AcousticWave

An acoustic wave equation for anisotropic media

A wave equation, derived under the acoustic medium assumption for P-waves in transversely isotropic media with a vertical symmetry axis (VTI media) yields a good kinematic approximation to the familiar elastic wave equation for VTI media. The wavefield solutions obtained using this VTI acoustic wave equation are free of shear waves; which significantly reduces the computation time compared to the elastic wavefield solutions for exploding-reflector type applications. From this VTI acoustic wave equation, the eikonal and transport equations that describe the ray theoretical aspects of wave propagation in a TI medium are derived. These equations, based on the acoustic assumption (shear wave velocity equals zero), are much simpler than their elastic counterparts, and yet yield an accurate description of traveltimes and geometrical amplitudes. Numerical examples prove the usefulness of this acoustic equation in simulating the kinematic aspects of wave propagation in complex TI models. Where the extrapolation in time t for the 2-D version in space with lateral x and depth z and medium parameters v, v_v, and eta is given by:

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Department of Physical Science and Engineering 4700 King Abdullah University of Science and Technology

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