Abstract

An acoustic approach to description of P-wave travel times in anisotropic media is needed in order to avoid the solution of elastic wave equations. Type of stone, lateral and vertical facies variations or preferential direction of fracturing, are some of the causes to produce wave velocity dependence with the angle of propagation in the medium. In this work, we present an equation to the approximation of the relation dispersion for a TTI media. The procedure used in the approximation reduces the fourth order differential equation used to model the P wave to a second order equation. Numerical examples of seismic modeling and migration of TTI media are used to validate the new equation. RTM migration, using the REM expansion in time and pseudoespectral method in space, shows that the P-wave equation improves the migrated image in a VTI media and produces also a stable numerical solutions.

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