Velocity Modelling for Depth Migration Using Exact-Time Migration

Velocity modelling is often done with pre-stack time migration, at least for weak lateral velocity variations. Iterating through the combination of common-offset DMO, zero-offset migration and velocity interpretation can yield a more accurate velocity model for depth migration. However, especially when lateral velocity variations increase, this method is compromised by errors incurred through the use of DMO and, in particular, constant velocity DMO. Consideration of these errors leads to the exact-time migration algorithm which is based on ray tracing through a velocity-depth model. In order to update the velocity-depth model based upon the residual errors after exact-time migration, a theoretical relationship between time migration stacking velocities and velocity-depth functions along image rays has been established.

The velocity building process with exact-time migration consists of taking the exact-time migrated gathers and interpreting stacking velocities. A generalised linear inversion scheme then inverts these velocities and updates the velocity-depth model. This procedure is iterated as required. At any stage the velocity-depth model can be used to create a pre-stack depth migrated image which can be used for interpretation and detailed updating of the model, or as the final image. The updates made by the inversion scheme are smooth and details from interpretation of depth images can be helpful.

Application of the exact-time migration approach to an Australian field data example resulted in obvious and significant velocity model improvements in each of two iterations. The effect of these improvements on pre-stack depth migrated images verify the ability of the exact-time migration algorithm as a velocity modelling option by improving the seismic image below a high velocity buried channel.