OC-seislet: seislet transform construction with differential offset continuation |
Figure 1 shows a 2-D slice out of the benchmark French model (French, 1974). We created a 2-D prestack dataset (Figure 2a) by Kirchhoff modeling. Three sections in Figure 2a show the time slice at time position 0.6 s (top section), common-offset section at offset position of 0.2 km (bottom-left section), and common-midpoint gather at midpoint position of 1.0 km (bottom-right section). The reflector with a round dome and corners creates complicated reflection events along both midpoint and offset axes. The inflection points of the reflector leads to traveltime triplications at some offsets. Figure 2b shows a preprocessed data cube in the - -offset domain after the log-stretched NMO correction and a double Fourier transform along the stretched time and midpoint axes. We apply the OC-seislet transform described above along the offset axis in Figure 2b. Thus, the offset axis becomes the scale axis. The cube of the transform coefficients is shown in Figure 3b and should be compared with the corresponding Fourier transform along the offset direction in Figure 3a. The OC-seislet transform coefficients get concentrated at small scales, which enables an effective compression. In contrast, the Fourier transform develops large coefficients at coarser scales but has small residual coefficients at fine scales. Figure 4 shows a comparison between the decay of coefficients (sorted from large to small) between the Fourier transform and the OC-seislet transform. A significantly faster decay of the OC-seislet coefficients is evident.
slice
Figure 1. 2-D slice out of the benchmark French model (French, 1974). |
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data,dinput
Figure 2. 2-D synthetic prestack data in - -offset domain (a) and in - -offset domain (b). |
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dfourier,dtran
Figure 3. Fourier transform (a) and OC-seislet transform (b) of the input data from Figure 2b along the offset axis. |
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compare
Figure 4. Transform coefficients sorted from large to small, normalized, and plotted on a decibel scale. Solid line: OC-seislet transform. Dashed line: Fourier transform. |
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OC-seislet: seislet transform construction with differential offset continuation |