This book is about the use of computer programs for the analysis of geophysical data to try to determine the constitution of the Earth's interior, a process which enables a geophysicist to locate petroleum and mineral prospects. Traditional concepts of data processing are thoroughly discussed to provide a good foundation on the subject. The general theory of mathematical-physical computations in stratified media leads to computational techniques for two- and three-dimensionally heterogeneous media. A feature of the book is the use of partial differential equations for reflection seismic data processing in petroleum prospecting. Professor Claerbout and his students have originated a great deal of this material, which thus cannot be found in any other book.