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Abstract:
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One of main assumption for solving wave equation either numerically or analytically is to compensate the anisotropic properties those are usually observed in the earth materials. Consequently, most conventional prestack depth migration techniques based on wave equation solution, are not sufficient for these anisotropic media. Asymptotic analysis of wave propagation in vertical transversely isotropic (VTI) media yields a dispersion relation of couple P- and SV wave modes that then can be converted to fourth order scalar partial difference (PDE) wave equation. By setting the shear velocity equal 0 and defining the auxilary function, the fourth order PDE acoustic wave equation for VTI media can be reduced to a system of coupled second order PDEs and then can be solved numerically by finite difference method (FDM). The result of this P wavefield simulation is kinematically similar to the one of elastic VTI wavefield simulation. Since the FDM approach can simulate the wavefield propagation in the VTI media, and reverse time migration (RTM) images the reflectors by using time extrapolation to synthesize source and receivers wavefield in the subsurface by FDM, the RTM technique is then promptly suggested to image the subsurface. The proposed algorithm has been shown the accuracy of subsurface imaging by VTI Marmousi synthetic example. |