Gazdag migration from an irregular surface

An algorithm for depth migration when the surface is nonflat is presented by Ji and Claerbout (1992) elsewhere in this report. If the surface fluctuates severely, the aperture of the wavefield varies with the surface. The varying aperture along the surface results in an amplitude change in the image. Figure (c) shows this effect caused by the undulating topography shown in Figure (a). In the portion of flat surface the reflector has imaged correctly, but in the portion of nonflat surface the image shows slight amplitude change with some background noise. The result of the least-squares imaging is shown in Figure (d); it is more correct than the image after migration.

 

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Figure 7 Least-squares Gazdag imaging from an irregular surface: (a) A syncline reflector model under the undulating surface (upper white line), (b) The data obtained by the Gazdag modeling using the algorithm introduced by Ji and Claerbout (1992), (c) The image obtained by the Gazdag migration for (b), (d) The image obtained by the least-squares Gazdag imaging for (b) (after 10 iterations).