A 2-D geologic model used for walkaway VSP ray-tracing modeling. (Images courtesy of VSFusion)

Conventional migration of primary reflections in vertical seismic profile (VSP) data provides only a narrow illumination/imaging zone below the deepest receiver. The first-order free-surface related multiples provide much wider seismic illumination than the primary seismic reflections. This article presents a methodology to perform three-component (3-C) vector migration for the first-order free-surface related multiples.

It is well recognized that the traditional 3-D migration of upgoing primary reflections in VSP data images only a very narrow cone-shaped zone around the borehole, with the cone tip centered at the shallowest receiver in the well. To extend this limited imaging zone, a few imaging methods (e.g., Yu and Schuster 2004, Jiang et. al. 2005) have recently been developed to migrate first-order downgoing multiples which can provide much wider imaging zones than migrating conventional primary reflections with only VSP data.

The multiples recorded by 3-C borehole receivers have the same 3-D vector characteristics as the reflected data. However, almost all current imaging methods migrate only a single scalar receiver component. As it is difficult to rotate the amplitude/energy of the multiple arrivals distributed on the three components onto a single scalar component due to their more complex ray paths (relative to primary reflected ray paths), migrating all three components simultaneously instead of one scalar component can significantly improve the image quality of the multiple reflections. The migration of all three components of the multiple data can also help reduce image ambiguity and the migration artifacts inherent to any single scalar component migration algorithm.

Methodology
The first-order free-surface related multiple arrivals are upgoing primary reflections that have been reflected back from the free surface and then propagate down to the borehole receivers. Seismic waves excited by a point source propagate down to the various geologic interfaces and are reflected from the interfaces. The primary reflections recorded by the borehole geophones provide only a narrow cone of illumination; most primary reflections, however, will continue to propagate past the receiver, back to the free surface. The free surface acts as an almost perfect seismic reflector, and the primary reflections from the free surface are strongly reflected back down to the borehole receivers. The first-order multiples are usually the dominant wave mode in the VSP wavefield as the higher-order multiples attenuate quickly due to their much longer travel distances relative to the first-order multiples. A comparison of the illumination zone generated by the upcoming primary reflections and the illumination zone generated by the first-order free-surface related multiples show that the multiples image a significantly wider geologic area.

The following steps were used to perform 3-C vector migration using the first-order free-surface related multiples:
1. Build a mirror-image velocity model symmetric about the free surface and project the borehole receivers to their virtual positions on the mirror-image velocity model.
2. Calculate and build travel-time tables from every source/virtual receiver position to each image point in the velocity model.
3. Perform three-component (x, y, z) vector summation of the 3-D Kirchhoff prestack depth migration for the first-order free-surface related multiples.

Numerical examples

The methodology was tested using a dataset generated by ray trace-modeling a 2-D layered model using walkaway VSP survey geometry. The model has seven layer interfaces with contrasting compressional (P)-wave velocities. The walkaway VSP survey has a total of 61 source positions ranging between the X coordinate locations of 2,000 and 8,000 ft (610 and 2,440 m) with a 100-ft (31-m) interval between each shot. The depth of all sources is 10 ft (3 m) below the free surface. A total of 30 3-C borehole receivers were modeled between the vertical depths of 5,000 and 6,450 ft (1,525 and 1,967 m), spaced at 50-ft (15-m) intervals. The wellhead position was at an X coordinate of 5,000 ft.

Conclusions

The first-order free-surface related multiples, which usually dominate the downgoing wavefields in VSP data, provide a much wider seismic illumination zone than conventional primary VSP reflections. We have developed a new methodology to perform 3-C vector migration for the first-order free-surface related multiples. The new method is based on the free-surface mirror image principle and a vector summation algorithm for Kirchhoff prestack depth migration. Synthetic modeling results suggest that our method can efficiently and accurately produce a much wider image zone than conventional VSP migration using primary reflections only. Image quality is also significantly enhanced by migrating all three vector components instead of one scalar component as is usually done in conventional VSP migration methods.

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