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Synthesis of Rayleigh‐wave envelope on the spherical Earth: Analytic solution of the single isotropic‐scattering model for a circular source radiation
Author(s) -
Maeda Takuto,
Sato Haruo,
Ohtake Masakazu
Publication year - 2003
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1029/2002gl016629
Subject(s) - physics , scattering , rayleigh wave , radiative transfer , envelope (radar) , isotropy , rayleigh scattering , point source , computational physics , classical mechanics , isotropic solid , surface wave , seismogram , optics , geology , telecommunications , radar , seismology , computer science
Surface waves propagating around the spherical Earth are scattered by medium heterogeneities and topographical variations. Wave trains appearing between the multiple arrivals of surface waves are interpreted as scattered waves. Mean‐Squared (MS) envelopes of vertical‐component seismograms in long periods can be explained by the single isotropic scattering process of Rayleigh waves of the fundamental mode based on the radiative transfer theory on the spherical Earth. For the case of circular radiation from a point source on the sphere, we can analytically solve the single scattering approximation of the radiative transfer equation. The resultant MS envelope is written by using an elliptic integral of the first kind.