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

该项目的目标是开发一种新技术，从卫星数据的反演中估计全球时空模型。这将使我们有机会更好地表征和分离外部和内部来源，因为它们具有不同的统计特性。由于新的卫星任务将提供大量的数据，因此有必要研究处理这些数据的新方法。如果必须考虑全时空协方差信息，则构造全局时空样条的经典方法将不可行。同时处理Swarm使命一年的数据所需的数据量将超出计算机能力的一般能力。因此，我们提出了一种基于Kaiman滤波和Kaiman平滑的方法，该方法允许我们将全球时空先验信息的字段，虽然实际的计算是在一个小得多的数据集上顺序进行。该滤波器的递归结构将根据全局先验协方差信息产生全局时空反演。该项目的目标有三个方面。第一步是设计递归的Kaiman滤波器，它近似于已建立的规则性磁规范。在这一步骤中使用的数据将是CHAMP现有数据和Swarm使命提供的未来数据。然而，这些技术也将应用于火星全球勘测者（MGS）和月球勘探者任务提供的磁性数据，这对于估计岩石圈对火星和月球磁场的贡献至关重要，我们也对此感兴趣。在第二步中，除了滤波器的数值设计之外，我们还希望解决所提出的估计器的统计特性的问题。我们的特点是凯曼过滤器作为一种有效的方式，最大化的可能性和最佳预测，并期待在估计的渐近性质。这可以应用于内场的时间变化及其预测。统计正则化和鲁棒性的方法进行了调查。这些调查将自然地反馈到Kaiman滤波器和更平滑的设计中。最后，在第三步，wc将使用新开发的模型，以提取更好的岩石圈组成部分的特征，特别是在地球，火星和月球的撞击crater周围。最近，由于行星探索，撞击坑在行星建造或行星改造过程中的作用得到了很大程度的研究，这表明可能所有行星表面都是行星际天体撞击的坑。大型撞击产生的加热和冲击压力足以消除现有的剩磁，大型撞击盆地往往具有非常弱的磁场。因此，在步骤2和步骤3中所做的所有工作将使我们能够正确地描述这些弱磁场，并获得行星体古老磁场的一些有趣特性，这对它们的形成和演化带来了新的和重要的限制。

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.