Elliptical velocity dependence on the direction of wavepropagation is the simplest type of anisotropy that might beencountered in the subsurface. When the symmetry axis isvertical, describing elliptical anisotropy (EA) requires onlyone parameter — the ellipticity coefficient — in addition tothe conventional isotropic velocity. It is tempting, therefore,to use elliptical anisotropy as a testing ground for various an-isotropic parameter-estimation techniques. This apparentlystraightforward thinking, however, fails to deliver satisfacto-ry results because traveltime inversion in certain EA media isknown to be nonunique. Here, I prove this nonuniqueness tobe a general property of all EA media and explicitly show thata constant depth stretch generates a family of kinematicallyequivalent EA models for any given spatial distribution of theellipticity coefficient and the velocity.
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