A UNIFIED APPROACH TO ACOUSTICAL REFLECTION IMAGING .3. EXTENSION TO THE ELASTIC SITUATION

The forward model, as derived in part I [ A. J. Berkhout, J. Acoust. S oc. Am. 93, 2005-2016 (1993) ], and the inversion scheme, as derived i n part II [A. J. Berkhout and C. P. A. Wapenaar, J. Acoust. Soc. Am. 9 3, 2017-2023 (1993) J, are extended to the elastic situation. The elas tic forward and inverse problem are formulated in terms of matrices, s imilar as in the acoustic situation. Unlike in the acoustic situation, the matrices involved in the elastic problem each consist of 3 X 3 su bmatrices. For instance, the submatrices of the multi-component data m atrix V represent single-component data matrices, each submatrix being related to a specific combination of source and receiver components. On the other hand, the submatrices of the multi-wavetype reflection ma trix R+/- represent single-wavetype reflection matrices, each submatri x being related to a specific combination of incident and reflected wa vetypes. In the discussion of the elastic forward model the multi-comp onent data matrix V at the acquisition surface is related to the multi -wavetype reflection matrices R+/- in the subsurface. In the discussio n of the inversion scheme it is shown how R+/- is obtained step by ste p from the multi-component data matrix V. Once the multi-wavetype refl ection matrices R+/- have been determined the medium parameters can be much better resolved than in the acoustic situation.