Amplitude Of Reflected Wave Research Articles

The mild-slope equations

In its original form the mild-slope equation, which approximates the motion of linear water waves over undulating topography, is a simplified version of the more recently derived modified mild-slope equation. However, the reduced equation does not deal adequately with rapidly varying small-amplitude perturbations about an otherwise slowly varying bedform and it does not produce free-surface profiles that inherit slope discontinuities from the topography, an intrinsic feature of the approximation on which both equations are based. The inconsistency between the two equations is rectified by the derivation of an alternative form of the mild-slope equation, having the simplicity of the standard form and yet containing all of the essential features of the full equation. In the process, a more transparent version of the modified mild-slope equation is identified. The standard and revised mild-slope equations are compared analytically in the context of two-dimensional plane wave scattering and it is found that they lead to values of the reflected wave amplitude that differ at lowest order in the mild-slope parameter, for a general topography. It is also confirmed that the revised mild-slope equation gives the dominant contribution in the solution of the new form of the modified mild-slope equation. Indeed, the two equations differ only by a term that is virtually negligible.

Fracture detection using land 3D seismic data from the Yellow River Delta, China

Over the past 10 years, there has been a consistent increase in using 3D P-wave data to characterize fractures, which is critical for ensuring economic oil and gas production in tight formations of otherwise low permeability. Here, we present a case study of fracture detection using 3D P-wave seismic data from the Yellow River Delta in East China. The target formation is a naturally fractured mud-rock reservoir. The field site has been in production for more than 10 years; however, virgin pressure wells are still being drilled. The purpose of the survey was the remote identification, for future well planning, of zones of high fracture density that are residual oil-charged. A major aspect of this study is to compare the different seismic attributes and different analysis techniques on a common data set for fracture detection. Our aim is to understand the merits of these different techniques, and to establish some basic guidelines for fracture detection using P-wave data. If we assume the fracture population consists of predominantly one major orientation, the azimuthal variation of P-wave seismic attributes, such as traveltime, stacking velocity, reflected wave amplitudes, impedance, etc. can be approximately described by an ellipse. The long axis of the ellipse indicates the fracture orientation, and the relative ratio of the long to short axes of this ellipse is proportional to the fracture density or intensity of the rock concerned. As we know, at least three data points are required to define an ellipse in azimuthal planes. Thus fracture orientation and intensity maps can be built from 3D P-wave data if there is sufficient azimuthal coverage. We shall call this technique azimuthal attribute analysis or the 3A technique. In the practical application of the 3A technique, two methods are often employed to extract the fracture information: full-azimuth surface fitting and narrow-azimuth …

EFFECTS OF EXERCISE TRAINING ON THE AMPLITUDE AND TIMING OF CENTRAL AORTIC PRESSURE WAVE REFLECTION IN CORONARY ARTERY DISEASE

Early return of wave reflection from peripheral reflecting sites augments systolic and pulse blood pressures and increases left ventricular external arterial load. Such changes are attributable to increased stiffening of the large elastic arteries and increased pulse wave velocity. PURPOSE The purpose of this study was to investigate the effects of 12 weeks of standard cardiac rehabilitation on the amplitude and timing of wave reflections in coronary artery disease. METHODS Ten coronary artery disease patients underwent 12 weeks of exercise training (ET) as part of a standard cardiac rehabilitation program and ten control patients (C) received 12 weeks of standard care and did not participate in supervised exercise. Brachial artery blood pressure was measured by sphygmomanometry and central aortic pressure was measured by noninvasive radial artery applanation tonometry and use of a generalized transfer function before and after the 12 week exercise or control period. Central aortic augmentation index (AIa) and delay of the reflected wave (Δt), indicators of arterial stiffness, were calculated from the aortic pressure waveform. RESULTS Twelve weeks of endurance exercise training did not alter heart rate, central or peripheral systolic, diastolic or pulse pressures but did result in a significant decrease in AIa (30.4% vs. 26.2%, p < 0.05) and a significant increase in Δt (136.2 vs. 144.4, p < 0.05) in the ET group. There were no changes in any of these parameters in the C group during the 12-weeks of standard care. CONCLUSION The present study is the first to investigate the effects of endurance training on arterial properties using pulse wave analysis in coronary artery disease patients. Pulse wave analysis demonstrated that 12-weeks of endurance training in coronary artery disease patients resulted in a reduction in arterial stiffness as evidenced by a reduction in AIa and an increase in Δt. Our results suggest that endurance exercise training improves systemic arterial stiffness.

Relation between the Hydrodynamic and Elastic Parameters in Surface Wave Diffraction on a Floating Plate

The problem of surface wave diffraction on a floating elastic plate is considered. The relation between the parameters of the elastic vibrations of the plate and the transmitted and reflected wave amplitudes is investigated. It is shown that the maximum amplitudes of the plate stresses and deflections depend nonmonotonically on the incident wave frequency and are reached simultaneously with the maxima of both the transmission coefficient and the length of the wave penetrating into the plate. This makes it possible to use the transmission coefficient as a parameter for investigating the maximum and minimum amplitudes of the hydroelastic vibrations of the plate. As an example, this criterion is used to minimize the vibrations of a plate whose leading edge is elastically connected to the bottom.

Augmentation index as a measure of peripheral vascular disease state.

Pulse pressure, especially in central arteries, is an independent predictor of adverse cardiovascular events in patients with increased elastic artery stiffness (or elastance). The central arterial pressure wave is composed of a forward traveling wave generated by left ventricular ejection and a later arriving reflected wave from the periphery. Increased stiffness of elastic arteries is the primary cause of increased pulse pressure in subjects with degeneration and hyperplasia of the arterial wall. As stiffness increases, transmission velocity of both forward and reflected waves increase, which causes the reflected wave to arrive earlier in the central aorta and augments pressure in late systole [ie, augmentation index = (augmented pressure/pulse pressure) increases]. These changes in wave reflection properties are associated with vascular disease and aging and cause an increase in left ventricular afterload, myocardial mass, and oxygen consumption. Vasoactive drugs have little direct effect on large elastic arteries but can markedly change wave reflection amplitude and augmentation index by altering stiffness of the muscular arteries and modifying transmission velocity of the reflected wave from the periphery to the heart. This change in amplitude and timing of the reflected wave causes a generalized change in central arterial systolic and pulse pressure that is not detected by cuff pressure measurements in the brachial artery.

Amplitude and timing of central aortic pressure wave reflections in heart transplant recipients

Background Hypertension (HTN) assessed by sphygmomanometer is a common finding in heart transplant recipients (HTR); however, little is known about the contribution of arterial wave reflection to central aortic pressure in these patients. The aim of this study was to measure the central aortic pressure wave in HTR on antihypertensive therapy and determine the effects of amplitude and timing of wave reflection on the various components of the wave. Methods A total of 53 stable adult HTR on antihypertensive medication underwent brachial artery blood pressure ([BP]; by sphygmomanometry) and central aortic pressure (by noninvasive radial artery applanation tonometry and use of a generalized transfer function) measurements at rest. Central aortic augmentation index (AIa), an indicator of arterial stiffness, was calculated from the aortic pressure waveform. Patients were divided into three groups (A, B, and C) based on the amplitude of AIa. Results Mean brachial BP was 136 ± 15/84 ± 9.4 mm Hg. Group A patients ( n = 25) had a higher AIa (average 21% ± 7.6%) than group B ( n = 18, AIa = 6.5% ± 3.0%, P < .001) or group C ( n = l0, AIa = −8.7% ± 8.1%, P < .001) patients. The amplitude of AIa was inversely related to the travel time (Δt p/2) of the reflected pressure wave from the periphery to the heart (r = −0.78, P < .001). Despite this clear stratification of patients by aortic pulse wave analysis, standard cuff pressure was similar among the groups. Conclusions Noninvasive analysis of the central aortic pressure wave identified a subgroup of hypertensive HTR with increased arterial stiffness, increased propagation of the reflected wave, and augmented aortic systolic and pulse pressure not identified with the sphygmomanometer.

Potential for use of pulse wave analysis in determining the interaction between sildenafil and glyceryl trinitrate.

The early part of the central aortic pressure pulse, with amplitude (PI - Pd), is generated by left ventricular ejection, while the latter part (or augmented pressure), with amplitude (Ps - Pi), is generated by the reflected wave arriving during systole. The effects of arterial vasodilator agents, especially nitrates, on central aortic systolic blood pressure are grossly underestimated by sphygmomanometric measurements of brachial artery pressure. The objective of this study was to investigate the potential for use of central arterial pulse wave analysis, obtained noninvasively from the radial pulse, in determining the interaction between sildenafil and the nitric oxide donor drug glyceryl trinitrate (GTN). Central aortic pressure waveforms were generated from noninvasively measured radial artery pressure wave-forms and subjected to pulse wave analysis to determine the interaction between sildenafil and transdermally applied GTN. Transdermal GTN (2.5, 5.0, and 15 mg per 24-h patches) alone caused no consistent change in sphygmomanometer-determined systolic or diastolic pressures, but there was a consistent, dose-related fall in amplitude of the augmented systolic pressure, (Ps - Pi), of 4.0, 7.0, and 11 mmHg, respectively, with little change in diastolic pressure. The 2.5 mg patch caused a fall of 4.0 mmHg in aortic systolic pressure, while augmentation index (AIx) fell from 20 to 11% and pulse pressure fell 18%. When oral sildenafil (50 mg) was administered after GTN (2.5 mg), aortic systolic pressure fell another 4.0 mmHg. This decrease in systolic pressure caused a fall in AIx to almost 0.0%; pulse pressure fell another 9.0%. These modifications in aortic systolic and pulse pressure are due primarily to reduction in wave-reflection amplitude and are not detected by sphygmomanometer-measured brachial artery pressure.

Arterial Elastance and Wave Reflection Augmentation of Systolic Blood Pressure: Deleterious Effects and Implications for Therapy

Systolic and pulse blood pressures are stronger predictors of stroke, coronary heart disease, myocardial infarction, heart failure, end-stage renal disease, and cardiovascular mortality than diastolic pressure. Furthermore, diastolic pressure is inversely related to coronary heart disease and cardiovascular mortality. Increased elastance (or stiffness, inverse of compliance) of the central elastic arteries is the primary cause of increased systolic and pulse pressure with advancing age and in patients with cardiovascular disease, including hypertension, and is due to degeneration and hyperplasia of the arterial wall; diastolic pressure decreases as arterial elastance increases. As elastance increases, transmission velocity of both forward and backward (or reflected) traveling waves increases, which causes the reflected wave to arrive earlier in the central aorta and augments pressure in late systole. These changes in arterial wall properties cause an increase in left ventricular afterload and myocardial oxygen consumption and a decrease in myocardial perfusion pressure, which may induce an imbalance in the supply-demand ratio, especially in hypertrophied hearts with coronary artery disease. Also, an increase in systolic pressure increases arterial wall circumferential stress, which promotes fatigue and development of atherosclerosis. Vasodilator drugs have little direct active effect on large elastic arteries but can markedly reduce wave reflection amplitude and augmentation index by decreasing elastance of the muscular arteries and reducing pulse wave velocity of the reflected wave from the periphery to the heart. This decrease in intensity (or amplitude) and increase in travel time (or delay) of the reflected wave causes a generalized decrease in systolic pressure and arterial wall stress and an increase in ascending aortic flow during the deceleration phase. The decrease in systolic pressure brought about by this mechanism is grossly underestimated when systolic pressure is measured in the brachial artery.

Radiation characteristics of wide-angle H-plane sectoral horn loaded with dielectric of multiangular shape

Radiation characteristics of H-plane sectoral horns can be improved or modified by inserting a proper dielectric loading. A study of the radiation of wide-angle sectoral horns with a multiangular dielectric insert that behaves as a lens is presented. Two types of loading are considered, the first in the waveguide feed, the second in the aperture. The method of analysis is the domain product technique utilizing Mathieu function expansions. Numerical investigation has shown that both configurations can provide improvements, but the first lens possesses certain advantages in comparison with the second one. Specifically, it has smaller dimensions and allows minimization of the reflected wave amplitude. Proper choice of the shape of the first insert and material of the dielectric can ensure reduction in the beamwidth, lowering the side lobe level and low return losses in a broad band of frequencies.

Estimation du coefficient de réflexion en canal à houle

A complex function F( t) containing the water surface levels in a fixed point in the real part and a function obtained from the slope of this surface in the imaginary part, is used to study the reflection wave in a flume. This complex function analysis by the discrete Fourier transform allows to separate the incident and the reflected wave amplitudes, which are respectively given by the amplitudes of the Fourier-series coefficients of positive and negative frequencies. Errors linked to the evaluation of the reflection coefficient by the measurement of the water surface level in three nearby points are numerically studied.

Microscopic theory of a transition layer on the ideal surface of semiinfinite dielectric media and the near-field effect

The microscopic theory of a transitional layer on the ideal surface of a semi-infinite absorbing or nonabsorbing isotropic dielectric is developed within the framework of classical optics when the polarization vector of the medium is a linear function of the electric field strength inside the medium. The concentration of atoms (molecules) of the medium and their polarizability are independent of coordinates and are constant inside the medium and close to its surface. The consideration is carried out within the framework of the concept of a discrete-continuous dielectric, in which the fields of dipoles of discretely distributed atoms (molecules) inside the Lorentz sphere surrounding the observation point are taken into account. The near-field effect is shown to result in a nonexponential behavior of the field nearby the surface. The thickness of the transitional layer can be found from experimental values of the reflected wave amplitude.

Stiffness of carotid artery wall material and blood pressure in humans: application to antihypertensive therapy and stroke prevention.

Because epidemiological studies show that increased pulse pressure and carotid wall-material stiffness are predictors of cardiovascular mortality independent of age, atherosclerosis, and conventional risk factors, the relationships between carotid wall stiffness and blood pressure are important to the optimization of cardiovascular prevention. In middle-aged hypertensive patients, mean and pulse pressures are increased, and systolic and diastolic pressures are increased to the same degree as mean pressure. Carotid hypertrophy is associated with normal wall stress, but no increased stiffness of wall material has been reported. With age, the normal wall stress is associated with a larger diameter and a stiffer material of carotid but not peripheral arteries. The stiffer wall involves calcifications, large amounts of collagen, and fragmentation and rupture of elastic tissue, which results in increased pulse-wave velocity and alterations of amplitude and timing of wave reflections and thus causes a disproportionate increase in systolic and pulse pressure. During this period, acutely administered nitrates in elderly subjects are able to reduce selectively systolic and pulse pressures without altering diastolic and mean blood pressure and composition of the carotid wall. New therapeutic approaches acting mainly on the wall of large arteries are needed to treat hypertension in elderly patients and prevent stroke and myocardial infarction. These drugs could either selectively lower pulse pressure through changes in wave reflections (as nitrates do) or decrease arterial wall stiffness through modification of the composition of material (such as compounds that act on collagen cross-linking).

Applications of the causality condition to one-dimensional acoustic reflection problems.

The causality condition is examined as a means of determining frequency-domain information about a submerged object from a partial knowledge of its acoustic reflection characteristics. A one-dimensional problem is considered in which an acoustic wave reflects from an object that is described by the impedance it presents to the fluid. Two new applications of the causality condition to the frequency-domain analysis of this problem are investigated and illustrated by numerical examples. In each application, the causality condition is used to find the object's complex impedance from a knowledge of the reflected wave's magnitude. The first application is to experimental studies where one desires a knowledge of an object's complex impedance but practical limitations only allow a measurement of the reflected wave amplitude. Analysis shows that the causality condition may be used to determine the phase of the reflected wave, and hence the object's impedance, if the reflection coefficient is minimum phase. When this is true, examples suggest that the phase of the reflection coefficient may be accurately determined from the causality condition even in the presence of noise and band-limited data. The second application is to design situations, where one wishes to create an object that reflects sound with a specified frequency-dependent magnitude. The causality condition may aid the designer by providing a knowledge of all causal object impedances that produce the same reflection coefficient magnitude. A numerical example is presented in which a variety of causal object impedances produce the same reflection coefficient magnitude over an infinite frequency range.

Propagation of solitary waves through significantly curved shallow water channels

Propagation of solitary waves in curved shallow water channels of constant depth and width is investigated by carrying out numerical simulations based on the generalized weakly nonlinear and weakly dispersive Boussinesq model. The objective is to investigate the effects of channel width and bending sharpness on the transmission and reflection of long waves propagating through significantly curved channels. Our numerical results show that, when travelling through narrow channel bends including both smooth and sharp-cornered 90°-bends, a solitary wave is transmitted almost completely with little reflection and scattering. For wide channel bends, we find that, if the bend is rounded and smooth, a solitary wave is still fully transmitted with little backward reflection, but the transmitted wave will no longer preserve the shape of the original solitary wave but will disintegrate into several smaller waves. For solitary waves travelling through wide sharp-cornered 90°-bends, wave reflection is seen to be very significant, and the wider the channel bend, the stronger the reflected wave amplitude. Our numerical results for waves in sharp-cornered 90°-bends revealed a similarity relationship which indicates that the ratios of the transmitted and reflected wave amplitude, excess mass and energy to the original wave amplitude, mass and energy all depend on one single dimensionless parameter, namely the ratio of the channel width b to the effective wavelength λe. Quantitative results for predicting wave transmission and reflection based on b/λe are presented.

CAD-oriented equivalent circuit modeling of step discontinuities in rectangular waveguides

A novel equivalent circuit model for step discontinuities in rectangular waveguides is presented. The equivalent circuit model is based on a modal analysis and enables full-wave characterization of the step-discontinuity by circuit analysis on commercial simulators. The equivalent circuit model of the H-plane step has been implemented on Libra to demonstrate its accuracy. Results of the circuit analysis were found to be in virtually perfect agreement with the conventional mode-matching solution based on incident and reflected wave amplitudes.

Nonlinear Interaction of Acoustical Waves Due to Cracks and Its Possible Usage for Cracks Detection

An interaction of a CW acoustic wave and a powerful acoustic pulse due to nonlinear properties of a crack-type discontinuity in a solid is considered. Characteristics of nonstationary variations of the reflected wave amplitude and the phase of the transmitted wave, which are induced by the powerful pulse, are determined. The effects should allow one to distinguish cracks from other scatterers and can be used as a base of a new method of crack detection and positioning. Demonstrative signal estimates based on two simplified crack models are presented.

An effective wave-trapping system

Abstract This is a theoretical study of a breakwater-seawall wave-trapping system. The breakwater, being flexible, porous and thin beam-like, is held fixed in the sea bed and idealized as one-dimensional beam of uniform flexural rigidity and uniform mass per unit length. The seawall, being vertical, rigid and impermeable, is located behind the breakwater by a distance of L . The velocity potentials of the wave motion are coupled with the equation of motion of the breakwater. Analytical solutions in closed forms are obtained for the reflected and transmitted velocity potentials together with the displacement of the breakwater. The free-surface elevation, hydrodynamic forces acting on both the breakwater and the seawall are determined. It is found that the values of L , at which the minimum reflected-wave amplitudes reach, are in the range of 2n+1 4 λ to 3n+2 6 λ for breakwaters with different rigidity and permeability. It is shown that, when the spacing L maintains values in the range of 2n+1 4 λ to 3n+2 6 λ, the resultant amplitudes in both regions can be reduced to a favorable amount for any wave and structural parameters. It is also shown that the hydrodynamic forces on the breakwater decrease as the structural flexibility and porosity increase. However, with increases of the structural porosity and flexibility, the seawall experiences an increase of the hydrodynamic forces. Various results are presented in this paper to illustrate the effects of the structural and perous parameters together with the spacing on the response and efficiency of the breakwater-seawall wave-trapping system.

Right ventricular-vascular interaction in congestive heart failure. Importance of low-frequency impedance.

Vasodilator agents are widely used in congestive heart failure. These agents may have important effects on the pulsatile aspects of right ventricular hydraulic load. Fifteen patients with severe congestive heart failure were studied during cardiac catheterization by use of high-fidelity pressure transducers and a catheter-mounted flow velocity probe. Three graded doses of nitroprusside were infused as pulmonary artery (PA) pressure and flow were continuously recorded. From Fourier transforms of signal-averaged waves, PA impedance, hydraulic power, and wave reflection indices were derived. At the highest dose of nitroprusside (66 +/- 41 micrograms/min), cardiac output was significantly improved, whereas PA mean and wedge pressure, resistance, impedance at the first harmonic, characteristic impedance, and wave reflection amplitude were all reduced. At the dose (32 +/- 20 micrograms/min) at which cardiac output first showed improvement, only PA mean pressure and first-harmonic impedance were significantly reduced. Hydraulic power cost per unit of forward flow was also lowered at this dose, despite lack of significant change in pulmonary vascular resistance. At the lowest dose of nitroprusside (11 +/- 4 micrograms/min), six patients experienced a decrease in stroke volume, whereas the other nine were either unchanged (n = 1) or showed an increase (n = 8). Multiple regression revealed that only the change in first-harmonic impedance correlated with this effect, increasing when stroke volume decreased and decreasing when stroke volume increased (P = .02). The change in first-harmonic impedance at this dose appeared to be caused by alterations in the amplitude of PA wave reflections. At higher doses, changes in mean PA pressure (but not in pulmonary vascular resistance) correlated with changes in stroke volume. Nitroprusside vasodilation at low doses alters PA hemodynamics in congestive heart failure primarily through changes in low-frequency impedance. In some patients, this effect is associated with decreased stroke output. At higher doses, favorable alterations in resistance, low- and high-frequency impedance, and wave reflections all contribute to increased forward flow and decreased power requirement per unit forward flow. These findings show that ventricular-vascular interaction is importantly affected by pulmonary vasodilation and that appreciation of pulsatile properties is required to understand the effects of pulmonary vasodilation on cardiac output.

Effect of zeroth-order density inhomogeneity on ion acoustic soliton reflection in a finite ion temperature plasma

Fourier transformation with respect to time is used to solve the differential equation for the amplitude of reflected waves generated as a result of an ion acoustic soliton incident on a density gradient. A general equation giving dependence of the reflected wave amplitude on the zeroth-order plasma density n0 is obtained. Reflection occurs for n0≤0.38, and the amplitude of the reflected wave increases with the increasing plasma density. The reflection coefficient for the reflected wave is defined, and it is shown that the tendency of reflection becomes weaker as the ion temperature is raised.

Reflection and attenuation of equatorial waves in the stratosphere and mesosphere

AbstractQuantitative theoretical estimates are made of the reflection and radiative damping of the Kelvin and Rossby‐gravity (RG) waves propagating upward in the 20–90 km altitude region. An atmosphere with realistic temperature, wind and cooling rate coefficient values is approximated by a model of vertically stacked, thin, homogeneous layers. The amplitude reflection coefficients are shown for different wave periods (T) and zonal wavenumbers (kx). Combining the attenuation due to radiative cooling with the growth due to density decrease, the net changes of wave amplitudes with height in the 20–90 km region are shown for various wave modes.For Kelvin waves the reflected wave energy is generally less than 15% of the incident wave energy, but the reflected wave amplitude can be 20%‐30% of the incident wave amplitude for many modes, at 20 km height. In contrast, many RG wave modes suffer strong or total reflection at various heights if they are not severely damped at lower heights. Calculations for January and July wind conditions reveal a good deal of sensitivity of RG wave reflection to wind conditions.Radiative damping is found to be severe in the mesosphere for Kelvin waves with T ⩾ 6–8 days, depending on wind conditions; it is severe even in the lower stratosphere for RG waves with T &gt; 4 days. Considerable changes in the damping rates and wave amplitudes at various heights take place from January to July owing to wind changes. Kelvin waves in the 2–8‐day period range and RG waves in the 1.5‐3‐day range can propagate into the upper mesosphere/lower thermosphere without large attenuation, depending upon wind conditions.It is shown that our theoretical results can explain several observed characteristics of equatorial waves in the stratosphere and mesosphere, including the recent results on wave disturbances in satellite‐measured temperatures. Further modelling studies based on our methodology can lead to a good physical insight and quantitative interpretations of the SAO‐ and the QBO‐generation processes.