We introduce a new operator for explicit wavefield extrapolation. We modify the commonly used locally homogeneous wavefield extrapolator to include a local vertical gradient, whose purpose is simply to enhance operator stability when spatially localized. The locally homogeneous operator assumes that wavefield extrapolation across a single depth step can be done with straight raypaths using the assumed constant velocity at the output point. Such operators can produce excellent seismic images but the straight ray assumption means that their spatial aperture is infinite, which leads to instability when the operator is localized by spatial windowing. Adjusting the operator to accommodate a suitably chosen positive vertical velocity gradient causes raypath curvature which naturally limits the operator within a finite aperture. The required modification to the locally homogeneous operator is essentially a WKBJ-style integrated phase. The resulting operator has a finite aperture and is sufficiently stable when localized to be used in an explicit depth migration scheme. We demonstrate operator fidelity with excellent images of the Marmousi model.

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