The TTI slowness surface approximation

Citation data:

SEG Technical Program Expanded Abstracts, ISSN: 1052-3812, Vol: 30, Issue: 1, Page: 222-226

Publication Year:
2011
Usage 4
Abstract Views 4
Citations 2
Citation Indexes 2
Repository URL:
http://hdl.handle.net/10754/575676
DOI:
10.1190/1.3627651
Author(s):
Stovas, A.; Alkhalifah, Tariq Ali
Publisher(s):
Society of Exploration Geophysicists
Tags:
Earth and Planetary Sciences; Anisotropy; Migration; TTI; Wave equation
book chapter description
The relation between the vertical and horizontal slownesses, better known as the dispersion relation, for a transversely isotropic media with titled symmetry axis {left parenthesis, less than bracket}TTI{right parenthesis, greater than bracket} requires solving a quartic polynomial, which does not admit a practical explicit solution to be used, for example, in downward continuation. Using a combination of 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 dispersion relation 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 small tilt in the symmetry angle. © 2011 Society of Exploration Geophysicists.