Monday, September 13, 2010

Kinds of Migration

[Note: A version of this blog entry appears in World Oil (September, 2010)]

In are earlier column (The Age of Migration) we discussed the history of seismic migration. Here we consider a related question: “What are the different kinds of migration, and which one should I choose?”

Migration is an important and expensive process applied to reflection seismic data before interpretation. It is the last major process to hit the data and likely to be blamed for everything from low resolution to inconsistent amplitudes, even though these problems may arise from acquisition or earlier processing steps.

To effectively discuss imaging it helps to know about kinds of migration. It is a waste of time and money to re-migrate data because an inappropriate migration technique was recommended or requested. Here we develop a classification scheme to bring order out of apparent chaos and get everyone talking the same language.

Dimensionality is the first consideration: Migration is either 2D or 3D.

  • 2D: Appropriate only for a pure dip-line. Even then, out-of-plane energy remains that can blur the data.
  • 3D: The right thing to do, but needs data acquired in 3D. A close grid of 2D lines can be merged into a 3D volume and migrated, but this is not really 3D data even if you have 100 square miles of the stuff. What makes data 3D is rich azimuth content; a 2D line has only one azimuth (the compass direction along the line).

Next we have to think about the form of the data being input to the migration: Poststack or prestack.

  • Poststack: Migration of the stack data volume, i.e., one trace per bin for 3D data. This is much less expensive than prestack migration, but also less accurate in structurally complex areas.
  • Prestack: Migration of the prestack data volume containing many traces per bin. Every blip of amplitude on every prestack trace is processed, requiring huge computational effort. Much more expensive than poststack migration.

Another consideration is the handling of lateral velocity variation. Across faults, salt boundaries, and steep dips, velocity can change dramatically over a short distance bending seismic rays. For small velocity contrast (e.g., Gulf of Mexico above salt), we can use shortcuts that save processing time and money. From the viewpoint of physics: Migration can be time or depth.

  • Time: Time migration gives the correct treatment of constant and depth-dependent velocity. Time migration can be interpolated for lateral velocity changes, but is inferior to depth migration for strong variations.
  • Depth: Correct physics treatment of strong lateral velocity variations, rays and wavefronts are accurately bent through the velocity field. Tends to be much more expensive that time migration.

Note the migration terms ‘time’ and ‘depth’ are unrelated to whether the ouput data have a time or depth axis. Any migration can be delivered in time or depth. In current practice it is common to interpret the migrated data in time and depth convert particular horizons using sonic logs and vertical seismic profiles. This makes depth conversion part of the interpretation process and depths can be guaranteed to match log tops at well locations. In areas of strong velocity variation, depth migration is used and output directly in depth. However, migration depth accuracy is limited and the depth section often needs final adjustment based on well data.

In the jargon of migration, a given method can be classified by concatenating the terms given above. For example, we can say 2D poststack time migration or 3D prestack depth migration.

It is important to realize that data are never migrated just once. Migration velocity analysis involves iterating the migration many times. There are clever ways of avoiding repeated migration of the entire data volume, but iterating even part of a large survey can add up. More input traces mean more cost. For a given number of input traces, depth migration will be more expensive and (we hope) more accurate than time migration.

When should we request depth migration and when will time migration suffice? What about prestack and poststack? The controlling factors are dimensionality of the data, structural complexity and velocity variation. The migration should be 2D or 3D depending on dimensionality of the data. However, to hold down costs, selected 2D lines are often extracted from the 3D data for detailed prestack depth migration. These 2D lines should be extracted in the dip direction, if one exists, to minimize out-of-plane effects. If a migration with too many shortcuts is used on properly acquired 3D data, the clue will be lack of geological sense in the final image volume. On the other hand, you can always overkill a job with prestack depth migration and incur unnecessary costs.

Note we have classified migration at a rather abstract level; there is nothing here about individual algorithms. Something like 3D prestack depth migration can be accomplished by many methods: Kirchhoff, beam, wave equation, reverse time, etc. Choosing an optimum method is the realm of the seismic imaging specialist.

At first sight, prestack time migration seems curiously unwise. Much extra expense is incurred by working with prestack data, but no improved image can be expected because only time migration physics is going into the algorithm. Prestack time migration’s main role in the world is to prepare data for prestack interpretation, primarily Amplitude Versus Offset (AVO) analysis. We want to migrate before AVO work to improve lateral resolution, but not spend big money on depth migration and related velocity analysis...plus we have more faith in time migration amplitude behavior.

In summary, two things make migration expensive: More data or more physics, or both. More data comes from 3D versus 2D and prestack versus poststack. The level of physics is implied by the terms ‘time migration’ (less physics) and ‘depth migration’ (more physics).

This column does not prepare you to write, or even use, complex migration software. But you might be able to deal with contractors, processors, and contribute to asset team discussions. By way of analogy, we are not out to build a car, just be a savvy, knowledgeable buyer who can kick the tires, peek under the hood, and make informed decisions.

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