F. Imaging by seismic migration3D Post-stack Time Migration3D Pre-ststack Depth MigrationData Courtesy of CGG- Depth migrationF - 24
For the next few slides, we discuss the task of seismic migration. First we show how the stacked traces are migrated using post-stack migration, and then how the traces are migrated prior to stack using pre-stack migration.
In this diagram, we compare the stacked (but un-migrated) image in red with the migrated image in blue. Migration has shifted the events up in space and time to be in the correct location on the reflector.
If they are properly migrated, the blue image places the reflection events in the correct position directly below the position the stacked source-receiver location. The key here is that it is a vertical image of the reflector.
For the present discussion, it is a vertical image in time. To convert it to depth, we would need to know the vertical velocity from the source-receiver location to the reflector.On the top of this diagram, we see a single un-migrated (stacked) trace.
Upon migrating the one trace (with post-stack time migration) we see that the reflection events have been swept out on circular trajectories into the location of the adjacent traces. In fact, every single sample in the original trace has been swept out on a circular trajectory.
This migration algorithm, referred to as Kirchhoff Summation, simply does this to every trace in the survey and then adds the sweep products together.
For a 3D survey, the sweeps must be in three dimensions.For a dipping reflector, the un-migrated traces are swept into all of the possible places of origin.
In this case, we see that all of the circular trajectories intersect the original reflector surface. So the migration process adds the reflection events in phase on the actual reflector and out of phase every where else.From the previous diagram, we see that the circular trajectories for all of the reflection events (shown in red) touch the original reflector (shown in green). All of the sweep trajectories have the point source in common because that is where the reflections actually came from.
Again, we are going to rely on constructively and destructively adding the sweeps together to image the reflector.
This process is shown in the next few slides.For this diagram, a diffraction has been migrated with a Kirchhoff Summation algorithm. In fact, any of the migration algorithms would have produced the same result.
We see that the diffraction has been exactly collapsed to a reflection event on a single trace.
In this case, the migration has worked perfectly, because the diffraction was created by a model in a constant velocity environment where the velocity was a known quantity.
The problem with migration in the real world is that the velocity has to be estimated.
The point here is that the potential limit of horizontal resolution is the trace (line) sample spacing if the process of migration has worked perfectly.
The next four diagrams show the process of Kirchhoff Summation as a large sum of ellipses.
The purpose of this sequence of diagrams is to show how effective constructive interference is in producing a migrated image.
In this diagram, we see two dipping layers that are presented here as an um-nigrated image.In this pre-stack time migrated model, we see that constructive interference has indeed built an image of the dipping reflectors.
With the rather coarse trace spacing used for the migration, we see that destructive interference has not really worked perfectly, resulting in migration noise.
We also see events curling up from the ends of each migrated layer. This is a legacy of the ellipse sweep on a model that had abrupt terminations rather than diffractions at the ends of each layer.
To further illustrate the ellipse sweep process, we will migrate a subset of the original model. In this case, we will migrate every fifth trace.
In actual fact, all of the traces in the entire profile were migrated, but only every fifth trace on the dipping reflector model contains an event. So the migration program did a lot of sweeping of zero sample values. The program simply does the sweeping and sums the results. It has no idea of what each of the traces contain.Here we see the migrated traces for a single offset (in this case a shot to receiver offset of 600 feet).
The ellipse sweeps can be seen, and also we see a hint of the ellipses starting to add together to form an image of the reflectors.
With all of the traces present in the model, we rely on constructive and destructive interference to build the migrated image.For a dipping reflector, the un-migrated traces are swept into all of the possible places of origin.
In this case, we see that all of the circular trajectories intersect the original reflector surface. So the migration process adds the reflection events in phase on the actual reflector and out of phase every where else.A graphical representation of the reflections from a dipping interface shows the problem with the old concept of stacking.
The reflections that would be traditionally stacked together have a common midpoint from their surface geometry. Here we see that in the presence of a dipping reflector, the reflection points all have a unique location that moves farther up dip as the shot-receiver offset increases.
Since we do not know the configuration of the subsurface, we correct for moveout and stack the trace producing a smear of reflection points on the reflector. This dramatically degrades the horizontal resolution of the data.
The solution to this problem is to migrate the traces to their correct reflection points before they are stacked.In this diagram, we see one pre-stack time migrated trace revealing the elliptical sweep trajectories. The source and receiver locations are at the two focus points of the ellipse.
The elliptical sweeps are symmetrical in this diagram because the data was generated from a constant velocity model. In real data, the ellipses are distorted by the velocity field. The amount of this distortion defines the difference between time and depth migration.
The sweeping associated with the separation of the source and receiver locations, are what defines pre-stack migration.This diagram compares the moveout from the previous diagram (the red traces) to traces that have been pre-stack migrated (the blue traces).
The traces in the midpoint gather have been migrated on elliptical trajectories so that the energy is coherent on the actual reflector.
When we look at the traces (blue traces) that have been swept into a single bin location we see that they are properly aligned and can be stacked.
The blue traces become a common image point gather.Here we compare the old method of imaging, that is stacking followed by migration, with the current method of migration prior to stack.
On the left hand side of the diagram, we see a common midpoint gather and the reflection ray paths in black. Immediately to the right of this display are the reflections shown as four red traces. These display the expected normal moveout. This would be corrected to flatten the traces then stacked and migrated to give the single trace shown at the right hand side of the diagram.
The current approach is to sweep the traces into their possible origin locations as shown by the red ellipses. We then assemble the traces in any given bin location, which are now migrated into their correct location on the reflector, and assuming that they are properly aligned (flattened), they are subsequently stacked.
In a subsequent section of this text, the imaging process is discussed in much greater detail. For the current discussion, we have now obtained a zero offset trace that has been migrated and stacked.Depth migration is totally reliant on an accurate velocity model of the subsurface.
The process involves ray tracing to determine the reflection travel times to every point in a three dimensional cube surrounding the trace being migrated.
The arrival times in the three dimensional depth grid are the same as the spherical sweeps that we had for time migration, but the sweeps are distorted by the velocity model.
We are now calculating the travel time to an image point in the depth domain.
A fundamental issue in seismic data is the relationship between an image in time and an image in depth.
The seismic section on the left shows an image in depth, with the velocity model shown as the colored layers. This would correspond to a pre-stack depth migrated image where the velocities have been correctly determined. The image therefore faithfully represents the subsurface structure.
The section on the right has been stretched into time with the velocity information in the model. In this case, the process is essentially trivial because the velocities are precisely known. This is never true in the real world.
To illustrate the problem with the image in time, the model on the left has been constructed with a perfectly flat layer at the bottom. When this image is stretched into time, this flat layer displays a dip from right to left, and we see structures that are a result of velocity pull-up generated from the thrusted high velocity layers in the upper part of the section.This comparison of post-stack time migration vs pre-stack depth migration very graphically shows that seismic migration is really a three dimensional problem.
One of the classic challenges to seismic migration is imaging below salt layers....