f Estimation of reflection co-efficients from zero-offset field data

The classical one-dimensional inverse problem consists of predicting reflection coefficients from surface seismic data using the one-dimensional wave equation. In one spatial dimension only plane waves propagating along one axis can be described. Spherical waves originating from a point source can not be adequately described. Many authors have considered this problem, and given examples of use on field data. An early example is Bamberger et.al. (1982). This work considers the inverse problem of predicting reflection coefficients from vertically travelling spherical waves in a one-dimensional horizontally layered medium. It is a more realistic problem than the classical one in the sense that point sources are commonly used in seismic exploration.