Seismic envelope inversion for long-wavelength structure recovery in FWI without low frequency source

2014 ◽  
Author(s):  
Ru-Shan Wu* ◽  
Jingrui Luo
Keyword(s):  
Low Frequency ◽  
Long Wavelength ◽  
Frequency Source

scholarly journals The Low-Frequency Array (LOFAR): Opening a New Window on the Universe

2002 ◽  
Vol 199 ◽  
pp. 474-483
Author(s):  
Namir E. Kassim ◽  
T. Joseph W. Lazio ◽  
William C. Erickson ◽  
Patrick C. Crane ◽  
R. A. Perley ◽  
...  
Keyword(s):  
Angular Resolution ◽  
Broad Band ◽  
Low Frequency ◽  
Electromagnetic Spectrum ◽  
Interferometric Imaging ◽  
Very Large Array ◽  
Long Wavelength ◽  
Calibration Techniques ◽  
Long Baselines ◽  
The Universe

Decametric wavelength imaging has been largely neglected in the quest for higher angular resolution because ionospheric structure limited interferometric imaging to short (< 5 km) baselines. The long wavelength (LW, 2—20 m or 15—150 MHz) portion of the electromagnetic spectrum thus remains poorly explored. The NRL-NRAO 74 MHz Very Large Array has demonstrated that self-calibration techniques can remove ionospheric distortions over arbitrarily long baselines. This has inspired the Low Frequency Array (LOFAR)—-a fully electronic, broad-band (15—150 MHz)antenna array which will provide an improvement of 2—3 orders of magnitude in resolution and sensitivity over the state of the art.

scholarly journals Kinetic extraordinary-mode eigenvalue equation for relativistic nonneutral electron flow in planar geometry

1989 ◽  
Vol 7 (1) ◽  
pp. 55-84 ◽  
Author(s):  
Ronald C. Davidson ◽  
Han S. Uhm
Keyword(s):  
Electron Flow ◽  
Low Frequency ◽  
Companion Paper ◽  
Field Configuration ◽  
Outer Edge ◽  
Eigenvalue Equation ◽  
Planar Geometry ◽  
Canonical Momentum ◽  
Stability Properties ◽  
Long Wavelength

Use is made of the Vlasov–Maxwell equations to derive an eigenvalue equation describing the extraordinary–mode stability properties of relativistic, non-neutral electron flow in high-voltage diodes. The analysis is based on well-established theoretical techniques developed in basic studies of the kinetic equilibrium and stability properties of nonneutral plasmas characterized by intense self fields. The formal eigenvalue equation is derived for extraordinary-mode flute perturbations in a planar diode. As a specific example, perturbations are considered about the choice of self-consistent Vlasov equilibrium , where . is the electron density at the cathode (x = 0), H is the energy, and Py is the canonical momentum in the Y-direction (the direction of the equilibrium electron flow). As a limiting case, the planar eigenvalue equation is further simplified for low-frequency long-wavelength perturbations with |ω − kvd, ≪ ωυ where and and ⋯c = eB0/mc, and B0ệz is the applied magnetic field in the vacuum region xb < x ≤ d. Here, the outer edge of the electron layer is located at x = xb; ω is complex oscillation frequency; k is the wavenumber in the y-direction; ωυ is the characteristic betatron frequency for oscillations in the x′-orbit about the equilibrium value x′ = x0 = xb/2; and Vd is the average electron flow velocity in the y-direction at x = x0. In simplifying the orbit integrals, a model is adopted in which the eigenfunction approximated by , where x′(t′) is the x′-orbit in the equilibrium field configuration. A detailed analysis of the resulting eigenvalue equation for , derived for low-frequency long-wavelength perturbations, is the subject of a companion paper.

scholarly journals On the dynamic homogenization of periodic media: Willis’ approach versus two-scale paradigm

2018 ◽  
Vol 474 (2213) ◽  
pp. 20170638 ◽  
Author(s):  
Shixu Meng ◽  
Bojan B. Guzina
Keyword(s):  
Low Frequency ◽  
Second Order ◽  
The Body ◽  
Clear Understanding ◽  
Periodic Media ◽  
Physical Sciences ◽  
Static Approximation ◽  
Long Wavelength ◽  
Modulation Factor ◽  
Effective Impedance

When considering an effective, i.e. homogenized description of waves in periodic media that transcends the usual quasi-static approximation, there are generally two schools of thought: (i) the two-scale approach that is prevalent in mathematics and (ii) the Willis’ homogenization framework that has been gaining popularity in engineering and physical sciences. Notwithstanding a mounting body of literature on the two competing paradigms, a clear understanding of their relationship is still lacking. In this study, we deploy an effective impedance of the scalar wave equation as a lens for comparison and establish a low-frequency, long-wavelength dispersive expansion of the Willis’ effective model, including terms up to the second order. Despite the intuitive expectation that such obtained effective impedance coincides with its two-scale counterpart, we find that the two descriptions differ by a modulation factor which is, up to the second order, expressible as a polynomial in frequency and wavenumber. We track down this inconsistency to the fact that the two-scale expansion is commonly restricted to the free-wave solutions and thus fails to account for the body source term which, as it turns out, must also be homogenized—by the reciprocal of the featured modulation factor. In the analysis, we also (i) reformulate for generality the Willis’ effective description in terms of the eigenfunction approach, and (ii) obtain the corresponding modulation factor for dipole body sources, which may be relevant to some recent efforts to manipulate waves in metamaterials.

scholarly journals 200Hz low frequency source for ocean acoustic tomography.

1994 ◽  
Vol 21 (3) ◽  
pp. 146-155
Author(s):  
Toshiaki NAKAMURA ◽  
Toshio TSUCHIYA ◽  
Iwao NAKANO ◽  
Toshiyuki NAKANISHI ◽  
Ieharu KAIHOU ◽  
...  
Keyword(s):  
Low Frequency ◽  
Acoustic Tomography ◽  
Frequency Source ◽  
Ocean Acoustic Tomography

scholarly journals An introductory guide to fluid models with anisotropic temperatures. Part 2. Kinetic theory, Padé approximants and Landau fluid closures

2019 ◽  
Vol 85 (6) ◽  
Author(s):  
P. Hunana ◽  
A. Tenerani ◽  
G. P. Zank ◽  
M. L. Goldstein ◽  
G. M. Webb ◽  
...  
Keyword(s):  
Kinetic Theory ◽  
Fourth Order ◽  
Low Frequency ◽  
Padé Approximants ◽  
Landau Damping ◽  
Order Moment ◽  
Fluid Models ◽  
Frequency Limit ◽  
Long Wavelength ◽  
Pade Approximants

In Part 2 of our guide to collisionless fluid models, we concentrate on Landau fluid closures. These closures were pioneered by Hammett and Perkins and allow for the rigorous incorporation of collisionless Landau damping into a fluid framework. It is Landau damping that sharply separates traditional fluid models and collisionless kinetic theory, and is the main reason why the usual fluid models do not converge to the kinetic description, even in the long-wavelength low-frequency limit. We start with a brief introduction to kinetic theory, where we discuss in detail the plasma dispersion function $Z(\unicode[STIX]{x1D701})$ , and the associated plasma response function $R(\unicode[STIX]{x1D701})=1+\unicode[STIX]{x1D701}Z(\unicode[STIX]{x1D701})=-Z^{\prime }(\unicode[STIX]{x1D701})/2$ . We then consider a one-dimensional (1-D) (electrostatic) geometry and make a significant effort to map all possible Landau fluid closures that can be constructed at the fourth-order moment level. These closures for parallel moments have general validity from the largest astrophysical scales down to the Debye length, and we verify their validity by considering examples of the (proton and electron) Landau damping of the ion-acoustic mode, and the electron Landau damping of the Langmuir mode. We proceed by considering 1-D closures at higher-order moments than the fourth order, and as was concluded in Part 1, this is not possible without Landau fluid closures. We show that it is possible to reproduce linear Landau damping in the fluid framework to any desired precision, thus showing the convergence of the fluid and collisionless kinetic descriptions. We then consider a 3-D (electromagnetic) geometry in the gyrotropic (long-wavelength low-frequency) limit and map all closures that are available at the fourth-order moment level. In appendix A, we provide comprehensive tables with Padé approximants of $R(\unicode[STIX]{x1D701})$ up to the eighth-pole order, with many given in an analytic form.

scholarly journals Instability of combined gravity-inertial-Rossby waves in atmospheres and oceans

2011 ◽  
Vol 29 (6) ◽  
pp. 997-1003 ◽  
Author(s):  
J. F. McKenzie
Keyword(s):  
Energy Exchange ◽  
Wave Speed ◽  
Rossby Waves ◽  
Low Frequency ◽  
Phase Speed ◽  
Ocean Dynamics ◽  
Stratified Medium ◽  
Instability Condition ◽  
Long Wavelength ◽  
Critical Latitude

Abstract. The properties of the instability of combined gravity-inertial-Rossby waves on a β-plane are investigated. The wave-energy exchange equation shows that there is an exchange of energy with the background stratified medium. The energy source driving the instability lies in the background enthalpy released by the gravitational buoyancy force. It is shown that if the phase speed of the westward propagating low frequency-long wavelength Rossby wave exceeds the Poincaré-Kelvin (or "equivalent" shallow water) wave speed, instability arises from the merging of Rossby and Poincaré modes. There are two key parameters in this instability condition; namely, the equatorial/rotational Mach (or Froude) number M and the latitude θ0 of the β-plane. In general waves equatorward of a critical latitude for given M can be driven unstable, with corresponding growth rates of the order of a day or so. Although these conclusions may only be safely drawn for short wavelengths corresponding to a JWKB wave packet propagating internally and located far from boundaries, nevertheless such a local instability may play a significant role in atmosphere-ocean dynamics.

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