Chapter 5
Migration
Because of the physics of wave propagation, the 3D nature of subsur-
face geology, and the techniques with which reflection seismic data are
acquired and processed, seismic data must be migrated, or repositioned, to
place reflections in their true subsurface positions. This migration, which
addresses the image-fidelity element of data quality, is done routinely as part
of a data-processing sequence for all 2D or 3D data before or after stacking
in the time or the depth domain, depending on the complexity of the geo-
logic structure and the subsurface velocity field.* As an interpreter, you are
concerned with migration because in every interpretation you describe the
size and position of the elements of geology that you see in your data, and
you cant accurately do this without taking migration into account, either in
data processing or as part of your interpretation work flow.
The need for migration is illustrated in Figure 1, which is a 2D model of
a single dipping reflector with constant P-wave velocity above the reflector
and seismic source and receiver coincident at point SR. By convention, the
recorded two-way traveltime t to the dipping reflector is plotted on a vertical
trace at point SR, even though the true normal-incidence reflecting point on
the reflector is not located vertically below point SR. The dashed red curve
in Figure 1, which is an arc of a circle with radius equal to t, represents
all possible positions for the reflector for a given value of t. This curve is
known as a wavefront, a locus of equal traveltimes through a propagating
medium for an impulse occurring at t0 = 0 (see Figure 2). The migration
*A paper by Gray et al. (2001) contains an excellent historical perspective of migra-
tion as well as practical treatment (with a minimum of high-level mathematics) of
migration problems and solutions, and a paper by Etgen et al. (2009) provides a
comprehensive overview of the current state and future direction of depth imaging
in exploration geophysics.
63
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64First Steps in Seismic Interpretation
X
SR
u
m
t
t
Migrated
Unmigrated
sin m = tan u
Figure 1. Schematic of migration of a dipping interface in a 2D constant-velocity
model, where u is unmigrated dip angle, m is migrated dip angle, t is two-way
traveltime, and X is horizontal distance.
Impulse at t0
t1
t2
t3
t3 > t2 > t1
Figure 2. Schematic (2D view) of the definitions of wavefronts and rays. A wavefront
is a locus of equal traveltimes for a pulse propagating through an elastic medium. The
shape of a wavefront depends on the velocity distribution in the transmitting medium;
in this example, the wavefronts are circular because the propagation velocity is
constant and isotropic. A ray (red arrow) is a line (or curve) everywhere perpendicular
to wavefronts that represents the travel path of a pulse from t0 to traveltime t.
operation moves the reflecting point from its position vertically below point
SR along this curve to its true subsurface position, that is, to its migrated
position at the point of normal incidence reflection. Notice in the very sim-
ple example of Figure 1 that the relationship between the dip angles of the
unmigrated and migrated reflectors is derived directly from trigonometry of
the triangles formed by the origin of the diagram, point SR, and the reflect-
ing points on the unmigrated and migrated reflectors.
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Chapter 5: Migration65
Datum
Unmigrated
Migrated
Figure 3. Migration of a horizon (dashed black curve) interpreted on a 2D unmigrated
seismic section. The final migrated horizon (solid red curve) connects points of
tangency to the arcs (wavefronts) constructed from the source positions.
A horizon interpreted on an unmigrated 2D seismic section can be
migrated by constructing arcs for many source points along the section and
then drawing a smooth curve connecting points of tangency to these arcs, as
shown in Figure 3. Think of this process as generating a wavefront for the
observed traveltime to the unmigrated reflection (horizon) at each individual
source point and then defining the migrated horizon as the surface tangent
to all of these wavefronts. The shapes of the arcs (wavefronts) depend on
the velocity distribution in the section above the dipping reflector. In the
simplest case of constant velocity, the arcs are circular; but they become
more complicated when the velocity distribution varies vertically or later-
ally (or both). Hence, repositioning reflections migration is a velocity-
dependent process.
Before the advent of 3D data or computerized migration as an essential
step in a standard data-processing sequence, migration of 2D seismic data
was addressed in several ways. One primary way was to interpret horizons
and faults on unmigrated data. The horizon maps constructed from the inter-
preted lines were then migrated using an appropriate velocity function or
distribution. This technique, called map migration, was done separately for
each interpreted horizon, requiring consistency of velocity trends, vertically
and laterally, from one horizon to the next to produce geometrically correct
and geologically reasonable maps.
Another way to migrate data was to interpret horizons and faults on
unmigrated data; then the interpreted lines were migrated individually using
an appropriate velocity function or distribution (as illustrated in Figure 3).
Because this migration could be done only in the plane of an individual 2D
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66First Steps in Seismic Interpretation
line, migration could not properly account for the effects of a 3D structure
for reflections from points located out of the vertical plane of the line. These
out-of-plane reflections (see Figures 4 and 5) are called sideswipe. Only in
the relatively uncommon case of a 2D line being true dip to actual subsur-
face structure can 2D migration be trusted to be accurate; even at that, its
results depend on the accuracy of the velocity used for migration. The failure
of 2D migration, whether manual or computerized, to handle 3D subsurface
structure accurately is the source of the mis-tie problem present in virtually
all 2D interpretation projects; 3D imaging is required to address this issue
properly.
An example of the power of migration to more accurately define true
subsurface geology is shown in Figure 6. Figure 6a is a 2D unmigrated
seismic line on which you see what is commonly referred to as a bow tie,
Figure 4. The antiformal feature within the red circle on this 2D time-migrated
display is an example of the out-of-plane effect known as sideswipe on 2D seismic
data. Apparent structural discordance such as this is an obvious positive indication
of sideswipe; the antiform and the dipping reflections that dominate the bottom half
of the display cannot coexist as reasonable subsurface geometries. Even the dipping
reflections on this display will be mispositioned (mismigrated) if the 2D line is not a
true dip line. Several fault-plane reflections also can be seen in this image (courtesy BP).
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Chapter 5: Migration67
a)
t
b)
t
Figure 5. (a) Image of a 2D time-migrated seismic line, showing sideswipe (crosscutting
antiformal reflections within the yellow circle). The red arrow marks the intersection
of this line with an orthogonal 2D time-migrated line. (b) Image of a 2D time-migrated
seismic line orthogonal to the line shown in (a). The red arrow marks the intersection of
the two lines. There is no sideswipe on this line, and the dipping salt body to the left of
the line is the source of the sideswipe reflections observed on the orthogonal line shown
in (a). The distance between the intersection of the two lines and the edge of the salt
body on this line is approximately 8000 ft (2450 m) (courtesy WesternGeco).
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68First Steps in Seismic Interpretation
a)
t
b)
t
Figure 6. (a) Image of a 2D unmigrated line exhibiting a classic bow-tie reflection
configuration. (b) Prestack time migration (PSTM) of the line shown in (a). The
crossing reflections in the center of the unmigrated image are resolved to reveal
a relatively simple syncline. Note also that small faults, especially on the left
side of the image, are more sharply defined. Focusing of reflections in general is
improved (courtesy PGS).
so named for the pattern of crossing reflections in the center of the image.
This reflection configuration as it appears cannot in all likelihood represent
real geology, so migration is needed to resolve the actual structure. Figure
6b is the migrated version of this 2D line; the bow-tie reflections have been
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Chapter 5: Migration69
repositioned to their true locations to reveal a relatively simple syncline.
This type of structure is called a buried focus syncline because the center of
curvature of the syncline is below the recording surface of the seismic data
(see Figure B-11 in Sheriff [2002] for illustrations of the raypath geometries
and a synthetic record section for this structure). Comparison of Figure 6a
and 6b shows that in addition to resolving the true structure of the syncline
correctly, migration more clearly defines small faults, especially to the left
of the syncline, and generally focuses reflections more sharply. The smooth-
ness and clarity of the migrated image in Figure 6b suggests that the orienta-
tion of this line is very nearly perpendicular to the axis of the syncline, that
is, the line is a dip line. Keep in mind, though, that this is still 2D migra-
tion, no matter how striking the results, and that 3D migrated data would be
needed for optimum imaging accuracy.
Reflection seismic data are migrated in the time or the depth domain,
depending on the complexity of the subsurface structure and the subsurface
velocity field (see Figure 7). As a result of progress in computer power and
sophistication of migration algorithms as well as in response to the advance
of exploration into more challenging subsurface settings, migration is now
done routinely on prestack data, although there are still many areas in which
poststack imaging in time or depth can provide acceptable results.
PoSTM PrSTM
Poststack time Prestack time
migration migration
Simple velocities Simple velocities
Simple structure Complex structure
PoSDM PrSDM
Poststack depth Prestack depth
migration migration
Complex velocities Complex velocities
Simple structure Complex structure
Figure 7. Different migration types for prestack and poststack time and depth
domains. Most seismic imaging is now done on prestack data, so the acronyms for
poststack time (PoSTM) and poststack depth (PoSDM) migration are no longer
commonly used. The shortened acronyms PSTM for prestack time migration and
PSDM for prestack depth migration are now widely accepted.
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70First Steps in Seismic Interpretation
Reflected S
Incident P
Reflected P
1 q1
VP1, 1
VP2, 2
Transmitted P
Refraction (P)
sin V1 Transmitted S
1
= Reflection (P)
sin 2 V2 q1 = q1
Figure 8. Snells law for reflection and refraction of P-wave energy at and across
an acoustic impedance (AI) boundary. The critical angle of incidence c is the
angle at which 2 = 90 (sin 2 = 1), that is, sin 1 = V1/V2, and no energy is
transmitted across the AI boundary into the deeper layer. Raypaths for reflected
and transmitted shear (S-wave) energy are shown by the dashed arrows.
Depth imaging is needed primarily for areas of large lateral velocity con-
trasts in the subsurface where ordinary time-domain imaging fails because
it does not account for refraction of seismic energy (defined by Snells law;
see Figure 8) at the boundaries across which these contrasts occur. Because
depth imaging includes the effects of refraction in calculating travel paths
by way of traveltimes through an interval-velocity model, its results more
accurately describe the true positions of subsurface reflectors. However, you
must be aware that migration output in depth does not guarantee one-to-one
correspondence with true geology. Depth imaging can fail when the depth-
migration velocity model is inaccurate, either in defining the geometries of
anomalously high- or low-velocity bodies or in assigning specific velocity
values, gradients, or anisotropy parameters in the velocity model. Figure 9
clearly illustrates the differences between time and depth migration, dem-
onstrating that accurate description of geology requires depth imaging in
areas where there are large lateral velocity contrasts, in this example caused
by salt bodies.
To produce an accurate image of subsurface features of interest, seis-
mic data must first be acquired in such a way that energy reflected from
those features is recorded at the surface. The term illumination is defined as
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Chapter 5: Migration71
a)
Two-way time below sea level (ms)
b)
Depth (m below sea level)
Figure 9. (a) A 2D PSTM seismic line, approximately 75 km (47 mi) long, from
offshore Brazil. (b) A 2D PSDM image of the line in (a).The differences between
the two images are striking. The PSDM image is a more accurate representation
of subsurface geology, certainly leading to a very reasonable explanation for the
location of the exploration well (annotated in green) on the right side of the line
(courtesy PGS).
the placement of seismic sources and receivers so that seismic energy will
fall on desired portions of reflectors and be recorded for processing. Obvi-
ously, you cannot migrate reflections to their true subsurface positions if the
energy reflected from those positions was never recorded. Often you will
find yourself correlating horizons through poorly imaged zones that were
only partially illuminated or not illuminated at all, so that you are effec-
tively conducting a model-guided interpretation, connecting illuminated
and properly migrated patches of the subsurface together in a geologically
reasonable way. This is to be expected, especially in frontier exploration or
in areas with severe imaging problems such as subsalt plays, and you must
be sure to risk your interpretation of these areas accordingly. If illumination
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72First Steps in Seismic Interpretation
Figure 10. Matrix of migration algorithms in modern depth-migration methods,
illustrating the range of migration algorithms that can be used to address different
subsurface imaging problems. In general, greater structural and/or velocity
complexity in the subsurface requires algorithms from the upper-right quadrant of
the matrix, which involve increased time and cost in their applications (Figure 1
by Biondi in Herron [2009]).
modeling was not done as part of acquisition design for your data, then it
is good practice to do this modeling using first-pass interpretation results to
identify the areas in which your correlations are probably less reliable and
to provide input for additional data acquisition.
Seismic migration has become more important as exploration targets
are being sought in increasingly challenging and complex settings. There
are many different migration approaches and algorithms, some better suited
to specific imaging problems than others, all having their own strengths/
limitations and corresponding cost implications (for example, see Figure
10). As an interpreter, you will often contribute to decisions involving which
migration algorithms to use for a given problem, so you will need to develop
at least a basic understanding of how the different algorithms work. This is
part of building experience, and it requires you to work closely and com-
municate effectively with processing geophysicists.
You will frequently be called on to assess the quality of migration out-
put. For all of the mathematical and computational complexity of migration,
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Chapter 5: Migration73
your assessment will often consist exclusively of visual and very non-
quantitative determination of improved S/N and reflection continuity
ultimately, whether the output appears to look more reasonable geologically
within the context of expectation or realization of some geologic concept
or model. At best, these will be subjective assessments, and you will make
them with greater confidence as you gain experience.
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