Except for a thin layer at the surface, all of our knowledge of the physical properties of the Earth at depth is based on observations collected at the surface. This creates what is known as an inverse problem, where indirect information must be used to constrain the interior, hidden from view. Such Inverse problems arise in many areas of the sciences including Engineering, Astronomy, Biology and Medicine. Although the applications differ the mathematical framework of inverse problems is similar across all fields meaning advances in one area can influence another in unexpected ways.

Mathematics has also revealed that Earth Science inverse problems are often `ill-posed’ which means that Earths properties at depth can only be partially determined from the surface. This creates major challenges in how to draw robust conclusions about what is actually going on down there. In addition Earth Science problems often involve complex and sometimes unfavourable mathematical relationships between the deep and the surface, requiring advanced computational resources and ingenuity to reach a solution. These issues will be explored in the presentation and some challenges highlighted.

This Public Lecture is run in conjunction with the Mathematics of Planet Earth 2013 Conference.