Changes

==What migration accomplishes==

==What migration accomplishes==

The migration problem is illustrated in Figure 1. The upper part of the figure depicts a zero-offset survey conducted over a subsurface medium that is homogeneous (constant P-wave velocity) with the exception of an isolated boulder at some depth. Also shown are the straight ray paths traveled by seismic waves from each of five different source positions down to the boulder and back up to receivers located at the sources. Clearly, reflections from the boulder will be observed at all the surface locations, not just the one directly above it. Also, the reflection time clearly increases as the source-receiver pair is moved farther from the point directly above the boulder. The bottom part of Figure 1 shows schematically the seismic section that would be obtained for this survey. Reflections occur along a hyperbolic ''diffraction'' pattern with the apex at the same CMP location as that of the boulder.

The migration problem is illustrated in [[:file:seismic-migration_fig1.png|Figure 1]]. The upper part of the figure depicts a zero-offset survey conducted over a subsurface medium that is homogeneous (constant P-wave velocity) with the exception of an isolated boulder at some depth. Also shown are the straight ray paths traveled by seismic waves from each of five different source positions down to the boulder and back up to receivers located at the sources. Clearly, reflections from the boulder will be observed at all the surface locations, not just the one directly above it. Also, the reflection time clearly increases as the source-receiver pair is moved farther from the point directly above the boulder. The bottom part of Figure 1 shows schematically the seismic section that would be obtained for this survey. Reflections occur along a hyperbolic ''diffraction'' pattern with the apex at the same CMP location as that of the boulder.

 

The task of migration here is to convert or ''map'' reflections along the diffraction into a single point at the position of the boulder. The reverse process, by which the boulder gives rise to the observed diffraction pattern, is called ''modeling''.

The task of migration here is to convert or ''map'' reflections along the diffraction into a single point at the position of the boulder. The reverse process, by which the boulder gives rise to the observed diffraction pattern, is called ''modeling''.

While the earth's subsurface is more complicated than that shown in Figure 1, the seismic data that would be obtained over the real earth can for all purposes be represented as a superposition of many diffraction curves generated by each of many boulder-like anomalies in the subsurface.

While the earth's subsurface is more complicated than that shown in [[:file:seismic-migration_fig1.png|Figure 1]], the seismic data that would be obtained over the real earth can for all purposes be represented as a superposition of many diffraction curves generated by each of many boulder-like anomalies in the subsurface.

 

 

 

Figure 3 shows another perspective on this mispositioning. Reflections recorded at zero source-receiver offset follow ray paths that are perpendicular to the reflector. As a result, the reflection from the point on the reflector beneath point P, for example, would be recorded by the geophone at location G, to the right.

[[file:seismic-migration_fig3.png|thumb|{{figure number|3}}Schematic depth section showing normal incidence ray paths for two-way travel between source-receiver positions and a dipping reflector.]]

[[:file:seismic-migration_fig2.png|Figure 2]] shows another depth section and associated seismic section for a subsurface consisting of a single dipping reflector. For a constant-velocity subsurface, the many weak diffractions from very closely spaced points along the reflector (of which five are shown in the figure) give rise, through constructive and destructive interference, to a net ''reflection'' along the straight-line envelope of the diffraction curves. Note that the reflection is displaced laterally from the true reflector position (the line connecting apexes of the diffraction curves). It is this lateral mispositioning of reflections from dipping reflectors that gave rise to the term ''migration'' for the process that corrects the positioning.

Figure 4 shows the application of migration to CMP-stacked field data. The superposition of diffraction curves evident in the unmigrated data of Figure 4a gives rise to crossing reflections that can not plausibly be interpreted as structure. By correcting for lateral mispositioning of dipping reflectors and “collapsing” diffraction curves to zones defined by the diffraction apex, migration converts the recorded waves to a subsurface picture (Figure 4b) depicting both broadly and tightly folded anticlines and synclines.

[[:file:seismic-migration_fig3.png|Figure 3]] shows another perspective on this mispositioning. Reflections recorded at zero source-receiver offset follow ray paths that are perpendicular to the reflector. As a result, the reflection from the point on the reflector beneath point P, for example, would be recorded by the geophone at location G, to the right.

[[file:seismic-migration_fig4-part1.jpg|thumb|{{figure number|4}}(a) CMP stack of data from the Santa Barbara Channel, offshore California.]]

[[:file:seismic-migration_fig4-part1.jpg|Figure 4]] shows the application of migration to CMP-stacked field data. The superposition of diffraction curves evident in the unmigrated data of [[:file:seismic-migration_fig4-part1.jpg|Figure 4a]] gives rise to crossing reflections that can not plausibly be interpreted as structure. By correcting for lateral mispositioning of dipping reflectors and “collapsing” diffraction curves to zones defined by the diffraction apex, migration converts the recorded waves to a subsurface picture ([[:file:seismic-migration_fig4-part2.jpg|Figure 4b]]) depicting both broadly and tightly folded anticlines and synclines.

[[file:seismic-migration_fig4-part2.jpg|thumb|Figure 4(b) Result of migration.]]

==How migration is accomplished==

==How migration is accomplished==