In this thesis, a theory is developed for the propagation of seismic surface waves in a laterally heterogeneous earth, based upon a single-scattering (Born) approximation. Correct to first order, finite-frequency effects of surface waves can be taken into account using three-dimensional Born sensitivity kernels. The sensitivity kernels are formulated for fundamental-mode surface-wave phase, amplitude and arrival angle measurements. They completely account for the effects of mode-coupling, directional-scattering, seismic source radiation and the effects of seismograms tapering in making surface-wave measurements. The three-dimensional sensitivity kernels are then applied to global long-period surface-wave tomography. It is shown that with wavefront healing effects properly accounted for, finite-frequency tomography fits dispersion data better than traditional ray-theoretical tomography; the recovered mantle anomalies are stronger, and the resolution of small-scale features is greatly improved compared to traditional ray-theoretical tomography.; The global structure of shear-wave velocity and radial anisotropy in the upper mantle is investigated using finite-frequency surface-wave tomography, based upon separate inversions of fundamental-mode Love (SH-type) and Rayleigh (SV-type) wave dispersion data. Globally averaged radial anisotropy shows a transition from positive anisotropy (horizontal mantle flow) to negative anisotropy (vertical mantle flow) at about 220 km depth, mainly due to increasing negative anisotropy beneath the mid-ocean ridges. The fast seismic anomalies beneath continental cratons as well as the old Pacific plate are mostly confined to the uppermost 250 km, and are characterized by positive anisotropy. The slow anomalies beneath mid-ocean spreading centers are characterized by negative anisotropy below 120 km, and anomalies beneath slow-spreading and fast-spreading mid-ocean ridges show distinctly different depth extent: anomalies at fast-spreading centers are mostly confined to the uppermost 250 km, in contrast, anomalies at slow-spreading centers extend much deeper, i.e., at least to the top of the transition zone. This different depth extent indicates that the primary driving force of slow-spreading seafloor may be different from that of fast-spreading seafloor, and that active upwelling beneath ridges may play a major role in the opening of slow-spreading seafloor.
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