## Promoting Sparsity and Localization in Geophysical Inverse Problems: Methodology and Case StudiesFrederik J. Simons Princeton University Sometimes we don't have enough information, sometimes we have too much and need to choose. Sometimes our data present a highly incomplete picture of the truth, and sometimes there is so much redundancy and overdeterminacy that we need to cull it down somehow. In this talk, I will discuss several ways to shed light on problems of this nature. I will talk about the problem of reconstructing global sea level from sparse, uncertain, scattered indicators of local sea level. I will introduce the design of flexible parameterizations to render inverse problems in geodesy and geomagnetics sparse. I will discuss sparsity-promoting algorithms in global seismology. Lastly, I will discuss how to weigh the Earth from space by monitoring the mass balance of the Greenland ice sheets using time-variable gravity. Each of these subtopics are connected by the mathematical approach with which we treat them - I will briefly highlight the key innovations and discuss the often widespread implications of the results. Department of Geosciences Virginia Polytechnic Institute and State University 4044 Derring Hall (0420) Blacksburg, VA 24061 |