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## Datuming from a planar datum to another planar datum, upward

To introduce datuming that uses a finite-difference method, let me first describe datuming from a lower planar datum to a higher planar datum. A scatterer is located at (z=0.15, y=0.32) in a constant velocity v=1 medium. The variables z and y denote depth and horizontal coordinates. I generate the synthetic zero-offset section in Figure 1 at the planar datum z=0.05 by ray tracing, for which only the traveltime is correct. The apex of the hyperbola is at time t=0.1. Then I use a grid in which nz=20, ny=128, dz=0.005, dy=0.005, and dt=0.001 to run the two-way wave equation forward in time with the synthetic record as the boundary condition at the lower recording datum. The desired wavefields at the higher planar datum are the absorbing history wavefields at the top iz=1 of the grid, or the history wavefields at the planar datum just one grid point below the top, so that the absorbing boundary conditions can be implemented efficiently. The results are shown in Figure 2. In this case, the datuming is done over 50 m. After the datuming process, the apex of the hyperbola is at time t=0.15. The time period for running the wave equation must be larger than the original record length by an amount that is long enough to account for the propagation time from the lower datum to the higher datum, because the actual earth wavefields expand up from the subsurface. There is a light ghost following the main event, which results from the reverberations between the input datum and the output datum. The ghost reflection can be removed by implementing better absorbing boundary conditions at the output datum, and implementing the recorded wavefields as a series of point sources instead of simple boundary conditions.

 d1 Figure 1 The wavefields recorded at the planar datum z=0.05

 d1.2 Figure 2 The extrapolated wavefields at the upper planar datum z=0. The apex of the hyperbola has been shifted by the datuming.

Next: Datuming from an irregular Up: POSTSTACK DATUMING Previous: POSTSTACK DATUMING
Stanford Exploration Project
11/17/1997