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Prestack and Postack Migration

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  • 9

    Chapter Nine Prestack Migration (and 3-D DMO) Introduction Objectives Know that prestack migration can eliminate errors of conflicting dips. Know that NMO, DMO, and poststack migration is considered by some to be

    prestack migration. Identify the main methods of prestack migration. Understand the iterative nature of prestack migrations that are based on CMP

    concepts. Understand the process of GDMO-PSI. Introduction to EOM (covered in detail in Chapter 11). Know that constant velocity 3-D prestack migration may be accomplished with

    2-D DMO and 3-D poststack migration.

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  • A Practical Understanding of Pre- and Poststack Migrations

    Page 9.2

    9.1 Introduction to Prestack Migration 9.1.1 Various views of the objectives of prestack migration 1. Put reflection back at the reflector position.

    Directly (model-based method) Using DMO and poststack migration

    2. Collapse Cheops pyramid to scatterpoint 3. Distribute energy from one input sample to the prestack migration ellipse or

    ellipsoid. 4. Energy in a trace could come from any scatterpoint in the surrounding volume.

    5. Formation of prestack migration gathers for velocity analysis: Using inverse NMO (INMO) Directly (Gardners or Bancrofts method)

    Depth

    Most desirable when the velocity field can be estimated. More accurate positioning of energy, especially if anisotropic affect are

    considered. Expensive. Requires an interpreter to maintain a reasonably accurate geological

    model for the velocities. Will produce the best focusing if the velocity model is known (exactly).

    Time Better focusing than poststack migration. Possibly better focusing than prestack depth migration with estimated

    velocities. Inexpensive. Focusing is independent of the velocity model. Reasonable results from a processor.

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  • Chapter 9 Prestack Migration

    Page 9.3

    NMO

    T0-NMO

    Th

    CMPS R

    NMO

    Th

    CMPS R

    DMOellipse

    Poststacksemicircle

    a) b)

    Front

    hx

    t

    NMO

    T0-NMO

    Th

    CMPS R

    c) d)

    NMOTh

    CMPS R

    e) f)

    Figure 9.1 Approaches to prestack migration, a) input direct, b) using DMO, c) summing Cheops pyramid, d) forming an ellipse, e) reflections come from anywhere, and f) CMP and CSP gathers.

    CMP CSP

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  • A Practical Understanding of Pre- and Poststack Migrations

    Page 9.4

    9.1.2 Prestack migration techniques DMO and poststack migration (two velocity functions)

    NMO-DMO-Constant offset poststack migration NMO-DMO-Source record migration NMO-DMO-MIG-INMO-velocity analysis-NMO NMO-DMO-TimeMIG, VA-Stack -> InvTMIG->Post-DepthMIG

    Prestack TimeMIG, -> Inv-Po-TimeMIG, -> Post-DepthMIG Direct Kirchhoff (Cheops summation) Source record migration

    Direct Kirchhoff Downward continuation of receivers

    o Kirchhoff imaging condition RMS velocities (time mig.) traveltime on grid or raypaths (depth mig.)

    o Forward modelling from source location cross correlation inversion

    SG (shot/geophone) method: Downward continuation of source and receiver records. Constant offset migration Stolt 3-D transform of 2-D data GDMO-PSI EOM Tau-p methods

    I usually use the term full or true prestack migration for those methods that use one velocity function. DMO methods use two; one for MO correction and another for migration. I consider these methods to be a pseudo prestack migration.

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  • Chapter 9 Prestack Migration

    Page 9.5

    h

    Tn

    Prestack migrationellipse

    DMO ellipse

    45

    T

    xS R

    t or z

    Poststackmigration

    a)

    Front

    hx

    t

    b)

    x

    h

    t

    Source record

    x

    h

    t

    Constant offset section

    c)

    Figure 9.2 Various methods of prestack migration, a) using DMO, b) full Kirchhoff migration, and c) using source records or constant offset sections.

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  • A Practical Understanding of Pre- and Poststack Migrations

    Page 9.6

    9.2 DMO and Prestack Migration In a constant velocity environment, MO, DMO, and poststack migration are kinematically equivalent to prestack migration ( Hale [101]). However, in a variable velocity environment, possible conflicts in velocity still occur when reflections overlap. DMO removes the dip effect on stacking velocities, i.e. no inverse cosine

    effect. DMO does not correct the problem of time varying velocities with conflicting

    dips. After DMO a single trace, source record, or constant offset section is essentially equivalent to zero-offset, i.e. P(x , h, tMO-DMO) = P(x, h = 0, t). After DMO, traces in the same CMP gather can be summed to produce a

    stacked section. The DMOd source records or constant offset sections may be poststack

    migrated to create the prestack migration ellipse as illustrated in Figure 9.3. After poststack migration, they may be called prestack migrated source

    records or prestack migrated constant offset sections. DMO and poststack migrated data may be sorted into CMP gathers, which may

    be referred to as common reflection point (CRP) gathers. In CRP gathers, energy from reflectors should be flat or have constant time

    with offset. Velocity analysis is required to ensure the flatness on events. Stacking the CRP gathers completes the prestack migration. The result would be identical if the DMOd data was first stacked then one

    poststack migration applied to the stacked section. Consequently there is some resistance to calling these DMO processes a prestack migration. Because of the DMO limitations to constant or smoothly varying velocities, this method of processing may be inferior to prestack migration methods that dont use DMO. The DMO method of analysis uses one application of velocities for MO and one for the poststack migrations. A number of iterations will be required to converge to one stable velocity.

    DMO and poststack migration computes much faster than full prestack migration and more time can be spent estimating NMO and migration velocities.

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  • Chapter 9 Prestack Migration

    Page 9.7

    h

    Tn

    Prestack migrationellipse

    DMO ellipse

    45

    T

    xS R

    t or z

    Poststack migration

    Figure 9.3 DMO and poststack migration recreate the prestack migration ellipse.

    When migration is applied to constant offset sections, there are no overlapping reflections as they are now in their approximate geological location. The problem of overlapping reflections is therefore resolved.

    The main purpose in forming migrated constant offset sections is velocity analysis. Inverse moveout (IMO) is applied before stacking to allow a refined velocity to be estimated. Although each DMOd trace is essentially zero-offset, an offset from the original geometry is assumed. The offset of the DMOd traces may be different, and depend on the processing geometry, either a source record, or a constant offset section. Any offset may be used for IMO, but it should be chosen to enhance the velocity analysis. After velocity analysis, the data may be stacked, or the entire process repeated for optimal imaging.

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  • A Practical Understanding of Pre- and Poststack Migrations

    Page 9.8

    9.3 DMO Prestack time, IMO to stack, poststack depth migration

    DMO and poststack time migration may be used to prepare an optimum stacked section for poststack depth migration. MO-DMO constant offset sections. Time migrate each constant offset section. IMO, estimate an improved velocity, and then MO. Stack the offset sections. Inverse time migrate (or model) the stacked section with the same velocities

    and algorithm as in the second step. Poststack depth migration. These processing schemes enable a more accurate positioning in space and time of the input data prior to a final velocity analysis. The stacked section is formed from data that is focused at the scatterpoint. The inverse time migration forms a zero-offset section that has prestack focusing, however, the approximations of time migration have been effectively removed (or reduced). Poststack depth migration completes the process and tends to an image produced by prestack depth migration. The extensive use of time migrations permit simplified velocity analysis and faster algorithms to be used, reducing the cost of processing. The DMO prestack migration steps are illustrated in Figure 9.4. With a constant velocity, the scatterpoint energies in Figure 9.4d are ideally focused to a constant time and position (x). When the velocities are in error, the energy will form on a surface that is spread laterally, and will curve away from constant time, as show