The relationship between Born inversion and migration for common‐midpoint stacked data

Abstract

The relationship between Born inversion and wave‐equation migration of common‐midpoint (CMP) stacked seismic reflection data is analytically determined. The three‐dimensional (3-D) velocity distribution obtained by Born inversion is shown to be directly related to the 3-D reflectivity function obtained by wave‐equation migration for full bandwidth or band‐limited data. The relationship is obtained by the reformulations of migration and Born inversion methods as inverse source problems for the 3-D wave equation. The reformulation leads to a definition of the reflectivity function as the source function for the wave equation. It also leads to determination of the Born inversion results by applying the algorithm for wave‐equation migration to modified surface data. The modified data are simply related to the CMP stacked data. Alternatively, Born inversion results may be obtained directly from the migrated section. Results from synthetic and recorded data are presented and found to be consistent with the theoretical developments.