The TTI slowness surface approximation

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2 Scopus citations

Abstract

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.
Original languageEnglish (US)
Pages (from-to)222-226
Number of pages5
JournalSEG Technical Program Expanded Abstracts 2011
Volume30
Issue number1
DOIs
StatePublished - May 25 2012

ASJC Scopus subject areas

  • Geotechnical Engineering and Engineering Geology
  • Geophysics

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