3-D prestack time migration

Seismic Data Analysis

Series	Investigations in Geophysics
Author	Öz Yilmaz
DOI	http://dx.doi.org/10.1190/1.9781560801580
ISBN	ISBN 978-1-56080-094-1
Store	SEG Online Store

In prestack time migration, we discussed 2-D prestack time migration as the rigorous solution to the problem of conflicting dips with different stacking velocities. When the reflector geometries that give rise to this problem have a 3-D behavior, it is necessary to image the subsurface using 3-D prestack time migration. Fault-plane reflections associated with rotated fault blocks are one such case that requires imaging in 3-D and before stack. Aside from solving the problem of conflicting dips with different stacking velocities and thus producing an improved migrated stack volume, 3-D prestack time migration produces common-reflection-point (CRP) gathers which can be used for amplitude variation with offset analysis.

As for the 2-D case, the robust alternative to 3-D prestack time migration in practice is to apply NMO and 3-D DMO corrections followed by 3-D poststack time migration. We shall begin this section by presenting a widely accepted procedure for 3-D prestack time migration that is based on a modification to this robust alternative. Specifically, it is assumed that following NMO and 3-D DMO corrections, each of the common-offset volumes of data is equivalent to a 3-D zero-offset wavefield, and thus can be migrated using a 3-D poststack time migration algorithm, individually. Also in this section, we shall review crossline migration as a process that reduces the imaging problem from three dimensions to two dimensions .

Figure 7.4-1 shows three inline sections from a 3-D CMP-stacked data volume associated with a marine 3-D survey with no 3-D DMO correction. Four time slices associated with the 3-D CMP-stacked data volume as in Figure 7.4-1 are shown in Figure 7.4-2. From the inline sections and the time slices, note that the subsurface structural setting involves highly complicated fault patterns. The cross-sections of the image volume from 3-D poststack time migration along the same inline traverses as in Figure 7.4-1 are shown in Figure 7.4-3. Although the fault planes themselves are not delineated, the presence of the complicated fault patterns is evident from the cross-sections (Figure 7.4-3) and the time slices (Figure 7.4-4) of the image volume.

A subset of the velocity spectra used to pick stacking velocities is shown in Figure 7.4-5. Figure 7.4-6 shows the cross-sections of the 3-D migration velocity field along three inline and three crossline traverses. This velocity field was derived by interpolating the vertical functions picked from the velocity spectra as in Figure 7.4-5 and spatially smoothing the resulting velocity volume.

Now apply 3-D DMO correction to preserve the fault-plane reflections. Figure 7.4-7 shows the three inline sections and Figure 7.4-8 shows the four time slices from the 3-D DMO-stack data volume. The cross-sections of the image volume from 3-D poststack time migration along the same inline traverses as in Figure 7.4-7 are shown in Figure 7.4-9 and the time slices from the same volume are shown in Figure 7.4-10. Note that 3-D DMO correction preserves the fault-plane reflections on stacked data and the subsequent 3-D poststack time migration delineates the fault blocks with improved imaging (compare Figure 7.4-3 with Figure 7.4-9).

A subset of the velocity spectra used to pick velocities after 3-D DMO correction is shown in Figure 7.4-11. Figure 7.4-12 shows the cross-sections of the 3-D migration velocity field along three inline and three crossline traverses. This velocity field was derived by spatially interpolating the vertical functions picked from the velocity spectra as in Figure 7.4-11.

The kinematics of 3-D prestack time migration can be formulated as an extension of the kinematics of 2-D prestack time migration (migration velocity analysis and E.5) in the same manner as for 3-D DMO correction. In fact, Figure 7.2-11, which describes the 3-D DMO process, can also be used to describe 3-D prestack time migration. Consider a trace from a common-cell gather with no NMO nor DMO correction and map the amplitude at time sample A to neighboring cells which are coincident with the source-receiver azimuthal direction associated with that input trace along the semi-elliptical trajectory that describes the kinematics of 3-D prestack time migration. The nonzero-offset migration ellipse is described by equation (5-33). Repeat the process for all the traces from the same common-cell gather and map the amplitudes in the same manner.

For the hypothetical recording geometry with a common-cell gather coincident with a common-midpoint gather and traces in the gather covering a 360-degree source-receiver azimuthal range, but having the same source-receiver separation, the elliptical trajectories associated with all the traces constitute an ellipsoid of revolution as shown in Figure 7.2-11a. This ellipsoid describes the kinematics of the impulse response of a 3-D prestack migration operator.

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  Figure 7.4-1  Three inline sections (from top to bottom: Inlines 105, 155, and 205 with 1250-m distance between them) from a 3-D CMP-stacked data volume associated with a marine 3-D survey.

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  Figure 7.4-2  Four time slices associated with the 3-D CMP-stacked data volume as in Figure 7.4-1 (from top to bottom at 1000, 1200, 1400, and 1600 ms). The vertical axis denotes the inlines and the horizontal axis denotes the crosslines.

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  Figure 7.4-3  Three inline sections (from top to bottom: Inlines 105, 155, and 205 with 1250-m distance between them) from a 3-D poststack time-migrated CMP-stacked data volume as in Figure 7.4-1.

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  Figure 7.4-4  Four time slices associated with the 3-D poststack time-migrated CMP-stacked data volume as in Figure 7.4-3 (from top to bottom at 1000, 1200, 1400, and 1600 ms). The vertical axis denotes the inlines and the horizontal axis denotes the crosslines.

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  Figure 7.4-5  Velocity analysis along inline 155 of the data as in Figure 7.4-1. Analysis locations are denoted by the crossline numbers.

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  Figure 7.4-6  Three inline and three crossline sections of the 3-D velocity field derived from the velocity analyses as in Figure 7.4-5 and used to do 3-D poststack time migration as in Figure 7.4-3.

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  Figure 7.4-7  Three inline sections (from top to bottom: Inlines 105, 155, and 205 with 1250-m distance between them) from a 3-D DMO-stacked data volume associated with a marine 3-D survey as with Figure 7.4-1.

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  Figure 7.4-8  Four time slices associated with the 3-D DMO-stacked data volume as in Figure 7.4-7 (from top to bottom at 1000, 1200, 1400, and 1600 ms). The vertical axis denotes the inlines and the horizontal axis denotes the crosslines.

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  Figure 7.4-9  Three inline sections (from top to bottom: Inlines 105, 155, and 205 with 1250-m distance between them) from a 3-D poststack time-migrated DMO-stacked data volume as in Figure 7.4-7.

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  Figure 7.4-10  Four time slices associated with the 3-D poststack time-migrated DMO-stacked data volume as in Figure 7.4-9 (from top to bottom at 1000, 1200, 1400, and 1600 ms). The vertical axis denotes the inlines and the horizontal axis denotes the crosslines.

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  Figure 7.4-11  Velocity analysis after 3-D DMO correction along inline 155 of the data as in Figure 7.4-7. Analysis locations are denoted by the crossline numbers.

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  Figure 7.4-12  Three inline and three crossline sections of the 3-D velocity field derived from the velocity analyses as in Figure 7.4-11 and used to do 3-D poststack time migration as in Figure 7.4-9.

In migration principles, we discussed semicircle superposition and diffraction summation concepts for 2-D zero-offset migration. Applying those concepts to the case of 3-D zero-offset migration, the latter can be conceptualized as the spreading of amplitudes on each input stacked trace in the (x, y, t) volume over the surface of a hollow hemisphere (Figure 7.3-11). Superposition of the resulting hemispherical surfaces yields the (x, y, z) image volume. Alternatively, for a given output sample of a trace in the (x, y, z) image volume, amplitudes over the surface of the hyperboloid of revolution in the (x, y, t) volume of the input 3-D zero-offset wavefield can be summed and placed on that output sample location. The Kirchhoff summation technique for migration incorporates the amplitude and phase factors described in Section H.1.

Similarly, for an input trace with a specific source-receiver azimuth and offset as depicted in Figure 7.2-11a, 3-D prestack time migration can be conceptualized either by way of a semi-elliptical superposition using equation (5-33) or a diffraction summation over the traveltime trajectory described by equation (5-32). The recording geometry of Figure 7.2-11a, however, never exists in reality. Instead, 3-D recording geometries give rise to nonuniform source-receiver azimuthal and offset coverage, and midpoint scattering over the survey area. 3-D DMO correction implicitly regularizes the spatial sampling of the prestack 3-D data. As a result, the data can be decoupled and sorted into common-offset volumes each of which is considered a replica of a 3-D zero-offset wavefield. This then enables us to adopt the robust approach for 2-D prestack time migration based on DMO correction and common-offset migration (prestack time migration) to develop an efficient workflow for 3-D prestack time migration as described below.

See also

• 3-D DMO correction combined with 3-D common-offset migration
• Crossline migration
• 3-D migration velocity analysis
• Aspects of 3-D prestack time migration — a summary

External links

find literature about 3-D prestack time migration