Lg waves are shown to be identified with higher mode Love wave propagation. The complete demonstration shows that the observations of Lg can be explained only by taking into account the anelasticity of the crust-mantle system, the selective frequency response of the seismograph, and above all, the complicated features of the propagation of Love waves for a number of higher modes, including the relative spectral excitations of these modes. It is not necessary to introduce crustal low-velocity channels to explain the character of the Lg seismogram.
The apparent initial phase of a point source of Rayleigh waves is shown to depend on the inclination of the source to the vertical. This effect is frequency dependent; the frequency dependence vanishes for a vertical or horizontal source. Corrections must therefore be applied to the phase velocities determined by the single-station method and, less significantly, to group velocities; these corrections depend on a knowledge of the angle of inclination of the source.
The characteristics of the Rayleigh wave response to dip-slip motion along a vertical fault plane are investigated. The sources are located at various depths in the crust of a shield structure. Results are given in the form of frequency spectra of the displacement at the free surface. Both individual modes and combinations of the modes are treated.
For a structure containing even a slight low-velocity channel in the upper mantle, the collection of higher mode Rayleigh waves decomposes naturally into a family of LVC channel waves and a family of crustal waves. Only the fundamental mode and the crustal waves need be considered as exciting Rayleigh waves significantly, since the channel waves do not generate significant amplitudes at the free surface.
Due to continuing improvement in instrumentation and data processing techniques, increasingly longer periods are being obtained in seismic surface wave measurements. Three aspects of surface wave propagation on a sphere, which become important at long periods, are treated in some detail: (1) the dependence of the spherical phase velocity on the relative positions of epicentre and station, (2) the importance of the polar component of Love waves, relative to the azimuthal component, and (3) the accuracy of the common practice of treating surface wave data as though they represent a continuous-frequency phenomenon.The original work on polar phase shift theory (Brune et al.) predated derivations of the response of a sphere to realistic models of the earthquake mechanism. We update the original theory by basing the development on these later derivations.I and em on I and 8. Long-period surface wave seismology pm(j3 0) = arg (&?/marg (Gm). 41 1 and define (2.15) Also, from the first term of the expansion for xp, for large 1, we have rm t
The hypothesis that one can assign the phase velocity calculated, from a tripartite net to one of the legs of the net exclusively, when that leg approximately coincides with the surface wave propagation vector, has been substantiated by experimental data. If more than one leg of an array of stations is parallel to the propagation vector, it is possible to make a quantitative estimate of the lateral heterogeneity of structure across the net. If, however, the propagation vector coincides with only one of the legs, one can only draw qualitative conclusions about lateral heterogeneity.
The seismic phase §a, on a shield structure, is interpreted using evidence from both group velocity dispersion and amplitude excitation functions.§a on a shield is explained in terms of stationary phases of higher-mode Love waves. It does not appear to be a low-velocity zone channel wave, but rather a phenomenon mainly influenced by the presence of a rapid increase in S-wave velocity at a depth of about 400-450km. The energy associated with the Sa stationary phases propagates much as though it were propagating through a single, homogeneous, low-velocity layer overlying the high-velocity material below the velocity increase.
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