# Dip moveout correction in three and two dimensions

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## Abstract

Any 3D survey with the shots and receivers in a horizontal plane, whatever the layout, can be interpolated to a regularly spaced sampling by a velocity independent procedure. The procedure creates an offset-versus-time panel at each (x, y) grid point which has the property that all reflections and diffractions have hyperbolic moveout with the rms velocity. This is exactly true if the velocity of propagation in the medium is constant. The derivation is based on the concept that an ellipsoidal wavefront is equivalent to the summation of a family of tangent spherical wavefronts. Migration of a single finite-offset trace (the ellipsoidal wavefront) can be achieved by migrating a family of zero-offset traces (spherical wavefronts). This step from finite offset to zero offset can be broken into two steps; the first is independent of velocity and introduces intermediate offsets, and the second is standard NMO and stack applied to the intermediate offsets. This concept for DM0, dip moveout correction, was applied to a 2D data set acquired over a constant velocity subsurface. A dip line was shot over a horizontal reflector and a ramp inclined at 60[degrees]. Before DMO the horizontal reflector showed a stacking velocity of 2 960 m/s and the ramp showed a stacking velocity of approximately 5 900 m/s. After DMO both reflections showed a stacking velocity of approximately 3 000 m/s. This velocity was used to stack and migrate the data. The depth section clearly images both events within the bounds of the limited data set. Prior knowledge of the propagation velocity was not essential to any processing steps nor was prior knowledge of the dip of the ramp. Velocity analysis was done simply with the normal moveout equation.