of squared residuals. A two-dimensional version of the fast field program (FFP), a widely accepted atmospheric propagation model, was used as comparison. Plots of the error surface were then made to show sensitivity bounds. Upward and downward refracting atmospheres were considered for a range of frequencies. The GFPE model was found to require a height increment parameter of about 0.05 wavelengths while the range increment parameter extended from 10 to 120 wavelengths depending on atmospheric profile and frequency. The thickness of the attenuation layer was found to be frequency dependent and ranged from 50 to over 200 wavelengths. The surface wave integral height was found to be a minimum of 30 and 13 wavelengths for the upward and downward atmospheres, respectively. The CPU time for the GFPE model ranged from 10 to 60 s, depending on frequency, and was approximately 60–1000× faster than the two-dimensional FFP.

High-resolution images of the lower crust: deep seismic reflections from 15 to 180 Hz

We report the results of an unconventional, broad-band deep-seismic reflection survey undertaken on land in southwest England. Previous marine seismic lines in this area have shown strong layered lower-crustal reflectivity. The broad-band survey shows near-normal-incidence P-wave reflections from the lower continental crust and from the Moho with frequencies that range from 15 to 180 Hz. High-frequency lower-crustal S-wave reflections were also observed. These high frequencies were obtained by placing both sources and receivers in boreholes up to 2 km deep, drilled within a large homogeneous granite pluton. Recording down-hole avoids loss of high frequency energy during transmission through heterogeneous and highly attenuative near-surface layers. The high frequencies were generated using explosive sources, and were recorded on sub-surface accelerometers and hydrophones, and on a conventional array of surface geophones. Seismic attenuation within the granite is low; the quality factor, Q, lies above 2000. These new, high-frequency observations show that the lower crust does not preferentially reflect particular frequencies. The data are most readily explained as resulting from the combination of a frequency-independent Q in the upper crust with a white reflectivity response in the lower crust. The data are not consistent with crustal models which are highly tuned to reflect preferentially the frequencies employed in conventional deep seismic reflection surveys. The data require relatively sharp boundaries within the lower crust; significant variation in physical properties must occur over vertical distances of not more than about 10 m. Sharp boundaries are most easily explained if the reflections result from lithological contrasts.

Acoustically sealing earmuff for an infant

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