An iterative inversion of back‐scattered acoustic waves

The application of the Born approximation to the scattered wave field, followed by a WKBJ and far-field approximation on the propagation Green's function for a slowly varying background medium, leads to a simple integral relation between the density and bulk-modulus anomalies superimposed on the background medium and the scattered wave field. An iterative inversion scheme based on successive back-projections of the wave field is used to reconstruct the two acoustic parameters. The scheme, when applied to data generated using the direct integral relation, shows that the variations of the parameters can be reconstructed. The procedure is readily applicable to actual data, since every iterative step is essentially a prestack Kirchhoff migration followed by the application of the direct Born approximation and far-field operator.