Energy mode distribution: An analysis of the ratio of anti-Stokes to Stokes amplitudes generated by a pair of counterpropagating Langmuir waves

Results from plasma wave experiments in spacecrafts give support to nonlinear interactions involving Langmuir, electromagnetic, and ion-acoustic waves in association with type III solar radio bursts. Starting from a general form of Zakharov equation (Zakharov, V.E., 1985. Collapse and self-focusing of Langmuir waves. Hand-book of Plasma Physics Cap.2, 81–121) the equations for electric fields and density fluctuations (density gratings) induced by a pair of counterpropagating Langmuir waves are obtained. We consider the coupling of four triplets. Each two triplets have in common the Langmuir pump wave (forward or backward wave) and a pair of independent density gratings. We numerically solve the dispersion relation for the system, extending the work of (Alves, M.V., Chian, A.C.L., Moraes, M.A.E., Abalde, J.R., Rizzato, F.B., 2002. A theory of the fundamental plasma emission of type- III solar radio bursts. Astronomy and Astrophysics 390, 351–357). The ratio of anti-Stokes (AS) (ω₀+ω) to Stokes (S) (ω₀-ω^*) electromagnetic mode amplitudes is obtained as a function of the pump wave frequency, wave number, and energy. We notice that the simultaneous excitation of AS and S distinguishable modes, i.e., with Re{ω}=ω_r≠0, only occurs when the ratio between the pump wave amplitudes, r is ≠1 and the pump wave vector k₀ is , W₀ being the forward pump wave energy. We also observe that the S mode always receives more energy.     

Simulation studies of processes associated with stimulated electromagnetic emission (SEE) in the ionosphere

Results of numerical simulation studies of processes associated with Stimulated Electromagnetic Emission (SEE) produced during ionospheric heating experiments are presented. A one-dimensional magnetized electrostatic Particle-In-Cell (PIC) simulation model with uniform plasma density is used to investigate electrostatic wave generation in the region where the pump frequency ω₀ approximately equals the upper hybrid frequency ω_uh. In particular, the simulation plasma is driven with a uniform oscillating electric field to represent the long wavelength pump wave and power spectra of the electrostatic waves produced are taken. The pump wave frequency and amplitude are varied to consider the effects on the simulation power spectrum. The upper hybrid frequency in the model is varied through harmonics of the electron cyclotron frequency Ω_ce to consider the effects of stepping the pump frequency through cyclotron harmonics. The power spectrum from the simulation plasma is richly structured. The resulting power spectra show sidebands upshifted and downshifted from the pump frequency by multiples of the lower hybrid frequency ω_lh. The structure of the spectrum is highly sensitive to the proximity of the upper hybrid frequency to the cyclotron harmonic frequencies.     

THE SPECTRAL FUNCTION OF A LAYERED SYSTEM AND THE DETERMINATION OF THE WAVEFORMS AT DEPTH*

Consider the mathematical model of a horizontally layered system subject to an initial downgoing source pulse in the upper layer and to the condition that no upgoing waveforms enter the layered system from below the deepest interface. The downgoing waveform (as measured from its first arrival) in each layer is necessarily minimum-phase. The net downgoing energy in any layer, defined as the difference of the energy spectrum of the downgoing wave minus the energy spectrum of the upgoing wave, is itself in the form of an energy spectrum, that is, it is non-negative for all frequencies. The z-transform of the autocorrelation function corresponding to the net downgoing energy spectrum is called the net downgoing spectral function for the layer in question. The net downgoing spectral functions of any two layers A and B are related as follows: the product of the net downgoing spectral function of layer A times the overall transmission coefficient from A to B equals the product of the net downgoing spectral function of layer B times the overall transmission coefficient from B to A. The net downgoing spectral function for the upper layer is called simply the spectral function of the system. In the case of a marine seismogram, the autocorrelation function corresponding to the spectral function can be used to recursively generate prediction error operators of successively increasing lengths, and at the same time the reflection coefficients at successively increasing depths. This recursive method is mathematically equivalent to that used in solving the normal equations in the case of Toeplitz forms. The upgoing wave-form in any given layer multiplied by the direct transmission coefficient from that layer to the surface is equal to the convolution of the corresponding prediction error operator with the surface seismogram. The downgoing waveform in this given layer multiplied by the direct transmission coefficient from that layer to the surface is equal to the convolution of the corresponding hindsight error operator (i.e., the time reverse of the prediction error operator) with the surface seismogram.     

Observations of Pc 3–4 and Pi 2 geomagnetic pulsations in the low-latitude ionosphere

Day-time Pc 3–4 (≃5–60 mHz) and night-time Pi 2 (≃5–20 mHz) ULF waves propagating down through the ionosphere can cause oscillations in the Doppler shift of HF radio transmissions that are correlated with the magnetic pulsations recorded on the ground. In order to examine properties of these correlated signals, we conducted a joint HF Doppler/magnetometer experiment for two six-month intervals at a location near L = 1.8. The magnetic pulsations were best correlated with ionospheric oscillations from near the F region peak. The Doppler oscillations were in phase at two different altitudes, and their amplitude increased in proportion to the radio sounding frequency. The same results were obtained for the O- and X-mode radio signals. A surprising finding was a constant phase difference between the pulsations in the ionosphere and on the ground for all frequencies below the local field line resonance frequency, independent of season or local time. These observations have been compared with theoretical predictions of the amplitude and phase of ionospheric Doppler oscillations driven by downgoing Alfvén mode waves. Our results agree with these predictions at or very near the field line resonance frequency but not at other frequencies. We conclude that the majority of the observations, which are for pulsations below the resonant frequency, are associated with downgoing fast mode waves, and models of the wave-ionosphere interaction need to be modified accordingly.     

Q-LOG DETERMINATION ON DOWNGOING WAVELETS AND TUBE WAVE ANALYSIS IN VERTICAL SEISMIC PROFILES1

Seismic attenuation introduces modifications in the wavelet shape in vertical seismic profiles. These modifications can be quantified by measuring particular signal attributes such as rise-time, period and shape index. Use of signal attributes leads to estimations of a seismic-attenuation log (Q-log). To obtain accurate signal attributes it is important to minimize noise influence and eliminate local interference between upgoing and downgoing waves at each probe location. When tube waves are present it is necessary to eliminate them before performing separation of upgoing and downgoing events. We used a trace-by-trace Wiener filter to minimize the influence of tube waves. The separation of upgoing and downgoing waves was then performed in the frequency domain using a trace-pair filter. We used three possible methods based on signal attribute measurements to obtain g-log from the extracted downgoing wavefield. The first one uses a minimum phasing filter and the arrival time of the first extremum. The two other methods determine the Q-factor from simple relations between the amplitudes of the first extrema and the pseudo-periods of the down-going wavelet. The relations determined between a signal attribute and traveltime over quality factor were then calibrated using field source signature and constant-Q models computed by Ganley's method. Q-logs thus obtained from real data are discussed and compared with geological information, specifically at reservoir level. Analysis of the tube wave arrivals at the level of the reservoir showed a tube wave attenuation that could not be explained by simple transmission effects. There was also a loss of signal coherence. This could be interpreted as tube wave diffusion in the porous reservoir, followed by dispersion. If this interpretation can be verified, tube wave analysis could lead to further characterization of porous permeable zones.     

WIND observations of coherent electrostatic waves in the solar wind

The time domain sampler (TDS) experiment on WIND measures electric and magnetic wave forms with a sampling rate which reaches 120 000 points per second. We analyse here observations made in the solar wind near the Lagrange point L1. In the range of frequencies above the proton plasma frequency f_pi and smaller than or of the order of the electron plasma frequency f_pe, TDS observed three kinds of electrostatic (e.s.) waves: coherent wave packets of Langmuir waves with frequencies f ≃ f_pe, coherent wave packets with frequencies in the ion acoustic range f_pi ≥ f ≥ f_pe, and more or less isolated non-sinusoidal spikes lasting less than 1 ms. We confirm that the observed frequency of the low frequency (LF) ion acoustic wave packets is dominated by the Doppler effect: the wavelengths are short, 10 to 50 electron Debye lengths λ_D. The electric field in the isolated electrostatic structures (IES) and in the LF wave packets is more or less aligned with the solar wind magnetic field. Across the IES, which have a spatial width of the order of ≃25_D, there is a small but finite electric potential drop, implying an average electric field generally directed away from the Sun. The IES wave forms, which have not been previously reported in the solar wind, are similar, although with a smaller amplitude, to the weak double layers observed in the auroral regions, and to the electrostatic solitary waves observed in other regions in the magnetosphere. We have also studied the solar wind conditions which favour the occurrence of the three kinds of waves: all these e.s. waves are observed more or less continuously in the whole solar wind (except in the densest regions where a parasite prevents the TDS observations). The type (wave packet or IES) of the observed LF waves is mainly determined by the proton temperature and by the direction of the magnetic field, which themselves depend on the latitude of WIND with respect to the heliospheric current sheet.     

ULF wave measurements onboard the Interball auroral probe

The IESP experiment implemented onboard the Interball auroral probe measures the six components (3B, 3E) of the waves in the ULF range: 0.1–10 Hz and from time to time 0–30 Hz. Two different kinds of waves have been observed in the auroral region at altitudes between 10 000 and 20 000 km: (1) electrostatic emissions which consist of quasi-monochromatic structures with frequencies above the oxygen gyrofrequency, superimposed on a wide band signal interpreted as a Doppler broadening, (2) electromagnetic wide band spectrum fluctuations. These emissions are interpreted as current-driven electromagnetic or electrostatic ion cyclotron waves. The electromagnetic/electrostatic character is controlled by the plasma parameter _i and by the O⁺ concentration.     

Hydromagnetic spectroscopy of the magnetosphere with Pc3 geomagnetic pulsations along the 210° meridian

Analysis of Pc3 observational data along the 210° magnetic meridian showed a complicated frequency-latitude structure at middle latitudes. The observed period-latitude distributions vary between events with a “noisy source”: the D component has a colored-noise spectrum, while the spectrum of H component exhibits regular peaks that vary with latitude, and events with a “band-limited source”: the spectral power density of the D component is enhanced at certain frequencies throughout the network. For most ULF events a local gap of the H component amplitude has been exhibited at both conjugate stations at L ≃ 2.1. A quantitative interpretation has been given assuming that band-limited MHD emission from an extra-magnetospheric source is distorted by local field line resonances. Resonant frequencies had been singled out with the use of the asymmetry between spectra of H and D components. Additionally, a local resonant frequency at L ≃ 1.6 was determined by the quasi-gradient method using the data from nearly conjugate stations. The experimentally determined local resonance frequencies agree satisfactorily with those obtained from a numerical model of the Alfven resonator with the equatorial plasma density taken by extrapolation of Carpenter-Anderson model. We demonstrate how simple methods of hydromagnetic spectroscopy enable us to monitor simultaneously both the magnitude of the IMF and the magnetospheric plasma density from ULF data.     

Density fluctuations measured by ISEE 1–2 in the Earth’s magnetosheath and the resultant scattering of radio waves

Radio waves undergo angular scattering when they propagate through a plasma with fluctuating density. We show how the angular scattering coefficient can be calculated as a function of the frequency spectrum of the local density fluctuations. In the Earths magnetosheath, the ISEE 1–2 propagation experiment measured the spectral power of the density fluctuations for periods in the range 300 to 1 s, which produce most of the scattering. The resultant local angular scattering coefficient can then be calculated for the first time with realistic density fluctuation spectra, which are neither Gaussian nor power laws. We present results on the variation of the local angular scattering coefficient during two crossings of the dayside magnetosheath, from the quasi-perpendicular bow shock to the magnetopause. For a radio wave at twice the local electron plasma frequency, the scattering coefficient in the major part of the magnetosheath is b(2f_p) 0.5–4 × 10^–9 rad²/m. The scattering coefficient is about ten times stronger in a thin sheet (0.1 to IR_E) just downstream of the shock ramp, and close to the magnetopause.     

VERTICAL SEISMIC PROFILING IN COAL*

The intellection of seismic wave propagation in coal measures demands direct observation of the wavefield progression. Two vertical seismic profiles with high spatial and temporal sampling, were recently recorded in the Sydney Basin coalfields as part of an experimental coal seismic program. Static corrections and interval velocities were obtained by an automated system to determine first kicks and pulse rise times. Upgoing and downgoing waves were separated in the f—k-plane using a novel technique of contour slice filtering. The isolated upgoing waves clearly display reflections from the major coal seams within the stratigraphic sequence. The downgoing wave spectra were subjected to attenuation analysis. The deduced specific quality factor Q for Permian coal measure rocks lies in the range 20–70. Similar estimates were obtained in the time domain from measurements of pulse broadening. Synthetic VSP seismograms, computed using an exact recursive formulation, are an indispensable aid to interpretation. They illustrate the filtering effects of coal seams and sequences, and the effects of the contribution of internal and free-surface multiple reflections in the recorded wavetrains.     

An absorbing boundary condition for wave propagation in saturated poroelastic media — Part II: Finite element formulation

In a finite element formulation for dynamic soil-structure interaction, an absorbing boundary condition is needed to model wave propagation towards infinity. When the soil is saturated, its dynamic behaviour can be modelled by means of Biot's poroelastic theory. In Part I (Degrande, G. & De Roeck, G., Soil Dynamics & Earthquake Eng., 1993, 12(7), 411-21), a local absorbing boundary condition for wave propagation in saturated poroelastic media has been developed. In the present paper, this boundary condition is implemented in an irreducible finite element formulation for a compressible pore fluid. Spurious reflections for oblique incident waves on the absorbing boundary contribute to the solution errors. Therefore, a spectral element method, based on classical analytical solution techniques, is used to assess the accuracy of the finite element formulation.     

Letter to the editor First direct observations of the reduced striations at pump frequencies close to the electron gyroharmonics

It is well known that the ionospheric plasma response to high-power HF radio waves changes drastically as the heater frequency approaches harmonics of the electron gyrofrequency. These include changes in the spectrum of the stimulated electromagnetic emission, reduction in the anomalous absorption of low-power diagnostic waves propagating through the heated volume, and reduction in the large scale F-region heating. Theoretical models as well as previous experimental evidence point towards the absence of small-scale field-aligned plasma density irregularities at pump frequencies close to electron gyroharmonics as the main cause of these changes. Results presented in this paper are the first direct observations of the reduced striations at the 3rd gyroharmonic made by the CUTLASS radar. In addition, simultaneous EISCAT observations have revealed that the “enhanced ion-line” usually present in the EISCAT ion-line spectrum during the first few seconds after heater switch on, persisted at varying strengths while the heater was transmitting at frequencies close to the 3rd electron gyroharmonics.     

The zonal E×B plasma drift effects on the low latitude ionosphere electron density at solar minimum near equinox

The F2-layer peak density, NmF2, and peak altitude, hmF2, which were observed by 12 ionospheric sounders during the 20 September 1964 geomagnetically quiet time period at solar minimum are compared with those calculated by the three-dimensional time-dependent theoretical model of the Earth's low and middle latitude ionosphere and plasmasphere. The modeled NmF2 are also compared with those measured during the geomagnetically quiet time periods of 12–15, 18–21, and 26 September 1964 to take into account observed day-to-day ionospheric variability. Major features of the data are reproduced by the model if the corrected HWM90 neutral wind is used. The changes in NmF2 due to the zonal E×B plasma drift are found to be less than 20% in the daytime low latitude ionosphere. The model, which does not take into account the zonal E×B plasma drift, underestimates night-time NmF2 up to the maximum factor of 2 at low geomagnetic latitudes. The night-time increase of NmF2 caused by the zonal E×B plasma drift is less pronounced at −20° and 20° geomagnetic latitudes in comparison with that between −10° and 10° geomagnetic latitude. The longitude dependence of the calculated night-time low latitude influence of the zonal E×B plasma drift on NmF2 is explained in terms of the longitudinal asymmetry in B (the eccentric magnetic dipole is displaced from the Earth's center and the Earth's eccentric tilted magnetic dipole moment is inclined with respect to the Earth's rotational axis), and the variations of the wind induced plasma drift and the meridional E×B plasma drift in geomagnetic longitude. The difference between the hmF2 values calculated by including the effect of zonal E×B drift and that obtained when it is excluded does not exceed 19 km in the low latitude ionosphere. Over the geomagnetic equator the zonal E×B plasma drift produces the maximum increase in the electron density by a factor of 1.06–1.48 and 1.05–1.30 at 700 and 1000 km altitude, respectively, and this increase is not significant above about 1500 km. Changes in the vertical electron content, VEC, caused by the zonal E×B plasma do not exceed 16% during the day, while the value of the night-time VEC is increased up to a factor of 1.4 due to this drift. The maximum effects of the zonal E×B plasma drift on the night-time electron density derived from the model results corresponding to solar minimum and maximum are quite comparable.     

Control of structures with friction controllable sliding isolation bearings

A friction controllable sliding isolation system was developed and experimentally and analytically investigated by Feng et al. (Feng, Q., Shinozuka, M. & Fujii, S. A. friction controllable sliding isolation system. J. Eng. Mech., ASCE, 1993, 119(6), in press), the control algorithm having been developed based on a key assumption that the structural motion is always in the sliding phase. However, this assumption may not be valid in cases where the sticking phase of the structural motion dominates. In this paper a new control algorithm is developed including the effects of stick—slip phases. Effect of time delay is included in the formulation. The developed algorithm is used to evaluate the accuracy and limitations of the algorithm with continuous sliding assumption. Response to various earthquake motions, simulated using the two control algorithms, is presented. Comparisons with experimental results are also presented. Effects of stick—slip phases on the response are evaluated.     

Interpretations and observations of ocean wave spectra

The paper starts with a discussion of the linear stochastic theory of ocean waves and its various nonlinear extensions. The directional spectrum, with its unique dispersion relation connecting frequency (ω) and wavenumber (k), is no longer valid for nonlinear waves, and examples of $\left( \mathbf{k},\omega\right) The paper starts with a discussion of the linear stochastic theory of ocean waves and its various nonlinear extensions. The directional spectrum, with its unique dispersion relation connecting frequency (ω) and wavenumber (k), is no longer valid for nonlinear waves, and examples of ( k,w)\left( \mathbf{k},\omega\right) -spectra based on analytical expressions and computer simulations of nonlinear waves are presented. Simulations of the dynamic nonlinear evolution of unidirectional free waves using the nonlinear Schr?dinger equation and its generalizations show that components above the spectral peak have larger phase and group velocities than anticipated by linear theory. Moreover, the spectrum does not maintain a thin well-defined dispersion surface, but rather develops into a continuous distribution in ( k,w)\left( \mathbf{k,}\omega\right) -space. The majority of existing measurement systems rely on linear theory for the interpretation of their data, and no measurement systems are currently able to measure the full spectrum in the open ocean with high accuracy. Nevertheless, there exist a few low-resolution systems where data may be interpreted within a minimal assumption of a non-restricted ( k,w)\left( \mathbf{k,}\omega\right) -spectrum. The theory is reviewed, and analyses based on conventional spectral analysis as well as a directional wavelet analysis are carried out on data from a compact laser array at the Ekofisk field in the North Sea. The investigation confirms the strong impact of the second order spectrum below the spectral peak, but is non-conclusive about the off-set in the support of the first order spectrum seen in the dynamical simulations.     

M m: Extension to Love waves of the concept of a variable-period mantle magnitude

We extend to Love waves the concept of the mantle magnitudeM _mintroduced recently for Rayleigh waves. Spectral amplitudesX() of Love waves in the 50–300 s period range are measured on broad-band records from major events. A distance correctionC _D, regionalized to reflect the influence of different tectonic paths, and a source correctionC _S, compensating for the variation of excitation with period are effected; the exact geometry and depth of the event are however ignored. The resulting expression

Sources of microseismicP waves

Summary Origin ofP waves detected earlier in microseisms of very quiet locations in the USSR is discussed in detail. It appears that the most pronounced sources ofP waves are tropical cyclones over the Pacific. The amplitude of the force in the source for a medium power typhoon is found to be of the order of 10¹⁶ dynes. The effective source area is estimated as 10⁴–10⁵ km² approximately. The shape of the amplitude spectrum ofP wave corrected for the absorption in the mantle does not contradict with the standing wave theory of microseisms generation. Results of observations at various epicentral distances give strong evidences of the predominant attenuation of the fundamental Rayleigh mode as compared with higher Rayleigh modes andP waves in the frequency band of 0.3–0.15 cps.     

Long period edge waves off Southern Africa

Long gravity wave height oscillations of up to 60 cm with periods between 12 min and 1 h have been observed on tide gauge recordings from the southern coast of South Africa. Short period (30 min to 1 h), small height (3 mb) air pressure pulses were recorded at stations along the same coastline. Two separate events of contrasting nature are described in detail. The simple model of Snodgrass et al. (1962, Journal of Marine Research, 20, 3–30) is used to explain the sea waves as resonant, coastally trapped, edge waves on the Agulhas Bank forced by the atmospheric pulses.     

Marine seismic wavefield measurement to remove sea-surface multiples

We propose a new method for removing sea-surface multiples from marine seismic reflection data in which, in essence, the reflection response of the earth, referred to a plane just above the sea-floor, is computed as the ratio of the plane-wave components of the upgoing wave and the downgoing wave. Using source measurements of the wavefield made during data acquisition, three problems associated with earlier work are solved: (i) the method accommodates source arrays, rather than point sources; (ii) the incident field is removed without simultaneously removing part of the scattered field; and (iii) the minimum-energy criterion to find a wavelet is eliminated. Pressure measurements are made in a horizontal plane in the water. The source can be a conventional array of airguns, but must have both in-line and cross-line symmetry, and its wavefield must be measured and be repeatable from shot to shot. The problem is formulated for multiple shots in a two-dimensional configuration for each receiver, and for multiple receivers in a two-dimensional configuration for each shot. The scattered field is obtained from the measurements by subtracting the incident field, known from measurements at the source. The scattered field response to a single incident plane wave at a single receiver is obtained by transforming the common-receiver gather to the frequency–wavenumber domain, and a single component of this response is obtained by Fourier transforming over all receiver coordinates. Each scattered field component is separated into an upgoing wave and a downgoing wave using the zero-pressure condition at the water-surface. The upgoing wave may then be expressed as a reflection coefficient multiplied by the incident downgoing wave plus a sum of scattered downgoing plane waves, each multiplied by the corresponding reflection coefficient. Keeping the upgoing scattered wave fixed, and using all possible incident plane waves for a given frequency, yields a set of linear simultaneous equations for the reflection coefficients which are solved for each plane wave and for each frequency. To create the shot records that would have been measured if the sea-surface had been absent, each reflection coefficient is multiplied by complex amplitude and phase factors, for source and receiver terms, before the five-dimensional Fourier transformation back to the space–time domain.