Showing papers on "Amplitude published in 1990"

Transmission of seismic waves across single natural fractures

Abstract: Fractures and other nonwelded contacts are important mechanical and hydrological features of rock masses. Their effects on seismic wave propagation can be modeled as a boundary condition in the seismic wave equation. Seismic stress is continuous across such a boundary, but seismic particle displacement and seismic particle velocity are not. The complete solutions for seismic wave reflection, conversion, and transmission across a displacement and velocity discontinuity between two half-spaces with different densities and elastic properties are derived for all angles of the incident wave. The ratio between the seismic stress across this boundary and the seismic particle displacement and velocity are described by a specific stiffness and a specific viscosity, respectively. A displacement discontinuity results in frequency-dependent reflection and transmission coefficients and a frequency-dependent group time delay. The velocity discontinuity results in frequency-independent coefficients and zero delay. Results of laboratory experiments on compressional and shear wave transmission across three different natural fractures in a quartz monzonite are described. Measurements were made at different effective stresses under dry and saturated conditions at room temperature. It is shown that the effect of these fractures on the spectral amplitudes for compressional and shear pulses transmitted across these fractures are described well by a displacement discontinuity for compressional pulses under dry and saturated conditions and by a combined displacement and velocity discontinuity for shear wave pulses under dry and saturated conditions. Values of specific stiffness and specific viscosity vary between fractures and increase with increasing effective stress, as does the static specific stiffness of these fractures. Changes in the spectral amplitudes of transmitted pulses are also analyzed in terms of attenuation using the seismic quality factor Q, which is found to be a function of frequency.

Laboratory Measurements of Deep-Water Breaking Waves

Abstract: The results of laboratory experiments on unsteady deep-water breaking waves are reported. The experiments exploit the dispersion of deep-water waves to generate a single breaking wave group. The direct effects of breaking are then confined to a finite region in the wave channel and the influence of breaking on the evolution of the wave field can be examined by measuring fluxes into and out of the breaking region. This technique was used by us in a preliminary series of measurements. The loss of excess momentum flux and energy flux from the wave group was measured and found to range from 10% for single spilling events to as much as 25% for plunging breakers. Mixing due to breaking was studied by photographing the evolution of a dye patch as it was mixed into the water column. It was found that the maximum depth of the dye cloud grew linearly in time for one to two wave periods, and then followed a t$^{\frac{1}{4}}$ power law (t is the time from breaking) over a range of breaking intensities and scales. The dyed region reached depths of two to three wave heights and horizontal lengths of approximately one wavelength within five wave periods of breaking. A detailed velocity survey of the breaking region was made and ensemble averages taken of the non-stationary flow. Mean surface currents in the range 0.02-0.03 C (C is the characteristic phase speed) were generated and took as many as 60 wave periods to decay to 0.005 C. A deeper return flow due to momentum lost from the forced long wave was measured. Together these flows gave a rotational region of approximately one wavelength. Turbulent root mean square velocities of approximately 0.02 C were measured near the surface and were still significant at depths of three to four wave heights. More than 90% of the energy lost from the waves was dissipated within four wave periods. Subsequently measured kinetic energy in the residual flow was found to have a t$^{-1}$ dependence. Correlation of all the above measurements with the amplitude, bandwidth and phase of the wave group was found to be good, as was scaling of the results with the centre frequency of the group. Local measures of the breaking wave were not found to correlate well with the dynamical measurements.

HOW TO CALCULATETHE ELASTICSCATFERINGMATRiX IN TWO-DIMENSIONALQUANTUMFIELD THEORIES BY NUMERICAL SIMULATION

Abstract: A method to calculate the elastic scattering amplitude at low energies in two-dimensional quantum field theories is proposed and tested in a numerical simulation of the 0(3) non-linear if-model on a simple square lattice. We also compute the isospin current form factor in this model and compare our results with the known exact expressions for the S-matrix and the form factor in the continuum limit. As a technical improvement, we introduce a two-cluster simulation algorithm which leads to significantly reduced statistical errors in the calculation of four-point correlation functions.

Experimental study of the Faraday instability

Abstract: An experimental study of surface waves parametrically excited by vertical vibrations is presented. The shape of the eigenmodes in a closed vessel, and the importance of the free-surface boundary conditions, are discussed. Stability boundaries, wave amplitude, and perturbation characteristic time of decay are measured and found to be in agreement with an amplitude equation derived by symmetry. The measurement of the amplitude equation coefficients explains why the observed transition is always supercritical, and shows the effect of the edge constraint on the dissipation and eigen frequency of the various modes. The fluid surface tension is obtained from the dispersion relation measurement. Several visualization methods in large-aspect-ratio cells are presented.

Anisotropy in seismic velocities and amplitudes from multiple parallel fractures

Abstract: Many rock structures include multiple, near-parallel, planar discontinuities such as bedding planes or joints. The effects of these nonwelded interfaces on seismic wave propagation are often analyzed using effective moduli, in terms of which seismic wave propagation is independent of frequency and without loss, unless the moduli include imaginary terms. An alternative approach is to treat these interfaces as a boundary condition in the seismic wave equation, across which seismic stress is continuous, but seismic particle displacements are discontinuous. The ratio of the stress to displacement is called the specific stiffness of the interface and characterizes the elastic properties of a fracture. For a completely elastic system this results in frequency-dependent reflection and transmission coefficients for each interface as well as a frequency-dependent group time delay. Using multiple, parallel displacement discontinuities and ignoring converted and reflected waves, expressions derived for transmitted wave amplitudes and group velocities show that these depend on frequency, angle of incidence, and polarization in the case of shear waves. Measurements on a laminated steel block show that shear pulses propagating parallel to the laminations and polarized parallel and perpendicular to the plane of the laminations both travel at the velocity for solid steel, although the spectra of these pulses differ considerably. However, the energy of the pulse polarized perpendicular to the laminations may propagate as an interface wave between each pair of laminations. Predictions of the displacement discontinuity model have features quite distinct from many crustal observations to date. We suggest that we are able to model dense populations of coplanar cracks that cannot be treated by effective moduli methods which require a dilute concentration of cracks.

Amplitude death in an array of limit-cycle oscillators

Abstract: We analyze a large system of limit-cycle oscillators with mean-field coupling and randomly distributed natural frequencies. We prove that when the coupling is sufficiently strong and the distribution of frequencies has sufficiently large variance, the system undergoes “amplitude death”-the oscillators pull each other off their limit cycles and into the origin, which in this case is astable equilibrium point for the coupled system. We determine the region in couplingvariance space for which amplitude death is stable, and present the first proof that the infinite system provides an accurate picture of amplitude death in the large but finite system.

Power-law shot noise

Abstract: The behavior of power-law shot noise, for which the associated impulse response functions assume a decaying power-law form, is explored. Expressions are obtained for the moments, moment generating functions, amplitude probability density functions, autocorrelation functions, and power spectral densities for a variety of parameters of the process. For certain parameters the power spectral density exhibits 1/f-type behavior over a substantial range of frequencies, so that the process serves as a source of 1/f/sup alpha / shot noise for alpha in the range 0 >

A Study of Self-excited Oscillations of the Tropical Ocean–Atmosphere System. Part II: Nonlinear Cases

Abstract: We analyze the linearized version of an analytical model, which combines linear ocean dynamics with a simple version of the Bjerknes hypothesis for El Nino. The ocean is represented by linear shallow water equations on an equatorial beta-plane. It is driven by zonal wind stress, which is assumed to have a fixed spatial form. Stress amplitude is set to be proportional to the thermocline displacement at the eastern boundary. It is shown that, for physically plausible parameter values, the model system can sustain growing Oscillations. Both growth rate and period scale directly with the time that an oceanic Kelvin wave needs to crow the basin. They are quite sensitive to the coupling parameter between thermocline displacement and wind stress, and the zonal location and meridional width of the wind. The most important parameter determining this behavior of the system is the coupling constant. For strong coupling the system exhibits exponential growth without oscillation. As the coupling is decreased ...

Shear-layer pressure fluctuations and superdirective acoustic sources

Abstract: We consider a sequence of boundary-value problems for the acoustic wave equation, with the pressure specified on the boundary as a function of space and time, and simulating features of the pressure field measured just outside a turbulent shear layer supporting large-scale coherent structures. The boundary pressure field has the form of a travelling subsonic plane wave, modulated by a large-scale envelope function. Three models for the envelope distribution are studied in detail, and the particular features which they exhibit are shown to be representative of large classes of amplitude functions.We start by looking at the hydrodynamic near field of the boundary pressure fluctuations, over spatial regions throughout which the motion can be taken as incompressible. Very close to the boundary, the pressure fluctuations decay exponentially with transverse distance, while at sufficiently large distances from the whole wave packet on the boundary, the pressure fluctuations have a dipole algebraic decay. We investigate the transition from exponential to algebraic decay, and find that it is effected through quite a complicated multilayer structure which depends crucially on the detailed form of the envelope.Acoustic fields are then determined both from exact solutions to the wave equation, and from matching arguments. In some cases, where the boundary source is compact, the distant acoustic fields have a simple compressible dipole type of behaviour. In other cases, however, when the boundary source is non-compact, the acoustic field has a superdirective character, the angular variation being described by exponentials of cosines of the angle with the streamwise direction. It is shown how the superdirective acoustic sources are completely compatible with the features of the inner incompressible field, and a criterion for the occurrence of the superdirective acoustic fields will be given. Superdirective fields of this kind have been observed in measurements by Laufer & Yen (1983) on a low-speed round jet of Mach number 0.1, and the general relation of our results to those experiments is explained.

Radiations by solitons at the zero group-dispersion wavelength of single-mode optical fibers

Abstract: Nonlinear pulse propagation at the zero group-dispersion wavelength is studied analytically. It is discovered that, after the characteristic initial frequency splitting, evolution of the pulse envelope that is shifted down to the anomalous regime is described by the nonlinear Schr\"odinger equation with higher-order dispersion as a perturbation. The effect of the perturbation on the pulse is to excite radiation at a frequency inversely proportional to the small parameter \ensuremath{\beta}. The amplitude of the radiation is exponentially small (\ensuremath{\propto}exp(-1/\ensuremath{\beta})] and can be calculated only by the perturbation method that goes beyond all orders.

On the origin of solar wind MHD turbulence: Helios data revisited

Abstract: We study the fluctuations of density, magnetic and velocity fields in the frequency range from (1 day)−1 ≈ 1.2×10−5 Hz to (2.8 min)−1≈ 6×10−3 Hz, as measured by the primary Helios mission (118 days), at heliocentric distances ranging from 0.3 to 1 AU. We address the question of the existence of nonlinear cascades in the observed turbulence, possibly separate for the two “inward” and “outward” components, corresponding to opposite directions of propagation along the large-scale magnetic field. We consider energies per unit mass, not per unit volume, in order to work with variables which are not very sensitive to the heliocentric distance variations. We find that while the whole spectrum of total (kinetic plus magnetic) turbulent energy undergoes very large daily variations both in its amplitude and spectral shape the instantaneous spectrum follows a power law in the frequency range 10−4 to 6×10−3 Hz. We show that both the amplitude and the spectral index m depend on the proton temperature, in a monotonic way, so that a large temperature (thermal speed about 60 km/s) leads to a low level of turbulence with a steep, Kolmogorov-like spectrum (m ≈ −1.8), while a low temperature (thermal speed about 16 km/s) leads to a flatter spectrum (m ≈ −1.2) with a high level of turbulence. This relation is independent from heliocentric distance, at least between 0.3 and 1 AU. Decomposing the turbulent energy into two components, “outward” and “inward,” we find that the spectrum of the outward component also follows very closely the daily proton temperature variations, while the inward component's spectrum is less sensitive to the temperature but also varies with the relative level of rms proton density fluctuations. As a consequence, Alfvenic periods (in which energy is dominated by the outgoing component) occur mainly when density fluctuations are low and temperature is high, which does not contradict the classical view that they are found in the “trailing edges of high-speed streams” (Belcher and Davis, 1971). The existence of inertial ranges controlled by the level of density fluctuations is not completely new (see the numerical simulations of purely hydrodynamic turbulence by Pouquet and Passot (1987)), but the strong dependence of both turbulent energy level and spectral slope on temperature is a new, unexpected property of solar wind turbulence which remains to be explained.

Method and apparatus for analyzing rotating machines

Abstract: A vibration transducer (22) is mounted to a rotating machine (20) for sensing vibration thereof. An output electrical signal from the vibration transducer is analyzed to generate a level display (18) of vibrational displacement per unit time, a speed display (22) indicative of rotational speed, and a bearing condition display (20) indicative of bearing condition, all displays derived directly from the vibration transducer signal. The electrical signal is transformed (36) into a frequency spectrum that has an amplitude for each of a plurality of narrow frequency ranges or bins. Each frequency bin has a characteristic center frequency and a predefined width or band of frequencies. A speed analysis program (38) identifies a set of at least first, second and third order related frequency bins, i.e. frequency bins whose center frequencies are an even multiple of each other, that have a significantly high amplitude and provides the lowest bin center frequency as a control signal to the speed display. A bearing condition analysis program (40) eliminates the bins that are integer multiples of the running speed and lower frequency, e.g. less than third order, identifies sets of bins with relatively large amplitudes that are integer multiples of each other, and selects the set of bins with the largest amplitude as being controlling of bearing condition. After elimination of frequencies not indicative of bearing condition, the bearing defect frequency remains. The amplitude of this frequency is displayed on bearing condition readout (22). The amplitude indicating the severity of the bearing defect.

Regimes in the wintertime circulation over northern extratropics. I: Observational evidence

Abstract: Regimes of the northern extratropical circulation in winter are identified in this paper as clusters of atmospheric states in a low-dimensional phase space generated by the leading EOFs of eddy geopotential fields In order to define the clusters, our algorithm seeks points corresponding to local maxima for the density of atmospheric states; subsequently, a cluster is defined around each density maximum as that portion of the phase space in which the observed density can be locally approximated by a unimodal function Two analyses were performed, using a 5-dimensional and a 3-dimensional space respectively, and they provided consistent results Six clusters were found the largest cluster includes 40% of the fields in our sample; its centroid is close to the climatological winter state, but it possesses a positive projection on the Pacific-North American (PNA) pattern the other five clusters represent anomalous flow regimes and include 52% of the fields One of them shows a low amplitude of the planetary waves; the remaining four represent states with large wave amplitude but different phases the variability between clusters accounts for the bimodality in the amplitude of planetary waves detected in previous observational studies Our analysis reveals that this bimodality is much enhanced in the region of the phase space where the PNA index is negative, and the separation among the clusters is stronger Finally, frequencies of transitions between clusters are presented, which show an asymmetric behaviour in the transitions between regimes with low and high amplitude of planetary waves

The time dependent amplitude equation for the Swift-Hohenberg problem

Abstract: Precise estimates for the validity of the amplitude approximation for the swift-Hohenberg equation are given, in a fully time dependent framework. It is shown that small solutions of orderO(ɛ) which are modulated like stationary solutions have an evolution which is well described in the amplitude approximation for a time of orderO(ɛ-2). For the proofs, we use techniques for nonlinear semigroups and oscillatory integrals.

Ion flux oscillations associated with a radially polarized transverse Pc 5 magnetic pulsation

Abstract: The AMPTE CCE spacecraft observed a transverse Pc 5 magnetic pulsation (period of about 200 s) at 2155-2310 UT on November 20, 1985, at a radial distance of 5.7 - 7.0 earth radii, at a magnetic latitude of 1.2 - 19 deg, and near 1300 magnetic local time. The magnetic pulsation exhibits properties consistent with a standing Alfven wave with a second-harmonic standing structure along the ambient magnetic field. The amplitude and the phase of the flux pulsation are found to be a function of the particle detector look direction and the particle energy. The observed energy dependence of the shift is interpreted as the result of a drift-bounce resonance of the ions with the wave. From this interpretation it follows that the wave propagated westward with an azimuthal wave number of approximately 100. Thus the study demonstrates that particle data can be useful for determining the spatial structure of some types of ULF waves.

Noise and critical behavior of the pupil light reflex at oscillation onset

Abstract: We have induced oscillations in the human pupil light reflex using two different kinds of external electronic feedback: smooth negative feedback (SNF) and piecewise constant negative feedback (PCNF). The behavior of the mean amplitude and period at oscillation onset are shown to be in good agreement with a model of this neural system incorporating the external feedback. The critical behavior displayed through amplitude and period fluctuations is different in each case. The observation that amplitude fluctuations are larger (smaller) than period fluctuations for SNF (PCNF) is explained theoretically and by numerical integration of a stochastic delay-differential equation with additive and multiplicative colored noise. We find that both types of noise postpone the Hopf bifurcation in SNF by an amount proportional to the noise intensity and inversely proportional to the correlation time. The implications for analyzing bifurcations in neural systems are discussed.

Frequency domain optical imaging using diffusion of intensity modulated radiation

Abstract: Arrangements are disclosed for producing images based upon diffusional wave theory and frequency domain analysis. A medium to be imaged is illuminated with amplitude modulated radiation, and diffusional radiation transmitted or reflected by the medium is detected at a plurality of detection locations, as by a television camera. The phase and also the amplitude demodulation of the amplitude modulated diffusional radiation is detected at each detection location. A relative phase image and also a demodulation amplitude image of the medium are then generated from respectively the detected relative phase values and the detected demodulation amplitudes of the diffusional radiation at the plurality of locations. The present invention is particularly suited for medical applications for generating images of internal anatomical details of the body by using a near infrared amplitude modulated source for illumination of the body. In such medical applications, the body is illuminated with near infrared radiation having a wavelength between 600 and 1200 nanometers which is amplitude modulated at a frequency in the megahertz to gegihertz range, and internal images of the patient are generated for medical diagnosis. In preferred embodiments, a laser is utilized to generate the near infrared radiation near or below a 10 watt power level which is coupled by fiber optic cables to the body of the patient. Detection is also with fiber optic cables placed in direct contact with an opposed surface of the body which couple the transmitted diffusional radiation to an image intensifier placed in front of a television camera detector. The gain of the image intensifier is modulated at a frequency to obtain a heterodyned output frequency of less than 60 hertz which is within the detection bandwidth of the television camera.

The amplitudes of interplanetary fluctuations: Stream structure, heliocentric distance, and frequency dependence

Abstract: A study is presented of the heliocentric distance, frequency, and stream structure dependence of the amplitudes of interplanetary fluctuations in the velocity and magnetic field from 0.3 to nearly 20 AU and for spacecraft-frame periods of 10 days to a few hours. Evidence is presented that, at a given heliocentric distance, the amplitude of the magnetic field fluctuations is proportional to the magnitude of the field, nearly independently of the solar wind speed. The radial evolution of magnetic fluctuations is shown to be nearly consistent with WKB expectations except at smaller scales in the inner heliosphere and at the largest scales in the outer heliosphere. While the large-scale velocity fluctuations are kinetic energy-dominated in the inner heliosphere due to the presence of streams, the magnetic fluctuation energy eventually comes to be slightly dominant over the kinetic energy at all scales. The theoretical implications of the results are considered.

Saturation of a single mode driven by an energetic injected beam. III. Alfven wave problem

Abstract: The saturation amplitude of Alfven waves, excited by alpha particles produced in an ignited tokamak, is estimated. The formalism that has been developed to describe the saturation of a single mode is generalized to toroidal geometry. The saturation level is estimated for the toroidal Alfven gap mode. The alpha particle radial flux resulting from the finite wave amplitude is found to produce relatively weak energy losses compared to the usual energy drag losses.

Ising model in a time-dependent magnetic field.

Abstract: We report the results of Monte Carlo simulations on a two-dimensional Ising model in a sinusoidally oscillating external magnetic field. We find evidence for a dynamical phase transition, supporting the results of recent mean-field and large-N analyses of this model. We also analyze the hysteresis loops as a function of the amplitude and frequency of the applied field, fitting our data to a proposed areal scaling law.

Improved correlation discrimination using an amplitude-modulated phase-only filter.

Abstract: A novel amplitude-modulated phase-only filter (AMPOF) is proposed for achieving improved correlation discrimination The proposed AMPOF has an amplitude spectrum which is the inverse of a biased amplitude spectrum of the object function and a phase spectrum which is a complex conjugate of the phase spectrum of the object function When compared with the phase-only filters, the AMPOF is found to have significantly superior correlation discrimination capability

The density and shear velocity contrast at the inner core boundary

Abstract: SUMMARY A systematic search of short-period GDSN seismograms from 1980 to 1984 at ranges from 20" to 90" identifies two probable PKiKP arrivals. PKiKPIPcP amplitude ratios for these phases are consistent with previous studies. However, more typically PKiKP is not observed, even when clear PcP arrivals are seen. We use these data to place upper bounds on PKiKPIPcP amplitude ratios for 100 event-station pairs. These bounds indicate that most measurements of PKiKP amplitudes are biased toward large values and predict reflection coefficients at the inner core boundary (ICB) which are too high. Our upper limits on PKiKP amplitudes roughly constrain the density jump at the ICB to be less than l.Og~m-~ and the shear velocity at the top of the inner core to be greater than 2.5 km s-l, assuming a sharp discontinuity at the ICB. Upper bounds on PKiKPIP amplitude ratios at ranges between 70" and 90" are consistent with these results but are less reliable due to take-off angle differences between P and PKiKP. Approximately 50 observed free oscillations of the Earth are sensitive to the structure of the inner core. Modem models derived from these and other mode data typically have a density jump at the ICB of 0.5-0.6 g ~m-~. An experiment in which we varied the mean density of the inner core indicates that the mode frequencies are roughly linear functionals of this parameter. The fit to the data is seriously degraded if the density jump is significantly different from 0.55 g ~m-~. Many of the modes are also strongly sensitive to the shear velocity in the inner core, and forward modelling indicates that the average inner-core shear velocity is probably 3.45 f 0.1 km s-'. These results are compatible with the short-period PKiKP amplitude bounds, indicating that there is no inconsistency between PKiKP and normal mode data regarding the density and shear velocity structure at the inner core boundary.

Single-mode Faraday waves in small cylinders

Abstract: Experiments on single-mode Faraday waves in small rectangular and circular cylinders in which both capillary and viscous effects were significant aie reported. Measurements of threshold forcing (for neutral stability) and steady-state wave amplitudes are compared with theoretical predictions. Theoretical predictions of the resonant frequency of a single mode and of the threshold amplitude for its excitation on the hypothesis of linear boundary-layer damping agree well with the measured data. (The theory must use the measured damping rate to predict these quantities for waves in the rectangular cylinder.) Theoretical predictions of wave amplitudes are in reasonable agreement with those observed in the circular cylinder; however, the theory provides only qualitative predictions of amplitudes for waves in the rectangular cylinder. In experiments in which two modes are theoretically admissible, the one with the smaller damping rate is observed; however, a single-mode calculation proves inadequate for the prediction of the stability boundary.

Vibrotactile intensity discrimination measured by three methods.

Abstract: The difference threshold for the detection of changes in vibration amplitude was measured as a function of the intensity and frequency of stimuli delivered through a 2.9‐cm2 contactor to the thenar eminence. Stimuli were either 25‐ or 250‐Hz sinusoids, narrow‐band noise centered at 250 Hz, or wideband noise. Thresholds were measured by two‐interval, forced‐choice tracking under three methods of stimulus presentation. In the gated‐pedestal method, subjects had to judge which of two 700‐ms bursts of vibration separated by 1000 ms was more intense. In the continuous‐pedestal method, subjects had to detect a 700‐ms increment in the amplitude of an ongoing pedestal of vibration. In the two‐burst–continuous‐pedestal method with 1500‐ms pedestals, the subject had to detect which of two successively presented pedestals contained a 500‐ms amplitude increment. Thresholds were consistently lower for detecting increments in the amplitude of a continuous pedestal of vibration than for detecting amplitude differences between briefly presented successive pedestals or amplitude increments in successive pedestals. A ‘‘near miss’’ to Weber’s law was found both for sinusoidal and for noise stimuli. The difference threshold was not affected by stimulus frequency condition.

Far-field pattern determination from the near-field amplitude on two surfaces

Abstract: The possibility of determining the far field of radiating systems by measuring only the near-field amplitude is investigated. The main difficulties of the problem are examined in some detail and a new near-field/far-field transformation technique is developed, based on the measurement of the near-field amplitude over two surfaces surrounding the antenna under test. The accuracy of the far-field reconstruction results are related both to the distance between such surfaces and to some a priori information concerning the near-field phase and/or the radiating system. The information on the radiating system allows relaxation of the need for any information on the near-field phase provided that the distance between the measurement surfaces is high enough. Conversely, the knowledge of a more or less corrupted near-field phase allows reduction of such distances without affecting the accuracy of the far-field reconstruction. Numerical examples validating the effectiveness of the developed algorithm are provided for the planar scanning case. >

Inter-subband scattering in a 2D electron gas

Abstract: A new technique, using the absolute amplitude of the low-field Shubnikov-de Haas oscillations, is presented which allows the direct measurement of inter-subband scattering in 2D heterojunction structures. When applied to a heterojunction with two subbands occupied the technique is used to show that inter-subband scattering is independent of temperature between 1 and 4 K. In agreement with previous reports frequency and amplitude intermodulation, which increases with temperature, is also observed. This is attributed to mixing, by thermal or impurity damping, between the two sets of oscillations in the Fermi energy. This explanation is supported by a model calculation which reproduces the features of the experimental results.