Anisotropy and attenuation are critical to the modeling and analysis of seismic amplitude, phase, and traveltime data. Neglect of either of these phenomena, which are often both operating simultaneously, diminishes the resolution and interpretability of migrated images. In order to obtain an accurate image of subsurface earth, it is necessary to include both anisotropy and attenuation in inversion procedures as subsurface materials are far from being isotropic or elastic. In this thesis, I address attenuation and anisotropy problems such as modeling of wave propagation and compensating for attenuation effects in seismic images. To develop such analysis, I derive a time domain viscoacoustic constant-Q wave equation in isotropic and anisotropic media using an un-split field PML's scheme that is practically efficient and accurately simulates the constant-Q attenuation behavior and developing an Q-compensated reverse-time migration approach to compensate for attenuation effects in seismic images during migration. First, I investigate the accuracy of the new approach of viscoacoustic wave equation based on constant-Q theory. Most importantly, this approach separates attenuation and dispersion operators that allow us to mitigate both amplitude attenuation and phase dispersion e ects in seismic imaging. This equation is the key modeling engine for seismic migration. Second, I present a method to improve image resolution by mitigating attenuation e ects. I develop a Q-compensated reverse-time migration imaging approach (Q-RTM) and demonstrate this approach using di erent synthetic models. In Q-RTM, amplitude compensation happens within the migration process through manipulation of attenuation and phase dispersion terms in the time domain di erential equations. Particularly, the back-propagation operator is constructed by reversing the sign only of the amplitude loss operators, but not the dispersion-related operators, a step made possible by reformulating the absorptive equations such that the two appear separately. Numerical results further verify that this Q-RTM approach can e ectively improve the resolution of seismic images, particularly beneath high-attenuation zones. Finally, I extend the viscoacoustic wave equations from isotropic media to transversely isotropic (TI) media. For imaging application, I discuss the stability condition and the artifacts of shear wave triplications. The results indicate that the stable anisotropic reverse time migration is accessible by taking off anisotropy around the selected high gradient points of tilt angle in areas of rapid changes in the symmetry axes.
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