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Authors: Mainardi, F.*
Tomirotti, M.*
Title: Seismic pulse propagation with constant Q and stable probability distributions
Issue Date: Oct-1997
Series/Report no.: 40/5
Keywords: Earth anelasticity
quality factor
wave propagation
fractional derivatives
stable probability distributions
Abstract: The one-dimensional propagation of seismic waves with constant Q is shown to be governed by an evolution equation of fractional order in time, which interpolates the heat equation and the wave equation. The fundamental solutions for the Cauchy and Signalling problems are expressed in terms of entire functions (of Wright type) in the similarity variable and their behaviours turn out to be intermediate between those for the limiting cases of a perfectly viscous fluid and a perfectly elastic solid. In view of the small dissipation exhibited by the seismic pulses, the nearly elastic limit is considered. Furthermore, the fundamental solutions for the Cauchy and Signalling problems are shown to be related to stable probability distributions with an index of stability determined by the order of the fractional time derivative in the evolution equation.
Appears in Collections:05.09.99. General or miscellaneous
Annals of Geophysics

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