In this thesis, a finite-frequency theory is developed to calculate Born sensitivity kernels for Rayleigh-wave phase and amplitude measurements that are valid in regions near seismic stations. Calculations of sensitivity kernels for inter-station measurements show that exact travelling-wave representation of Green tensor is necessary when station spacing is close to or smaller than the seismic wavelength. This finite-frequency theory will allow us to take advantage of dense seismic arrays to obtain high-resolution surface-wave tomography using inter-station measurements. The non-linear dependence of surface wave phase upon large perturbations in crustal thickness as well as finite-frequency effects in global surface-wave tomography are investigated using wave propagation simulations. Calculations show that non-linearity as well as finite-frequency effects can be accounted for by using 2D phase-velocity kernels for boundary perturbations. A 3D-reference tomographic approach is developed for iterative inversions of global crustal structure where Frechet kernels are calculated in 3D reference models. A global dataset of minor-arc and major-arc Rayleigh wave dispersion measurements at periods between 25 seconds and 100 seconds are built and global phase velocity maps based on the dataset are obtained using diffractional tomography. The phase velocity model confirms many general features associated with surface tectonics including the ocean-continent dichotomy and the signature of lithospheric cooling in oceanic plates. There are significant differences between the phase velocity model and calculations based on a current global model CRUST2.0+S20RTS in oceanic regions, Archean and Proterozoic cratons as well as orogenic belts. In addition, the high resolution phase velocity maps reveal a major change in the distribution of small scale anomalies in the Pacific at different wave periods. / Ph. D.