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## Examples of three-dimensional lateral prediction

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.

yplanesld
Figure 5
A comparison of smearing with one- and two-pass t-x prediction. The top cube is the input, the middle cube is the result of a one-pass 3-dimensional t-x prediction, and the bottom cube is the result of two passes of one-dimensional t-x prediction in the inline and crossline directions. The one-pass result shows no smearing of the fault; the two-pass result shows a smeared fault image.

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.

Arcoorig
Figure 6
The input to the t-x and f-x predictions. A significant amount of noise is seen here. In this figure and the ones that follow, the vertical axis is time and the horizontal axes are space.

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.

Arcotx2d
Figure 7
The result of two passes of 2-dimensional t-x prediction processing. While this result is an improvement over the input, some of the details are seen to be lost when compared to the 3-dimensional t-x prediction. More noise has been attenuated than with the two-pass f-x prediction.

Arcotx3d
Figure 8
The result of 3-dimensional t-x prediction processing. This result preserves the details lost in the two-pass t-x prediction.

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.

Arcofx2d
Figure 9
The result of two passes of 2-dimensional f-x prediction processing. While this result is an improvement over the input, some of the details are seen to be lost when compared to the 3-dimensional f-x prediction.

Arcofx3d
Figure 10
The result of 3-dimensional f-x prediction processing. This result preserves the details lost in the two-pass f-x prediction.

Next: Conclusions Up: Three-dimensional lateral prediction Previous: The three-dimensional extension of
Stanford Exploration Project
2/9/2001