Time-to-depth conversion and seismic velocity estimation using time-migration velocity

Introduction

Time-domain seismic imaging is a robust and efficient process routinely applied to seismic data (Robein, 2003; Yilmaz, 2001). Rapid scanning and determination of time-migration velocity can be accomplished either by repeated migrations (Yilmaz et al., 2001) or by velocity continuation (Fomel, 2003). Time migration is considered adequate for seismic imaging in areas with mild lateral velocity variations. However, even mild variations can cause structural distortions of time-migrated images and render them inadequate for accurate geological interpretation of subsurface structures.

To remove structural errors inherent in time migration, it is necessary to convert time-migrated images into the depth domain either by migrating the original data with a prestack depth migration algorithm or by depth migrating post-stack data after time demigration (Kim et al., 1997). Each of these options requires converting the time migration velocity to a velocity model in depth.

The connection between the time- and depth-domain coordinates is provided by the concept of image ray, introduced by Hubral (1977). Image rays are seismic rays that arrive normal to the Earth's surface. Hubral's theory explains how a depth velocity model can be converted to the time coordinates. However, it does not explain how a depth velocity model can be converted to the time-migration velocity. Moreover, image-ray tracing is a numerically inconvenient procedure for achieving uniform coverage of the subsurface. This may explain why simplified image-ray-tracing algorithms (Hatton et al., 1981; Larner et al., 1981) did not find widespread application in practice. Other limitations of image rays are related to the inability of time migration to handle large lateral variations in velocity (Robein, 2003; Bevc et al., 1995).

The objective of the present work is to find an efficient method for building a velocity model from time-migration velocity. We establish new ray-theoretic connections between time-migration velocity and seismic velocity in 2-D and 3-D. These results are based on the image ray theory and the paraxial ray tracing theory (Popov, 2002; Popov and Pšencik, 1978; Cervený, 2001). Our results can be viewed as an extension of the Dix formula (Dix, 1955) to laterally inhomogeneous media. We show that the Dix velocity is seismic velocity divided by the geometrical spreading of the image rays. Hence, we use the Dix velocity instead of time migration velocity as a more convenient input. We develop a numerical approach to find (a) seismic velocity from the Dix velocity, and (b) transition matrices from the time-domain coordinates to the depth-domain coordinates. We test our approach on synthetic and field data examples.

Our approach is complementary to more traditional velocity estimation methods and can be used as the first step in a velocity model building process.

Time-to-depth conversion and seismic velocity estimation using time-migration velocity