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# Designing 3D seismic surveys

The imaging deficiencies of 2D seismic profiling were remedied by the implementation of 3D seismic data acquisition, which allows data processing to migrate reflections to their correct image coordinates in 3D space. Industry largely abandoned 2D seismic profiling in the 1990s and now relies almost entirely on 3D seismic data acquisition. This article talks about some of the basic concepts that it is important to understand to properly design a 3D seismic survey. Understanding these design issues will help with interpretation as well.

## Stacking bins

The horizontal resolution a 3D seismic image provides is a function of the trace spacing within the 3D data volume. As the separation between adjacent traces decreases, horizontal resolution increases. At the conclusion of 3D data processing, the area spanned by a 3D seismic image is divided into a grid of small, abutted subareas called stacking bins. Each trace in a 3D seismic data volume is positioned so that it passes vertically through the midpoint of a stacking bin.

In Fig. 1, each stacking bin has lateral dimensions of Δx and Δy. The horizontal separations between adjacent processed traces in the 3D data volume are also Δx and Δy. The term inline is defined as the direction in which receiver cables are deployed, which is north/south in this example. Inline coordinates increase from west to east as shown. Crossline refers to the direction that is perpendicular to the orientation of receiver cables; thus, the crossline coordinates increase from south to north.[1] These stacking bins can be square or rectangular, depending on an interpreter’s preferences. The dimension of the trace spacing in a given direction across a 3D image is the same as the horizontal dimension of the stacking bin in that direction. As a result, horizontal resolution is controlled by the areal size of the stacking bin.[2]

The imaging objective dictates how small a stacking bin should be. Smaller stacking bins are required if the resolution of small stratigraphic features is the primary imaging requirement. As a general rule, there should be a minimum of three stacking bins, and preferably at least four bins, across the narrowest stratigraphic feature that needs to be resolved in the 3D data volume. This imaging principle causes the targeted stratigraphic anomaly to be expressed on three or four adjacent seismic traces.

As Fig. 2 illustrates, the critical parameter to be defined in 3D seismic design is the smallest (narrowest) horizontal dimension of a stratigraphic feature that must be seen in the 3D data volume. For purposes of illustration, it is assumed that the narrowest feature to be interpreted is a meander channel. At least three, and ideally four, stacking bins (that is, seismic traces) must lie within the narrowest dimension, W, of this channel if the channel is to be reliably seen in the seismic image during workstation interpretation. Once W is defined, the dimensions of the stacking bins are also defined. The bin dimensions should be no wider than W/3. Ideally, they should be approximately W/4.[1] A variation in seismic reflection character on three to four adjacent traces is usually noticed by most interpreters, whereas anomalous behavior on fewer traces tends to be ignored or may not even be seen when a 3D data volume is viewed.

For example, if the interpretation objective is to image meandering channels that are as narrow as 200 ft, then the stacking bins should have lateral dimensions of approximately 50 ft (Fig. 2). This would cause a 200-ft channel to affect four adjacent traces. One of the first 3D design parameters to define, therefore, is the physical size of the stacking bin to be created. The bin size, in turn, can be determined by developing a stratigraphic model of the target that is to be imaged and then using that model to define the narrowest feature that needs to be seen. Once this minimum target dimension is defined, stacking bins with lengths and widths that are approximately one-fourth the minimum target width must be created if the target is to be recognized in a 3D data volume. Conversely, once a stacking-bin size is established, the narrowest stratigraphic feature that most interpreters can recognize will be a facies condition that spans at least three or four adjacent stacking bins.

## Station spacing

The distance between adjacent source points along a seismic line is the source-station spacing; the distance between adjacent receiver arrays along that same line is the receiver-station spacing. Previous publications on the topic of seismic acquisition[3] show that the trace spacing (i.e., the stacking-bin dimension) along a 2D seismic profile is one-half the receiver-station spacing (assuming the usual condition that the source-station spacing along the line is equal to or greater than the receiver-station spacing). Applying this principle to 3D seismic design leads to the following: the dimension of a 3D stacking bin in the direction in which receiver lines are deployed in a 3D grid is one-half the receiver-station spacing along these receiver lines, and the dimension of the stacking bin in the direction in which source lines are oriented is one-half the source-station spacing along the source lines.

As stated previously, once a decision has been made about the narrowest target that must be imaged, the required size of a stacking bin is automatically set at one-third or one-fourth that target dimension (Fig. 2). As a result, the source-station and receiver-station spacings are also defined because source-station spacing is twice the horizontal dimension of the chosen stacking bin in the source-line direction, and receiver-station spacing is twice the dimension of the stacking bin in the receiver-line direction. Stated another way, the source-station and receiver-station spacings should be one-half the narrowest horizontal dimension that needs to be interpreted from the 3D data.

When the geology involves steep dips or large changes in rock velocity across a fixed horizontal plane, rigorous calculations of station spacing (or bin size) should be made with commercial 3D seismic design software rather than by following the simple relationships described here.

## Stacking fold

The stacking fold associated with a particular 3D stacking bin is the number of field traces that are summed during data processing to create the single image trace positioned at the center of that bin (Fig. 1). In other words, the stacking fold is the number of distinct reflection points that are positioned inside a bin because of the particular source-receiver grid that is used.

At any given stacking-bin coordinate, the stacking fold inside that bin varies with depth. Fig. 3 illustrates vertical variation in stacking fold. The source-station and receiver-station spacings along this 2D profile both have the same value for Δx, which results in a stacking bin width of Δx/2. The vertical column shows the coordinate position of one particular stacking bin. For a deep target at depth Z2, the stacking fold in this bin is a high number because there is a large number, N2, of source-receiver pairs that each produce a raypath that reflects from subsurface point B. Only one of these raypaths, CBG, is shown. For a shallow target depth, Z1 , the stacking fold is low because there is only a small number, N1, of source-receiver pairs that can produce individual raypaths that reflect from point A. One of these shallow raypaths, DAF, is shown. When a 3D seismic data volume is described as a 20-fold or 30-fold volume, the designers are usually referring to the maximum stacking fold created by the 3D geometry, which is the stacking fold at the deepest target.[1]

In Fig. 3, when the stacking bin is centered around deep reflection point B, the stacking fold is at its maximum because the largest number of source and receiver pairs can be used to produce individual reflection field traces that pass through 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 by a distance that is no larger than depth Z2 to reflection point B. Thus, the distances CE and EG are each equal to Z2.

With this offset criterion to determine the number of source-receiver pairs that can contribute to the seismic image at any subsurface point, we see that the stacking fold at depth Z2 would be N2 , as Fig. 3 shows, because N2 unique source-receiver pairs can be found that produce N2 distinct field traces that reflect from point B. When the stacking bin is kept at the same x and y coordinates but moved to shallower depth, Z1, the stacking fold decreases to the smaller number, N1. Only N1 source-receiver pairs generate field traces that reflect from A and still satisfy the geometrical constraint that these pairs are offset by distance DE (or EF) that does not result in critical wavefield refractions at interfaces above A. When critical refraction occurs, the transmitted raypath, bent at an angle of 90°, follows a horizontal interface rather than continuing to propagate downward and illuminating deeper targets.

In 2D acquisition geometry, the inline stacking fold, FIL, is a function of two geometrical properties: the number of active receiver channels and the ratio between the source-station interval and the receiver-station interval. The raypath diagrams in Figs. 4 and 5 illustrate the manner in which each of these geometrical parameters affects inline stacking fold. Fig. 4 establishes the principle that inline stacking fold is one-half of the active receiver stations when the source-station interval equals the receiver-station interval.

....................(1)

The raypaths in Fig. 4a show the distribution of reflection points (the solid circles on the subsurface interface) when there are four active receiver channels and the source-station interval is the same as the receiver-station interval. The vertical dashed lines pass through successive reflection points. The stacking-fold numbers at the bottom of the diagram define the number of distinct source-receiver pairs that create a reflection image at each subsurface point, that is, the number of reflection points that each vertical dashed line intersects.

The maximum stacking-fold for this four-receiver situation is 2. The raypaths in Fig. 4b show the distribution of reflection points and the stacking fold that results when there are six-receiver channels. The maximum stacking fold for this six-receiver geometry is 3.

Fig. 5 expands the inline stacking-fold analysis to show that for geometries in which the source-station interval does not equal the receiver-station interval, then

....................(2)

where ~ means "is proportional to."

The raypath diagram in Fig. 5a shows the distribution of subsurface reflection points (the solid circles on the subsurface interface) when there are four active receiver channels and the source-station spacing equals the receiver-station spacing. The inline stacking fold is the number of independent reflection points that occur at the same subsurface coordinates, which is the same as the number of reflection points intersected by each vertical dashed line. The stacking fold is shown by the sequence of numbers at the base of the diagram and, in this geometry, the maximum fold is 2.

The raypath picture in Fig. 5b shows the distribution of reflection points when the number of active receiver channels is the same as in Fig. 5a; that is, there are four receiver groups, but the source-station spacing is now twice the receiver-station spacing. (Note that the incremental movement of the source-station flag in Fig. 5b is two times greater than the flag movement in Fig. 5a.) The resulting stacking fold is shown by the number written below each vertical dashed line, which is the number of reflection points intersected by each of those lines. The maximum stacking fold in this geometry is only 1. These two diagrams establish the principle that inline stacking fold is proportional to the ratio of the receiver-station interval to the source-station interval.

Combining Eqs. 1 and 2 leads to the design equation for inline stacking fold:

....................(3)

In 2D seismic profiling, the source-station interval is usually the same as the receiver-station interval, making the ratio term in the brackets in Eq. 3 equal to 1. However, in 3D 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. Crossline fold, FXL, is given by

....................(4)

In a 3D context, the stacking fold is the product of the inline stacking fold (the fold in the direction in which the receiver cables are deployed) and the crossline stacking fold (the fold perpendicular to the direction in which the receiver cables are positioned). This principle leads to the important design equation:

....................(5)

To build a high-quality 3D image, it is critical not only to create the proper stacking fold across the image space but also to ensure that the traces involved in that fold have a wide range of offset distances and azimuths. Eq. 5 provides no information about the distribution of either the source-to-receiver offset distances or azimuths that are involved in the stacking fold. When it is critical to know the magnitudes and azimuth orientations of these offsets, commercial 3D seismic design software must be used. Offset analysis is a technical topic that goes beyond the scope of this discussion. Galbraith[4] describes the parameters involved in onshore 3D seismic survey design.

## Nomenclature

 FIL = inline stacking fold FXL = crossline stacking fold ir = receiver-station interval, L, ft or m is = source-station interval, L, ft or m nc = number of receiving channels nl = number of receiver lines in the recording patch

## References

1. Hardage, B.A. 1997. Principles of Onshore 3-D Seismic Design. Geological Circular 97 – 5. Austin, Texas: Bureau of Economic Geology, University of Texas.
2. Ebrom, D., Li, X., and McDonald, J. 1995. Bin Spacing in Land 3-D Seismic Surveys and Horizontal Resolution in Time Slices. The Leading Edge 14 (1): 37-41. http://dx.doi.org/10.1190/1.1437061
3. Cordsen, A., Galbraith, M., and Peirce, J. 2000. Planning Land 3-D Seismic Surveys, Vol. 9. Tulsa, Oklahoma: Geophysical Developments, Soc. of Exploration Geophysicists.
4. Galbraith, M. 1994. Land 3-D Survey Design by Computer. Exploration Geophysics 25 (2): 71–77. http://dx.doi.org/10.1071/EG994071