Parabolic Approximation

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Haruo Sato - One of the best experts on this subject based on the ideXlab platform.

  • Parabolic equation and envelope synthesis based on the markov Approximation
    2012
    Co-Authors: Haruo Sato, Michael Fehler, Takuto Maeda
    Abstract:

    The inhomogeneity of the earth’s lithosphere has a broad spectrum compared with the wavelength of regional seismic waves. We will now present a model for wave propagation through random media having long-wavelength components of velocity inhomogeneity compared with the dominant wavelength of seismic waves. We focus on diffraction and multiple forward-scattering effects upon the waveform formation. In such a case we can apply the Parabolic Approximation for the wave equation.

  • seismic wave propagation and scattering in the heterogeneous earth
    1997
    Co-Authors: Haruo Sato, Michael Fehler
    Abstract:

    Introduction.- Heterogeneity in the Lithosphere.- Phenomenological Approaches to Seismogram Envelopes in short-periods.- Born Approximation for Wave Scattering in Random Media.- Attenuation of High-Frequency Seismic Waves.- Synthesis of Three-Component Seismogram Envelopes for Earthquakes Using Scattering Amplitudes from the Born Approximation.- Envelope Synthesis Based on the Radiative Transfer Theory: Multiple Scattering Models.- Parabolic Approximation and Envelope Synthesis based on the Markov Approximation. Summary and Epilogue.

  • regional differences of random inhomogeneities around the volcanic front in the kanto tokai area japan revealed from the broadening of s wave seismogram envelopes
    Journal of Geophysical Research, 1995
    Co-Authors: Kazushige Obara, Haruo Sato
    Abstract:

    Broadening of seismogram envelopes around direct S waves of deep earthquakes that occurred in a lithospheric slab reveals random inhomogeneities in the upper mantle and crust. Regional differences in the character of envelope broadening were studied in relation to the volcanic front in the central part of Japan. A total of 58 earthquakes that occurred along the subducting Pacific plate ranging from 80 to 500 km in depth were observed at 73 stations of the Kanto-Tokai seismic observation network and used in this analysis. Time lags of the maximum peak arrival and the half-maximum arrival were measured from the onset of the direct S wave on root-mean-squared traces of horizontal component seismograms in frequency bands of 1, 2, 4, and 8 Hz. The envelope broadening is weak at stations located along the coastline of the Pacific Ocean, however, the dependence of time lags on the hypocentral distance and frequency becomes strong at stations near the volcanic front. Moreover, the time lags become very long with increasing hypocentral distances and frequencies west of the volcanic front. This broadening of the seismogram envelope can be interpreted as the effect of the diffraction and multiple forward scattering on the seismic wave propagation through random inhomogeneities. The Parabolic Approximation is applied to simulate the envelope broadening when the correlation distance of velocity inhomogeneities is longer than the seismic wavelength. The numerical simulation indicates that the dependence of the envelope broadening on the travel distance and frequency depends greatly on the type of the autocorrelation function for the randomness. By comparing the observed frequency dependence of the envelope broadening with the result of the numerical simulation, the type of the autocorrelation function was estimated to be close to Gaussian at stations east of the volcanic front and close to exponential west of the volcanic front. The regional difference in the randomness on both sides of the volcanic front might reflect the difference in the short-wavelength component inhomogeneities.

  • inversion of full seismogram envelopes based on the Parabolic Approximation estimation of randomness and attenuation in southeast honshu japan
    Journal of Geophysical Research, 1991
    Co-Authors: Frank Scherbaum, Haruo Sato
    Abstract:

    The envelope shape around the arrival of the direct waves of seismic signals traveling in a randomly inhomogeneous medium has been predicted, based on the Parabolic Approximation, to be a measure of the long-wavelength components of the randomness as well as the attenuation properties of the medium. We use a nonlinear Marquardt-Levenberg inversion technique in order to model the SH wave envelopes of 119 earthquakes in the frequency band 2–6 Hz for lapse times less than 1.5 times the shear wave travel time. We attempted to obtain the ratio of the mean square fractional velocity fluctuation to the correlation length (e2V/a) estimates as well as estimates of attenuation Qs−1. For the majority of the events we found a good correlation between the envelope shape and the hypocentral distances. The resultant e2V/a of 10−3.27±0.32 km−1 is independent of frequency. It agrees well with the choice of the Gaussian autocorrelation function for the long-wavelength components of the random velocity fluctuations. The resultant attenuation Qs−1 is roughly proportional to the reciprocal of frequency. We may interpret it as either the scattering loss due to short-wavelength components of randomness or intrinsic loss. We have performed numerical simulations of the inversion process to quantify the model parameter uncertainties and to obtain a better understanding of the model parameter resolution. By modeling the wave envelopes as a superposition of noise-free wave envelopes and band-pass-filtered Gaussian noise we were able to reproduce the visual appearance of the observed envelopes as well as the observed features in the model parameter dependency. We find that for long hypocentral distances the envelope shape is controlled by the attenuation coefficient, while for short hypocentral distances the velocity fluctuations contribute dominantly.

Amir M. Sodagar - One of the best experts on this subject based on the ideXlab platform.

G.r. Lahiji - One of the best experts on this subject based on the ideXlab platform.

A Fiasconaro - One of the best experts on this subject based on the ideXlab platform.

  • single particle spectrum and binding energy of nuclear matter
    Physics Letters B, 2000
    Co-Authors: M Baldo, A Fiasconaro
    Abstract:

    Abstract In non-relativistic Brueckner calculations of nuclear matter, the self-consistent single particle potential is strongly momentum dependent. To simplify the calculations, a Parabolic Approximation is often used in the literature. The variation in the binding energy value introduced by the Parabolic Approximation is quantitatively analyzed in detail. It is found that the Approximation can introduce an uncertainty at best of 1–2 MeV already around the saturation density, and therefore it should be avoided in Brueckner calculations.

  • single particle spectrum and binding energy of nuclear matter
    arXiv: Nuclear Theory, 2000
    Co-Authors: M Baldo, A Fiasconaro
    Abstract:

    In non-relativistic Brueckner calculations of nuclear matter, the self-consistent single particle potential is strongly momentum dependent. To simplify the calculations, a Parabolic Approximation is often used in the literature. The variation in the binding energy value introduced by the Parabolic Approximation is quantitatively analyzed in detail. It is found that the Approximation can introduce an uncertainty of 1-2 MeV near the saturation density.

M Baldo - One of the best experts on this subject based on the ideXlab platform.

  • single particle spectrum and binding energy of nuclear matter
    Physics Letters B, 2000
    Co-Authors: M Baldo, A Fiasconaro
    Abstract:

    Abstract In non-relativistic Brueckner calculations of nuclear matter, the self-consistent single particle potential is strongly momentum dependent. To simplify the calculations, a Parabolic Approximation is often used in the literature. The variation in the binding energy value introduced by the Parabolic Approximation is quantitatively analyzed in detail. It is found that the Approximation can introduce an uncertainty at best of 1–2 MeV already around the saturation density, and therefore it should be avoided in Brueckner calculations.

  • single particle spectrum and binding energy of nuclear matter
    arXiv: Nuclear Theory, 2000
    Co-Authors: M Baldo, A Fiasconaro
    Abstract:

    In non-relativistic Brueckner calculations of nuclear matter, the self-consistent single particle potential is strongly momentum dependent. To simplify the calculations, a Parabolic Approximation is often used in the literature. The variation in the binding energy value introduced by the Parabolic Approximation is quantitatively analyzed in detail. It is found that the Approximation can introduce an uncertainty of 1-2 MeV near the saturation density.