This reference is for an abstract only. A full paper was not submitted for this conference.
The word "resolution" is often assumed to refer to the specific case of temporal resolution. In that regard, Kallweit & Wood (1982) observed that when two octaves of bandwidth are present, the limit of temporal resolution can be expressed as 1/(1.4 x FMAX). However, equally important is the issue of spatial resolution. One of the methods proposed by Berkhout (1984) for quantifying spatial resolution is via the use of the "spatial wavelet". Such wavelets demonstrate that better temporal resolution leads to better spatial resolution. A key point in this paper, though, is that this relationship works the other way too. That is, better spatial resolution leads to better temporal resolution. For instance, of great interest spanning from the Gulf of Mexico to the Red Sea is the exploration for reservoirs beneath salt. In order for the migration process to be able to produce high temporal frequencies in the images of reflections beneath salt, the corrugated nature of the top-salt boundary needs to be portrayed faithfully in the velocity model. However, if a smoothed version of that boundary is used instead (as would certainly be the case in the first round of tomography), the spatial resolution of the top salt is lost. This is what leads to a forfeiture of the subsalt temporal resolution.
The formulas for spatial wavelets are computed from calculus via the analytic integration of continuous functions. However, seismic data are sampled in time and space, and the imaging calculations use discrete summations. This means the spatial resolution in real surveys is more limited than indicated by the spatial wavelets - and the limitation gets worse when the sampling is coarse. One of the key reasons for the loss of bandwidth with large midpoint bins is due to the anti-alias filtering of the migration operators that must be done. As discussed by Abma et al. (1999), such filtering is needed to prevent the generation of artifacts. The resolution implications are demonstrated in Figure 1. A depth-varying velocity function from an onshore survey was used to model diffractions from two closely spaced points in the zone of interest. Those diffractions were then migrated and stacked. The results from two candidate survey designs are shown. The macro designs were identical. However, the source and receiver intervals were selected to yield the 40-ft (12 m) and 80-ft (24 m) CMP bin dimensions in the two surveys respectively. We can see that the 40-ft CMP bin design clearly resolves the two points that are 200 ft (61 m) apart, but the 80-ft design does not. Also, analyses of spectra (not shown) reveal that the temporal bandwidth for the 40-ft case is better than that from the 80-ft scenario - again confirming the inter-relationship of temporal and lateral resolution. This situation is definitely shared in marine surveys too. Such examples not only demonstrate the benefits of the more detailed structural interpretation that can be obtained from small-bin surveys, they also demonstrate the more detailed identification of reservoir properties that can be derived from inversion.
Of course hand-in-hand with the drive for greater spatial resolution should be the drive for greater accuracy in source and receiver coordinate information. That is understandably more challenging in the offshore case. To investigate this issue, modeling and subsequent migration tests similar to those performed for Figure 1 were executed for a marine survey design. A velocity function was used from a field where the target was 6130 m deep. After the modeling of the diffraction surfaces was performed, the source and receiver coordinates were perturbed. This caused the migration to be conducted with inaccurate coordinate information. Three scenarios are featured in Figure 2. The panel on the left is used for reference. In that case, the correct coordinates were used for the migration. The panel in the middle shows the results obtained when the receiver coordinates were perturbed using a Gaussian distribution characterized by a 3-m standard deviation. That is similar to the type of accuracy that is available from leading-edge acoustic positioning systems. The panel on the right shows the result when the standard deviation was 20 m. That is akin to the type of accuracy that was available in early surveys that relied solely on compasses for streamer navigation data. We can see that the loss of resolution induced by the 3-m inaccuracy is no great consequence. The two point diffractors that are separated by 30 m are easily resolved. However, those diffractors are not resolved when the standard deviation is 20 m. Note that in this exercise the bin dimensions are 5 m. So, the right-most panel in the figure demonstrates that small bins by themselves are not sufficient for good resolution. Accuracy in coordinates is required too.
Improved (temporal and spatial) resolution requires denser spatial sampling. This naturally implies that massively more shots (via continuous recording techniques) and/or higher channel counts are required in acquisition. Indeed such strategies would seem to be ideal for onshore programs in the Middle East and North Africa where the desert environments place minimal restriction on access. However, in other regions, topography, vegetation, infrastructure, and many other things often severely restrict where shot points can be placed. In those cases, the burden of denser spatial sampling would have to be placed primarily on the channel count. Whatever the case, the quest for better sampling also implies that each shot should ideally be a point (as in the case of a single vibrator) and each receiver should be recorded by a separate channel - otherwise there will be smearing of the signal. But this is not to say that it would be sufficient simply to use more channels and more computers. An order of magnitude increase in the number of live channels requires paradigm shifts in data QC, data transfer, and processing. It also requires improvements in things like positioning accuracy - as mentioned above. So assuming all hurdles are overcome, how many live channels would we like to have in each shot? Well frankly, most geophysicists would probably take all that they could get. Today, large "conventional" land and marine acquisition systems might have 4,000 to 5,000 channels. However, some single-sensor land systems have offered up to 30,000 live channels - with further advances to 150,000 channels recently launched. Similarly, marine singlesensor systems can record tens of thousands of live channels - with the main limitation being how many streamers can be towed by the vessel.
What we have said here is that resolution is multifaceted. Good temporal resolution does not depend simply on how much high-frequency energy our seismic sources can pump into the ground. Good temporal resolution in the 3D migrated image also requires good spatial sampling. Good spatial sampling requires high channel counts. High channel counts require a paradigm shift in everything from QC procedures to final interpretation. Also, the very definition of "sampling" implies discrete sampling - not mixing. And finally, the big questions of course are just how small do the bins have to be, and how many channels are needed? In other words, what are the requirements in the field design that are needed to meet the requirements in resolution? Projects with which the authors have been involved employed bins as small as 3 m or so. Such density is certainly not yet required in most areas, but it might very well be appropriate for specific instances ranging from the SAGD programs of the heavy oil province in Canada to high-resolution surveys in heavily karsted zones of the Middle East. As a matter of practice, proper survey evaluation and design studies need be conducted to answer these field-specific questions.
Abma, R., Sun, J., & Bernitsas, N., 1999, Antialiasing methods in Kirchhoff migration: Geophysics, 64. 1783–1792
Berkhout, A. J., 1984, Seismic exploration - seismic resolution: a quantitative analysis of resolving power of acoustical echo techniques. Geophys. Press, London.
Kallweit, R. S. & Wood, L. C. 1982. The limits of resolution of zero-phase wavelets. Geophysics. 47. 1035–1046.