Model with low-relief structure
In this section, we shall review velocity estimation via stacking velocity inversion and coherency inversion in the presence of low-relief structures. Figure 9.2-1 shows a velocity-depth model with such characteristics. The model simulates a transgressive depositional sequence within the first 1-km depth, a deltaic sequence between 1.5-2 km, and a deeper depositional sequence between 2-2.5 km. Our goal is to detect the subtle lateral velocity variations within the individual sequences.
A total of 154 shot records was modeled using the two-way acoustic wave equation. The simulated recording geometry consists of a split-spread cable with 97 receivers and an offset range of 0-2350 m. Shot and receiver intervals are both 50 m. Figure 9.2-2 shows the CMP-stacked section with and without the interpreted time horizons. Assuming that the CMP-stacked section is largely equivalent to a zero-offset section, these time horizons correspond to two-way zero-offset time picks which are used in stacking velocity inversion and coherency inversion.
The color-coded true velocity-depth model is shown in Figure 9.2-3. Using coherency inversion and stacking velocity inversion to estimate layer velocities, the velocity-depth models also shown in Figure 9.2-3 are obtained. In both cases, normal-incidence traveltime inversion is used to delineate the reflector geometries. Note that both techniques are able to delineate the shallow transgressive sequence. The individual units within the deltaic sequence are not included in the velocity-depth model estimation. Instead, only the top (Horizon 5) and base (Horizon 6) of the sequence are included in the model. Nevertheless, both techniques are able to detect the existence of velocity variations from one unit to the next. The deltaic sequence, however, is delineated by coherency inversion more accurately. Finally, stacking velocity inversion fails to estimate the internal velocity distribution of the deepest sequence between 2-2.5 km, correctly. Coherency inversion, on the other hand, has at least been able to detect the relative magnitude of the velocity variations within this sequence with reasonable accuracy. In the following paragraphs, we shall discuss how the two velocity-depth model estimates in Figure 9.2-3 were made.