Mathematics of Reflection Seismology / Математика сейсмологии отраженных волн

This chapter develops mathematical concepts and tools underlying techniques for estimation of material structures from observations of reflected waves. These techniques belong in some sense to the theory of inverse problems for partial dierential equations, but many of them have their origins outside of modern mathematics. Most of the ideas developed in this chapter arose rst in the seismology, particularly in that branch devoted to exploration for petroleum. Therefore I shall take viewpoint and terminology from exploration seismology. A principal goal of this chapter is to provide a natural \Courant|Hilbert" setting for these ideas and terms, which play a very important role in the following chapters.<...>