Downward continuation

In Figure , the upward continued synthetics of Figure  have been downward continued back to the original recording surface using the adjoint datuming operators. The Kirchhoff method has most faithfully reproduced the original synthetic. Both the finite-difference and the phase-shift result have a pronounced stair-step effect along the events. This does not occur after upward continuation, but after downward continuation, the discretisation of the topography has introduced an error. This error can be reduced at the cost of a finer grid step size in $\Delta z$. Aside from the stair-step effect, both the finite-difference and phase-shift results reasonably restore the original kinematics, although the finite-difference result exhibits more artifacts.

The result of downward continuing the original synthetic (Figure a) from the topography to a flat datum below the topography with the Kirchhoff algorithm is displayed in Figure . Downward continuing the data in constant (or depth-variable) velocity does not require trace padding because all dip components are propagated downward and inward and the steep dips do not propagate off the computational grid. Therefore, the flanks of the syncline/anticline structure are well imaged without requiring any trace padding.

 

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Figure 10 (a) Synthetic data, and downward continuation of the upward continued synthetics from Figure with (b) Kirchhoff, (c) finite-difference, and (d) phase-shift methods.

 

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Figure 11 Downward continuation and migration of downward continued synthetic with the Kirchhoff algorithm.