| Summary: | The thermal and mechanical structure of the lithosphere is the primary control on a planet’s geology, and is most commonly investigated using global or regional topography and gravity data. In this dissertation, the relationship between the two is used to investigate the lithosphere on the Moon and under the Earth’s ocean basins. Analysis of the relationship between gravity and topography on the nearside of the Moon, using line-of-sight accelerations from Doppler tracking of the Lunar Prospector spacecraft, indicates that <i>T<sub>e</sub></i> increased from less than 7 km to greater than 40 km between the time the oldest terrain formed and the most recent giant impacts. The increase is most simply interpreted in terms of the cooling and thickening of the lunar lithosphere, although the variation of <i>T<sub>e</sub></i><sub> </sub>is not well-described using simple thermal history models. Modelling of sometimes sparse topographic measurements above large seamounts using grids of satellite-derived sea-surface gravity indicates that, in the Earth’s oceans, <i>T<sub>e</sub></i> coincides roughly with the depth to the 300 ± 100°C isotherm at the time of loading. However, there is considerable scatter, and the interpretation is complicated by viscous relaxation, breaks in the plate, and uncertainty about the density of the load. The cooling thermal plate model has been used for the last 30 years to describe the subsidence of the ocean floor. However, an analysis of the average seafloor depth as a function of age shows that, in the absence of thickened crust and dynamic topography generated by mantle convection, the plate model does not provide a good description of the average topography of the ocean floor at ages greater than approximately 85 million years. There is evidence for a slight, temporary swallowing between the ages of 85-130 million years in the Pacific and Atlantic oceans, which is consistent with the outcome of early numerical experiments on the instability of a cooling thermal boundary layer. Nevertheless, the thermal plate model, with a plate thickness of approximately 90 km, does appear to provide a good description of the average subsidence of, and heat flux through, the oldest sea floor. An analysis of the relationship between gravity and topography over dynamic swells and depressions in the Pacific Ocean, Atlantic Ocean, and Central Africa indicates that gravity and topography are highly coherent at intermediate and long wavelengths, and that the admittance does not vary significantly with wavelength. This is in contrast to the predictions of early theoretical calculations. The long-wavelength admittance over marine dynamic topography is 30 ± 5 mGal km<sup>-1</sup>, and the admittance over dynamic topography in central Africa is approximately 40 mGal km<sup>-1</sup>. An analysis of the results of asthenospheric seismic tomography under the Pacific Ocean, using a recently-published parameterisation of SV-velocity in terms of temperature and depth, indicates that the intermediate and long-wavelength gravity field does not result primarily from temperature anomalies within the lower part of the asthenosphere.
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