Time-variant dip filtering
The slant-stack domain is convenient for implementing dip filtering. To illustrate this, consider the problem of attenuating the strong ground roll in the field record in Figure 6.3-20a, which was obtained from a walkaway noise test. For simplicity, ignore the backscattered Rayleigh waves, since removing them would mean computing negative p traces. Figure 6.3-20b shows the τ − p gather obtained from this field data set. Phase velocity is varied from 500 m/s to over 10 000 m/s. The ground roll generally has very low phase velocity and is mapped to the left of the solid line at 2500 m/s, labeled as E in Figure 6.3-20b.
Suppose that the τ − p gather traces that contain the ground roll are used to reconstruct the t − x gather with the original offsets. The reconstructed gather shown in Figure 6.3-20c contains only the dips that we want to remove from the original wavefield. If this reconstructed gather is subtracted from the original gather (Figure 6.3-20a), the result is the dip-filtered shot record shown in Figure 6.3-20d. An alternate way to compute the dip-filtered shot record is to use, for reconstruction, the slant-stack traces that are only within zone F to the right of the solid line in Figure 6.3-20b. With either approach, the amplitudes at the boundary between the pass and reject zones, the solid line at 2500 m/s in Figure 6.3-20b, must be tapered to reduce artifacts in the reconstructed t − x gather.
Dip filtering in the slant-stack domain should be nearly equivalent to the f − k dip filtering process described in frequency-wavenumber filtering. Figure 6.2-1b shows the 2-D amplitude spectrum of the original field record of Figure 6.2-1a, which is the same data set as in Figure 6.3-20a. The reject zone is defined by the fan in Figure 6.2-1c, which is equivalent to zone E to the left of the vertical line in Figure 6.3-20b.
Figure 6.3-17 Panels (a), (d), and (g) are the input CMP gathers, which contain a single dipping event EF. Panels (b), (e), and (h) are the corresponding slant-stack gathers. Panels (c), (f), and (i) are the reconstructed offset gathers. The slant-stack and reconstructed gathers are displayed at a higher gain than the input gathers.
Figure 6.2-1 (a) Composite field record obtained from a walk-away noise test. Trace spacing = 10 m, A = ground roll, B = a backscattered component of A, C = dispersive guided waves, D = primary reflection. Event E is referred to in Exercise 6-4. (b) The f − k spectrum of this field record, (c) The f − k spectrum of the field record after rejecting ground roll energy A. Compare this with the f − k spectrum (b) of the original record. For display purposes, each spectrum is normalized with respect to its own maximum. (d) Dip-filtered field record whose f − k spectrum is shown in (c). Compare this record with the original in (a). (Data courtesy Turkish Petroleum Corp.)
Figure 6.3-20 (a) A field data set with strong ground-roll energy A, its backscattered component B, guided waves C, and a strong reflection D; (b) τ − p gather obtained from this field data set; (c) reconstruction of the field record using the portion to the left of the solid vertical line in (b) (zone E); (d) dip-filtered data obtained by subtracting the gather in (c) from the original data in (a); (e) the original data set (a) after f − k dip filtering. (Data courtesy Turkish Petroleum Corporation.)
When compared with the slant-stack output (Figure 6.3-20d), the result of f − k dip filtering of the field data set in Figure 6.3-20e suggests basically no difference in performance. However, with the slant-stack approach, dip filtering can be applied in a time-variant manner. This means that the boundary between the pass and reject zones need not be vertical as in Figure 6.3-20b. Also, with the slant-stack technique, we can work with data that are irregularly spaced along the offset axis. This is not the case for the f − k method of dip filtering, since the fast Fourier transform requires data with equal trace spacing. On occasion, dip filtering also is incorporated into multiple attenuation in the slant-stack domain to further eliminate multiples.
An application of time-variant dip filtering to reduce the cable truncation effects on slant-stack gathers (Figure 6.3-17) is provided by Kelamis and Mitchell . Their procedure is outlined below:
- Map a single trace in the offset domain to the slant-stack domain over a specified range of p-values (equations 4a, 4b).
- Apply a time-varying filter by muting inner and outer portions of the slant-stack gather. The mute functions are prescribed using a velocity filter that depends on time and offset.
- Repeat steps (a) and (b) for all offset traces in the input gather and sum the resulting slant-stack gathers.
- Apply rho filtering to the summed slant-stack gather.
- Following a specific process in the slant-stack domain, such as deconvolution, apply inverse linear moveout correction for a specified offset value, and sum over the p-range (equations 5a, 5b). Repeat for all offsets; the output is the slant-stack processed offset data.
- Kelamis and Mitchell (1989), Kelamis, P. G. and Mitchell, A. R., 1989, Slant-stack processing: First Break, 7, 43–54.
- Physical aspects of slant stacking
- Slant-stack transformation
- Practical aspects of slant stacking
- Slant-stack parameters
- Slant-stack multiple attenuation