My Smudge is Better Than Your Smudge

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The means by which 'migrated' seismic images are formed is used to illustrate how easily the final images can be degraded by the seismic migration process itself. I mention a few key considerations to avoid the degradation of seismic image quality and resolution during traditional workflows.


The Superposition of Partial Seismic Images

The animated illustration below of Kirchhoff migration for one offset plane illustrates how the superposition of 'partial images' from discrete trace locations builds up a seismic image. 


Kirchhoff migration of individual seismic traces, each corresponding to a common source-receiver offset (i.e., 'offset plane'), is used to build an increasing higher quality 'summed' image by superimposing each 'partial image' from more closely-spaced traces. As trace spacing decreases (i.e., spatial sampling improves), the reconstructed seismic image more closely represents the subsurface geology. The final result represents a single fold migration of one offset plane. When this process has been completed for all offset planes represented in the overall data, each result is summed to form the final 'full fold migrated image'. If every step of the workflow was executed optimally, the final image will exceed everywhere the result shown here in terms of image quality and resolution. Data courtesy of PGS.

I find it particularly illustrative to look at the partial image for the initial migration of only one seismic trace as the shape of the 'Kirchhoff operator' is clear.

The steeply-dipping (or curved) 'limbs' of each operator corresponds to the subsurface data points used to reconstruct the dipping geological features not immediately below the surface location of the (common midpoint or CMP) trace being migrated.

The physical 'width' of each migration operator increases with increasing depth below the surface (units of depth for 'depth' migration and units of two-way travel time for 'time' migration). The lateral distance at any depth (or time) between the surface trace location and the widest lateral extent of the limbs of the migration operator is referred to as the migration 'aperture'.

In principle, the larger the migration aperture, the greater the ability of seismic migration to properly reconstruct the deepest and steepest geological features on the final seismic image.

Note, however, that vertical resolution in seismic images may often be improved by decreasing the aperture size--at the cost of degraded resolution and reconstruction of any dipping geological features.

There is No Free Lunch in Seismic Imaging

It is computationally more expensive to migrate data with a large migration aperture than a small migration aperture.

Furthermore, if geological targets are deep and a large migration operator will expectably be used in the project workflow (determined during the survey planning stage), it is necessary to acquire a large amount of additional data to deliver a 'fully migrated, full fold' 3D seismic image volume.

As an example, if the primary survey area of interest is 20 x 50 kilometers in dimensions (1,000 square kilometers) and a maximum seismic aperture of 5 kilometers is anticipated, the survey dimensions must be expanded to 30 (5 + 20 + 5) x 60 (5 + 50 + 5) kilometers, i.e., 1,800 square kilometers--an 80% increase!

Today the migration operator for evert CMP location may be unique for Kirchhoff pre-stack depth migration (PSDM), determined by the vertical and lateral spatial variation in the velocity model everywhere.

It follows that if the velocity model is not accurate each partial image will incorrectly position the data in space and the superposition of the partial images will be smeared. The common terminology is this case is that the image is imperfectly focused. Such considerations influence the growth of FWI (full waveform inversion) for building the most accurate velocity models in recent years.

Although I have used Kirchhoff migration to illustrate the principles here, the mis-focusing and mis-positioning of seismic events will similarly occur for other seismic migration methods such a RTM (reverse time migration), but are not discussed here.

Incorporating Both Amplitude and Phase Changes in Seismic Migration

In my article titled "The Inconvenient Truth About High Frequencies" I describe how to incorporate corrections for both amplitude and phase distortion into seismic migration.


Horizontal slice through a 3D wavefront being propagated in a constant velocity model. In contrast to acoustic modeling (upper left), incorporation of the amplitude term related to attenuation (upper right) reduces amplitude with increasing propagation distance, incorporation of the phase term related to attenuation (lower left) affects phase and therefore travel time with increasing propagation distance, and viscoacoustic modeling includes both the amplitude and phase terms. Correspondingly, viscoacoustic migration accounts for both (frequency-dependent) amplitude and phase changes within the migration operator.

Optimizing the Reflectivity Model from Seismic Migration Whilst Simultaneously Optimizing the Velocity Model Used to Migrate the Data

In my article titled "Least Squares Migration: 1 of 2 Articles" I discussed both image domain and data domain implementations of Least Squares Migration (LSM). in the traditional implementation, LSM does not update the velocity model.

Therefore, although the overall amplitude balance may be enhanced, the mis-positioning and mis-focusing issues mentioned above will not be addressed.

However, in my subsequent article titled "Least Squares Migration: 2 of 2 Articles", I  describe an elegant process to simultaneously recover high-resolution subsurface models of reflectivity and velocity.

Paraphrased into layman's terms, each iteration of the solution described updates the reflectivity in a manner that benefits from the update in velocity, and conversely, the same velocity model updates benefit from the update in reflectivity within the same iteration.

Overall, this modern and sophisticated implementation of seismic imaging should yield the most optimum seismic images according to all possible descriptors.

Disclaimer

The content discussed here represents the opinion of Andrew Long only and may not be indicative of the opinions of Petroleum Geophysical AS or its affiliates ("PGS") or any other entity. Furthermore, material presented here is subject to copyright by Andrew Long, PGS, or other owners (with permission), and no content shall be used anywhere else without explicit permission. The content of this website is for general information purposes only and should not be used for making any business, technical or other decisions. 

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