The synthetic data are sorted into common midpoint gathers and NMO corrected. The resulting data cube is displayed in Figure 3. The effect of the velocity anomaly is seen as a symmetric ``X'' pattern visible in the top panel of the data cube. This top panel is a time slice through one of the reflection events.

Figure 3

Kjartansson 1979 made plots of trace power in midpoint-offset coordinates and observed ``V'' shaped patterns due to shallow velocity or absorption anomalies in the Grand Isle data set (see also Claerbout 1993). In Figure 4, I have plotted trace power for three different synthetic data sets with velocity anomalies centered at depths of , and . The trace power is calculated by taking the square root of the sum of the squares of the trace amplitudes. The ``X'' patterns arise because the synthetics are split spread to simulate land data acquisition. For deeper anomalies the legs of the ``X'' are closer to the midpoint axis. For shallower anomalies the legs of the ``X'' are closer to the lines representing the shot and group axes.

The qualitative observation that the trajectory of the ``X'' patterns is a function of anomaly depth gives rise to the slant stack imaging method of the next section.

Figure 4

11/16/1997