The quality of residual static corrections greatly depends on the cross-correlation window and maximum allowable static shift used.
The cross-correlation window is the time gate that defines the part of trace that has to be cross-correlated in order to estimate the residual static corrections. It must contain as many reflections as possible to reduce the discrepancy from the time invariance assump- tion. In addition it should avoid the reflection events with poor S/N and muted zone. Its choice is a critical step which can often be resolved only after some trial-and-error attempts.
The maximum allowable static shift is the amount of time shift between traces allowed during their cross-correlation. In principle it should be adequate to accommodate all possible combined shot and receiver static shifts at any given location. However, static shifts greater than the dominant period of the data may induce cycle skips errors es- pecially for poor S/N ratio data. Conversely, small static shifts may be inadequate to account for all possible shot and receiver static shifts. Attempting to use small time intervals in sequence to avoid the possibility of cycle skipping errors without reducing the possibility of solving large time shifts is an alternative that unfortunately does not work properly [Yilmaz, 1987]. For shallow and ultrashallow seismic reflection dataset Steeples and Miller [1998] suggest to limit the maximum allowable static shifts to one- quarter of the dominant wavelet period, ensuring at least two (but preferably more) reflection events within the correlation window. However, as the frequency content of the reflection signals increases it becomes more and more difficult to compensate for the static anomalies minimizing the chance of generating static artefacts. This could be approached with some degree of confidence only when a large number of reflections are present. Unfortunately, this is not the case of shallow seismic reflection data where generally the number of reflection events is very low, often no more than two or three. In these cases, unsuitable cross-correlation window and/or allowable static shift could even set the stage for production of artefacts as bogus structures and coherent events from noise.
Further considerations concerning the pitfalls commonly faced in residual static correc- tions of shallow and ultrashallow seismic reflection data are reported in the introduction of this thesis.
Chapter 4
The CRS stack method
In this chapter I introduce the concepts of the CRS stack process and of the related CRS-based processing tools for deriving velocity information, residual static corrections and for event-consistent smoothing of CRS parameters. These processing tools permit the establishment of CRS processing chains based entirely on the same assumptions, operators, and apertures.
4.1
Introduction
The Common Reflection Surface (CRS) stack method [e.g. J¨ager et al., 2001; Mann et al.,1999] is a seismic reflection imaging technique that produces the zero-offset section, stacking the traces whose sources and receivers are within the limits of a certain aperture in the vicinity of a central point x0. Therefore, unlike the conventional CMP stack which
evaluates the reflections within individual CMP gathers, the CRS stack spans several neighbouring CMP gathers to produce the so-called CRS-supergathers. Each CRS- supergather covers all the traces stemming from a common reflector segment centred in depth at the reflection point of the image ray, i.e. of the zero-offset ray which emerges at the image point location x0[Hubral,1983]. The stack result is then placed at the location
of the imaging point x0. Since the number of traces falling into the CRS-supergather can
significantly exceed the number of traces belonging to one CMP gather, the resulting CRS stacked section generally shows higher S/N ratio and better reflection continuity compared to its CMP counterpart. This is especially true in complex and/or low- coverage areas. Moreover, the high number of traces allows for the implementation of a stable data-driven process to determine accurate stacking parameters, velocity information and residual static corrections. This makes the CRS stack a much faster and less user interactive time-imaging procedure than the conventional CMP processing. To fully understand the reason for using the traces of neighbouring CMP gathers to pro- duce single ZO stacked traces, it is helpful to consider a laterally inhomogeneous model with dipping and/or curved reflectors and marked velocity variations in the overburden. In such conditions, the signals reflected from a common-reflection-point (CRP) in depth are not confined to single CMP gathers bacause it occurs the so-called reflection-point
Distance [m] Depth [m] 0 500 1000 1500 2000 0 1000 2000 3000 (a) Depth [m] 1750 1700 1650 1600 1550 1500 1450 1400 200 300 400 500 600 700 Distance [m] (b)
Figure 4.1: (a) Ray families (in colour) for five neighbouring CMP gathers; (b) detail showing the regions covered by reflection points [Hertweck et al., 2007].
smearing [e.g. Yilmaz,1987]. This is well illustrated in Figure 4.1a, where the ray fam- ilies of few neighbouring CMP gathers together with their respective range of reflection points are shown above a curved reflector. Rays with the same colour belong to the same CMP family. Since that some reflection points are sampled by the rays of differ- ent CMP gathers (see Figure 4.1b), in principle it is not so strange to look for signals reflected from the same CRP in neighbouring CMP gathers. In practice however, this is never possible as it presupposes a perfect knowledge of the geometry and characteristics of the subsurface which, obviously, are themeselves the objective of the seismic survey. To recover the equivalence between CRP and CMP dip-moveout (DMO) correction can be used [e.g. Deregowski, 1986], which however will remove only the effect due to the reflector dip but not the reflection point dispersal caused by the reflector curvature or by the velocity variations on the overburden. Accordingly, as geology becomes complex the DMO corrections fails and a residual reflection point dispersal remains. In these cases thus, the CMP stack method uses events that are reflected in a certain vicinity of a central reflection point, i.e. the reflection point of the image ray, relying implicitly on the continuity of the reflector around it. Since this same assumption also underlies the DMO correction, using events that are reflected in the vicinity of a reflection point under consideration does not violate the principles underlying the CMP stack.
It is well known that since the seismic energy propagates into the ground with a finite- frequency content, its propagation affects not only the structures along the ray paths, as implied by the ray theory approximation, but rather a finite volume of space around the geometrical ray path. The intersection of this volume with a reflector yields the so-called first interface Fresnel zone, which defines the maximum achievable resolution in terms of reflector properties. The first interface Fresnel zone in the depth domain cor- responds to the projected first Fresnel zone in the time domain. Accordingly, the major contribution stemming from a particular reflector segment in the depth domain can be found inside the associated projected first Fresnel zone in the time domain. Stacking the traces stemming from a common-reflector-segment (a common reflection surface for 3D surveys) within the first Fresnel zone around the supposed central reflection point, would improve the fold coverage of the central CMP gather without sacrificing the resolution on the final stacked section. This is what the CRS stack actually does: it uses the traces
of neighbouring CMP gathers to evaluate the reflection response of a reflection portion within the first Fresnel zone of arbitrary dip and curvature, including diffraction points and planar reflectors. Obviously, to take into account neighbouring CMPs the CRS stack has to add an additional data dimension along CMP direction, i.e. the midpoint direction. As a result, the stacking trajectories in the time-offset plane are replaced by stacking surfaces in the time-offset-midpoint volume. This implies the existence of continuous reflection events over several neighbouring CMP gathers, i.e. the considered reflector segment has to be continuous over at least the range of reflection points. This assumption, however, underlies also the NMO/DMO processing chain, which requires continuity of the reflector at least with regards to the portion on which the reflection point dispersal occurs. The CRS stack therefore is not a new stacking concept but simply the generalization, along the midpoint direction, of the conventional CMP stack method.