Migration and line length
For one reason or another, a seismic line may have to be recorded in the field with a shorter length than desired. To see the effect of line length on migration, we will examine the migrations of the decreasing lengths of the same CMP stack (Figure 4.6-34). Migration of the smaller portions, BD and CD, results in an increasingly smeared section, particularly in the deeper parts. We conclude that short seismic lines really are not suited for migration.
If the line traverse is too short, two effects occur. First, there is not enough space in the section for dipping events to move during migration. This problem may be alleviated by padding the stacked section with zero traces on both sides before migration. Second, side boundary effects contaminate a significant portion of the migrated section. The real solution to circumvent the boundary effects is to record data with sufficient line length.
Figure 4.6-34 Migrations of a portion of a CMP stack with different lateral extents.
Figure 4.6-36 A CMP stack (a) before and (b) after migration.
With a general idea of structural dip in an area, the geophysicist must consider the additional spatial extent that is required by migration. (Refer to the discussion on Figure 4.1-1.) This is especially important in 3-D surveys in which the surface areal coverage must be extended beyond the subsurface areal coverage so that steep dips and structural discontinuities can be recorded and imaged properly (3-D survey design and acquisition). The problem with 3-D is that cost increases as the square of the survey dimension, so that temptation to record too small a survey is great.
Regardless of line lengths, there are additional problems associated with the side boundaries of the stacked section input to migration. All migration algorithms implicitly make some assumption about the nature of data outside the side boundaries of the input stacked section. The simple assumptions, zero amplitude or zero gradient at the side boundaries of the section, cause data that should migrate past the edge to be reflected back into the section. To prevent this, traces of zero amplitude often are appended to the edges of the input section. This allows the dipping events to move freely into the zero-amplitude region during migration. If the events that would migrate off the input section are not needed, they often are suppressed by using absorbing side boundary conditions .
Figure 4.6-35 shows a section with significant smearing caused by side boundary effects. The wavefront character that dominates the left boundary of the migrated section down to the bottom of the mute zone can be explained using the principle of semicircle superposition for migration. Consider a dipping event A that extends down to the edge of the section as in the sketch in Figure 4.6-35. After migration B, note the remainder of the semicircular wavefront C on the left side. This wavefront did not cancel out during superposition because no data were available beyond the left boundary of the section.
Another source of edge effects is the presence of amplitude bursts at or near the edge of the stacked section associated with a low signal-to-noise ratio that results from low fold. The edge effects on the left boundary below the mute zone in the migrated section (Figure 4.6-35) probably stem from the lack of amplitude balance on the CMP stacked section. The latter is caused by changes in fold at the end of the line.
Figure 4.6-36 shows a CMP stack with an imbricate structure associated with overthrust tectonics. After migration, note that there are two zones with no reflections. The zone to the left of CMP 100 resulted from finite line length. Specifically, the events on the left flank of the imbricate structure are migrated to the right in the up-dip direction, thus leaving behind a zone of no events into which no energy is moved since the line ends to the left of the structure. The zone of no events between CMP 200 and 300 is a direct consequence of the overthrusting that has given rise to a culminating structure with very steep, almost overturned events. Migration of such steep dips is possible only if they exist in the recorded data and are imaged using algorithms which handle dips beyond 90 degrees.