Wave theory justifies both pre- and post-NMO deconvolution, but the filters should be estimated simultaneously, not sequentially. A linearized theory enables simultaneous estimation of the two filters. The theory incorporates spherical divergence independently from statistical weighting. Field data test cases show the expected interaction between NMO and deconvolution. The tests were not able to establish that simultaneous estimation is superior to sequential estimation. The difficulty is ascribed to the inadequacy of NMO as a downward continuation process.

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