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On mathematical modelling of absorption and dispersion of seismic waves for low frequencies
Author(s) -
Von Wolfersdorf L.,
Rost L.
Publication year - 1991
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670140804
Subject(s) - anelastic attenuation factor , mathematics , mathematical analysis , attenuation , dispersion (optics) , plane (geometry) , plane wave , phase velocity , absorption (acoustics) , seismic wave , dispersion relation , limit (mathematics) , attenuation coefficient , hilbert transform , riemann hypothesis , quality (philosophy) , geometry , physics , geophysics , acoustics , optics , statistics , quantum mechanics , spectral density
The problem of determining the dispersion and absorption of plane seismic waves by a given seismic quality factor is dealt with in the case that the quality factor tends to a positive limit as the frequency goes to zero. General formulae are derived for the phase velocity and the attenuation coefficient by solving the corresponding Riemann–Hilbert problems for analytic functions in the upper half‐plane.