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A tilted transversely isotropic slowness surface approximation
Author(s) -
Stovas A.,
Alkhalifah T.
Publication year - 2013
Publication title -
geophysical prospecting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.735
H-Index - 79
eISSN - 1365-2478
pISSN - 0016-8025
DOI - 10.1111/j.1365-2478.2012.01078.x
Subject(s) - slowness , transverse isotropy , quartic function , dispersion relation , anisotropy , axis of symmetry , mathematical analysis , dispersion (optics) , tilt (camera) , isotropy , mathematics , symmetry (geometry) , geology , geometry , optics , physics , seismology , pure mathematics
The relation between vertical and horizontal slownesses, better known as the dispersion relation, for transversely isotropic media with a tilted symmetry axis (TTI) requires solving a quartic polynomial equation, which does not admit a practical explicit solution to be used, for example, in downward continuation. Using a combination of the perturbation theory with respect to the anelliptic parameter and Shanks transform to improve the accuracy of the expansion, we develop an explicit formula for the vertical slowness that is highly accurate for all practical purposes. It also reveals some insights into the anisotropy parameter dependency of the dispersion relation including the low impact that the anelliptic parameter has on the vertical placement of reflectors for a small tilt in the symmetry angle.