Principles of Migration Using Wavefield-continuation Methods
For depth-migration problems, wavefield-continuation migration methods can yield better images than Kirchhoff methods do. Wavefield-continuation methods provide accurate solutions of the wave equation over the whole range of seismic frequencies, whereas Kirchhoff methods are based on a high-frequency approximation of the wave equation. Furthermore, wavefield-continuation methods naturally handle multipathing of the reflected energy induced by complex velocity functions. In contrast, when multipathing occurs, Kirchhoff methods require summation of the data over complex multivalued surfaces. That process can be cumbersome and error-prone.
The following example illustrates a case in which severe multipathing of the wave-field makes wavefield-continuation methods advisable. Figure 1 shows a crossline section through the SEG-EAGE salt velocity model. Figure 2 compares the images obtained by 3D prestack migration with (a) a wavefield-continuation method and (b) a Kirchhoff method using the SEG-EAGE C3-NA data set. The location of this section coincides with that of the section shown in Figure 1. Improvements achieved by wavefield-continuation migration in the subsalt image (Figure 2a) are evident. Image (a) shows several reflectors that are not visible in image (b). Furthermore, several imaging artifacts that degrade image (b) are not in image (a). The wavefield-continuation image was computed by applying a computational algorithm called common-azimuth migration (Chapter 5), the cost of which is comparable to that of using Kirchhoff migration for full-volume images.
The superior image quality achieved by wavefield-continuation migration can be understood by analyzing results of wavefield modeling in the vertical section