## Abstract

Three-dimensional (3-D) seismic surveys have become a major tool in the exploration and exploitation of hydrocarbons. The first few 3-D seismic surveys were acquired in the late 1970s, but it took until the early 1990s before they gained general acceptance throughout the industry. Until then, the subsurface was being mapped using two-dimensional (2-D) seismic surveys.

Theories on the best way of sampling 2-D seismic lines were not published until the late 1980s, notably by Anstey, Ongkiehong and Askin, and Vermeer. These theories were all based on the insight that offset forms a third dimension, for which sampling rules must be given.

The design of the first 3-D surveys was severely limited by what technology could offer. Gradually, the number of channels that could be used increased, leading to discussions on what constitutes a good 3-D acquisition geometry. The general philosophy was to expand lessons learned from 2-D acquisition to 3-D. This approach led to much emphasis on the properties of the CMP gather (or bin), because good sampling of offsets in a CMP gather was the main criterion in 2-D design. Three-D design programs were developed that concentrated mainly on analysis of bin attributes and, in particular, on offset sampling (regularity, effective fold, azimuth distribution, etc.).

This conventional approach to 3-D survey design is limited by an incomplete understanding of the differing properties of the many geometries that can be used in 3-D seismic surveys. In particular, the sampling requirements for optimal prestack imaging were not properly taken into account. This book addresses these problems and provides a new methodology for the design of 3-D seismic surveys.

The approach used in this book is the same as employed in my Seismic Wavefield Sampling, a book on 2-D seismic survey design published in 1990: Before the sampling problem can be addressed, it is essential to develop a good understanding of the continuous wavefield to be sampled. In 2-D acquisition, only a 3-D wavefield has to be studied, consisting of temporal coordinate *t*, and two spatial coordinates: shot coordinate *x** _{s}*, and receiver coordinate

*x*

*. In 3-D acquisition, the prestack wavefield is 5-D with two extra spatial coordinates, shot coordinate*

_{r}*y*

*, and receiver coordinate*

_{s}*y*

*.*

_{r}In practice, not all four spatial coordinates of the prestack wavefield can be properly sampled (proper sampling is defined as a sampling technique which allows the faithful reconstruction of the underlying continuous wavefield). Instead, it is possible to define three-dimensional subsets of the 5-D prestack wavefield which can be properly sampled. In fact, the 2-D seismic line is but one example of such 3-D subsets.

- Page 1Abstract
Three-dimensional (3-D) seismic surveys have become a major tool in the exploration and exploitation of hydrocarbons. The first few 3-D seismic surveys were acquired in the late 1970s, but it took until the early 1990s before they gained general acceptance throughout the industry. Until then, the subsurface was being mapped using two-dimensional (2-D) seismic surveys.

Theories on the best way of sampling 2-D seismic lines were not published until the late 1980s, notably by Anstey, Ongkiehong and Askin, and Vermeer. These theories were all based on the insight that offset forms a third dimension, for which sampling rules must be given.

The design of the first 3-D surveys was severely limited by what technology could offer. Gradually, the number of channels that could be used increased, leading to discussions on what constitutes a good 3-D acquisition geometry. The general philosophy was to expand lessons learned from 2-D acquisition to 3-D. This approach led to much emphasis on the properties of the CMP gather (or bin), because good sampling of offsets in a CMP gather was the main criterion in 2-D design. Three-D design programs were developed that concentrated mainly on analysis of bin attributes and, in particular, on offset sampling (regularity, effective fold, azimuth distribution, etc.).

This conventional approach to 3-D survey design is limited by an incomplete understanding of the differing properties of the many geometries that can be used in 3-D seismic surveys. In particular, the sampling requirements for optimal prestack imaging were not properly taken into account. This book addresses these problems and provides a new methodology for the design of 3-D seismic surveys.

- Page 5Abstract
In the 1980s, the theory of seismic data acquisition techniques received renewed interest. In particular, Anstey (1986) and Ongkiehong and Askin (1988) introduced new ideas. These authors argued that ground roll suppression is optimal if the acquisition technique insures a regular distribution of geophones over the common midpoint.

Using field data examples, Morse and Hildebrandt (1989) and Ak (1990) demonstrated the superior performance of the stack-array approach over techniques in which there is no such regular distribution of geophones.

In my book,

*Seismic Wavefield Sampling*(Vermeer, 1990), I expand the idea of regularity to the sampling of both receivers and shots. This chapter deals with some highlights of that book, concentrating on the concept of symmetric sampling as the best compromise data acquisition technique.The shot/receiver and midpoint/offset coordinate systems in 2-D

Along the 2-D line, each shot with coordinate

*x*is recorded by a receiver spread with receiver coordinates_{s}*x*. The collection of all common-shot gathers forms the prestack wavefield_{r}*W*(*t*,*x*,_{s}*x*), which is a 3-D data set. The prestack wavefield is smooth and continuous (apart from shot and geophone coupling variations)._{r}The 3-D prestack wavefield (corresponding to a 2-D seismic line) can also be described by traveltime

*t*, mid-point*x*and shot-to-receiver offset_{m}*x*. These variables are illustrated in Figure 1.1. The two pairs of spatial coordinates are related by_{o}A description of a prestack seismic data set in the two coordinate systems is shown in Figures 1.2a and 2b. Each “×” corresponds to a single trace.

- Page 17Abstract
Since the early 1980s, there has been a steady increase in the number of acquired 3-D surveys. Continuing improvements in technology have made it possible to make 3-D seismic data acquisition more and more efficient and cost-effective. Yet, a clear theory as to what constitutes a good 3-D acquisition geometry has not been available, and much of the design of 3-D acquisition geometries has been based on earlier experience—what seemed to have worked in the past was adopted for the future—and on the possibilities and limitations of the available equipment (Stone, 1994). Cordsen et al. (2000) rely on some rules of thumb and guidelines to help them “through the maze of different parameters that need to be considered.” In this chapter, I will provide a theoretical framework for the design of 3-D acquisition geometries suitable for both marine and land data acquisition.

Quite rightly, many current design techniques for 3-D geometries attempt to extend to 3-D what had been learned from the design of 2-D geometries. A breakthrough in thinking about 2-D geometries was provided in Anstey's paper (1986) “Whatever happened to ground roll?” Anstey argued that the combination of field arrays and stacking takes care of adequate suppression of ground roll, provided the offset distribution in the common midpoint (CMP) is regular and dense—the so-called stack-array concept. Ongkiehong and Askin (1988) proposed the hands-off seismic data acquisition concept. They argued that the distance between elements in an array and the length of the contiguous arrays is fully determined by signal velocity and required bandwidth.

- Page 49Abstract
A 3-D acquisition geometry should be designed such that at the end of the acquisition and processing sequence the desired signal can be reliably interpreted and the noise is suppressed as much as possible. This chapter focuses on noise suppression.

The main types of noise are multiples and low-velocity noise such as ground roll and scattered energy. How much low-velocity noise can be suppressed depends on the choice of field arrays, the stack response (implicitly also on fold) and on various processing steps. One of the reasons to select a

*wide*orthogonal geometry is that it allows tackling low-velocity noise by filtering in the shot as well as in the receiver domain. The total amount of multiple suppression depends on the stack response (implicitly also on range of offsets) and on the success of multiple elimination programs, but not on field arrays. At present there is no clear theory on how much noise can be removed in processing. As a consequence, the required noise suppression by field arrays and stacking is relatively unknown, and, to a large extent, the choice of field arrays and fold is dependent on experience.In this chapter, the effect of field arrays on low-velocity noise and of the stack response on low-velocity noise and multiples is discussed. This chapter begins with a discussion of the properties of the low-velocity noise as essential knowledge for the optimal choice of field arrays (linear or areal, shot and/or receiver arrays). Another very useful piece of knowledge would be a quantitative assessment of the amount of noise (ground roll and scattered energy) relative to the desired primary energy.

- Page 69Abstract
In this chapter the symmetric sampling criteria are expanded into guidelines for parameter selection for the survey geometry.

Often, geophysicists dealing with the design of 3-D seismic surveys concentrate on the properties of the bin: offset distribution, azimuth mix, midpoint scatter. In my approach, even more emphasis is put on the spatial properties of a geometry across the bins. These spatial aspects are so important because most seismic processing programs operate in some spatial domain, i.e., combine neighboring traces into new output traces, and because it is the spatial behavior of the 3-D seismic volume which the interpreter has to translate into maps.

These guidelines start with a brief description of the knowledge base, which has to be built to allow a satisfactory choice of all parameters. The first choice to be made is the type of geometry. In general, orthogonal geometry is the geometry of choice for land data acquisition and for marine data acquisition in combination with ocean-bottom cables. Yet, other geometries may also be selected, and a short review outlines pros and cons of various geometries that may be chosen.

This chapter focuses on orthogonal geometry. If 3-D symmetric sampling is taken as a starting point, the choice of parameters for this geometry is simplified considerably. Instead of having to decide on the shot interval and on the receiver interval, a decision need only be made as to the sampling interval. Similarly, the maximum inline and maximum crossline offsets can be made equal. It is also recommended to see what the consequences are of making the shot-line interval and the receiverline interval the same.

- Page 103Abstract
Marine 3-D seismic data acquisition technology is progressing rapidly. On the one hand, there has been a very rapid increase in the number of streamers that can be towed by modern seismic vessels, and on the other hand, the variety of stationary-receiver (seabed) systems is mushrooming. As a consequence, 3-D seismic surveys may be carried out using quite different techniques, and the question of which technique is most appropriate for a given problem needs to be addressed. This chapter reviews pros and cons of the various techniques.

There is a great deal of similarity between a 2-D grid of seismic lines acquired on land and offshore. In both cases sources and receivers are arranged along coinciding straight lines leading to seismic traces, all having the same shot-to-receiver azimuth within one seismic line. The main difference, as far as geometry is concerned, is that in streamer acquisition an end-on geometry is used whereas in land data acquisition a center-spread geome-try is possible.

With the advent of 3-D acquisition, marine and land data acquisition geometries started to diverge. In marine acquisition, 3-D was most efficiently achieved by repeating the 2-D geometry, whereas on land, sources and receivers can be decoupled so that other geometries such as orthogonal and zigzag geometries are also feasible, and in fact, more cost-effective.

Acquiring parallel lines in 3-D marine acquisition means that at the start of the survey, the best direction of those lines must be decided. Assuming a dominant dip and strike direction, various authors have discussed the pros and cons of dip or strike acquisition (Larner and Ng, 1984; Manin and Hun, 1992; Arbi et al., 1995).

- Page 125Abstract
Multicomponent surface seismic has a long history on land, whereas multicomponent marine data acquisition was virtually unheard of until a few years ago. Then, the interest in multicomponent marine data acquisition received a great stimulus by the pioneering work of Sta-toil with their SUMIC technique (Section 5.4.4.2; Berg et al., 1994; Johansen et al., 1995; Berg and Arntsen, 1996; Granli et al., 1999). Imaging of gas chimneys was the main application of the technique (Berg et al., 1994; Granli et al., 1999). The

*PS*-wave data produced sections suitable for structural interpretation, whereas the*P*-wave sections only produced jumble across the gas chimneys.In SUMIC, ROVs were still used to plant the geo-phones, but since then a less expensive technique, based on using a dragged bottom cable, was developed. This technique was first tested for 2-D/4-C applications (Kommedal et al., 1997; Kristiansen, 1998). Kristiansen (1998) lists a large number of applications for 4-C (three geophones plus hydrophone) data.

Full-scale tests of the dragged bottom cable technique for 3-D/4-C surveys have been reported for three differ-ent surveys acquired in the North Sea (Rognø et al., 1999; McHugo et al., 1999; Rosland et al., 1999). The geometries used in these surveys were all different.

In all marine applications,

*P*-wave energy converted to*S-*wave energy at the reflecting horizons is the main wave type being analyzed. These*PS*-waves have asymmetric raypaths leading to special requirements for the survey geometry. - Page 141Abstract
Traditionally, a microspread or noise spread has been the tool for detailed investigation of the properties of the wavefield to be recorded in 2-D seismic data acquisition. Ideally, the noisespread consists of a single shot recorded by a receiver spread with receiver station intervals that are small enough for alias-free recording of the total wavefield, including ground roll. Such a data set allows analysis of the noise in relation to the signal and serves as a tool for the design of field arrays. Examples of noise spreads are shown in Figure 4.16 of Vermeer (1990).

In 1979, a noise spread with extremely fine receiver station sampling was acquired in the Paris basin by the field crew of Shell's E&P Lab. With its 0.25-m sampling interval, it was appropriately called the nanospread. Berni and Roever (1989) used this data set to illustrate the effect of statics variation across field arrays (intra-array statics). This paper showed an important application of noise spreads: the investigation of recording effects which cannot be analyzed after acquisition with usual spatial sampling intervals and arrays.

A disadvantage of the 2-D noisespread is that it does not allow the investigation of 3-D effects. Instead, one would need a 3-D microspread. Therefore, in the context of Shell's research project, “Fundamentals of 3D seismic data acquisition,” it was decided to acquire such a data set. Originally, the idea was to acquire a 3-D shot with a dense coverage of geophone stations around it. This would involve months of acquisition time.

- Page 159Abstract
The theory of spatial resolution has been dealt with in great detail by various authors on prestack migration and inversion (e.g., Berkhout, 1984; Beylkin, 1985; Beylkin et al., 1985; Cohen et al., 1986; Bleistein, 1987), and on diffraction tomography (e.g., Wu and Toksoz, 1987). Despite all this work, the practical consequences of the theory are still open to much debate.

Von Seggern (1994) discusses resolution for various 3-D geometries, and concludes: “ Uniform 3-D patterns, asymmetric patterns, and both narrow and wide swath 3-D patterns all produce nearly equivalent images of a point scatterer, without significantly better resolution in one or the other horizontal direction.” These results were obtained using quite a coarse measurement technique; moreover, fold varied across the midpoint range. As a consequence, the considerable differences in resolution that do occur between different geometries were overlooked.

Neidell (1994) submitted that coarse sampling, if compensated by high fold (24-fold or higher), does not sacrifice resolution. His conjecture led to a flurry of reactions (Vermeer, 1995; Neidell, 1995; Ebrom et al., 1995b; Markley et al., 1996;, Shin et al., 1997).

Ebrom et al. (1995b) and Markley et al. (1996) investigate resolution using a tank model consisting of a number of vertical rods. The time slices at the level of the top of the rods are compared for various sampling intervals and folds of coverage. Whereas Ebrom et al. (1995b) showed that the resolution in the timeslice could be finer than the acquisition common midpoint (CMP) binning, Markley et al. (1996)

- Page 175Abstract
In this chapter the paper “DMO in arbitrary 3-D acquisition geometries” is reproduced (Vermeer et al., 1995). It describes the result of research carried out in 1992 within the context of Shell Research's project “Fundamentals of 3-D seismic data acquisition.” The initial project results pointed to advantages of using wide geometries when an orthogonal geometry was chosen for the 3-D survey. However, there was a general feeling that DMO would produce best results for narrow-azimuth geometries. For instance, Beasley and Klotz (1992) wrote, “For DMO purposes, good offset distribution within each azimuth range should be a survey design goal,” and: “… wide-azimuth surveys should be higher in fold than narrow-azimuth surveys to avoid artifacts from applying 3-D DMO.” In 1988, den Rooijen had written a Shell report which advocated the use of narrow-azimuth geometry because of DMO. Because this prescription did not fit in with the budding theory of 3-D symmetric sampling, den Rooijen and I set out to investigate DMO in cross-spreads, and soon we found that DMO can indeed be applied successfully in those single-fold data sets.

In 1989, Padhi published the theory of DMO in cross-spreads and other minimal data sets in a Shell Oil research summary. Also in that summary the term minimal data set was introduced. Unfortunately, the significance of that work was not recognized on our side of the ocean, so we had to reinvent the wheel. Collins (1997a, 1997b, submitted to Geophysics in April 1994) elaborated on Padhi’s work and Padhi and Holley (1997) provides a simplified version of Padhi’s original paper.

- Page 185Abstract
The relation between acquisition geometry and imaging is of great interest as the leitmotiv of this book. First and foremost is the influence of sampling on a good imaging result. The relation is also apparent in the velocity-model updating procedure, when subsets of the data have to be selected for imaging. A good understanding of the properties of the acquisition geometry is necessary for successful true-amplitude migration. This chapter focuses on this relation between acquisition geometry and imaging. It is based on three earlier papers (Vermeer, 1998a, 1998b, and 2000).

The influence of sampling on the imaging result was already mentioned at various places in this book. In particular, Section 8.3.7 illustrated that coarse sampling generates migration noise. Section 4.5 mentioned that the size of the survey area depends on the migration distance and the zone of influence. Often, Fresnel zone is used in this context, but Fresnel zone has a very specific meaning and does not quite express the zone around the imaging point that is required for a complete image. The expression “zone of influence” is a better term for this requirement. It was introduced in Brühl et al. (1996) for modeling and can readily be extended to migration.

The process of velocity-model updating can be subdivided into two major steps: (1) the creation of images using subsets of the total data set, followed by (2) an analysis procedure to find an improved velocity model. The collection of all image traces for a given output point is called common-image gather (CIG).