Translations:Mathematical foundation of 3-D migration/24/en

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Mathematically, the two-pass approach is based on the idea of full separation [1] of migration operators in the inline and crossline directions. The separation is strictly valid for the constant-velocity medium. When velocities vary spatially, splitting [1] of the inline and crossline operators is necessary (Figure 7.3-1). A rigorous mathematical treatment of separation and splitting of extrapolation operators can be found in a paper by Brown /> [2].

  1. 1.0 1.1 Claerbout, 1985, Claerbout, J. F., 1985, Imaging the earth’s interior: Blackwell Scientific Publications.
  2. Brown, 1983, Brown, D. L., 1983, Applications of operator separation in reflection seismology: Geophysics, 48, 288–294.