Model building

**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

Earth modeling in depth

Although doing it right the first time is most desirable, there is never a situation where this is possible when estimating an earth model in depth. The velocity-depth ambiguity that is inherent to inversion makes it very difficult getting the right answer — the true geological model, let alone the first time. Limitations in the resolving power of the methods to estimate layer velocities that arise from the band-limited nature of the recorded data and finite cable length used in recording further compound the problem. Finally, traveltime picking that is needed for most velocity estimation techniques and time-to-depth conversion as well as picking depth horizons from depth-migrated data to delineate reflector geometries are all adversely affected by noise present in the data.

All things considered, we can only expect to do our best in estimating what may be called an initial model, and update this model to get an acceptable final model. In this section, we shall discuss ways to estimate an initial model, and in the next section, we shall discuss application of residual moveout analysis and reflection traveltime tomography to update the initial model.

We shall discuss two strategies applicable to both 2-D and 3-D seismic data for initial model building:

A time-to-depth conversion strategy based on interpretation in the time domain, and
A layer-by-layer inversion strategy based on interpretation in the depth domain.

Practical methods to estimate layer velocities and delineate reflector geometries used in implementing the two strategies are listed in Table 9-1. A widely used combination for time-to-depth conversion is Dix conversion to estimate layer velocities and image-ray depth conversion to delineate reflector geometries. Whereas for layer-by-layer inversion, a widely used combination is coherency inversion to estimate layer velocities and poststack depth migration to delineate reflector geometries.

**Table 9-1.** A set of inversion procedures for earth modeling in depth to estimate layer velocities and delineate reflector geometries.
Layer Velocities	Reflector Geometries
Dix conversion of rms velocities	vertical-ray time-to-depth conversion (vertical stretch)
stacking velocity inversion	image-ray time-to-depth conversion (map migration)
coherency inversion	poststack depth migration
image gather analysis	prestack depth migration

3-D structural inversion applied to seismic data from offshore Indonesia

To build the model, we shall apply the structure-independent inversion strategy discussed in model building. The steps for model building are outlined below.

As for the time-to-depth conversion sequence described in model building, the Dix equation (9-1) is used to derive a 3-D interval velocity field from a 3-D rms velocity field. The latter is preferably estimated from prestack time-migrated data. Recall the sequence for 3-D prestack time migration described in 3-D prestack time migration. Following the application of NMO and 3-D DMO correction, each common-offset volume of data is migrated using an initial velocity field derived from the DMO-corrected data. The migrated data are then used to perform velocity analysis, once again, over the survey area at specified grid locations (Figure 7.4-19). The picked rms velocity functions are then used to create a 3-D rms velocity field. Figure 10.8-1 shows selected time slices from the 3-D rms velocity volume.
Perform Dix conversion to derive the 3-D interval velocity field (Figure 10.8-2).
By using this structure-independent 3-D interval velocity field, create an image volume from 3-D poststack depth migration. Figure 10.8-3 shows three inline sections from the image volume. The same inline sections with reverse polarity for better identification of some of the fault planes are shown in Figure 10.8-4. Selected depth slices from the image volume shown in Figure 10.8-5 exhibit a complex fault pattern.
Interpret a set of depth horizons from the image volume of 3-D poststack depth migration created in step (c). The resulting depth structure maps for six horizons that correspond to layer boundaries with significant velocity contrast are shown in Figure 10.8-6.
Intersect the 3-D interval velocity field from step (b) with the depth horizons from step (d) and extract a horizon-consistent interval velocity map for each layer (Figure 10.8-6).
Combine the interval velocity maps from step (e) with the depth horizon maps from step (d) to construct an initial 3-D velocity-depth model.

Figure 7.4-19 Velocity analysis after 3-D prestack time migration along Inline 155 of the data as in Figures 7.4-16, 7.4-17 and 7.4-18. Analysis locations are denoted by the crossline numbers.
Figure 10.8-1 Horizontal slices from the 3-D rms velocity field associated with the image volume shown in Figure 9.4-1.
Figure 10.8-2 Depth slices from the 3-D interval velocity field derived from Dix conversion of the 3-D rms velocity field as in Figure 10.8-1.
Figure 10.8-3 Three inline sections (from top to bottom: Inlines 105, 155, and 205 with 1250-m distance between them) from an image volume derived from 3-D poststack depth migration using the 3-D interval velocity field as in Figure 10.8-2.
Figure 10.8-4 The same three inline sections as in Figure 10.8-3 with reverse polarity.
Figure 10.8-5 Four depth slices from the image volume derived from 3-D poststack depth migration as in Figure 10.8-3 (from top to bottom at 1000, 1200, 1400, and 1600 m). The vertical axis denotes the inlines and the horizontal axis denotes the crosslines.
Figure 10.8-6 Maps of layer velocities (left column) and reflector geometries (right column) associated with the data as in Figure 10.8-3 before tomographic update. Refer to Figure 10.8-12 for the same maps after the tomographic update.