Linearized Inversion of Seismic Reflection Data*

A bstract This is the first of a series of papers giving the solution of the inverse problem in seismic exploration. The acoustic approximation is used together with the assumption that the velocity field has the form image . The forward problem is then linearized (thus neglecting multiple reflected waves) and the inverse problem of estimating δ is set up. Its rigorous solution can be obtained using an iterative algorithm, each step consisting of a classical Kirchhoff migration (hyperbola summation) plus a classical forward modeling step (circle summation).