The Interpreter’s Guide to Depth Imaging Scott MacKay; MacKay Consulting Summary During the relatively velocity-insensitive process of time imaging, the interpreter often relinquishes processing oversight to the processor or third-party “bird dogs” with little interpretive background. However, as depth imaging grows in importance, it has become clear that it cannot be considered a “product”. Depth imaging is intimately linked with the interpretative process. Therefore, the interpreter must be invested in the QC process and be prepared to guide it. This paper discusses a methodology for depth-imaging QC that establishes an appropriate dialogue between the interpreter and the processor. Effective communication is critical if a risk-mitigating depth volume is to be formed. The Interpreter’s Goals At the onset of a project it is important to establish a set of quality-control procedures for the formation of stable depth images. The iterative velocity-updating and data-QC process includes the following: -Choice of algorithms: Migration and velocity updating -Tomographic updates and velocity resolution -Forming the initial velocity model -Initial model PSDM -First iteration of tomography -Subsequent iterations of tomography and imaging -Anisotropy and well calibration Choice of algorithms: Migration and velocity updating The first decision for the interpreter involves the choice of the migration algorithm. Theoretically, the algorithmic choice is simple—reverse time migration (RTM). RTM images over 90 degrees and is ideal for overturned and far-offset reflectors illuminated by diving or turning waves. RTM is also wave-based, as such all paths taken by the data to illuminate the subsurface are used. Practically, RTM is still computationally intensive and expensive, making it a probable candidate for the final volume. Therefore, Kirchhoff methods, using rays, and wave-equation migration (WEM) are still tools that can yield suitable solutions in most geologies. Importantly, even simple geologies need depth imaging since we are looking for proportionally subtler targets (Young, 2009). The next algorithmic choice is velocity updating. RTM and WEM are powerful engines for wave-equation imaging, but the velocity-update process, tomography, has been slow to keep up. Full-waveform inversion (FWI), not to be confused with common AVO inversion, attempts to directly match the seismic gathers after imaging with the velocity update. This is opposed to picking residual curvature on

gathers for a ray-based tomography. As with RTM, FWI is still a computationally intensive process. Therefore, ray-based tomography is still the main engine for velocity refinement. However, RTM and WEM can still be used to generate angle gathers for picking and input to tomography. There are two main forms of ray-based tomography. Layered tomography typically analyzes hyperbolic residual moveout along interpreted horizons using semblance methods. Gridded tomography customarily uses non-hyperbolic picks along coherent events within the gather. The applicability of the two methods is discussed in the next section. Tomographic updates and velocity resolution For tomographic velocity updates, a realistic spatial velocity resolution should be established. Spatial (X, Y) resolution is simplistically visualized as the ability to solve for a full “wavelength” of velocity anomaly. Vertical resolution (Z) is more difficult to define as it is impacted by the density of the picks and the acquisition geometry. It is common to define vertical resolution as an arbitrary fraction of the spatial resolution. For hyperbolic-scanning methods, the minimum spatial resolution is equal to twice the offset mute. The mute is typically equal to the target depth. It is the low-resolution nature of hyperbolic scanning that usually results in a fairly stable solution, although at diminished image quality due to poorly-resolved velocities. Non-hyperbolic scanning (multiparameter) methods have the promise of extracting finer velocity resolution, at the risk of introducing instability in the form of velocity “bubbles” and local, false structure. The QCs described below help to mitigate the above issues. Forming the initial velocity model Depth imaging should be data driven. Therefore, minimal detail should be included in the initial velocity model. If PSTM was performed, the time-migration velocity field may be leveraged by conversion to interval velocity, imposing geologic interval-velocity constraints, and applying spatial smoothing approximately equal to the time-migration aperture. An alternative to PSTM velocities is a smoothed velocity function derived from synthetic ties, with care taken to define the shallow velocity gradient. There is a temptation to add refractor velocities, or even a refraction-tomography solution to the shallow portion of the initial model. This implies adding details that the PSDM reflection tomography may not be able to remove or update. This practice is not recommended and, if employed, should be done with smoothed solutions.

Interpreter’s Guide to Depth Imaging

A critical QC for the initial model is comparing the time migration to a vertical time-to-depth version with the initial velocity field. No local structuring should be introduced. Figure 1 is an example of a conditioned interval-velocity field. Figure 2 (left) shows the PSTM image in time and on the right is the vertical depth conversion. This example illustrates the subtle differences to be expected.

Fig. 1: Conditioned initial PSDM velocity field

Fig. 2: PSTM in time (left), PSTM in vertical depth (right) Initial model PSDM The initial velocity model is used to generate common-image point (CIP) gathers and target lines. In terms of the structural imaging, the initial-model PSDM should be quite similar to the PSTM converted to vertical depth. Figure 3 shows a comparison between the PSTM in vertical depth (top) and the PSDM with the initial model. The two are structurally similar and the PSDM is more poorly focused, as expected, due to the initial nature of the velocity field. First iteration of tomography Regardless of the type of tomography employed, the first-iteration update is typically of low spatial resolution, e.g. 5 km by 5 km (X, Y) by 2.5 km (Z). The goal is to debias the initial velocities and avoid adding detail too early in the iterative process. Once the resolution of the update is chosen, the first-iteration velocity update is formed and a new series of CIPs and target lines are created. The

suggested QCs between the interpreter and processor, to be reviewed sequentially through the iterations, include: -Inlines, Xlines, and depth slices of images -Inlines, Xlines, and depth slices of velocities -Common-image point (CIP) gathers The PSTM in vertical depth and initial PSDM are the starting points for the comparisons. As the iterative process continues, the new iterations are added to the sequence. To detect the possible introduction of local velocity instabilities into the solution two more QCs are suggested: -Delta-velocity sections -Tomographic “ray-density” sections The delta velocity, or change in velocity, allows more attention to be paid to the details of the update. The ray-density plot shows the population of the tomographic velocity-update cells defined by the picks and their ray trace to the acquisition geometry. Low-density values typically give rise to erroneous velocities along the edges and at depth. Figure 4 shows a depth slice of the interval velocities from an advanced iteration of tomography. Note the ring of high velocities around the edge of the survey (black dashes). Eliminating updates with low ray density along the edges and at depth, then extrapolating values with better statistics, minimizes the impact of this issue.

Fig. 3: PSTM in vertical depth (top), initial PSDM (bottom)

Interpreter’s Guide to Depth Imaging

Fig. 4: High velocity anomaly caused by low ray density Subsequent iterations of tomography and imaging During each iteration of tomography, the target resolution is refined. Commonly, thirty percent finer resolution is introduced in each iteration. The QC comparisons are the same as those previously defined. The newer updates are simply added and reviewed in sequence. During the update process, too aggressive a solution may result in velocity and structural distortions. Figure 5 (top) shows the image and velocity of an early iteration of tomography. Figure 5 (bottom) shows the impact of adding too much detail to the solution. Local velocity anomalies (yellow) and local structural oscillations are visible in the later update. For this reason, a final target resolution should be established at the beginning of the project. A reasonable target resolution would be twice the nominal receiver-line spacing. When evaluating the iterations there should be a consistent improvement in focusing with each update. Additionally, the structural response should become simpler. Figure 6 shows relative-amplitude plots exhibiting the expected improvement between initial and later phases of tomography.

Fig. 6: Sequential improvement in focusing with iterations

Fig. 5: Early iteration update (top). Late iteration update (bottom) with local velocity and structural anomalies. During the iterative velocity updates, the gathers should also become flatter. However, the final goal is not to completely flatten the gathers. This would likely indicate that too much detail, and potential instability in the velocities, has been introduced. Figure 7 shows sequential flattening of gathers during the iterations. The final iteration panel (right), shows the goal of overall, but not exact, flattening within the target resolution. In general, if the final depth image is not better focused and structurally simpler than the PSTM in vertical depth, the project was unsuccessful and a review warranted.

Interpreter’s Guide to Depth Imaging

Fig. 7: Sequential flattening of gathers with iterations. Final gathers (right) approximately flat within target resolution Anisotropy and well calibration Depth imaging has embraced another aspect of geology, that of anisotropy. In its simplest form, anisotropy implies that waves travel faster horizontally than vertically. For isotropic imaging, the far-offset contributions result in seismic velocities being too fast. Figure 8 is an example of isotropic depth imaging. The left panel shows two CIPs from the initial migration. Note the classic “hockey stick” anisotropic response of upward curvature in the far offsets. The right panel shows the impact of performing a tomographic update without defining the anisotropic parameters. Note the near- to far-offset downward curvature changing back upward at the farthest offsets. This is an example of a failed tomographic update due to anisotropic contamination in the picks. To properly image, and to better tie the well tops, anisotropy must be incorporated early in the process.

Fig. 8: Two isotropic CIP gathers, offset increases to right. Left panel is initial isotropic migration, right is after update showing introduction of anisotropic contamination Well calibration, once done after isotropic depth imaging, consisted of vertical corrections of the depth volume to be consistent with the well tops (MacKay, 2006). Anisotropic imaging now implies tying tops. An example of the

importance of interpretive QC for anisotropic imaging is seen in Figure 9, showing depth-difference maps before and after editing. The map on the left contains local bulls-eyes that indicate problematic well tops. Corrections were made to the KBs, deviation surveys, and interpreted well tops resulting in the smoother map on the right. The difference maps are proxies for the anisotropic parameter delta. Errors in delta, introduced early in the imaging process, will result in a compromised depth image. In the same manner that too much detail is undesirable in the velocity update, exact ties to the wells using delta are also undesirable. Therefore, smoothed versions of the parameter should be employed, leaving a minor adjustment to the depth volumes after imaging.

Fig. 9: Unedited depth-difference map (left), edited (right) Conclusions I have presented an overall strategy for the implementation and quality control of a depth-imaging project. The topics covered include the choice of the imaging tools, the formation of the initial velocity model, the QC steps for the iterations of tomography, and the impact of anisotropy on the well-calibration process. Author contact information: swmackay@gmail.com