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We prove a sharp-in-time dispersive estimate of the Dirac equation on spinor bundles over the real hyperbolic space. Compared with the Euclidean counterparts, our result shows that the dispersive estimate differs between short and long times, reflecting the intuitive influence of negative curvature on the dispersion. Moreover, the well-known equivalence between dispersive estimates for Dirac and wave propagators in the Euclidean setting no longer holds in this context. This finding suggests that spinor fields are affected by the geometry at infinity of the manifold. As a key application, we establish an improved global-in-time Strichartz estimate, in the sense that there is no loss of angular derivatives and the admissible set is larger than previously known results in other settings.

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Seismic guided drilling (SGD) is a workflow that uses drilling information from a well being drilled and existing surface seismic data plus offset well information, to recalibrate and update the existing 3D earth model, including seismic image, pore pressure, fracture gradient, and geological hazards in order to reduce drilling uncertainty and mitigate drilling risk ahead of bit. The modern practices in drilling heavily rely on the predrill earth models. The predrill models often are not precise due to the inherent non-uniqueness in our remote sensing techniques. While LWD/SWD and WL provide useful information along the borehole, they offer little understanding about the rock property ahead of bit. SGD is such a technology that constantly improves the 3D earth model ahead of the bit through the integration of current well measurements with existing surface seismic data, with a turnaround time on the order of 24hours. It not only corrects the model error behind the bit but also improve predictions ahead of the bit. The lack of adequate technologies, measurements, and turnaround time limitations, has made this type of optimum utilization/integration of seismic data and well data impractical until now. Recent developments in model building, rapid and accurate imaging technologies, and the availability of new well measurements, aided with modern engineering and computation, have made this optimum combination a reality. SGD has been used in several high-profile deep water HPHT wells worldwide with considerable successes. The technology is especially valuable in areas of low exploration activity or high geological complexity. The paper focuses on illustrating the concept of SGD technology and presenting a field example in the Gulf of Mexico, USA.

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