Reducing source-generated noise in shallow seismic data ... - CiteSeerX

GEOPHYSICS, VOL. 66, NO. 5 (SEPTEMBER-OCTOBER 2001); P. 1612–1621, 8 FIGS., 2 TABLES.

Reducing source-generated noise in shallow seismic data using linear and hyperbolic τ -p transformations Roman Spitzer∗ , Frank O. Nitsche∗ , and Alan G. Green∗

ABSTRACT

source-generated noise throughout the entire data set. Following inverse linear τ -p transformation and removal of the linear moveout terms, the filtered shot gathers contain reflections and residual elements of the sourcegenerated noise. Because summing along hyperbolas favors reflections, transforming the filtered shot gathers into the hyperbolic τ -p domain leads to significant enhancements in the S/N ratio. A simple rescaling of data values in the hyperbolic τ -p domain, which results in the loss of true amplitude information, increases further the relative strength of the reflected signals. Finally, inverse hyperbolic transformation yields shot gathers dominated by reflections. In tests of the combined τ -p processing scheme on a synthetic shot gather and on a complete shallow seismic reflection data set recorded in northern Switzerland, significant improvements in the quality of reflections in the prestacked data and on a fully processed section are readily apparent. According to the results of these tests, the new scheme works well for reflections originating from flat and dipping horizons.

High-resolution seismic reflection data recorded at many locations on the earth are plagued by the overwhelming effects of direct, refracted, guided, and surface waves. These different components of source-generated noise may completely mask reflections at traveltimes 0 in reduced traveltime sections are unlikely to be reflections because most true reflections have p values less than those of the first arrivals.

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We may therefore filter out signals with p > 0. Based on these considerations and the results of tests conducted on a series of selected shot gathers recorded along the length of the profile, we adopt the τ -p filter displayed in Figure 6b. Results of applying the selected τ -p filter, followed by inverse linear τ -p transformation and removal of the linear moveout terms, are displayed in the shot gather of Figure 6c. This figure reveals well-defined reflections throughout the time range 25–80 ms. To illustrate the effect of the τ -p filter, Figure 6d shows the difference between Figures 5c and 6c. Note the large amount of linear source-generated noise removed from the latter figure. Remnants of linear source-generated noise in Figure 6c (marked by arrows) are a consequence of minor aliasing in the τ -p domain (Figure 6b). Spatially aliased events in the t-x domain may spread over a range of slownesses in the τ -p domain, including the pass region of the filter. They cannot therefore be eliminated entirely in the linear τ -p domain without affecting the true reflections. To suppress the remnants of source-generated noise in Figure 6c, we again apply a simple scaling scheme to the data in the hyperbolic τ -p domain (Figure 7a). Moderately strong amplitudes at p < 0.2 ms/m are related to the remnants of the source-generated noise. Nonetheless, the S/N ratio is ∼10, similar to the synthetic example in Figure 4a. Squaring each sample value in the hyperbolic τ -p domain, while preserving the signs, once more enhances the amplitudes of reflections relative to other events (Figure 7b). Inverse hyperbolic τ -p transformation and square rooting each sample value results in a shot gather containing mostly reflections (Figure 7c). Remnant source-generated noise and artifacts observed after linear τ -p processing (Figure 6c) are suppressed successfully.

Stacks We have shown that a combination of processing techniques applied in the linear and hyperbolic τ -p domains has the potential to improve significantly S/N ratios in shot gathers (compare Figures 7c and 5c). To examine the effects of these improvements on final seismic images, we processed the entire Rhine Valley profile data set twice, once using carefully selected mute functions in the t-x domain and a second time using the new τ -p strategy. Except for the optional items in Table 2, we used the same processing sequence with identical processing parameters for the two stacks. Refraction- and residual-static Table 2. Processing sequence applied to high-resolution seismic data set, which includes τ -p processing outlined in Table 1.

FIG. 5. (a) Typical raw shot gather recorded along a highresolution seismic line in northern Switzerland. Receiver spacing is uniformly 2.5 m. Static corrections are applied and traces are normalized with respect to the maximum amplitude of the entire shot gather. (b) As for (a), except for the application of time- and offset-varying gain functions based on average amplitude-versus-time curves computed for traces over 40 m distance ranges. (c) As for (b), except spectral balancing (80–250 Hz) is applied. Shallow reflections at ∼25 to ∼80 ms become evident, (e.g., Refl at ∼25 ms). To allow direct comparisons to be made, no additional scaling is applied to Figures 5c, 6a, 6c, 6d, and 7c.

Geometry Editing First-break picking Optional mute functions Refraction-static corrections Amplitude scaling Spectral balancing (80–250 Hz) Optional τ -p processing (Table 1) Velocity analyses Residual-static corrections NMO corrections Stack

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corrections, average first-break velocities, and stacking velocities were derived from the conventionally processed data (i.e., Figure 8a). Differences between the stacks in Figures 8a and 8b are solely a function of the optional items in Table 2. Figure 8a shows the stacked section obtained with carefully selected mute functions. Top mutes were designed to eliminate the first arrivals and related source-generated noise, and bottom mutes were designed to remove the surface waves. Figure 8b shows the result of applying the new strategy with the combined linear and hyperbolic τ -p processing scheme (Table 1). Reflections on the section of Figure 8b are uniformly more continuous than those on the section of Figure 8a. The advantages of the new strategy for mapping very shallow structures are particularly evident. A strong reflection at 25–30 ms on the right side of Figure 8b is hardly recognizable

on Figure 8a. Moreover, the onlap structure mapped on the former (marked elliptical area) would not have been so interpreted on the basis of information contained in the latter. CONCLUSIONS

Our ability to image seismically the very shallow subsurface at numerous locations worldwide is limited by the dominant effects of source-generated noise. To address this issue, we propose a processing strategy that markedly suppresses the effects of such noise in high-resolution seismic data. Essential elements of this strategy are 1) average apparent velocities of first arrivals vave are determined via standard refraction-static analyses—in general, these velocities vary across the survey area;

FIG. 6. (a) As for Figure 5c, except plotted with reduced traveltimes t 0 = t + 30 −(x/2180), where 2180 m/s is the first-arrival velocity estimated from refraction-static analyses. (b) Result of linear τ -p transformation applied to (a). Reflections are not as clear as in Figure 3b, but source-generated noise is well defined. The pass region of the filter, designed in the τ -p domain on the basis of shot gathers recorded along the entire line, is outlined by the solid black line. (c) Result of τ -p filtering source-generated noise in (b), applying inverse linear τ -p transformation, and plotting as total traveltime. Note remnants of source-generated noise and transformation artifacts, indicated by arrows. (d) Differences between Figures 5c and 6c, showing level of source-generated noise eliminated from the latter.

Linear and Hyperbolic τ-p Processing

2) simple linear moveout terms [equation (1)] based on vave are applied to each trace—first arrivals and associated guided waves appear as horizontal to subhorizontal events on the resultant reduced traveltime shot gathers;

FIG. 7. (a) Result of hyperbolic τ -p transformations applied to shot gather shown in Figure 6c. The S/N ratio is about 10. (b) As for (a), except the amplitude of each sample is squared, such that the S/N ratio is about 100. For display purposes, each trace in Figures 7a and 7b is normalized with respect to the maximum amplitude of the respective section. Note the reduced noise level in (b) relative to (a). (c) Result of inverse hyperbolic τ -p transformation applied to (b) followed by square rooting the modulus of each value (sign is preserved) yields a shot gather ready for final processing (CMP sorting, NMO corrections, NMO stretch mute, and stack).

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3) the reduced traveltime shot gathers are transformed into the linear τ -p domain using a range of p values that excludes most of the surface waves and other slow traveling source-generated noise (e.g., air waves); 4) a 2-D filter is designed and applied in the linear τ -p domain to eliminate most of the direct, refracted and guided waves, and in addition to the well-defined wave types certain other forms of source-generated noise (e.g., signals with p > 0) may also be removed at this stage of processing; 5) the filtered data in the linear τ -p domain are transformed back into the t-x domain and the linear moveout terms are removed; 6) the filtered shot gathers are transformed into the hyperbolic τ -p domain—reflections are much more prominent than other signals (e.g., any remaining source-generated noise) in this domain; 7) by squaring each value in the hyperbolic τ -p domain (with signs preserved), the ratio of reflected signal to source-generated noise is increased; and 8) inverse hyperbolic transformation and square rooting of the resultant values (with signs preserved) yields high-quality shot gathers ready for further processing. The suggested processing strategy has been tested on synthetic and observed data sets. Reflections and sourcegenerated noise on the synthetic shot gather were well delineated in the linear τ -p domain. Although reflections on the observed shot gather were rather difficult to discern in this domain, the clearly defined source-generated noise allowed a suitable τ -p filter to be designed. Filtering the synthetic and observed data in the linear τ -p domain followed by inverse τ -p transformation yielded shot gathers with numerous reflected events (e.g., compare Figure 3c with Figure 2c and Figure 6c with Figure 5c). Nevertheless, small amounts of source-generated noise continued to contaminate these shot gathers; because aliased source-generated noise extended over the entire linear τ -p domain, including the pass region of the τ -p filter, it could not be removed completely without negatively affecting the true reflections—hence the need for additional data massaging in the hyperbolic τ -p domain. Transformation of both shot gathers into the hyperbolic τ -p domain using an appropriately broad range of positive and negative p values resulted in noticeable enhancements in the S/N ratios (Figures 4a and 7a). Coincidentally, these ratios were found to be ∼10 for both data sets. Further increases in these ratios to ∼100 were obtained by squaring each value in the hyperbolic τ -p domain (Figures 4b and 7b). Although the improvements in S/N ratio were diminished somewhat after inverse transformation, the final shot gathers (Figures 4c and 7c) were superior to those obtained after filtering in the linear τ -p domain (Figures 3c and 6c). One notable disadvantage of rescaling in the hyperbolic τ -p domain was a loss of amplitude information. Finally, reflections on the τ -p processed stacked section (Figure 8b) were found to extend to shallower depths and to be markedly more continuous than those on the conventionally processed section that included the time-consuming design and application of various conventional mute functions (Figure 8a). We conclude that the suggested τ -p processing strategy is useful for improving the quality of seismic images of the

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FIG. 8. Stacked sections obtained by (a) applying standard top and bottom mutes and (b) combined linear and hyperbolic τ -p processing (Table 1). Except for muting and τ -p processing, the same processing sequence (Table 2) with identical parameters was used for both sections. shallow subsurface. The decomposition of high-resolution seismic data into reflections and source-generated noise is a critical processing step that can be performed more efficiently and effectively in the linear and hyperbolic τ -p domains than in the t-x domain. Although we have only described the application of the proposed τ -p processing strategy to shot gathers recorded along profiles, it is relatively straightforward to extend the procedure to handle CMP gathers and shallow 3-D seismic reflection data. ACKNOWLEDGMENTS

We thank Michael Roth for performing the finite-difference simulations and Heinrich Horstmeyer for advice on the use of our processing software. This project was supported financially by Swiss National Science Foundation grants 20-50714.97 and 20-56799.99. REFERENCES Buker, ¨ F., Green, A. G., and Horstmeyer, H., 1998, Shallow seismic reflection study of a glaciated valley: Geophysics, 63, 1395–1407. Diebold, J. B., and Stoffa, P. L., 1981, The traveltime equation, tau- p mapping, and inversion of common midpoint data: Geophysics, 46, 238–254.

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