Layer-by-layer inversion

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Seismic Data Analysis
Series Investigations in Geophysics
Author Öz Yilmaz
ISBN ISBN 978-1-56080-094-1
Store SEG Online Store

The second strategy for initial model building involves a layer-by-layer application of an appropriate combination of inversion methods listed in Table 9-1. Layer-by-layer inversion involves the following steps:

  1. Interpret a set of time horizons from unmigrated data to be used in lieu of zero-offset reflection traveltimes required by coherency inversion. Alternatively, interpret a set of time horizons from time-migrated data and perform forward modeling to obtain the required zero-offset traveltimes.
  2. Assume that interval velocities and reflector geometries for the first n − 1 layers have been estimated, and that we want to estimate the same for the nth layer. By using the time horizons from step (a), first apply one of the inversion methods listed in the left-hand column of Table 9-1 to estimate the interval velocity field.
  3. Assign the estimated interval velocity field for the nth layer to the half space that includes the unknown part of the model — the nth layer and the layers below, and perform depth migration. Often, it is sufficient to do poststack depth migration.
  4. Interpret the depth horizon associated with the base of the nth layer from the depth image and incorporate it into the velocity-depth model.
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

The layer-by-layer inversion strategy alternates between layer velocity estimation and reflector geometry delineation for each layer starting from the earth’s surface and moving down one layer at a time. The layer-by-layer estimation strategy facilitates checking the results of inversion for one layer before moving down to the next. As such model updating can be interleaved with model estimation to circumvent accumulation of errors in layer velocities and reflector geometries as the analysis proceeds from the top down.

We shall demonstrate the layer-by-layer inversion strategy by applying a combination of coherency inversion to estimate layer velocities and poststack depth migration to delineate reflector geometries to the marine data set shown in Figure 9.4-15. Superimposed on the stacked section are the segments of interpreted reflection traveltime horizons. Starting from the top, H1 is the water bottom whereas H6 is the top-salt boundary. The abundance of diffractions within the salt layer is associated with high-velocity anhydrite-dolomite rafts. Input to coherency inversion is the zero-offset reflection traveltimes associated with normal-incidence rays and unmigrated data as shown in Figure 9.4-15. Diffraction flanks present in the unmigrated data must be avoided when interpreting the reflection traveltime segments from unmigrated data.

Details of coherency inversion for interval velocity estimation are provided in models with horizontal layers. Results of the layer-by-layer analysis have been compiled in Figures 9.4-16 through 9.4-21. Begin with the trivial task of modeling the water layer by normal-incidence time-to-depth conversion of the time horizon H1 in Figure 9.4-15 using a constant layer velocity of 1500 m/s. For each layer H2 through H6, and one layer at a time, the analysis includes the following steps:

  1. Apply coherency inversion to compute the horizon-consistent semblance spectrum (panel (a) in Figures 9.4-16 through 9.4-21), and
  2. pick the interval velocity profile from the semblance spectrum by tracking the semblance peaks.
  3. Assign the interval velocity profile to the half space that includes the unknown layer itself and use the known overburden layer velocities and reflector geometries to create the intermediate velocity-depth model (panel (b) in Figures 9.4-16 through 9.4-21).
  4. Perform poststack depth migration using the intermediate velocity-depth model (panel (c) in Figures 9.4-16 through 9.4-21).
  5. Interpret the depth horizon that corresponds to the base boundary of the layer under consideration.
  6. Incorporate the interpreted depth horizon into the intermediate velocity-depth model (panel (d) in Figures 9.4-16 through 9.4-21).
  7. Proceed to the next layer below and repeat the above steps.

The coherency semblance spectra shown in panel (a) of Figures 9.4-16 through 9.4-21 have been compiled into a single panel as shown in Figure 9.4-22. First, note the gradual decrease in resolution as we move down to the deeper layers. Much like conventional stacking velocity analysis, the resolving power of coherency inversion is governed by the cable length, the reflector depth, the layer velocity, and bandwidth of the data. Second, observe the short-wavelength variations in the velocity profiles defined by the semblance peaks. As was demonstrated by the synthetic data experiments in models with horizontal layers, these are caused by lateral velocity variations in the overlying layers that are much less than a cable length (Figures 9.1-13 and 9.1-20). In the present case shown in Figure 9.4-22, note that the interval velocity profiles for layers H6 and H7 exhibit much more pronounced fluctuations compared to the layers above. This is caused by the strong lateral variations in the interval velocity profile for layer H5. In practice, the interval velocity profile picked from the semblance spectrum must exclude such rapid fluctuations. Otherwise, the reflector geometry associated with the base of the layer under consideration will be corrupted by geologically implausable variations. Also note from the semblance spectra that we have to interpolate the interval velocity profiles through the zones with missing reflection events.

The accuracy in velocity estimation by coherency inversion can be monitored closely by examining the modeled CMP traveltimes and the associated raypaths. Shown in Figure 9.4-23 are the CMP gathers at a selected analysis location for each of the layers H2 through H7. Superimposed on these gathers are the modeled CMP traveltime trajectories that correspond to the optimum layer velocities picked from the semblance spectra shown in Figure 9.4-24. The raypaths associated with the modeled CMP traveltimes shown in Figure 9.4-25 illustrate the ray bending at layer boundaries. As such, the modeled traveltimes in Figure 9.4-23 are in general nonhyperbolic. From the surface lateral extent of the raypath family for each layer in Figure 9.4-25 and the offset range of the modeled traveltimes in Figure 9.4-23, we note the resolution that can be attained from the semblance spectra. Specifically, note that the sharpness of the spectra in Figure 9.4-24 decreases with increasing layer velocity, decreasing cable length, and increasing reflector depth.

The results of the alternating steps of layer velocity estimation and reflector geometry delineation involved in layer-by-layer model building have been compiled in Figure 9.4-26. The left and the right columns correspond to the compilations of panels (b) and (c) of Figures 9.4-16 through 9.4-21, respectively. The analysis sequence illustrated by Figure 9.4-26 begins with panel (a) and ends with panel (l). As outlined above, perform coherency inversion to generate the interval velocity profile and, hence, the intermediate velocity-depth model for layer H2 (panel (a)). Next, perform poststack depth migration and delineate the reflector geometry associated with the base of layer H2 (panel (b)). Then move down to the next layer and repeat the same analysis (panels (c) and (d)), until you reach the last layer in the sequence (panels (k) and (l)).

The final form of the velocity-depth model estimated by applying the layer-by-layer inversion strategy is shown in Figure 9.4-27a. Check the consistency of this velocity-depth model with the depth image derived from poststack depth migration (Figure 9.4-27b) and the stacked section (Figure 9.4-27c). Specifically, overlay the depth horizons from the velocity-depth model onto the depth image and note that the reflector geometries implied by the latter are in agreement with the depth horizons. Then, perform zero-offset normal-incident modeling of the traveltimes associated with the layer boundaries included in the velocity-depth model and overlay them onto the stacked section. Again, note that the actual reflection traveltimes on the stacked section are in good agreement with the modeled traveltimes. This exercise confirms the consistency of the estimated velocity-depth model with the input stacked data. Yet, the estimated model is but one of the many possible solutions. It can only be considered an initial model; thus, it needs to be verified by checking its consistency with prestack data and, finally, it needs to be updated (model updating).

We now examine the performance of the layer-by-layer inversion strategy applied to structurally complex data. Figure 9.4-28a shows a time-migrated stacked section with a complex overburden structure associated with salt tectonics. The top-salt boundary is represented by horizon H6. The section has been interpreted to identify the layer boundaries with significant velocity contrast. For coherency inversion to estimate interval velocities layer by layer, the required zero-offset traveltimes were modeled from the time horizons interpreted from the time-migrated section. The modeled zero-offset traveltimes are shown in Figure 9.4-28 superimposed on the unmigrated stacked section; note that they are consistent with the observed reflection times. The alternative to using the modeled zero-offset times for coherency inversion is clearly the reflection times picked directly from the unmigrated stacked data. While this alternative may be appropriate for cases of simple structures (Figure 9.4-15), in the present case of a complex structure it is easier and safer to interpret the time-migrated data.

Results of the alternating steps of layer velocity estimation using coherency inversion and reflector geometry delineation using poststack depth migration involved in layer-by-layer model building have been compiled in Figure 9.4-29. The left column shows the intermediate models for layers H2 to H5 (H1 is the water layer), and the right column shows the intermediate depth images from poststack depth migration. Start with the intermediate velocity-depth model in panel (a) and perform poststack depth migration to get the depth image in panel (b). Interpret the depth horizon associated with the base of layer H2 and insert this horizon into the velocity-depth model in panel (c). Then, move down to the next layer and perform coherency inversion to derive the interval velocity profile for it. Assign this velocity profile to the half space below the base of layer H2. This constitutes the updated intermediate velocity-depth model (panel (c)) which is used to obtain the depth image in panel (d). Continue in this alternating manner for estimating the layer velocities and delineating the reflector geometries until you reach horizon H5 (panel (h)).

We do not intend to proceed further and complete the model building for all the layers. Instead, we shall examine the accuracy of velocity estimation for the next layer H6 just above the salt layer. Figure 9.4-30 shows the coherency semblance spectra for layers within the overburden from H2 to H6. We observe that the quality of the semblance peaks is very good for layer H2, while it begins to degrade almost immediately for the layers below. Specifically, in the case of layer H3, the semblance peaks lose their sharpness at the center portion of the line where layer H3 becomes very thin (Figure 9.4-28a) causing instability in ray tracing. Next, the lateral velocity variation in layer H4 has caused rapid ondulations in the semblance spectrum for layer H5. Finally, note that the quality of the semblance peaks has deteriorated significantly for layer H6.

To closely examine this rapid degradation in the quality of semblance, we shall conduct velocity estimation for layer H6 at four selected locations. For each location, Figures 9.4-31 to 9.4-34 show the modeled CMP raypaths that correspond to the modeled CMP traveltime trajectory computed by assigning the velocity associated with the semblance peak to the half space below horizon H5. Where the overburden is relatively less complex, we note that the semblance peak is distinctive and thus the estimate velocity is not ambiguous (Figure 9.4-31). At CMP locations where the overburden is sufficiently complex to cause significant ray bending at layer boundaries, however, the semblance curves have poor quality (Figures 9.4-32 to 9.4-34). Note that, at these locations, reflection point dispersal at the vicinity of the normal-incidence point is large and raypaths are complex. As a result, the complex layer boundaries adversely affect the quality of interval velocity estimation using methods that rely on ray tracing. Also recall from the model experiments in models with horizontal layers that lateral velocity variations in the layers above cause rapid fluctuations in the semblance profile for the layer below. We conclude that all known practical velocity estimation techniques based on ray theory alone suffer from a degradation of lateral resolution in areas with complex overburden structures.

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