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Accurate and efficient imaging of complex structures by semirecursive Kirchhoff migration

Presented at the 59th Ann. Internat. Mtg., Euro. Assoc. Geo. Eng., Expanded abstracts, E037, May 1997.

Dimitri Bevc, 3DGeo Development Inc., 465 Fairchild Drive, Suite 226, Mountain View, CA 94043, USA, Email: dimitri@3DGeo.com.

Introduction
Kirchhoff migration is generally accepted to be the most practical and efficient method of imaging 2-D and 3-D prestack seismic data. However, in practice, standard Kirchhoff algorithms often do a poor job of imaging complex structures such as subsalt targets (Geoltrain and Brac, 1993; Nichols, 1994). I present a new semirecursive Kirchhoff migration algorithm which is capable of obtaining accurate images of complex structures by combining Kirchhoff datuming and Kirchhoff migration. The semirecursive method is successful because breaking up the complex velocity structure into smaller depth regions allows traveltimes to be calculated in simple regions where they are well behaved, and where they correspond to energetic arrivals. Because traveltimes are computed for simple depth regions, the adverse effects of caustics, head waves, and multivalued arrivals do not develop.

The semirecursive Kirchhoff method has the advantage of being able to use any simple first-arrival traveltime algorithm, thus benefiting from the computational efficiency, robustness, and simplicity of such methods. The method is efficient and offers substantial cost advantages and imaging improvements over conventional methods.

Semirecursive Kirchoff Migration
A well-known example of a complicated imaging objective is the Marmousi synthetic data set. The Marmousi velocity model generates complex propagation paths in which late energetic arrivals are not fit well by first-arrival finite-difference traveltimes. At late times, as the wavefield evolves, complex propagation effects begin to manifest themselves and the arrivals become multivalued, so that the first-arrival traveltimes no longer match the most energetic wavefront. By starting the traveltime calculation from a depth level deeper in the velocity model, it is possible to compute first-arrival traveltime tables which match the acoustic wavefield propagation and accurately parameterize the asymptotic Green's functions required for Kirchhoff imaging (Bevc, 1995).

The top image in Figure 1 is the result of standard Kirchhoff migration of the Marmousi synthetic using first-arrival traveltimes calculated with a finite-difference eikonal equation solver. The faults and beds in the upper portion are well imaged; however, the anticlinal structure below 2300 m and the target zone at a lateral position of about 6500 m and depth of 2500 m are not well imaged. The central portion of the image, at the target zone, corresponds to regions where the acoustic wavefield and first-arrival traveltime do not match. The propagation here is complicated by the overlying faults which contain fast and slow velocity regions, and by the high velocity salt which partially overlays the target, resulting in multivalued arrivals.

The result of applying the semirecursive algorithm to the Marmousi synthetic data set is displayed in the bottom image of Figure 1. It is generated by downward continuing the data to a depth of 1500 m in three datuming steps. The downward continued data are then migrated and combined with the previous image of the upper 2000 m. The bottom image in Figure 1 is a clear improvement over the previous migration result. The anticlinal structure below the salt and the target are now clearly imaged. Events which unconformably define the top of the anticline, the anticline events themselves, and the target events, are clearly imaged. The resolution is so good that the flat spot in the reservoir and the strongly reflective cap stand out clearly.

References
Bevc, D., 1995, Imaging under rugged topography and complex velocity structure: Ph.D. thesis, Stanford Univ.

Geoltrain, S. and Brac, J., 1993, Can we image complex structure with first-arrival traveltime?: Geophysics 58, 564--575.

Nichols, D., 1994, Imaging complex structures using band limited Green's functions: Ph.D. thesis, Stanford Univ.

Figure 1. Migrated image using traveltimes calculated from the surface, and traveltimes calculated from a depth of 1500 m. The lower part of the image was obtained by migrating data which was redatumed to a depth of 1500 m in three steps of 500 m each.

For a more detailed article on this subject, download my Geophysics preprint, or thesis.