Seismic Inverse Problems: Recent Developments in Theory and Practice
William W. Symes (The Rice Inversion Project, USA)

In the last fifteen years, advances in computer hardware and algorithm design have permitted geophysicists to pose the inference of three-dimensional earth structure from seismic data as an inverse problem via least-squares data-fit. Successful solutions have yielded dramatic improvements in the quality of seismic inference, and initiated an explosion of interest in both industrial and academic
research communities. However, fundamentally mathematical obstacles still limit the potential of seismic inversion. This paper will review both conventional and unconventional strategies for mitigation of these impediments. In particular I will explain how relaxation by mapping extension, an idea originating in industrial seismology, leads to algorithms that derive the same information about subsurface structure from standard time series data as has previously been obtained from time-of-flight information, a derived data type.