In the current study we use acoustic prestack depth migration for imaging base of salt and subsalt reflection events with energy that converted to the shear mode and back during propagation. A discussion of the method addresses migration algorithm modifications, prediction of AVO using elastic modeling, prestack processing for specific converted mode paths, and the use of two-pass prestack depth imaging. Prestack depth migrations of a 2D multi-shot elastic data set are included as examples.
In their 1996 paper, Ogilvie and Purnell demonstrate with theoretical calculations, synthetic models and field data that in seismic exploration of salt dominated regions, mode conversion is a significant phenomenon that cannot be neglected during processing and interpretation. Besides alerting the interpreter that these events exist and should be identified, their paper also describes methods for incorporating mode converted energy into the sequence for processing and interpreting the base of salt reflector.
As Ogilvie and Purnell demonstrate in their Figure 5, there is good theoretical basis for expecting that at the top and base of salt bodies, the percentage of the wavefield that is reflected and transmitted in a converted mode is relatively high when compared to that leaving the interface as unconverted energy. Furthermore, because the conversion varies greatly with angle of incidence, it is likely that base of salt in some areas can only be observed using converted energy.
Given the probable widespread occurrence of mode conversion during seismic exploration of salt bodies, an elastic migration algorithm would seem like an obvious object of desire. Although not generally available, algorithms have been described in the literature (for example, Kuo and Dai, 1984). However, multi-component data is a requirement for most, if not all, of these algorithms. Because the majority of data collected in the field today are not multi-component, it is also desirable to try to refine our methods for applying acoustic migration algorithms to imaging energy that has undergone mode conversions.
Salt bodies commonly introduce abrupt and severe velocity discontinuities into the subsurface which cannot be properly handled by stacking or time migration. As a result, prestack depth migration is coming to be regarded as a necessity for general problems in subsalt imaging (Lee and House-Finch, 1994; Lewis, et al., 1994). It seems reasonable, then, that in attempting to use mode-converted energy for subsalt imaging we should look for ways to apply existing prestack depth migration software.
By limiting ourselves to the use of existing acoustic algorithms, we also limit the imaging problem to correctly migrating only one mode conversion "path" per migration. For base of salt, we consider four such paths: PPPP, PSSP, PSPP and PPSP. In this notation, "P" indicates propagation in the compressional mode and "S" indicates propagation in the shear mode. The path is divided into four segments, namely surface to TOS (top of salt), TOS to BOS (base of salt), BOS to TOS, and TOS to surface. Note that the second, third and fourth paths all include two mode conversions.
The first path, PPPP, is handled by normal prestack depth migration using the correct acoustic velocity model. Likewise, the PSSP path can also be handled by existing algorithms, but the salt structure should be represented by its shear velocity rather than its acoustic velocity. Acoustic velocities are used to represent all other structures in this second model.
The prestack migration algorithm must be altered slightly to image energy which travels by the third and fourth paths. The migration must use both of the above velocity models: the down-going wavefield must be propagated through one while the up-going wavefield is propagated through the other. This modification is fairly straightforward for most depth migration algorithms. For Kirchhoff migrations, a set of tables for travel times from the surface to every subsurface point must be calculated for each velocity model. During migration, the travel times for the source location are taken from one table and combined with the times from the other table to produce the migration times for each trace. Likewise, for finite difference shot-receiver migrations, shot gathers must be downward continued for each migration depth step with one model whereas receiver gathers must be downward continued with the other.
Although algorithmically simple, imaging mode converted energy using acoustic algorithms is problematic because primary compressional energy dominates near offsets. Even with grossly incorrect (compressional) migration velocities, this energy tends to stack into the image, improperly positioned, and obscure events which propagated in mixed modes and have been positioned correctly. Imaging these events may be improved, however, by applying selective muting and gain functions before migration to take advantage of the separation of the various propagation modes in offset space.
Muting and offset-weighting can be applied in a target-oriented manner on the basis of predicted energy distribution at base of salt or subsalt reflectors. For complicated structures, reasonable estimates of energy distribution may be obtained by elastic modeling and subsequent AVO analysis of these events. Comparison of acoustic and elastic modeling may be necessary to identify the events of interest.
Unfortunately, many propagation paths will closely overlap in offset and time; one example is the PPSP and PSPP paths described above. In these cases, it is only possible to alert the interpreter to the presence of improperly positioned energy.
Of course, another truism of imaging through salt is that raypath distortions make 3D acquisition and processing mandatory. The suggestion, therefore, that we carry out multiple specialty prestack processing sequences to separately image individual mode conversion paths may seem daunting, if not outright impractical. Fortunately, this can be reduced to a manageable process using two-pass prestack depth imaging (Canning and Gardner, 1996). In this process, cross-line velocity independent prestack time migration is performed before 2D prestack depth migration. In this method, the cross-line migration removes, or at least greatly reduces, three dimensional effects in a 3D prestack data set. One or more 2D prestack in-lines can then be extracted from the data and satisfactorily migrated through iterative 2D prestack depth migrations. Specialty processing for converted modes can then be accomplished at little additional cost.
In 1994, an SEG research committee defined a structure and velocity model for a fictitious but realistic Gulf of Mexico salt body. This is a non-proprietary and widely available model; it is therefore also an appropriate choice for performing salt modeling and imaging studies. In July 1995, GTRI acquired a copy of the gridded 3D velocity volume that was generated from that model (Kessinger, et al., 1995).
We selected one 2D profile out of the 3D SEG/EAEG acoustic velocity model to use as the basis of our 2D modeling and imaging experiments. For the sake of a convenient reference, we chose the profile immediately under the source locations used for the east- west trending acquisition line in Phase A of the National Laboratory GONII project.
Before we could generate our 2D data set, it was necessary for us to define elastic parameters corresponding to the SEG/EAEG model. Using the 2D acoustic velocity profile as a template, we defined corresponding shear velocity and density profiles by assigning values for Vs and r.
We then generated two 138 shot multichannel 2D prestack data sets: one using 2D acoustic modeling code, the other using 2D elastic modeling code. These data were then used in imaging experiments involving 2D prestack depth migration. After muting the direct arrival from all of the shot events, we depth migrated both the acoustic and elastic data sets using the correct acoustic velocity field. The image of the elastic migration is shown in Figure 1.
Unlike the migrated acoustic data, the elastic data have illumination problems where the base of salt is thickest. Because of the stretching due to the velocity function, it is immediately obvious where the base of salt should be located. However, there is not a very good reflector all along that boundary, particularly in comparison to the acoustic results. This lack of energy would make it nearly impossible to correctly locate the base of salt in this area if we had tried to derive the model from the data during imaging.
It should also be noted that in the subsalt region in general, migration focusing analysis produced very clear and interpretable results for the acoustic data, but practically no coherency for the elastic data.
We also carried out one further imaging experiment. We modified the acoustic velocity grid by replacing the salt velocities in the section with the salt shear wave velocities. The 2D prestack depth migration using this modified velocity profile is shown in Figure 2. As the labeling shows, there is now a clear image along much of the base of salt in the correct location where we have imaged energy which traveled through the model in the PSSP mode. This image is best precisely in the area where the image was weakest using the unmodified acoustic velocities. There is also a mispositioned, but easily identified image of the direct P-wave reflection from the base of salt.
Between the PPPP and PSSP images is a strong event which probably corresponds to energy which propagated downward through the salt as S-wave energy and back up through the salt as P-wave energy: i.e., an image of the PSPP propagating energy.
At present, mode converted energy represents an important but largely untapped resource for defining base of salt and subsalt reflector locations. "On-the-shelf" acoustic algorithms can be used with little difficulty to image base of salt reflectors that underwent mode conversion during propagation. Whether these methods are useful for imaging subsalt reflectors requires further study.
Kessinger, W., Strahilevitz, R., and Ramaswamy, M., 1995, Subsalt response of elastic wavefield modeling: Expanded Abstracts, 65th Annual SEG Exposition and International Meeting.
Kuo, J.T., and Dai, T., 1984, Kirchhoff elastic wave migration for the case of noncoincident source and receiver: Geophysics, 49, no. 8, 1223-1238.
Lee, S., and House-Finch, N., 1994, Imaging alternatives around salt bodies in the Gulf of Mexico: The Leading Edge, 13, no. 8, 853-857.
Lewis, G.G., Young, K.T., Finn, C.J., and Schneider, W.A., 1994, Analysis of subsalt reflections at a Gulf of Mexico salt sheet through 3-D depth migration and 3-D seismic modeling: The Leading Edge, 13, no. 8, 873-878.
Ogilvie, J.S., and Purnell, G.W., 1996, Effects of salt-related mode conversions on subsalt prospecting: Geophysics, 61, no. 2, 331-348.
Figure 2: 2D prestack depth migration of elastic data using shear velocities for salt and compressional velocities elsewhere.
Figure 3: 2D prestack depth migration of acoustic data.
