We introduce a new viscoacoustic Wave Equation Migration (WEM) for media with attenuation. Our solution is based on a Fourier Finite-Difference (FFD) scheme for migration by wavefield continuation. Similarly to the acoustic solution, the viscoacoustic migration consists of three terms: a phase-shift extrapolation, a thin-lens correction, and a finite-differences operation. The viscoacoustic migration is also extended to account for anisotropy (VTI and TTI). The anisotropic effects are incorporated in the migration by using odd and even rational function terms in the finite differences solution. The dispersion relation, in presence of attenuation, includes both real and imaginary terms. While the real part controls the kinematics of the image, the imaginary part recovers the high vertical wave numbers in the seismic image; therefore improving resolution and amplitude balance. The implementation is stable, efficient, and very flexible. In absence of attenuation or anisotropy, the solution reduces to the familiar isotropic acoustic case. Results from synthetic example and two dual sensor field surveys from the North Sea and the Gulf of Mexico demonstrate the importance of incorporating the attenuation effects in isotropic and anisotropic migration algorithms.

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