Showing papers on "Amplitude published in 1983"

Stochastic simulation of high-frequency ground motions based on seismological models of the radiated spectra

Abstract: Theoretical predictions of seismic motions as a function of source strength are often expressed as frequency-domain scaling models. The observations of interest to strong-motion seismology, however, are usually in the time domain (e.g., various peak motions, including magnitude). The method of simulation presented here makes use of both domains; its essence is to filter a suite of windowed, stochastic time series so that the amplitude spectra are equal, on the average, to the specified spectra. Because of its success in predicting peak and rms accelerations (Hanks and McGuire, 1981), an ω -squared spectrum with a high-frequency cutoff ( f m), in addition to the usual whole-path anelastic attenuation, and with a constant stress parameter (Δ σ ) has been used in the applications of the simulation method. With these assumptions, the model is particularly simple: the scaling with source size depends on only one parameter—seismic moment or, equivalently, moment magnitude. Besides peak acceleration, the model gives a good fit to a number of ground motion amplitude measures derived from previous analyses of hundreds of recordings from earthquakes in western North America, ranging from a moment magnitude of 5.0 to 7.7. These measures of ground motion include peak velocity, Wood-Anderson instrument response, and response spectra. The model also fits peak velocities and peak accelerations for South African earthquakes with moment magnitudes of 0.4 to 2.4 (with f m = 400 Hz and Δ σ = 50 bars, compared to f m = 15 Hz and Δ σ = 100 bars for the western North America data). Remarkably, the model seems to fit all essential aspects of high-frequency ground motions for earthquakes over a very large magnitude range . Although the simulation method is useful for applications requiring one or more time series, a simpler, less costly method based on various formulas from random vibration theory will often suffice for applications requiring only peak motions. Hanks and McGuire (1981) used such an approach in their prediction of peak acceleration. This paper contains a generalization of their approach; the formulas used depend on the moments (in the statistical sense) of the squared amplitude spectra, and therefore can be applied to any time series having a stochastic character, including ground acceleration, velocity, and the oscillator outputs on which response spectra and magnitude are based .

Reverse time migration

Abstract: Migration of stacked or zero-offset sections is based on deriving the wave amplitude in space from wave field observations at the surface. Conventionally this calculation has been carried out through a depth extrapolation. We examine the alternative of carrying out the migration through a reverse time extrapolation. This approach may offer improvements over existing migration methods, especially in cases of steeply dipping structures with strong velocity contrasts. This migration method is tested using appropriate synthetic data sets.

Ionisation of atoms by ion impact

Abstract: Total cross sections are calculated for the ionisation of a hydrogen atom by multicharged fully-stripped ions in the 20-1000 keV amu-1 impact energy range. Distortion is accounted for in the entrance channel (via the eikonal approximation) and in the exit channel (via the continuum distorted-wave approximation). The transition amplitude is calculated in the post form so that the electronic nonorthogonal kinetic energy is treated as the perturbation. It is concluded that of the currently available models this theory is the most successful and versatile over a considerable range of energies and charges. Specifically for ionisation of a hydrogen atom by 50 keV protons the authors present doubly differential cross sections for electrons ejected in the forward direction and singly differential cross sections as a function of emission energy. The question of cusps and peaks in the differential cross sections is considered as is the question of charged scaling of the total cross section.

Sampling Theory and Wave Propagation

Abstract: In the seismic reflection method, the seismic signal does vary in amplitude, shape, frequency and phase versus the propagation time

Relation between shapes of post-synaptic potentials and changes in firing probability of cat motoneurones

Abstract: 1. The shapes of post-synaptic potentials (p.s.p.s) in cat motoneurones were compared with the time course of changes in firing probability during repetitive firing. Excitatory and inhibitory post-synaptic potentials (e.p.s.p.s and i.p.s.p.s) were evoked by electrical stimulation of peripheral nerve filaments. With the motoneurone quiescent, the shape of each p.s.p. was obtained by compiling post-stimulus averages of the membrane potential. Depolarizing current was then injected to evoke repetitive firing, and the post-stimulus time histogram of motoneurone spikes was obtained; this histogram reveals the primary features (peak and/or trough) of the cross-correlogram between stimulus and spike trains. The time course of the correlogram features produced by each p.s.p. was compared with the p.s.p. shape and its temporal derivative. 2. E.p.s.p.s of different sizes (0.15-3.1 mV, mean 0.75 mV) and shapes were investigated. The primary correlogram peak began, on the average, 0.48 msec after onset of the e.p.s.p., and reached a maximum 0.29 msec before the summit of the e.p.s.p; in many cases the correlogram peak was followed by a trough, in which firing rate fell below base-line rate. The height of the correlogram peak with respect to base-line firing rate increased in proportion to both the amplitude of the e.p.s.p.s and the magnitude of their rising slope (in these data, amplitude and rising slope also covaried). 3. The mean half-width of the correlogram peaks (0.65±0.28 msec (S.D.)) agreed better with the average half-width of the e.p.s.p. derivatives (0.55±0.33 msec) than with the half-width of the e.p.s.p.s (4.31±1.50 msec). The shape of the primary correlogram peak produced by simple e.p.s.p.s often resembled the temporal derivative of the e.p.s.p. rise. For larger e.p.s.p.s, the shape of the correlogram peak closely matched the e.p.s.p. derivative, while smaller e.p.s.p.s in appreciable synaptic noise often generated correlogram peaks somewhat wider than their derivatives. On the other hand, the match between the correlogram trough that followed the peak and the negative slope of the e.p.s.p. was better for the small e.p.s.p.s than for the large e.p.s.p.s; for large e.p.s.p.s the drop in firing rate during the trough was typically limited at zero. These relations were tested further by comparing the integral of the correlogram with the time course of the e.p.s.p. For large e.p.s.p.s, the correlogram integral matched the rising phase of the e.p.s.p. quite well, although it underestimated the rate of decline of the e.p.s.p. 4. Complex e.p.s.p.s with distinct components during their rising phase often produced correlogram peaks that did not accurately reflect the features in their temporal derivative. Temporal summation of large e.p.s.p.s and summation of their derivatives was linear, but the resulting correlogram peaks did not add linearly; the second correlogram peak was often smaller than the first. However, when small e.p.s.p.s were summed, the correlogram peaks more closely matched the e.p.s.p. derivatives. 5. Compound i.p.s.p.s produced primary correlogram troughs followed by a shallow compensatory peak. The width of the trough extended through the peak of the i.p.s.p., well into the falling phase of the i.p.s.p. During the trough the firing rate usually dropped to zero. Thus, the primary correlogram features produced by large i.p.s.p.s did not resemble any linear combination of the shape of the i.p.s.p. and/or its temporal derivative. Moreover, the integral of the correlogram did not resemble the i.p.s.p. 6. The major observations are consistent with a motoneurone model in which a membrane potential ramp approaches a voltage threshold for spike initiation. Near threshold, e.p.s.p.s superimposed on the ramp advance the occurrence of spikes to their rising phase, producing a correlogram peak resembling their temporal derivative. Synaptic noise would increase the probability of sampling the peak of the e.p.s.p., leading to wider correlogram peaks. I.p.s.p.s would delay the occurrence of spikes to their falling phase.

Method and apparatus for evaluating rhythmic oscillations in aperiodic physiological response systems.

Abstract: A method and apparatus for detecting amplitude variations in the rhythmic oscillations of a physiological response pattern in a frequency range of interest. A sensor (1) is used to detect an occurrence of an event in the cycle of a physiological response and the interval between each reoccurring event is timed and placed in a buffer (9). The output from the buffer (9) is read out at predetermined time intervals and fed to a filter (90) which determines the aperiodic portion of the signal and substracts that aperiodic portion to output a residual data signal. The residual data signal is fed to a band pass filter (94) which filters in a region determined by the predetermined frequency range of interest and which outputs to a calculation and display device (96) wherein the variance of the rhythmic oscillation is calculated and displayed.

Theory of the phase noise and power spectrum of a single mode injection laser

Abstract: Spontaneous emission alters the phase and amplitude of the laser field. The amplitude changes induce relaxation oscillations, which cause additional phase changes while restoring the field amplitude to the steady state value. It was previously shown that the additional phase changes greatly enhance the linewidth. We show here that the additional phase changes also give rise to line shape structure in the form of additional peaks separated from the main peak by multiples of the relaxation oscillation frequency. The calculated mean square phase change and power spectrum are in good agreement with published observations.

On the Joint Distribution of Wave Periods and Amplitudes in a Random Wave Field

Abstract: A theoretical probability density is derived for the joint distribution of wave periods and amplitudes which has the following properties: (1) the distribution is asymmetric, in accordance with observation; (2) it depends only on three lowest moments m 0 , m 1 , m 2 of the spectral density function. It is therefore independent of the fourth moment m 4 , which previously was used to define the spectral width (Cavanie et al . 1976). In the present model the width is defined by the lower-order parameter v = ( m 0 m 2 / m 2 1 - 1) ½ . The distribution agrees quite well with wave data taken in the North Atlantic (Chakrabarti & Cooley 1977) and with other data from the Sea of Japan (Goda 1978). Among the features predicted is that the total distri­bution of wave heights is slightly non-Rayleigh, and that the interquartile range of the conditional wave period distribution tends to zero as the wave amplitude diminishes. The analytic expressions are simpler than those derived previously, and may be useful in handling real statistical data.

The apparent attenuation of a scattering medium

Abstract: We report the results of some numerical experiments that bring out the lowpass characteristics of a purely elastic medium with a heterogeneous velocity structure. Although the typical fluctuation is spatially confined within less than a wavelength, waves propagating over a sufficiently long path suffer major cumulative effects. We summarize the removal of high frequencies during transmission by a frequency-independent apparent Q, and show that attenuation by intrinsic friction and scattering are approximately additive. We propose some diagnostics that might help to distinguish the presence of velocity fluctuations and resultant scattering from the presence of anelasticity and true dissipation. When scattering dominates over intrinsic friction: (1) the coda of a transmitted wave contains relatively higher frequencies than the initial pulse; (2) the attenuation deduced from the power spectrum of the transmitted wave is greater than that deduced from the phase spectrum; (3) compressional and shear wave apparent Q's are approximately equal; and (4) estimates of apparent Q made from reflected coda vary with frequency, while estimates made from the transmitted waves do not. We also outline several topics in the theory of wave propagation that will be relevant in a satisfactory interpretation of short-period observations, if the amplitude of such signals is affected by scattering.

A model relating ultrasonic scattering measurements through liquid–solid interfaces to unbounded medium scattering amplitudes

Abstract: The relationship between scattering data obtained from ultrasonic experiments, in which the waves are excited and detected in a finite measurement geometry, and unbounded medium, farfield scattering amplitudes is considered. For a scatterer in a single fluid medium, a Green’s function approach is used to develop an approximate, but absolute, relationship between these experimental and theoretical cases. Electromechanical reciprocity relationships are then employed to generalize to a two medium case in which the scatterer is located in an elastic solid which, along with the ultrasonic transducer, is immersed in a fluid medium. The case explicitly considered is one in which the incident waves are quasiplanar over the volume of the flaw and the scattering amplitudes are slowly varying over the range of angles subtended by the receiving transducer. Analytic approximations are developed for the absolute relationship of the received transducer signal to the unbounded medium scattering amplitudes, and formal exp...

Nonlinear oscillations of inviscid drops and bubbles

Abstract: Moderate-amplitude axisymmetric oscillations of incompressible inviscid drops and bubbles are studied using a Poincare–Lindstedt expansion technique. The corrections to the drop shape and velocity potential caused by mode coupling at second order in amplitude are predicted for two-, three- and four-lobed motions. The frequency of oscillation is found to decrease with the square of the amplitude; this result compares well with experiments and numerical calculations for drops undergoing two-lobed oscillations.

Chaotic vibrations of a beam with non-linear boundary conditions

Abstract: Forced vibrations of an elastic beam with non-linear boundary conditions are shown to exhibit chaotic behavior of the strange attractor type for a sinusoidal input force The beam is clamped at one end, and the other end is pinned for the tip displacement less than some fixed value and is free for displacements greater than this value The stiffness of the beam has the properties of a bi-linear spring The results may be typical of a class of mechanical oscillators with play or amplitude constraining stops Subharmonic oscillations are found to be characteristic of these types of motions For certain values of forcing frequency and amplitude the periodic motion becomes unstable and nonperiodic bounded vibrations result These chaotic motions have a narrow band spectrum of frequency components near the subharmonic frequencies Digital simulation of a single mode mathematical model of the beam using a Runge-Kutta algorithm is shown to give results qualitatively similar to experimental observations

Amplitude Equations for Systems with Competing Instabilities

Abstract: We describe how to derive ordinary differential equations to predict the time dependence of a system governed by partial differential equations when that system is near to the polycritical condition for the onset of several instabilities. The method is illustrated for the general case of two competing instabilities and then a specific physical example of this case is worked out in detail. The basic idea is to extend the Krylov–Bogolyubov–Mitropolsky method of nonlinear mechanics to bifurcation problems.

A parabolic equation for the combined refraction-diffraction of Stokes waves by mildly varying topography

Abstract: A parabolic equation governing the leading-order amplitude for a forward-scattered Stokes wave is derived using a multiple-scale perturbation method, and the connection between the linearized version and a previously derived approximation of the linear mild slope equation is investigated. Two examples are studied numerically for the situation where linear refraction theory leads to caustics, and the nonlinear model is shown to predict the development of wave-jump conditions and significant reductions in amplitude in the vicinity of caustics.

Cavitation Events in Thuja occidentalis L.? : Utrasonic Acoustic Emissions from the Sapwood Can Be Measured.

Abstract: Ultrasonic acoustic emissions (AE) in the frequency range of 0.1 to 1 megahertz appear to originate in the sapwood of Thuja occidentalis L. The AE are vibrations of an impulsive nature. The vibrations can be transduced to a voltage waveform and amplified. The vibrations of each AE event begin at a large amplitude which decays over 20 to 100 microseconds. Strong circumstantial evidence indicates that the ultrasonic AE result from cavitation events because: (a) they occur only when the xylem pressure potential Ψxp is more negative than a threshold level of about —1 megapascal; (b) the rate of AE events increases as Ψxp decreases and when the net rate of water loss increases; (c) the AE can be stopped by raising Ψxp above —1 megapascal. Ultrasonic AE have been measured in whole terminal shoots allowed to dry in the laboratory, in isolated pieces of sapwood as they dried in the laboratory, and in whole terminal shoots in a pressure bomb when Ψxp was decreased by lowering the gas pressure in the pressure bomb.

Wave modulation and breakdown

Abstract: Time series of amplitude, frequency, wavenumber and phase speed are measured in an unstable deep-water wavetrain using a Hilbert-transform technique. The modulation variables evolve from sinusoidal perturbations that are well described as slowly varying Stokes waves, through increasingly asymmetric modulations that finally result in very rapid jumps or ‘phase reversals’. These anomalies appear to correspond to the ‘crest pairing’ described by Ramamonjiarisoa & Mollo-Christensen (1979). The measurements offer a novel local description of the instability of deep-water waves which contrasts markedly with the description afforded by conventional Fourier decomposition. The measurements display very large local modulations in the phase speed, modulations that may not be anticipated from measurements of the phase speeds of individual Fourier components travelling (to leading order) at the linear phase speed (Lake & Yuen 1978).

Meander Bends of High Amplitude

Abstract: Meander bends of high amplitude in alluvial rivers often display a high degree of coherency. The only analytical equation heretofore available to describe such bends is the sine‐generated curve, which has no rigorous derivation in the context of rivers. Herein a nonlinear “bend equation,” based on a dynamical description of flow in bends and a kinematical description of bank erosion, is used to describe channel migration. This equation admits solutions of constant amplitude that migrate downstream with constant speed. The solution at high amplitude displays a prominent skewing that reveals the direction of flow. At low amplitude, the solution reduces to the sine‐generated curve.

Solitary and Periodic Gravity-Capillary Waves of Finite Amplitude,

Abstract: Two-dimensional solitary and periodic waves in water of finite depth are considered. The waves propagate under the combined influence of gravity and surface tension. The flow, the surface profile and the phase velocity are functions of the amplitude of the wave and the parameters l = λ/H and τ = T/ρgH2. Here λ is the wavelength, H the depth, T the surface tension, ρ the density and g the acceleration due to gravity. For . In addition, it is shown that elevation solitary waves cannot be obtained as the continuous limit of periodic waves as the wavelength tends to infinity. Graphs of the results are included.

Quantitative studies of stimulus coding in first-order vibrissa afferents of rats. 2. Adaptation and coding of stimulus parameters

Abstract: Mechanosensory neurons are often classified as either rapidly adapting or slowly adapting. We examined response decay (adaptation) during constant deflection of the vibrissae with quantitative, repeatable, ad hoc measures. We found that first-order vibrissa-activated neurons of the fifth ganglion exhibit a variety of adaptation rates that appear to be distributed continuously between the rapidly and slowly adapting extremes. Also, adaptation rate is influenced markedly by stimulus magnitude. We found no evidence for a dichotomy within the more slowly adapting neurons on the basis of discharge regularity. Threshold tuning curves were used to evaluate vibration sensitivity. Both the best frequencies and 1:1 discharge thresholds for sinusoidal stimulation ranged over two orders of magnitude and were continuously distributed. First-order vibrissa-activated afferents exhibit a broad variety of response patterns to constant-velocity stimulation. The pattern of discharge varied both as a function of time during constant-velocity (ramp) deflection and as a function of stimulus velocity. Although information about the parameters of a stimulus may be conveyed by any of several features of the response pattern, it appears that few if any neurons function as "pure" encoders of any particular stimulus parameter. We examined quantitatively the relationship between discharge rate and both velocity and amplitude of vibrissa deflection with the aid of a computer-based curve-fitting procedure. We found that about half the observed rate-level functions were best described by a power function; the remainder were best fit by a logarithmic function. The parameters of the best-fitting functions varied widely and continuously, emphasizing further the diversity of coding properties of the rat's vibrissa afferents. Rate-level curves for stimulus magnitude generally exhibited saturation; some were nonmonotonic. None were described adequately by either a logarithmic function or a power function.

Exploring the functional significance of physiological tremor: A biospectroscopic approach

Abstract: The functional significance of physiological tremor — the high frequency (8–12 Hz), low amplitude oscillation that occurs during the maintenance of steady limb postures — is not known. Often tremor, perhaps because of its pathological manifestations, is considered a source of unwanted noise in the system, something to be damped out or controlled. An examination of the phase relationship between tremor and rapid voluntary finger movement in normal subjects suggests a very different view. In four experiments in which tremor displacement and accompanying electromyographic activity were simultaneously monitored, we show a clear and systematic relationship between tremor and movement initiation. Empirically obtained frequency distributions of tremor peak-to-movement initiation time were most closely aligned to a probability density function (derived via numerical integration techniques) that assumed movements were initiated when the muscle-joint system possessed peak momentum. This relationship — evaluated by Chisquare goodness-of-fit tests — was evident regardless of whether the movements were self-paced (Experiments 1 and 2) or in response to an auditory reaction time signal (Experiments 3 and 4). The addition of a load to the finger in Experiments 2 and 4, though tending to reduce tremor frequency, did not prove disruptive, nor did a fractionated reaction time analysis reveal any significant inertial contribution to the maintenance of the phase relationship. These data are consistent with an emerging view that the motor control system is sensitive to its own dynamics, and suggest that under certain conditions normal physiological tremor is a potentially exploitable oscillation intrinsic to the motor system.

Solitary waves and double layers on auroral field lines

Abstract: Time stationary solutions to the Vlasov-Poisson equations for ion holes and double layers are examined along with particle simulations that pertain to recent observations of small amplitude electric field structures on auroral field lines. Both the time stationary analysis and the simulations suggest that the observed double layers evolve from holes in ion phase space. Multiple small amplitude double layers, as seen in long simulation systems, are observed to propagate past the spacecraft and may account for the acceleration of plasma sheet electrons to produce inverted-V precipitation.

A second-order theory for solitary waves in shallow fluids

Abstract: Solitary waves in density stratified fluids of shallow depth are described, to first order in wave amplitude, by the Korteweg–de Vries equation; the solution for a single solitary wave has the familiar ‘‘sech2’’ profile and a phase speed which varies linearly with the wave amplitude. This theory is here extended to second order in wave amplitude. The second‐order correction to the wave profile and the phase speed and the first‐order correction to the wavelength are all determined. Four special cases are discussed in detail. In certain special circumstances the first‐order theory may fail due to the vanishing of the nonlinear coefficient in the Korteweg–de Vries equation. When this occurs a different theory is required which leads to an equation with both quadratic and cubic nonlinearities.

Observation of relaxation resonance effects in the field spectrum of semiconductor lasers

Abstract: Subsidiary maxima are observed in the field spectra of single mode semiconductor lasers Measurements of their power dependence show they are linked to the relaxation resonance We attribute these maxima to combined phase and amplitude fluctuations at the relaxation resonance A theoretical calculation of the field spectrum using the results of a noise analysisincorporating carrier dynamics agrees very well with observations

Asymptotic behavior of the fixed-angle on-shell quark scattering amplitudes in non-Abelian gauge theories

Abstract: In this paper we find the asymptotic behavior of the fixed-angle on-shell quark-quark scattering amplitude in non-Abelian gauge theories in the limit of very large center-of-mass energy ..sqrt..s . We sum the perturbation series to all orders in the coupling constant and all powers of lns, but ignore terms which are suppressed by a power of s order by order in perturbation theory. In the s..-->..infinity limit the amplitude vanishes as exp(-..cap alpha.. lns ln lns), where ..cap alpha.. is a constant. The phase of the amplitude is shown to be free from infrared divergences. Hence the phase is a perturbatively calculable function and may provide important tests of QCD.

Variation in light intensity with height and time from subsequent lightning return strokes

Abstract: Photographic measurements of relative light intensity as a function of height and time have been conducted for seven return strokes in two lightning flashes at 7.8 and 8.7 km ranges, using film which possesses an approximately constant spectral response in the 300-670 nm range. The amplitude of the initial light peak is noted to decrease exponentially with height, with a decay constant of 0.6-0.8 km. The logarithm of the peak light intensity near the ground is found to be approximately proportional to the initial peak electric field intensity, implying that the current decrease with height may be much slower than the light decrease. Absolute light intensity is presently estimated through the integration of the photographic signals from individual channel segments, in order to simulate the calibrated, all-sky photoelectric data of Guo and Krider (1982).

Effects of crossed‐olivocochlear‐bundle stimulation on cat auditory nerve fiber responses to tones

Abstract: Phase, synchronization index, and average firing rate were calculated from period histograms of tone burst responses obtained from sound level series with and without electrical stimulation of the cross‐olivocochlear‐bundle (COCB). For most fibers, at low sound levels, COCB stimulation shifted the rate and synochronization index level functions up in sound level but did not shift the phase‐level function in the same way. These effects can be accounted for if the stage at which the COCB acts precedes the stage at which analog signals are changed into neural firing patterns with a given rate and synchronization index, but does not precede the stage at which the level dependence of phase is introduced. Some level series show an abrupt phase change and ‘‘dips’’ in rate and synchronization‐index level functions at high sound levels. COCB stimulation shifted these abrupt phase changes and dips down in sound level and usually had little effect at sound levels above these abrupt phase changes and dips. The following explanatory hypothesis is developed: excitation of an auditory‐nerve fiber is the result of two factors which are out of phase and have different growth functions. The two factors cancel when they are equal in amplitude producing the dips and phase changes. COCB stimulation reduces the more sensitive factor but does not change the other factor so the two factors cancel at a lower sound level with COCB stimulation.