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.     

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.     

Computer simulations for direct conversion of the HF electromagnetic wave into the upper hybrid wave in ionospheric heating experiments

Excitation of upper hybrid waves associated with the ionospheric heating experiments is assumed to be essential in explaining some of the features of stimulated electromagnetic emissions (SEE). A direct conversion process is proposed as an excitation mechanism of the upper hybrid waves where the energy of an obliquely propagating electromagnetic pump wave is converted into the electrostatic upper hybrid waves due to small-scale density irregularities. We performed electromagnetic particle-in-cell simulations to investigate the energy conversion process in the ionospheric heating experiments. We studied dependence of the amplitude of the excited wave on the propagation angle of the pump wave, scale length of the density irregularity, degree of the irregularity, and thermal velocity of the plasma. The maximum amplitude is found to be 37% of the pump amplitude under an optimum condition.     

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.     

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.     

Plasma wave radiation in the main ionospheric trough in the region of the terminator from the APEX satellite data

The data of measurements of broadband wave radiation in the main ionospheric trough in the subauroral zone of the topside ionosphere in the region of the day-night terminator (APEX satellite experiment) are presented. It is shown that the observed attenuation of electrostatic radiation in a broad frequency band and fluctuations (variations) in the cutoff frequency of the electrostatic mode spectrum at the level of the local plasma or upper hybrid frequency are related to plasma heating by damping electrostatic oscillations in the ionospheric trough. Waveguide channels for propagation of electromagnetic whistler-mode waves observed on the satellite can be generated during the propagation of a gravity-thermal disturbance from the terminator.     

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.     

Theory of convective saturation of Langmuir waves during ionospheric modification of a barium cloud

In recent experiments (Djuth, F. T., Sulzer, M. P., Elder, J. H. and Groves, K. M. (1995) Journal of Geophysical Research, 100, 17,347), a parametric decay instability was excited by an ordinarywave HF pump during an ionospheric chemical release from a rocket over Arecibo, PR, which created an artificial ‘barium ionosphere,’ with peak plasma frequency above the pump frequency, and a density gradient with a (short) 5 km scale length. Simultaneous incoherent scattering measurements revealed a strong initial asymmetry in the amplitudes of almost vertically upgoing versus downgoing measured plasma waves. We can account for this asymmetry in terms of linear convective saturation of parametrically unstable plasma waves propagating over a range of altitudes along geometric optics ray paths. Qualitative features of the frequency spectrum of the measured downgoing wave are in agreement with this model, although the theoretically predicted spectrum is narrower than observed. The observed altitude localization of the enhanced spectrum to a few range cells is consistent with the theory.     

Effective barometric admittance and gravity residuals

In the analysis of surface gravity signals that may originate from the Earth's core, the step of correcting for the atmospheric pressure fluctuations is one that must be done carefully. We apply two techniques for determining the local, or effective, barometric admittance function between simultaneous observations of surface gravity and pressure. The first is a frequency domain fit that computes the admittance on a band-by-band basis. Using data from both the Canadian and French superconducting gravimeters we determined that the magnitude of the local, or background, admittance increases smoothly and monotonically from about 0.2 μgal mbar⁻¹ at long periods (> 10 days) to about 0.35 μgal mbar⁻¹ at frequencies greater than 3 cycles per day (c.p.d.); the phase lag is within a few degrees of 180°. By comparison, the effective admittances of the large-scale harmonics of the solar heating tide (S₁---S₇) are much smaller, between 0.1 and 0.3 μgal mbar⁻¹, for most of the harmonics of a day. In the second approach we fit a symmetrical time domain admittance function having lengths between 1 and 19 h using both a standard least-squares fit to a white noise residual and a new, and clearly superior, fit assuming a brown noise residual. Both time and frequency domain approaches give comparable results and contribute to a significant lowering of the residual level in non-tidal bands.     

The fractal nature of the inhomogeneities in the lithosphere evidenced from seismic wave scattering

In this paper we show evidences of the fractal nature of the 3-D inhomogeneities in the lithosphere from the study of seismic wave scattering and discuss the relation between the fractal dimension of the 3-D inhomogeneities and that of the fault surfaces. Two methods are introduced to measure the inhomogeneity spectrum of a random medium: 1. the coda excitation spectrum method, and 2. the method of measuring the frequency dependence of scattering attenuation. The fractal dimension can be obtained from the inhomogeneity spectrum of the medium. The coda excitation method is applied to the Hindu-Kush data. Based on the observed coda excitation spectra (for frequencies 1–25 Hz) and the past observations on the frequency dependence of scattering attenuation, we infer that the lithospheric inhomogeneities are multiple scaled and can be modeled as a bandlimited fractal random medium (BLFRM) with an outer scale of about 1 km. The fractal dimension of the 3-D inhomogeneities isD ₃=31/2–32/3, which corresponds to a scaling exponent (Hurst number)H=1/2–1/3. The corresponding 1-D inhomogeneity spectra obey the power law with a powerp=2H+1=2–5/3. The intersection between the earth surface and the isostrength surface of the 3-D inhomogeneities will have fractal dimensionD ₁=1.5–1.67. If we consider the earthquake fault surface as developed from the isosurface of the 3-D inhomogeneities and smoothed by the rupture dynamics, the fractal dimension of the fault trace on the surface must be smaller thanD ₁, in agreement with recent measurements of fractal dimension along the San Andreas fault.     

Beach water table fluctuations due to spring–neap tides: moving boundary effects

Tidal water table fluctuations in a coastal aquifer are driven by tides on a moving boundary that varies with the beach slope. One-dimensional models based on the Boussinesq equation are often used to analyse tidal signals in coastal aquifers. The moving boundary condition hinders analytical solutions to even the linearised Boussinesq equation. This paper presents a new perturbation approach to the problem that maintains the simplicity of the linearised one-dimensional Boussinesq model. Our method involves transforming the Boussinesq equation to an ADE (advection–diffusion equation) with an oscillating velocity. The perturbation method is applied to the propagation of spring–neap tides (a bichromatic tidal system with the fundamental frequencies ω₁andω₂) in the aquifer. The results demonstrate analytically, for the first time, that the moving boundary induces interactions between the two primary tidal oscillations, generating a slowly damped water table fluctuation of frequency ω₁−ω₂, i.e., the spring–neap tidal water table fluctuation. The analytical predictions are found to be consistent with recently published field observations.     

Wave propagation in a seven-story reinforced concrete building: I. Theoretical models

For transient, high frequency, and pulse like excitation of structures in the near field of strong earthquakes, the classical design approach based on relative response spectrum and mode superposition may not be conservative. For such excitations, it is more natural to use wave propagation methods. In this paper (Part I), we review several two-dimensional wave propagation models of buildings and show results for theoretical dispersion curves computed for these models. We also estimate the parameters of these models that would correspond to a seven-story reinforced concrete building in Van Nuys, California. Ambient vibration tests data for this building imply vertical shear wave velocity β_z=112 m/s and anisotropy factor β_x/β_z=0.55 for NS vibrations, and β_z=88 m/s and β_x/β_z=1 for EW vibrations. The velocity of shear waves propagating through the slabs is estimated to be about 2000 m/s. In the companion paper (Part II), we estimate phase velocities of vertically and horizontally propagating waves between seven pairs of recording points in the building using recorded response to four earthquakes.     

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.     

Spectral parameters of ground motion in different regions: comparison of empirical models

Fourier-amplitude spectrum is one of the most important parameters describing earthquake ground motion, and it is widely used for strong ground motion prediction and seismic hazard estimation. The relationships between Fourier-acceleration spectra, earthquake magnitude and distance were analysed for different seismic regions (the Caucasus and Taiwan island) on the basis of ground motion recordings of small to moderate (3.5≤M_L≤6.5) earthquakes. It has been found that the acceleration spectra of the most significant part of the records, starting from S-wave arrival, can be modelled accurately by the Brune's “ω-squared” point-source model. Parameters of the model are found to be region-dependent. Peak ground accelerations and response spectra for condition of rock sites were calculated using stochastic simulation technique and obtained models of source spectra. The modelled ground-motion parameters are compared with those predicted by recent empirical attenuation relationship for California.     

A mode filter for plasma waves in the Hall-MHD approximation

A filter method is presented which allows a qualitative and quantitative identification of wave modes observed with plasma experiments on satellites. Hitherto existing mode filters are based on the MHD theory and thus they are restricted to low frequencies well below the ion cyclotron frequency. The present method is generalized to cover wave modes up to the characteristic ion frequencies. The spectral density matrix determined by the observations is decomposed using the eigenvectors of the linearized Hall-MHD equations. As the wave modes are dispersive in this formalism, a precise determination of the κ-vectors requires the use of multi-point measurements. Therefore the method is particularly relevant to multi-satellite missions. The method is tested using simulated plasma data. The Hall-MHD filter is able to identify the modes excited in the model plasma and to assign the correct energetic contributions. By comparison with the former method it is shown that the simple MHD filter leads to large errors if the frequency is not well below the ion cyclotron frequency. Further the range of validity of the linear theory is examined rising the simulated wave amplitudes.     

Scaling model experiments on propagation of electromagnetic waves using salt solution to simulate the Earth's crust: Loma Prieta and Kobe earthquakes

Propagation of electromagnetic (EM) waves from an earthquake focus in the conductive Earth has been investigated using 1/1,000,000 scaling models taking earth-ionosphere and ocean-Moho plane parallel-plate waveguides into account. Microwaves at a frequency, ω_m, a million times higher than that of seismic EM signal (SEMS), ω, were generated at the model focus. They are propagated in a salt solution modeling the earth's crust and reflected by ocean, fault planes, ionosphere and Moho plane all made by aluminum. Distribution of EM power was mapped by scanning a detector antenna over the model Earth's surface. The skin depth, δ, calculated by the exact skin depth equation, 1/δ=ω(μ/2)^1/2 [(1+(1/ωρ)²)^1/2 −1]^1/2 where dielectric constant, and permeability, μ are the same but resistivity, ρ, 10⁻⁶ times smaller than that of Earth, gave 10⁻⁶ times small skin depth validating the model scaling index. Images for evanescent and wave-ripple standing waves disturbed by normal, strike-slip and dip-slip conductive fault planes have been obtained using an aluminum plate. The co-circular contour map above the epicenter due to evanescence was pushed to the north east direction from the epicenter by the presence of ocean for the Loma Prieta earthquake, while to north direction for the Kobe earthquake. The intensity of EM ULF emissions for the Loma Prieta earthquake is discussed quantitatively.     

Q and high-frequency strong motion spectra

Empirical scaling equations for Fourier amplitude spectra of strong ground motion are used to describe A₀ and τ in the assumed (high-frequency) shape of strong motion amplitudes: FS(_φ) = A₀e-^πτφ. The res of computed A₀ and τ with other related estimates of spectral amplitudes; (2) smooth decay of strong motion spectral amplitudes up to φ = 25 Hz, without an abrupt low-pass filtering of high frequecies; and (3) good agreement with other estimates of the regionally specific attenuation of high-frequncy seismic waves.As the recorded strong earthquake shaking in the western United States typically samples only the shallow (10 km) and local (100km) characteristics of wave attenuation, the processed strong motion accelerograms can be used as the most direct means of describing the nature of the high-frequency attenuation of the entire strong motion signal for use in earthquake engineering applications. Seismological body wave, Lg and coda wave estimates of Q sample different volumes of the crust surrounding the station, and involve different paths of the waves. These differences must be carefully documented and understood before the results can be used in earthquake engineering characterization of strong motion amplitudes.     

Diurnal sea breeze effects on inner-shelf cross-shore exchange

Cross-shore exchange by strong (cross-shore wind stress, τ_sx>0.05 Pa) diurnal (7–25 h) sea breeze events are investigated using two years of continuous wind, wave, and ocean velocity profiles in 13 m water depth on the inner-shelf in Marina, Monterey bay, California. The diurnal surface wind stress, waves, and currents have spectral peaks at 1, 2, and 3 cpd and the diurnal variability represents about 50% of the total variability. During sea breeze relaxation (−0.05<τ_sx<0.05 Pa), a background wave-driven inner-shelf Eulerian undertow profile exists, which is equal and opposite to the Lagrangian Stokes drift profile, resulting in a net zero Lagrangian transport at depth. In the presence of a sea breeze (τ_sx>0.05 Pa), a uniform offshore profile develops that is different from the background undertow profile allowing cross-shore Lagrangian transport to develop, while including Lagrangian Stokes drift. The diurnal cross-shore current response is similar to subtidal (>25 h) cross-shore current response, as found by Fewings et al. (2008). The seasonality of waves and winds modify the diurnal sea breeze impact. It is suggested that material is not transported cross-shore except during sea breeze events owing to near zero transport during relaxation periods. During sea breeze events, cross-shore exchange of material appears to occur onshore near the surface and offshore near the sea bed. Since sea breeze events last for a few hours, the long-term cross-shore transport is incremental each day.     

Probabilistic versus deterministic seismic hazard analysis: an integrated approach for siting problems

A methodology is proposed to determine design earthquakes for site-specific studies such as the siting of critical structures (power plants, waste disposals, large dams, etc.), strategic structures (fire stations, military commands, hospitals, etc.), or for seismic microzoning studies, matching the results of probabilistic seismic hazard analyses. This goal is achieved by calculating the source contribution to hazard and the magnitude–distance deaggregation, showing that, varying the selected frequency and the level of hazard, the reference earthquakes are changed as a result. A procedure is then adopted to minimize the residuals between the uniform hazard spectrum (target motion) and the design earthquake spectrum, to provide a specific earthquake scenario encompassing all the frequencies of the target motion. Finally, some considerations on the use and the influence exerted by ground motion uncertainty (σ) on hazard deaggregation are outlined.     

Oxygen cyclotron harmonic waves observed using Van Allen Probes

Fine structured multiple-harmonic electromagnetic emissions at frequencies around the equatorial oxygen cyclotron harmonics are observed by Van Allen Probe A outside the core plasmasphere(L~5) off the magnetic equator(MLAT~.7.5°)during a geomagnetic storm. We find that the multiple-harmonic emissions have power spectrum density(PSD) peaks during 2–8equatorial oxygen gyroharmonics( f ~ n fO+, n=2–8), while the fundamental mode(n=1) is absent, implying that the harmonic waves are generated near the equator and propagate into the observation region. Additionally, these electromagnetic emissions are linearly polarized. Different from the equatorial noise emission that propagates considerably obliquely, these emissions have moderate wave normal angles(approximately 40°–60°), which predominately increase as the harmonic number increases.Considering their frequency and wave normal angle characteristics, it is suggested that these multiple-harmonic emissions play an important role in the dynamic variation of radiation belt electrons.