The presence of spatially varying low velocity thin layers in the near surface can account for the surface consistent terms in the description of reflection times. If the same low velocity material occurs at a greater depth in the section then its effect on reflections will vary with reflector depth. The dynamic characteristics of such a "buried static" feature is discussed and a subsurface consistent, time variant static description is given.
The description that is obtained of this moveout phenomenon is asymtotically static, which is to say, as the buried LVT approaches the surface, the description is identical to surface consistent statics. Thus, conventional statics modeling is a special case of STAR corrections. Furthermore, like statics, the fundamental information required is the vertical transmission time through the anomaly. However, this simplified theory makes no attempt to account for the effects of wave front "healing" which wig modify predictions based on ray considerations only. This aspect is investigated using wave equation modeling.
The effect on the reflection time curve of a reflector, due to the presence of buried stream channels, shallow gas "pockets" and erosional (or dissolved) surfaces with low velocity fill, can be modelled as a low velocity thin layer (LVT). The distortion of RMS velocity measurements and of the structure picture represented by the stack section, due to such buried static anomalies, could be substantially reduced.
The total moveout effect on a seismic reflection as observed on a CDP gather record, derives from the fundamentally dynamic process of wave propagation of the source field from the recording process of wave propagation of the source field from the recording surface to the reflector and back. From general principles, it is known that the arrival time of the event is given by the square-root of an even polynomial in the offset. This moveout- polynomial is a description of the effect of refractive spreading of the propagating wave front or, equivalently, the refractive bending A the wavefront normals or rays, according to Snell's law.
In many practical instances, the moveout which varies between reflection, the so-caged dynamic component can be adequately described by the first two terms in the general polynomial expression. This approximation is known as normal moveout. The moveout which does not vary observably between reflections is known as the static component or merely the static. Such an ad hoc division of the description of a dynamic process can be physically motivated by introducing the notion of a low-velocity thin layer, referred to henceforth as an underscore.
The essential property of an LVT is that it causes a negligible dis-placement of a reflected ray yet there can be a significant associat time delay. This is due to the ray displacement being controlled to first order by the thickness-velocity product whereas the time delay is determined to first order by the thickness/velocity ratio. Thus, the LVT acts as a thin lens would in optics and the effect on a wavefront is to cause a time delay depending on the point at which the wavefront crosses the LVT. If the delay varies across the wavefront, the associated rays undergo refractive bending. However, if the LVT does not vary across the impinging wavefront, the result is a constant delay with no refractive bending which is to say a static shift on the arrival time of the wavefront.
Whether this situation holds for the down-going field depends on the variability of the LVT over the extend of the wavefront. Because of the geometric spreading of the down-going field, an LVT must be increasing smooth with increasing depth of burial in order to effect a simple static delay. Conversely, the nearer the LVT is to the source, the more rapid can its spatial variations be, while still causing only a source static.
The usefulness of this description of an LVT as a "buried" static must be measured in terms of its effect on reflections. Two factors influencing this effect are wavefront spreading and a fixed length of recording cable which together imply the deeper the reflector, the less oblique are the rays from the source beam which give rise to the observed reflection. This situation is depicted in Figure 1. For the down-going wavefront defined by the limiting ray pair (A1, B1), the LVT must be smoother (to cause only a static) rather than for the wavefront associated with the ray pair (A2. B2). Consequently, for an LVT to cause a static (and surface consistent) moveout effect on a given reflection, the depth of burial of the LVT must be "small" compared to the reflector depth. How small will depend on the velocity depth function which controls the amount of geometric and refractive spreading, and on the recording geometry and the band-width of the signal which determines the sensitivity of measurement of moveout.
For the up-coming wavefront, a constant delay across the wavefront would seem to require a smoothness criterion for the LVT that would be too restrictive to be practical. Thus, significant refraction of the reflected wavefront might occur. Yet, it is clear that if the LVT is very shallow, i.e. near the detector, the delay will be the same for all reflections and simply a function of the surface position of the detector, viz. a static. How shallow can be understood by considering the associated common detector record. Referring to Figure 1, let the A-detector be common to a set of source-detector pairs. By the reciprocity principle, the wavefronts observed are the pairs. By the reciprocity principle, the wavefronts observed are the same that would be recorded if the A-detector was replaced by an equivalent source and the other sources replaced by equivalent detectors. Hence, the effect of the LVT at the detector can he treated in the same fashion for a source at that location so that the results of the discussion of the down-going wavefront apply for the upcoming wavefront in the vicinity of the A-detector. Thus, it follows that an LVT causes only a static effect on a reflection, provided the ratio of the depth of burial to the reflector depth is sufficiently small.