3-D residual statics corrections

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

The surface-consistent residual statics model that we discussed in residual statics corrections does not restrict shot and receiver stations to a survey line; they can be situated anywhere as in a 3-D survey. Hence, equation (3-25), which is re-written below, can be used to model the static shifts at all shot and receiver stations over the entire 3-D survey area as

$t_{ij}^{\prime }=s_{j}+r_{i}+G_{k}+4M_{k}h_{ij}^{2}.$

(10)

Here, $t_{ij}^{\prime }$ are the modeled traveltime deviations associated with a moveout-corrected reflection event within a specified time gate, s_j is the shot residual statics, r_i is the receiver residual statics, G_k is the structure term at the kth midpoint location, where k = (i + j)/2, and $4M_{k}h_{ij}^{2}$ is the residual parabolic moveout term, with 2h_ij being the shot-receiver separation. The idea is to decompose the reflection time deviations picked from moveout-corrected cell-gathers into surface-consistent shot and receiver residual statics shifts, as well as structure and residual moveout terms. The procedure is based on a formulation (residual statics corrections), where the residual statics terms in equation (10) are estimated such that the difference between the modeled times t′ and the actual times t picked from moveout-corrected cell-gathers is minimum in the least-squares sense.

As it is for the 2-D case, the critical step is in picking the traveltime deviations from the common-cell gathers. For 3-D seismic data, an initial pilot trace is built from the common-cell gather of a selected line where the signal-to-noise ratio is good. Pilot traces for other common-cell gathers are computed from both local input traces and neighboring pilot traces. Note that land recording geometry must accommodate some overlap between adjacent swaths to ensure statics coupling between the swaths.

A fundamental question arises regarding 3-D DMO correction in relation to residual statics corrections. Specifically, which one should follow the other? We note from Figure 7.2-8 and Levin’s equation (2) that reflection times need to be corrected for the source-receiver azimuth effect by way of the 3-D DMO process. If 3-D DMO correction were to follow residual statics estimation, traveltime variations caused by the source-receiver azimuth effect would influence the statics estimates. In contrast, if 3-D DMO were to precede residual statics estimation, the moveout-corrected times used in DMO correction would be contaminated by statics errors. Nevertheless, this problem is of a lesser degree than the problem caused by the effect of traveltimes that were not corrected for source-receiver azimuth on statics estimates. Therefore, it is advisable to apply 3-D DMO correction prior to residual statics estimation.

$t^{2}=t_{0}^{2}+{\frac {4h^{2}(1-\sin ^{2}\phi \cos ^{2}\theta )}{v^{2}}},$

(2)

Figures 7.2-6b and 7.2-7b show the shot and receiver residual statics over the survey area. Figure 7.2-13 shows a crossline from the 3-D survey of Figure 7.2-1 with and without residual statics corrections. Note the improvement in the reflection continuity at times below 2 s.

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  Figure 7.2-6  Shot statics associated with the 3-D survey of Figure 7.2-1. Top: field statics, middle: residual statics, and bottom: total statics as the sum of field and residual statics.

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  Figure 7.2-7  Receiver statics associated with the 3-D survey of Figure 7.2-1. Top: field statics, middle: residual statics, and bottom: total statics as the sum of field and residual statics.

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  Figure 7.2-13  A crossline from the volume of stacked data associated with the 3-D survey of Figure 7.2-1, (a) without, and (b) with residual statics corrections.

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  Figure 7.2-1  Base map of a land 3-D survey. East is to the right. Shot locations follow the irregular patterns and receiver locations follow the more-or-less regular lines in the east-west direction. Sketch on the bottom right is the recording geometry. See text for details.

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  Figure 7.2-8  Geometry for a dipping planar interface used in deriving the 3-D moveout equation (2), where ϕ is the dip angle, and θ is the source-receiver azimuth angle measured from the dip line .

Following 3-D DMO correction and residual statics corrections, a final velocity analysis is carried out using a grid of the size that may be as small as 500 × 500 m. Figure 7.2-14 shows velocity panels from selected analysis locations over the survey area. Velocity analysis for land data often requires more than just a velocity spectrum (Figure 7.2-14d). A set of guide velocity functions that differ by a certain percentage from one another is specified. These functions are used to apply moveout correction to a set of CMP gathers (along, say, the inline direction) on both sides of the analysis location. The center CMP gather (Figure 7.2-14a) after moveout correction using the guide functions constitute one part of the velocity panel (Figure 7.2-14b). The CMP stack of the selected gathers at the analysis location with the guide functions constitute another part of the panel (Figure 7.2-14c). The velocity spectrum associated with the center CMP gather also is included in the panel (Figure 7.2-14d). Combined analysis of the gather, stack, and spectrum enables reliable picking of a velocity function at the analysis location.

By combining the velocity functions picked at analysis locations over the survey area, a 3-D velocity field is created. Figure 7.2-15 shows selected time slices from the 3-D velocity field. A thorough check on the velocity field is essential for stacking and time migration. For the latter, DMO-stacking velocity field (Figure 7.2-15) usually is smoothed spatially so as to eliminate lateral velocity variations that are judged to be unacceptable for time migration.

Figure 7.2-16 shows selected crosslines from the volume of stacked data without and with 3-D DMO correction. For the location of these crosslines, refer to the base map in Figure 7.2-1. Note that the differences between the sections with and without 3-D DMO correction are seen to the right of inline location 300. Specifically, note the enhanced flanks of diffractions associated with the tight imbricate structure that conflict with the near-flat reflections on the DMO-stacked data.

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  Figure 7.2-13  A crossline from the volume of stacked data associated with the 3-D survey of Figure 7.2-1, (a) without, and (b) with residual statics corrections.

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  Figure 7.2-14  Part 1: Velocity panels from selected analysis locations over the 3-D survey area of Figure 7.2-1. (a) center cell-gather (CMP gather) at the analysis location; (b) the same gather after moveout correction using nine guide velocity functions which are plotted over the velocity spectrum shown in (d); (c) CMP stack over a small range of midpoints along the inline direction using the guide functions shown in (d).

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  Figure 7.2-14  Part 2: Velocity panels from selected analysis locations over the 3-D survey area of Figure 7.2-1. (a) center cell-gather (CMP gather) at the analysis location; (b) the same gather after moveout correction using nine guide velocity functions which are plotted over the velocity spectrum shown in (d); (c) CMP stack over a small range of midpoints along the inline direction using the guide functions shown in (d).

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  Figure 7.2-14  Part 3: Velocity panels from selected analysis locations over the 3-D survey area of Figure 7.2-1. (a) center cell-gather (CMP gather) at the analysis location; (b) the same gather after moveout correction using nine guide velocity functions which are plotted over the velocity spectrum shown in (d); (c) CMP stack over a small range of midpoints along the inline direction using the guide functions shown in (d).

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  Figure 7.2-15  Time slices from the 3-D velocity field that was derived from vertical functions at analysis locations (Figure 7.2-12) over the survey area of Figure 7.2-1 using 3-D DMO-corrected data. A smooth version of this velocity field is used for time migration. Hexagonal symbols indicate the velocity analysis locations.

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  Figure 7.2-16  Part 1: Selected crosslines from the volume of stacked data without (left) and with (right) 3-D DMO correction. The base map is shown in Figure 7.2-1, and the time slices from the 3-D velocity field are shown in Figure 7.2-13. The annotation on top of the sections refer to the inline numbers.

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  Figure 7.2-16  Part 2: Selected crosslines from the volume of stacked data without (left) and with (right) 3-D DMO correction. The base map is shown in Figure 7.2-1, and the time slices from the 3-D velocity field are shown in Figure 7.2-13. The annotation on top of the sections refer to the inline numbers.

See also

• 3-D refraction statics corrections
• Azimuth dependence of moveout velocities
• 3-D dip-moveout correction
• Inversion to zero offset
• Aspects of 3-D DMO correction — a summary
• Velocity analysis
• 3-D migration
• Trace interpolation

External links

find literature about 3-D residual statics corrections