Space-time models of planetary magnetic fields for characterisation of regional lithospheric features and impact craters

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The goal of this project is to develop a new technique to estimate global space-time models from the inversion of satellite data. This will give us the opportunity to better characterize and separate the external and the internal sources due do their different statistical properties. The enormous amount of data that will be available thanks to new satellite missions, will it make necessary to investigate new ways of treating them. The classical way of constructing global space time splines will be unfeasible if full space-time covariance information has to be taken into account. The data volume necessary to treat, say one year of data of the Swarm mission in a simultaneous way would be beyond the common capacities of computer powers. Therefore, we propose an approach based on Kaiman filtering and Kaiman smoothing, that allows us to incorporate global space-time prior information about the fields although the actual computation is carried out sequentially on a much smaller data set. It is the recursive structure of the filter, that will produce the global space-time inversion based on global prior covariance informations. The aim of this project is three fold. The first step consists to design recursive Kaiman filters, that approximate the established magnetic norms of regularity. The used data during this step will be the CHAMP available data and the future data provided by the Swarm mission. The techniques, however, will be also applied to magnetic data provided by missions as Mars Global Surveyor (MGS) and Lunar Prospector, crucial in estimating the lithospheric contributions in the Martian and Lunar magnetic fields, in which we are also interested. During the second step, besides the numerical design of the filters we also want to address the question of the statistical properties of the proposed estimators. We characterize the Kaiman filter as an effective way of both maximizing the likelihood and optimal prediction and look at the asymptotic properties of the estimates. This can be applied to the temporal changes and their prediction of the internal fields. The statistical regularization and robustness of the methods is to be investigated. These investigations will naturally feed-back into the Kaiman filter and smoother design. Finally, during the third step, wc will use the newly developed models, to extract better characterization of the lithospheric component in particular around the impact crators of Earth, Mars and Moon. Recently, the role of impact cratering in planet-building or planet-modifying processes has been largely investigated due to planetary exploration, indicating that possibly all planetary surfaces are cratered from impacts of interplanetary bodies. The heating and shock pressures generated by large impacts are more than sufficient to erase existing magnetic remanence, large impact basins tending to have very weak fields. So, all the work done during steps 2 and 3 will allow us to properly describe these weak magnetic fields and obtain some interesting properties of the ancient fields of planetary bodies, which brings new and important constraints on their formation and evolution.