Migration

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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 can’t 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.

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64 First Steps in Seismic Interpretation

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.

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.

X

u m

sin m = tan u

SR

MigratedUnmigrated

t

t

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.

t2

t1

t3

Impulse at t0

t3 > t2 > t1



Chapter 5: Migration 65

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

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.

Unmigrated

Migrated

Datum

t




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).

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).

t

ta)

b)




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

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).

t

t

a)

b)




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.

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.

Simple velocitiesSimple structure

PoSTMPoststack time

migration

Simple velocitiesComplex structure

PrSTMPrestack time

migration

Complex velocitiesSimple structure

PoSDMPoststack depth

migration

Complex velocitiesComplex structure

PrSDMPrestack depth

migration




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 Snell’s 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

Figure 8. Snell’s law for reflection and refraction of P-wave energy at and across an acoustic impedance (AI) boundary. The critical angle of incidence θc is the angle at which θ2 = 90° (sin θ2 = 1), that is, sin θ1 = 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.

sin 1

sin 2

=V1

V2

Refraction (P)

Reflection (P)

2

VP1, 1

VP2, 2

Incident P

Transmitted P

Reflected P

Reflected S

Transmitted S

1

q1 = q1´

q1´




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

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).

a)Tw

o-w

ay ti

me

belo

w s

ea le

vel (

ms)

D

epth

(m

bel

ow s

ea le

vel)

b)




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,

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]).




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.





Migration

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