Considering that geologic structures disturb prestack amplitude relationships, anisotropic migration is thus advocated not only for extracting azimuth-preserved common image gathers (CIGs), but also for preserving fracture-induced amplitude responses. However, most conventional anisotropic migration methods are hindered by their inefficiency in either modeling azimuthal traveltime variations at large offsets or characterizing subsurface reflections. Given that prestack time migration is widely applied for most practical purposes, we began with reformulations on a quartic traveltime formula, through which a new set of anisotropic parameters was developed. Then, an anisotropic migration method was established in the local-angle domain (LAD) for more reasonable uses of subsurface wavefield information. We also used a traveltime inversion scheme to estimate those anisotropic parameters required by anisotropic migration. Using this methodology on a physical model with a fracture medium, we derived better focused CIGs by thoroughly correcting the anisotropic effects of overburden. As a result, predicted properties of the fracture medium showed fewer interventions of geologic impacts. In a field example, a comprehensive study was performed on a deep carbonate reservoir to examine influences of different anisotropic migration algorithms on ultimate fracture prediction. Comparisons of the signal-to-noise ratio and agreements with formation microimage information reconfirmed the superiority of LAD anisotropic migration in recovering true properties of subsurface fractures, relative to routine methods (i.e., azimuth-sectored migration and anisotropic migration in the surface-offset domain).