Structure-independent inversion

**Seismic Data Analysis**
Series	Investigations in Geophysics
Author	Öz Yilmaz
DOI	http://dx.doi.org/10.1190/1.9781560801580
ISBN	ISBN 978-1-56080-094-1
Store	SEG Online Store

In areas with low-relief structures and moderate lateral velocity variations, a structure-independent inversion strategy can be used to circumvent interpretation of time horizons when deriving an initial estimate of the earth model. Compared to a layer-by-layer inversion strategy, it can prove to be robust and less labor-intensive. We shall outline a procedure for structure-independent earth model estimation using a field data example.

Shown in Figure 9.4-35a is a time-migrated CMP-stacked section that exhibits a highly developed deltaic depositional sequence. Note from the stacking velocity field shown in Figure 9.4-35b that the lateral velocity variations are mild to moderate. Because the dips are gentle and the structures have low reliefs, we may substitute the stacking velocity field in Figure 9.4-35b for the rms velocity field that we need for Dix conversion.

Consider a set of fictitious, flat time horizons as displayed in Figure 9.4-36a, and extract the rms velocity profiles along these horizons from the rms velocity section (Figure 9.4-36b).
Perform Dix conversion to generate interval velocity profiles from the rms velocity profiles (Figure 9.4-37a). Note that for deeper horizons, lateral velocity variations in the layers above have caused oscillations in the interval velocity profiles.
Apply lateral smoothing to remove these oscillations and use the edited interval velocity profiles to convert the flat time horizons (Figure 9.4-36a) to depth horizons.
Combine the interval velocity profiles (Figure 9.4-37a) with the depth horizons to build an initial interval velocity field as shown in Figure 9.4-37b. Note that lateral velocity variations have caused the flat time horizons (Figure 9.4-36a) to transform to nonflat depth horizons.
Perform poststack depth migration (Figure 9.4-38a) using the initial interval velocity field (Figure 9.4-37b) and overlay the depth horizons derived in step (c) onto the depth section. Note that the depth horizons do not conform to the geometry of the reflectors inferred by depth migration; thus, the term structure-independent model estimation.
Discard the structure-independent depth horizons and replace them with the depth horizons interpreted from the depth-migrated section (Figure 9.4-38b).
Overlay the depth horizons from step (f) onto the interval velocity section from step (d) (Figure 9.4-39a).
Extract the interval velocity profiles along the depth horizons from the interval velocity section (Figure 9.4-39b).
Eliminate the oscillations from these profiles and combine them with the depth horizons from step (f) to build a structurally consistent earth model in depth (Figure 9.4-40a).
Perform prestack depth migration and obtain the image section shown in Figure 9.4-40b from the image gathers as in Figure 9.4-41.

Events on image gathers, except for the multiples, are mostly flat. This means that the estimated earth model in depth (Figure 9.4-40a) is fairly accurate. In practice, to attain consistency of the estimated model with the input data, depth migration may have to be iterated a few times (2-D poststack depth migration). This then is followed by model updating with reflection tomography, which is discussed in the next section.

Figure 9.4-35 (a) A CMP-stacked section, and (b) the stacking velocity field.
Figure 9.4-36 (a) The stacking velocity field as in Figure 9.4-35b with fictitious flat time horizons superimposed, and (b) the rms velocity profiles extracted from the section in (a) along the fictitious flat time horizons.
Figure 9.4-37 (a) The interval velocity profiles derived from the rms velocity profiles in Figure 9.4-36b by way of Dix conversion, and (b) a structure-independent velocity-depth model created by combining the interval velocity profiles as in (a) with the fictitious depth horizons that correspond to the flat time horizons as in Figure 9.4-36a.
Figure 9.4-38 (a) Depth migration of the stacked section in Figure 9.4-35 using the velocity-depth model in Figure 9.4-37b with its associated structure-independent depth horizons superimposed, and (b) the same section as in (a) with a set of interpreted structurally consistent depth horizons.
Figure 9.4-39 (a) The velocity-depth model as in Figure 9.4-37b with a set of interpreted structurally consistent depth horizons as in Figure 9.4-38b, and (b) the interval velocity profiles extracted from the section in (a) along the structurally consistent depth horizons superimposed onto the same section.
Figure 9.4-40 (a) A structurally consistent velocity-depth model created by combining the interval velocity profiles as in Figure 9.4-39b with the depth horizons as in Figure 9.4-38b, and (b) prestack depth migration of the data associated with the stacked section in Figure 9.4-35.
Figure 9.4-41 Selected image gathers associated with the image section derived from prestack depth migration shown in Figure 9.4-40.