In SEP-60, the technique I used was to downward continue the wavefields, then sum power in the images at each depth, looking for the large power values that would result when energy is focused to a point in space, the source location. While that method is reasonable, I decided to backtrack and try to do the same imaging with a conceptually simpler scheme, used by Nikolaev (1987) to image scatterers using teleseismic data and ambient noise data with the NORSAR array.
In Nikolaev's scheme, we create a 3-D grid of possible scatterer locations in the subsurface. For each location, we find the moveout trajectory for energy coming from that point, and compute semblance over time along this trajectory in our data. We can then look at the average semblance over time, or the maximum semblance observed over all times, to get an idea of the scatterers that may lie in the subsurface.
An important first question is, given the size of our array, how far away can scatterers be identified as such? The limited size of the array will make it impossible to see any moveout for events coming from scatterers beyond a certain distance. Beyond this distance, scattered energy will be indistinguishable from plane waves. Nikolaev was using the NORSAR array, 110 km across, and was therefore theoretically able to image very deep structures. Our array is only 500 meters across, so our scattering analysis will be more localized. Figure shows the moveout across the array for a scattered event versus distance of the scatterer from the array. This figure assumes a constant velocity of 2000 meters/sec, a very favorable choice. For higher velocities the dropoff will be sharper. The time difference drops to less than four milliseconds at around 5 kilometers from the array, so our scattering analysis definitely cannot go beyond that point. I have chosen one kilometer as an upper bound in the analysis that follows, to avoid coming too close to the limit.
Figure shows the image that is obtained for the z=0 depth level when this scattering algorithm is applied to portions of several different nighttime and daytime records. The x and y dimensions of the grid of scattering locations shown are three times the size of the survey. Thus points up to 750 meters from the array center are shown in this plot. The dominant features in this plot are the radial streaks. These are due to the fact that as we get further from the array center, our summation path becomes flatter and flatter. Eventually we reach the point where we are summing along a plane wave path, and from there out we would just get a radial streak.
Figures and show the results for depths of 500 and 1000 meters. A feature worth noting in all of these is the general agreement among the daytime blast records, and among the nighttime records, but not between the two groups. The reason for this is that what we are seeing when we sum along these hyperbolic paths is, predominantly, plane wave energy, which was quite different during day and night recording periods. In Figure , I've performed the same computation as for Figure , but I've summed along plane wave paths rather than hyperbolic paths. The fact that these two plots are quite similar is disappointing; it means that the algorithm is seeing mainly plane wave energy imperfectly stacked along hyperbolic paths, rather than scattered energy.
If we are to see scattered energy, probably it is necessary to filter out the strong plane waves present throughout our dataset.