Image rays and lateral velocity variations

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Seismic Data Analysis
Series Investigations in Geophysics
Author Öz Yilmaz
ISBN ISBN 978-1-56080-094-1
Store SEG Online Store

Normal-incidence rays are associated with zero-offset traveltimes and therefore can be used to examine the degree of complexity in velocity-depth models as demonstrated in Figure 8.2-4. For a quantitative assessment of lateral velocity variations, however, image rays need to be examined as shown in Figure 8.2-5. By definition, image rays emerge at the right angle to the surface. As shown in Figure 8.0-11, the lateral shift between the point of departure of the image ray at the reflector position and the point of emergence of the image ray at the surface provides a measure of lateral velocity variation.

Consider the image rays departing from the top-salt layer boundary in Figure 8.2-5. These rays show no lateral shift, and therefore, imaging the top-salt boundary does not require depth migration; instead, it can be achieved by time migration. The image rays from the base-salt boundary, however, show significant lateral shifts, especially beneath the flanks of the diapir. The stronger the lateral velocity variations, the more the lateral shifts in image rays. This behavior of the image rays indicate that the lateral velocity variations caused by the salt diapir require depth migration to image the base-salt boundary, accurately.

The image rays associated with the flat reflector below the salt diapir also show significant lateral shifts (Figure 8.2-5). Again, this reflector can only be imaged accurately by depth migration, rather than time migration. Note that image rays do not sample the reflector boundaries uniformly — there are regions that contain densely and sparsely populated image rays.

In principal, an earth image in depth can be obtained by first migrating a stacked section in time, then converting the time-migrated section to depth along image rays using the appropriate velocity-depth model [1] [2]. This ray-theoretical two-step depth migration to obtain an earth image in depth is rarely used in practice. However, it is common practice to perform time-to-depth conversion of time horizons using image rays. Specifically, 3-D volume of stacked data first is migrated in time and selected time horizons are interpreted. These time horizons are then converted to depth horizons along image rays, again, using an appropriate velocity-depth model. Creating depth structure maps using this procedure is called map migration.

In conclusion, by examining the behavior of image rays through the salt diapir model, we can judge as to which layer boundary requires imaging in depth (Figure 8.2-5). The image rays down to the top-salt boundary are not distorted laterally; therefore, time migration is adequate for imaging the overburden above the salt diapir. Significant ray bending, however, takes place at the top-salt boundary; this results in lateral distortions of the image rays down to the base-salt boundary and the deeper reflector. Depth migration, therefore, is needed for accurate imaging of the base-salt boundary and the subsalt region.


  1. Hubral (1977), Hubral, P., 1977, Time migration — some ray-theoretical aspects: Geophys. Prosp., 25, 738–745.
  2. Larner et al., 1981, Larner, K. L., Hatton, L., and Gibson, B., 1981, Depth migration of imaged time sections: Geophysics, 46, 734–750.

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