Model fusion under probabilistic and interval uncertainty, with application to Earth sciences

One of the most important studies of the earth sciences is that of the Earth's interior structure. There are many sources of data for the construction of tomographic models of earth structure. These include the time of the first arriving waves from earthquakes and from man‐made sources, measurements of the earth's gravity field and measurements of the dispersion of surface waves generated from earthquakes. Formally integrating the information derived from multiple types of data sources is an important theoretical and practical challenge. While such combination methods are being developed, as a first step, we propose a practical solution: to fuse the Earth models coming from different data sets. The models used in this paper contain measurements that have not only different accuracy and coverage but also different spatial resolution. We describe how to fuse such models under interval and probabilistic uncertainty. The resulting techniques can be used in other situations when we need to merge models of different accuracy and spatial resolution.