An approximate solution is presented to the seismic inverse problem for two-dimensional (2-D) velocity variations. The solution is given as a multiple integral over the reflection data observed at the upper surface. An acoustic model is used, and the reflections are assumed to be sufficiently weak to allow a 'linearization' procedure in the otherwise nonlinear inverse problem. Synthetic examples are presented demonstrating the accuracy of the method with dipping planes at angles up to 45 degrees and with velocity variations up to 20 percent. The method was also tested under automatic gain control, in which case velocity estimates were lost but the method nonetheless successfully migrated the data.

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