f Removal of inhomogeneous internal multiples

Removal of surface-related multiples and interral multiples can be considered as the first step in the inversion of seismic data. The removal of surface-related multiples can be formulated by means of Rayleigh's reciprocity theorem, which leads to an integral equation of the second kind for the reflected pressure wavefield (Fokkema and van den Berg, 1993). The method requires no a priori information about the subsurface geology, nor structural nor material. In this paper a method is proposed to remove interral multiples of the first layer. Application of Rayleigh's reciprocity theorem leads to two integral relations that must be satisfied simultaneously: the first requires consistency in the first layer, implemented as an integral equation, while the other requires consistency with the measured data in the form of an integral representation. The result of simultaneous manipulation of the two integral relations is that the homogeneous domain has been extended downwardly, removing the first layer. This process can be continued to deeper levels to remove internal multiples from deeper layers. The method presented requires a priori infomation on the material properties in the layer from which the internal multiples are to be removed.