Abstract
Rayleigh waves in an elastic medium lying over a rigid basement were analyzed in the frequency-wavenumber domain. First, the Rayleigh function and representation of displacements were derived. Next, the function was closely investigated with respect to causality and locations of its zeros in the complex wavenumber plane. This is because, in case of the elastic and rigid basement model, all the singularities of the representation of the displacements are due to the zeros of the Rayleigh function. The Rayleigh function for the rigid basement model is known to have the Rayleigh poles with negative group velocity. In this study, it was shown that these poles violate causality. Finally, surface displacements were calculated by means of both the mode superposition and the discrete wavenumber method for several epicentral distances, and compared with each other in the frequency and time domain. The comparison showed that the mode superposition method tends to give considerable errors due to neglected complex poles especially at a short epicentral distance and in a low frequency range.
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Schedule a callMore From: Zisin (Journal of the Seismological Society of Japan. 2nd ser.)
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