An example of the 3-dimensional prediction's ability to predict nonlinear events is shown in Figure , where the input consists of several dipping layers cut by a fault in the crossline direction, so that events are nonlinear in the inline direction. In the cubes in Figure and the figures that follow, the vertical direction is the time axis, the horizontal direction is the inline spatial axis, and the direction running into the page is the crossline spatial axis. The lines on the cubes indicate the position of the slices shown on the faces of the cube. The one-pass 3-dimensional prediction did not smear the fault, because the calculated 3-dimensional filter created a prediction in the crossline direction that preserved the discontinuity in the inline direction. With the two-pass prediction, the inline pass smeared the reflections across the fault. For the noiseless case of Figure , the f-x prediction is not shown because it gave the same results as the t-x prediction.

Figure 5

The results of applying f-x prediction and t-x prediction to a 3-dimensional land survey provided by ARCO are shown in Figures to to demonstrate the differences between the two processes. This data set is interesting because it has a significant noise level with fairly flat, predictable events.

Figure 6

For both two-pass applications, the filter size was five elements in the spatial direction. For both 3-dimensional one-pass applications, I employed a filter with five elements in both spatial directions. The t-x prediction used a five-element filter length in the time direction for both one- and two-pass applications. The window sizes were 60 traces in the inline direction, 60 traces in the crossline direction, and 200 samples, or 0.4 seconds in time.

Both the two-pass and the one-pass t-x prediction results in Figures and show less noise than the corresponding f-x results; otherwise the results are similar. While the one-pass t-x prediction and f-x prediction results are much the same, the t-x prediction output shows somewhat less noise.

Figure 7

Figure 8

The advantage of using 3-dimensional lateral prediction is especially clear in Figures and . Both the one-pass results show significantly less smearing of the structure. On the top faces of the cubes in Figures and , the one-pass results appear clean and reasonable, whereas the two-pass results show smearing along the inline and crossline directions. An example of the smearing of the detail can be seen at point A of these figures, where a small doughnut-shaped feature is badly smeared in both the two-pass results. The front face of the cubes in Figures to are significantly different for the one- and two-pass results; with the one-pass results showing much more detail. The features at point B in the figures once again demonstrate the loss of detail. Although the differences between the 3-dimensional t-x and f-x results in Figures and are less than those between the 2-dimensional t-x and f-x results in Figure , the results of the 3-dimensional t-x prediction appear slightly cleaner than those of the 3-dimensional f-x prediction.

Figure 9

Figure 10

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