Mapping landforms on the Moon is of great interest and importance for future human settlements and resources exploration. One of the first steps is to map the topography and investigate their shape and geometry in great detail and resolution, which would provide the first conditions for assessing their suitability for future on-site analysis. However, data from the Lunar Orbiter Laser Altimeter (LOLA) provide low resolution elevation maps in comparison to the size of detailed geological features. To improve resolution, we developed an inverse method to upscale topographic maps to a higher resolution using photographic data from the Lunar Reconnaissance Orbiter Camera (LROC). The method, which exploits the relation between topographic gradients and degrees of shading of incoming sunlight, shows an improvement from ~60 metres per pixel to 0.9 metres per pixel, bringing it to the same resolution as the optical images from LROC. Our method can detect craters as small as ~3 metres of diameter and, if illumination from several angles are available, is potentially a way to remove shades from complex features such as caves. It is also possible to estimate the error of the model due to uncertainties in the albedo.

We developed a method for quantification of uncertainties on spatial data acquired at points with uncertain location coordinates. We applied it to well-log data from wells with uncertain trajectories. The method is fully probabilistic and requires few a priori assumptions on the Earth model and the wellbore geometry. We performed simulations of well trace and well-logging showing how the total uncertainty of well-log data vary according to the variability of subsurface properties, and how the reliability of well-log interpretations close to layer boundaries may be compromised.

Inversion of seismic data using information from horizontal wells is often is hampered by cumulative well- location errors. These errors can be significant and propagate to the well-log measurements in the borehole. To achieve a proper data integration and arrive at correct uncertainty estimates, we formulate the problem in a fully probabilistic framework and present a numerical approach for improving subsurface imaging using uncertain well-log data and their uncertain locations, as well as uncertain seismic data. The result is improved model error quantification in the seismic inversion process.