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GC3-D Design Philosophy – Part 3: Is Stacking Fold Acceptable?*
Bob Hardage1
Search and Discovery Article #40663 (2010)
Posted December 17, 2010
*Adapted from the Geophysical Corner column, prepared by the author, in AAPG Explorer, November, 2010, and entitled “Next Step: Is Stacking Fold Acceptable?”. Editor of Geophysical Corner is Bob A. Hardage ([email protected]). Managing Editor of AAPG Explorer is Vern Stefanic; Larry Nation is Communications Director. Click for remainder of series: Part 1 Part 2 Part 4
1Bureau of Economic Geology, The University of Texas at Austin ([email protected])
This article is the third of a four-article series – this topic considers Part 3 and Part 4 labeled on the Figure 1 flow chart of 3-D seismic design methodology.
Stacking fold is the number of field traces that are summed during data processing to create a single image trace positioned at the center of each bin. At any stacking bin coordinate, the stacking fold inside the bin varies with depth. Referring to Figure 2, when a stacking bin is centered about a deep reflection point B, the stacking fold is a maximum at depth B because the largest number of source and receiver pairs can be utilized to produce individual reflection field traces inside the bin.
The number of source-receiver pairs that can contribute to the image at B is typically confined to those source and receiver stations that are offset horizontally from B a distance that is no larger than depth Z2 to reflection point B. Thus, distances CE and EG shown on Figure 2 are each equal to Z2.
Using this offset criterion to determine the number of source-receiver pairs that contribute to a seismic image at any subsurface point, the stacking fold at depth Z2 would be N2 – because N2 unique source-receiver pairs can be found that produce distinct field traces reflecting from point B.
When the stacking bin moves to a shallower depth Z1, the stacking fold decreases to a smaller number N1 – because only N1 source-receiver pairs generate field traces that reflect from A and still satisfy the geometrical constraint that the source-receiver pairs are offset a distance DE (or EF) or less that does not exceed depth Z1.
In a 3-D context, stacking fold is the product of in-line stacking fold (the fold in the direction that receiver cables are deployed) and cross-line stacking fold (the fold perpendicular to the direction that receiver cables are positioned). Defining F as 3-D stacking fold, FIL as in-line fold and FXL as cross-line fold, this principle leads to the design equation:
(1) F = FIL x FXL.
To build a high-quality 3-D image, it is critical to not only create a proper stacking fold across the image space but also to ensure the traces involved in that fold have a wide range of offset distances and azimuths. Equation 1 provides no information about the distribution of source-to-receiver offset distances or azimuths that are involved in a stacking fold. If it is critical to know the magnitudes and azimuth orientations of source-receiver offsets, then commercial 3-D design software must be used.
Offset 
analysis
is a topic that goes beyond the scope of this discussion, which is structured to provide simple explanations of the basic principles of 3-D seismic design. All discussions of 3-D stacking fold will be based totally on equation 1. It is the simplicity of this equation that makes it appealing to use to explain to non-geophysicists how stacking fold and 3-D recording geometry link together.
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2-D vs 3-D Stacking Fold Considerations
In 2-D and 3-D acquisition geometry, in-line stacking fold FIL is a function of two geometrical properties:
● The number of active receiver channels.
● The ratio of the source-station interval and the receiver-station interval.
Specifically, in-line stacking fold is given by the equation:
(2) FIL = (1/2) (Number of receiver channels) X [(receiver-station interval)/ (source-station interval)].
In 2-D seismic profiling, the source-station interval is usually the same as the receiver-station interval, making the ratio term in the square brackets equal to unity. However, in 3-D profiling, the source-station spacing along a receiver line is the same as the source-line spacing, which is several times larger than the receiver-station spacing. For example, if the receiver-station spacing is 110 feet, and the interval between the source lines is 1,320 feet, then there is a source station every 1,320 feet along each receiver line – and the square bracket term in equation 2 has a value of (1/12).
The in-line fold for 3-D data acquisition is thus considerably less than it is for 2-D recording geometries. In this hypothetical example, it is 12 times less. Cross-line stacking fold FXL – created by a 3-D acquisition geometry – is controlled by the number of receiver lines that are incorporated into the 3-D recording swath and is given by:
(3) FXL = (1/2) (Number of receiver lines in recording swath).
The last step in the 3-D design
There are several ways to answer this question. The ideal situation is to have access to 3-D seismic data previously recorded near the prospect area. If those data have good signal-to-noise character, then one should simply define the stacking fold that was used in recording these older 3-D data as being the stacking-fold objective for the new 3-D data acquisition program.
If the signal-to-noise character of these pre-existing 3-D data is not acceptable, a higher stacking fold should be considered. If only 2-D seismic data are available in the area of interest – and these 2-D data adequately image the subsurface geology – a popular design guideline is:
(4) 3D stacking fold = (1/2) (2D stacking fold)
This is a statement of a commonly observed condition that 3-D stacking fold often needs to be only one-half the value of 2-D stacking fold to cause 3-D data to have equivalent signal quality. If neither 2-D nor 3-D data are available, the only recourses are to ask advice of people who have recorded data in the area – or to guess.
If the calculated stacking fold is significantly different from the intended value of stacking fold, then the design EXPLORER
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Stacking Fold 
