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On the geometrical spreading of viscoelastic waves

DEPARTMENT OF GEOLOGY AND GEOPHYSICS UNIVERSITY OF CALGARY, CALGARY, ALBERTA, Canada , T2N 1N4

Abstract

Krebes and Hron (1980) derived a formula for the geometrical spreading factor L for a seismic wave propagating through a layered viscoelastic medium. They assumed the angle ₀ between the propagation and attenuation vectors of the initial ray segment was constant. In this paper, the general formula for L is derived, in which ₀ is a function of the take-off angle ₀ (the functional form depends on source conditions). For the special case ₀ = ₀, which corresponds, for example, to an air-shot source just above the surface, the formula for L simplifies considerably. A few numerical evaluations of L for certain cases are also presented to illustrate the differences between elastic and viscoelastic geometrical spreading. The differences are small or negligible at small enough source-receiver offsets but can be large at greater offsets in cases where viscoelastic critical angles are different enough from elastic ones or do not exist. These cases, however, may not be very representative of true anelastic effects in the earth.

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