ESTIMATION OF MULTIPLE-SCATTERING BY ITERATIVE INVERSION .1. THEORETICAL CONSIDERATIONS

A review has been given of the surface-related multiple problem by mak ing use of the so-called feedback model. From the resulting equations it has been concluded that the proposed solution does not require any properties of the subsurface. However, sourer-detector and reflectivit y properties of the surface need be specified. Those properties have b een quantified in a surface operator and this operator is estimated as part of the multiple removal problem. The surface-related multiple re moval algorithm has been formulated in terms of a Neumann series and i n terms of an iterative equation. The Neumann formulation requires a n onlinear optimization process for the surface operator;while the itera tive formulation needs a number of linear optimizations. The iterative formulation also has the advantage that it can be integrated easily w ith another multiple removal method. An algorithm for the removal of i nternal multiples has been proposed as well. This algorithm is an exte nsion of the surface-related method. Removal of internal multiples req uires knowledge of the macro velocity model between the surface and th e upper boundary of the multiple generating layer.In Part II (also pub lished in this issue) the success of the proposed algorithms has been demonstrated on numerical experiments and field data examples.