automatic editing of noisy seismic data

Geophysical Prospecting 37,875-892, 1989

AUTOMATIC EDITING OF NOISY SEISMIC DATA’

RICHARD G. ANDERSON and G E O R G E A. McMECHAN’

ABSTRACT ANDERSON, R.G. and MCMECHAN, G.A. 1989. Automatic editing of noisy seismic data. Geo- physical Prospecting 37, 875-892.

Seismic data often contain traces that are dominated by noise; these traces should be removed (edited) before multichannel filtering or stacking. Noise bursts and spikes should be edited before single channel filtering. Spikes can be edited using a running median filter with a threshold; noise bursts can be edited by comparing the amplitudes of each trace to those of traces that are nearby in offset-common midpoint space. Relative amplitude decay rates of traces are diagnostic of their signal-to-noise (S/N) ratios and can be used to define trace editing criteria. The relative amplitude decay rate is calculated by comparing the time-gated trace amplitudes to a control function that is the median trace amplitude as a function of time, offset, and common midpoint. The editing threshold is set using a data-adaptive procedure that analyses a histogram of the amplitude decay rates.

A performance evaluation shows that the algorithm makes slightly fewer incorrect trace editing decisions than human editors. The procedure for threshold setting achieves a good balance between preserving the fold of the data and removing the noisiest traces. Tests using a synthetic seismic line show that the relative amplitude decay rates are diagnostic of the traces’ S/N ratios. However, the S/N ratios cannot be accurately usefully estimated at the start of processing, where noisy-trace editing is most needed; this is the fundamental limit to the accuracy of noisy trace editing.

When trace equalization is omitted from the processing flow (as in amplitude-versus- offset analysis), precise noisy-trace editing is critical. The S/N ratio of the stack is more sensitive to type 2 errors (failing to reject noisy traces) than it is to type 1 errors (rejecting good traces). However, as the fold of the data decreases, the S/N ratio of the stack becomes increasingly sensitive to type 1 errors.

INTRODUCTION Seismic reflection data are contaminated by a variety of noise, i.e. energy that is not a primary P-wave reflection. Some seismic traces have signal-to-noise (S/N) ratios

Paper read at the 50th EAEG meeting, The Hague, June 1988; revision accepted January 1989. Center for Lithospheric Studies, The University of Texas at Dallas, P.O. Box 83 06 88, Richardson, TX 75083-0688, U.S.A.

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876 RICHARD G. ANDERSON AND GEORGE A. McMECHAN

that are so low that they should be removed (edited) at the beginning of processing. Editing is usually done by a human interpreter using paper plots or an interactive workstation. Because of the large size of modern seismic data sets (especially from marine and 3D surveys), the editing process can be time consuming. This paper develops and evaluates a computer algorithm for automatically editing noisy seismic data.

The goal of noisy-trace editing is to maximize the S/N ratio of the stacked traces in the zone of interest. Whether or not a given trace should be edited depends on the relation between the S/N ratios of the unstacked traces in a CMP gather and the S/N ratio of the stacked trace. The relevant equations have been derived by White (1977) and Rietsch (1980) for spatially incoherent noise and signal amplitudes that are constant for all the traces in the CMP gather. If the S/N energy ratio for the ith trace is Ri and the number of traces in the CMP gather is n, the S/N energy ratio of the stacked trace is

R” = n n (l/Ri) . [ I i:, 1 (The S/N energy ratio is defined as the sum of the squares of the signal amplitudes divided by the sum of the squares of the noise amplitudes.) Thus, the S/N energy ratio of the stacked trace is the product of the number of traces in the CMP gather and the harmonic mean of the S/N energy ratios of the unstacked traces. Since the harmonic mean is biased toward the smaller values in a set of numbers, a single noisy trace can significantly degrade the S/N ratio of the stacked trace. However, editing too many traces will cause a reduction in the stacked traces’ S/N ratios by reducing n, the fold of the stack.

Trace amplitudes are often equalized before stack (i.e. the amplitudes are nor- malized so that the mean-squared amplitude over a selected time gate is the same for all traces). Then the S/N energy ratio of the stacked trace is

Trace equalization is applied more often than not in processing, but there are sig- nificant cases where it is not applied. When the variation of amplitude-versus-offset is analysed it is important to preserve the true amplitudes, so trace equalization should be avoided. Equations (1) and (2) show that the criteria for editing a given trace depends not on the absolute value of the trace’s S/N ratio, but on the relation between the trace’s S/N ratio and the average S/N ratio of all traces in the CMP gather. If the traces’ S/N ratios are uniformly low, no trace editing should be done. Noisy-trace editing is inherently a comparative process.

Noisy-trace editing is done at the beginning of processing because noisy traces can degrade the performance of prestack multichannel processes such as velocity analysis and residual statics analysis. However, (1) and (2) apply to the S/N ratios of the traces during the stacking process. These S / N ratios cannot be usefully estimated at the beginning of processing because subsequent signal-enhancing

A U T O M A T I C NOISY-TRACE E D I T I N G 811

processes, such as deconvolution and filtering, can change them. This lack of information about the S/N ratios limits the effectiveness of noisy-trace editing. Noisy trace editing is an interpretive, ‘best guess ’ procedure.

There are three distinct noise types that must be attacked during the editing process: spikes, noise bursts, and noisy traces. Spikes are high-amplitude noise with a maximum duration of a few sample intervals. Noise bursts are high-amplitude noise with a duration of ten to several hundred milliseconds. Noisy traces are dominated by noise over most of the trace. Spikes should be removed and replaced by temporally interpolated data. Ideally, noisy traces and noise bursts should be replaced by spatially interpolated data, but this is often unnecessary. Noisy traces are usually removed from the data set; noise bursts are usually muted (i.e. replaced by zeroes).

Spikes, noise bursts, and noisy traces are usually spatially incoherent. On some seismic lines, the primary noise problem is source-generated noise, which is spatially coherent. The best way to remove source-generated noise is by filtering (e.g. Hu and McMechan 1987; Beresford-Smith and Rango 1988) rather than editing. Traces that are dominated by source-generated noise should not be edited because these traces may have their S/N ratios enhanced by subsequent multichannel filtering.

Most non-source-generated noise is spatially incoherent, but the signal is spatially coherent, both along the offset axis and the common midpoint (CMP) axis. This distinction underlies our method for noisy-trace editing, which is implemented by eliminating data with amplitudes that are anomalous when compared to amplitudes that are nearby in offset-CMP space. This approach is similar to the methods developed by Akbulut et al. (1984) and Berni (1987). These authors addressed the problem of editing noise bursts; other methods for noise-burst editing were developed by Wiggins and Miller (1972), Neff and Wyatt (1986) and Mavko (1988). Ergas (1982) developed a method for editing noisy traces. Our method is distinct from previous published work: all three noise types (spikes, noise bursts, and noisy traces) are deleted and the trace-editing threshold is set using a data-adaptive procedure.

Comparisons between the performance of the automatic editing algorithm and the behaviour of human editors show that the algorithm makes errors at about the same rate as human editors. The adaptive threshold procedure achieves a good compromise between eliminating noisy traces and maximizing the fold of the data.

THE ALGORITHMS A complete system for automatic noisy-trace editing should edit all three types of noise. Our method treats each noise type separately. The threshold for noisy-trace editing is set by a data-adaptive procedure; the thresholds for noise-burst editing and despiking are fixed values that were determined by empirical testing.

Although the three stages of our algorithm are separated, the amplitude measure- ments are made in a single pass through the data. The amplitudes are measured over time gates that are about 200 ms long; the locations of the time gates are defined by the first arrival times. The median, mean, and maximum absolute amplitude are measured in each time gate.

878 RICHARD G . A N D E R S O N A N D G E O R G E A. M c M E C H A N

Despiking

The first algorithm, which implements the single-channel despiking process, is similar to Evans’s (1982) median filtering algorithm. For each time gate, the ratio of the maximum absolute value to the median absolute value is calculated. If the ratio exceeds 26 dB, a running median filter is applied to the trace absolute values and the ratio of the trace absolute value to the median absolute value is calculated at each sample. If this ratio exceeds 26 dB, the sample(s) are replaced by values interpolated using a cubic polynomial. If a time gate is despiked, the amplitudes are recalculated; these amplitudes are passed to the next stages of the algorithm. The threshold value was determined by empirical testing; the performance of the despiking algorithm is fairly insensitive to the precise value in the range 26-32 dB. It is best to use a low value for the threshold to assure detection of all anomalous amplitudes. For other applications of median filtering to seismic data, see Bednar (1983).

N oise-burst editing

The noise-burst editing algorithm is a multichannel process that uses the maximum absolute values measured in each time gate. The use of the maximum absolute amplitudes assures that the algorithm can detect noise bursts that have durations that are much shorter than the time gates. The time-gated maximum amplitudes are trace equalized to compensate for variations in source and receiver coupling. (This trace equalization does not affect the amplitudes of the output seismic data.) Each time-gated maximum amplitude on each trace is compared to the maximum amplitude of the two previous time gates; if the maximum amplitude does not exceed either of the two previous time-gated maximum amplitudes by more than 8 dB, the algorithm proceeds to the next time gate. If the 8 dB threshold is exceeded, a median amplitude is calculated using amplitudes from the same time gate on traces that are nearby in offset-CMP space. The aperture is limited to plus or minus one group interval along the offset axis and enough CMP intervals to get at least 15 traces in the median bin.

If the ratio of the time-gated amplitude to the median amplitude exceeds 12 dB, the data in that time gate are set equal to zero (with a taper at the ends of the time gate), the time gate is flagged before being passed to the noisy-trace editing stage, and the time-gated maximum amplitude is set equal to the amplitude from the previous time gate before the next time gate is analysed. (A good alternative to zeroing the noise bursts was suggested by Mavko (1988), who applied an amplitude scaling factor and band-pass filter to the noise bursts and then spliced them back into the trace.) The performance of the noise-burst editing algorithm is not significantly affected if the thresholds are varied by plus or minus 2 dB.

Noisy-tracing editing

The noisy-trace editing criterion is based on the fact that signal amplitudes decrease with time (because of geometrical divergence, transmission loss, and anelas-

A U T O M A T I C NOISY-TRACE E D I T I N G 879

tic attenuation), whereas many types of spatially incoherent noise are stationary (Anderson and McMechan 1988) and so have constant amplitudes. Hence, the amplitude decay rate of a trace, relative to traces that are nearby in offset-CMP space, is diagnostic of the trace's S/N ratio.

First, the time-gated mean amplitudes are trace equalized to compensate for variations in source-receiver coupling. (This trace equalization does not affect the amplitudes of the ontput seismic data.) Then a control function is constructed that approximates the median of the time-gated mean amplitudes as a function of time, offset and CMP. For most seismic data, amplitudes vary slowly along the CMP and offset axes. Therefore, instead of using a running 3D median filter, the median amplitude is calculated at selected points in offset-CMP space and linearly interpolated. The relative amplitude decay rate D for each trace is

where C is the control function described above; A is the time-gated mean amplitudes for each trace; i, j and k are time, offset and CMP indices, respectively; and q is the number of time gates. Relative amplitude decay rates greater than or close to zero correspond to large S / N ratios; negative relative amplitude decay rates correspond to small S/N ratios.

Two methods for setting the editing threshold were investigated. An extreme Studentized-deviate many-outlier procedure (Rosner 1983) was tested, but it edited too few traces when compared to the performance of a human editor. The method that was finally chosen is based on a simple model: the probability density function of the S/N ratios for a noisy seismic line tends to be multimodal, with the main peak corresponding to the non-noisy traces, and one or more smaller peaks corresponding to the noisy traces. At some point between the peaks, the slope of the probability density function goes to zero. This point can be determined by analysing a histogram of the relative amplitude decay rates.

Determining an appropriate bin size for a histogram can be diffkult when the population contains outliers; if the bins are too large, small-scale features of the histogram are obscured and if the bins are too small, the histogram will have spurious notches and spikes because of oversampling. The following formula (Freedman and Diaconis 1981) was used:

h = 1.66s [(ln n)/n]'l3, (4) where h is the bin width, s is the mean absolute deviation from the mean, and n is the number of samples.

Once the histogram has been calculated, the algorithm begins a search starting at the bin corresponding to the lower 20th percentile. At each bin, the slope of the histogram is estimated by doing a least-squares line fit to four adjacent bins. When


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a point is found where the slope is less than or equal to zero, the editing threshold is set at the corresponding relative amplitude decay rate.

In practice, the histogram is not often distinctly bimodal because the number of noisy traces is usually only a few percent of the population. However, the algorithm is effective because there is usually some point on the tail of the histogram where the slope is less than or equal to zero. Figure 1 shows where the algorithm set the threshold on data from a seismic line shot on land with a dynamite source. This threshold is a good compromise between rejecting noisy traces and preserving the fold of the data.

EXAMPLES

Synthetic examples

The despiking and noise-burst editing algorithms were tested by adding synthetic spikes, noise bursts, and noise recorded by a seismic field crew to a synthetic seismic line. Figure 2 shows a portion of a shot gather before and after automatic editing. Where the noise bursts have short durations, the despiking algorithm estimated the signal using interpolation. Longer period noise bursts were muted by the noise-burst editing algorithm. Although the noise-burst editing algorithm performed well on this example, it is less stable than the despiking or trace editing algorithms, and has a higher error rate.

A test seismic line was constructed by summing synthetic seismograms and noise recorded by a seismic field crew. On 3% of the traces the noise amplitudes were boosted to levels typical of noisy traces. For each trace, the S/N ratio was calculated

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over the zone of interest. The range of the S/N ratios is 80 dB (see Fig. 3), which is close to the dynamic range of most seismic field systems. The negative skewness of the data reflects the presence of two processes (signal and noise).

These data were used to compare the performance of the trace editing algorithm to optimum trace editing. Optimum trace editing is defined as the editing decisions that maximize Rs in (1) or (2); optimum editing can only be done when the traces’ S/N ratios are known, as in this synthetic example. Figures 4a and 4c show the results obtained by assuming that no trace equalization was applied; Figs 4b and 4d show the results obtained by assuming that trace equalization was applied before stack. Table 1 is a summary of the averaged data from Fig. 4.

The automatic editing algorithm enhanced the S/N ratios of the stacked traces; however, the algorithm made some errors (e.g. CMP number 99 on Fig. 4a). Figure 4 shows that, when the data are trace equalized before stack, the effect of noisy-trace editing on the stack is small. However, when trace equalization is not done, as in

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amplitude-versus-offset analysis, precise noisy-trace editing is crucial. This corrobo- rates previously published work on non-linear stacking (cf. Figs 3 and 4 of Klem- perer 1987).

Automatic trace editing did not improve the S / N ratios as much as optimum trace editing. However, optimum trace editing reduced the fold of the stack severely when there was no trace equalization, removing almost one third of the traces. When the fold is reduced, the ability of the stack to attenuate spatially coherent noise is degraded (see Anstey 1986). Thus, maximizing the stacked traces’ S/N ratios, as defined by (1) and (2), at the cost of reducing the fold, may not be optimal in the presence of spatially coherent noise. The goal of noisy-trace editing is to eliminate only the traces that are outliers compared to the rest of the data.

The assumption that the relative amplitude decay rates are diagnostic of the traces’ S / N ratios was tested by cross-plotting these two quantities (Fig. 5). The linear correlation coefficient for these data is 0.857; this supports the assertion that relative amplitude decay rates are diagnostic of S/N ratios. However, there is con-

TABLE 1. Comparison of automatic editing and optimum editing (summary of the data in Fig. 4)

No trace equalization Trace equalization

Average signal-to-noise Per cent Average Per cent ratio (dB) traces edited ratio (dB) traces edited

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siderable scatter at low SIN ratios, which is the critical region for editing decisions. The performance of the algorithm could be improved if the editing criteria were more strongly correlated with the traces’ S/N ratios.

Field data example Although it is simple to calculate SIN ratios for synthetic data, it is dificult to

determine S/N ratios for field data, especially when the data are noisy (White 1977). The noisy-trace editing algorithm was tested on field data by comparing its performance with the performance of human trace editors. A seismic line shot on land with a dynamite source was edited independently by three professional seismic processors. Out of a total of 3849 traces, 12 were edited by all three processors, 14 were edited by two processors, and 92 were edited by only one processor. If, for a given trace, we assume that the majority of the human editors made the correct decision, then the algorithm correctly deleted 19 traces, correctly passed 3799 traces, made 27 type 1 errors (incorrectly deleted a trace), and 9 type 2 errors (incorrectly passed a trace). There were five traces that were deleted by the majority of the human editors because the traces contained noise bursts. The program muted these noise bursts and passed the traces, and so was given credit both for correctly deleting and correctly passing those traces. (This is why the sum of the above numbers is greater than 3849.)

The human editors’ decisions to delete a noisy trace was seldom unanimous, which shows that noisy-trace editing is inherently subjective. Display parameters (e.g. trace equalization) can influence processors’ editing decisions. Seismic processors have varying perceptions of the tradeoff between the penalty for reducing

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the stack fold and the penalty for accepting a noisy trace. Out of 3854 editing decisions, the algorithm made 27 type 1 errors (0.70%), whereas out of 11,547 editing decisions, the human editors made 92 type 1 errors (0.80%). Thus, the number of errors made by the algorithm is comparable to the number of errors made by the human editors.

On some of the profiles, the performance of the automatic editing algorithm was distinctly superior to the performance of the human editors; Fig. 6 shows one example. The traces marked by the arrows were deleted by all three of the human editors, but the algorithm simply muted the noisy portions of the traces and pre- served the rest of the traces. This detailed surgical muting is time consuming when done by hand, but it is preferable to removing the entire trace.

SENSITIVITY ANALYSIS

The response of the S/N ratios of the stacked traces to noisy-trace editing was analysed using the synthetic seismic section that was used to generate Fig. 4. The data were grouped into CMP gathers, the S/N ratios of the stacked traces were calculated using (1) and (2), and the average S/N ratios for the stacked sections were calculated. Then the noisiest trace was eliminated from each CMP gather and the average S/N ratios of the stacked sections were recalculated. The calculations were repeated for different nominal stack folds using the same data. These calculations yield the expected S/N ratio of the stacked trace as a function of the number of traces removed from the gather, assuming that the editing is done with knowledge of the traces’ S/N ratios.

Figure 7a shows the results for the stack without trace equalization; Fig. 7b shows the results for the trace-equalized stack. In both there is an optimum (maximum S/N ratio) point that is controlled by the tradeoff between reducing the stack fold by deleting too many traces and contaminating the stacked trace by deleting too few traces. In Fig. 7, the penalty (i.e. reduction in S/N ratio) for a type 2 error is more severe than the penalty for a type 1 error. When editing noisy traces, the maxim to follow is ‘when in doubt, throw it out ’. This justifies the tendency for the noisy-trace editing algorithm to make more type 1 errors than type 2 errors on the described field data example.

Figure 7 shows that the sensitivity of the S/N ratio of the stack to noisy-trace editing is strongly affected by the fold of the data as well as trace equalization. As the stack fold decreases, the penalty for making a type 1 error increases, so precise noisy-trace editing is most critical on low-fold seismic lines.

Since the S/N ratios of the traces cannot be usefully estimated at the beginning of processing, it is difficult to estimate how much noisy-trace editing will increase the S/N ratios of the stacked traces. However, representative estimates can be made using synthetic data. A synthetic seismic line was generated by adding synthetic noise to synthetic seismograms, and the data were edited using the automatic trace editing algorithm. The average S/N ratio of the stacked traces was calculated with

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and without trace editing. The procedure was repeated for varying amounts of noise, and the results were plotted as a function of the quantity

where Ri is the S/N ratio, in decibels, of the ith trace (before editing or stacking), n is the number of traces, and p is the mean of the S/N ratios. The quantity GI is the fourth root of the fourth moment about the mean of the S/N ratios of the unedited, unstacked traces; it is related to the noisiness of the data. The results of these calculations are shown in Fig. 8.

888 RICHARD G. ANDERSON AND G E O R G E A. McMECHAN

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FIG. 8. (a) Difference between the average signal-to-noise ratio of the stacked traces with and without automatic noisy trace editing for ten synthetic seismic lines with varying levels of noise. (b) The percentage of traces that were edited by the automatic trace editing algorithm for the ten synthetic seismic lines. The x-coordinate is a, defined in (5), and is related to the noisiness of the data. The points marked A are data derived from the synthetic seismic line used to construct Fig. 4. Point B is the theoretical average gain in signal-to-noise ratio due to optimum stacking of field data generated by 16 vibrator sweeps at the same location (Rietsch 1980, Figs 5, 6 and 7a).

The points labelled A in Fig. 8 are data derived from the data used to generate Fig. 3. The point labelled B is the theoretical improvement in S / N ratio from optimum stacking of field data; these data were taken from Rietsch (1980), Figs 5, 6 and 7a. The data at point B are not representative of typical seismic data because these data were taken from 16 vibrator sweeps at the same location. Our experience in seismic data processing is that even the noisiest seismic data require that only

AUTOMATIC NOISY-TRACE EDITING 889

about 5-6% of the traces be deleted. Thus, Fig. 8 probably represents the range of conditions encountered in field data.

Figure 8 suggests that, unless the data are extremely noisy, only a cursory noisy- trace editing is suffcient if the data are trace equalized before multichannel processing. (Despiking and noise-burst editing may still be necessary.) However, when the data are very noisy and trace equalization is omitted, noisy-trace editing can increase the average S/N ratio of the stacked traces by up to 8 dB.

DISCUSSION A major criticism of the algorithms described in this paper is that they are arbitrary and have little physical justification. This criticism can be generalized to any noisy- trace editing procedure: since accurate estimates of the traces’ S / N ratios are not avail- able, noisy-trace editing is essentially an interpretive process. However, there is some physical justification for the proposed procedures. The basic technique is to delete data whose amplitude decay rates are anomalous compared to nearby data. Since the physical processes that control the amplitude decay rate of the signal vary slowly in space, a rapid spatial variation in amplitude decay rate is most likely due to noise.

Tests with synthetic data and theoretical response curves show that trace editing is most critical when the data are low fold and trace equalization is not applied. Hence, human processors should consider the fold of the data and the subsequent amplitude processing when making editing decisions. When the data are high fold, processors should edit ‘ liberally ’ (i.e. err on the side of editing too many traces) since the penalty for making a type 1 error is small for these data. When trace equalization is applied before stacking and multichannel filtering, the S / N ratio of the stacked section is relatively insensitive to both type 1 and type 2 errors, so a cursory noisy-trace edit is suffcient.

One important issue is how the sensitivity of the S / N ratio of the stacked data to noisy-trace editing is affected by other prestack processes. The effect of trace equalization was discussed above; other processes that might affect the trace editing decisions include dip moveout (Hale 1984) and non-linear stacking (Katz, Landrum and Schick 1985; Naess and Bruland 1985; McFadden, Drummond and Kravis 1986; Waltham and Boyce 1986). When dip moveout is applied, a single high-amplitude noisy trace can contaminate adjacent CMPs, whereas during stacking, the noise from a single trace is confined to a single CMP. Therefore, the penalty for making a type 2 error is greater when dip moveout is applied to the data. Non-linear stacking reduces the effect of noisy traces and increases the penalty for making a type 1 error, so more conservative editing is recommended if non-linear stacking is used. However, non-linear stacking is not a substitute for noisy-trace editing. Noisy traces can degrade the performance of all multichannel prestack processes, so they should be eliminated at the beginning of processing.

For an automatic editing algorithm to replace human editors in a production line environment, the cost of the computer time consumed by the algorithm must

890 R I C H A R D G. A N D E R S O N AND GEORGE A . M c M E C H A N

not exceed the cost of plotting and hand editing the data. Although a vectorized median search subroutine was implemented, much of the computer code did not vectorize well and the run time is comparable to the run time of a deconvolution algorithm. Whether the algorithm is cost-effective depends on the particular processing environment in which it is implemented.

Noisy-trace editing is a form of outlier rejection, which has been the subject of many studies in statistics (see Beckman and Cook 1983). An alternative to outlier rejection is to use robust estimation, i.e. a procedure that is minimally affected by the presence of outliers. According to Huber (1981), “ I t is an empirical fact that the best rejection procedures do not quite reach the performance of the best robust procedures. The latter apparently are superior because they can make a smooth transition between full acceptance and full rejection of an observation ”.

In order to replace noisy-trace editing with a robust procedure, CMP stacking and all multichannel prestack processes would have to be modified to use robust estimators such as the median or diversity-stack weighted mean (see Klemperer 1987) instead of the mean trace amplitude. This might be the ideal way to cope with noisy traces, but it would entail a complete overhaul of the seismic system and increased processing costs. Noisy-trace editing is cheaper and easier to monitor and control.

CONCLUSIONS

The relative amplitude decay rate of a trace is diagnostic of its S/N ratio and can be used for making trace editing decisions. The automatic noisy-trace editing algorithm makes some errors, but only at about the same rate as human editors. When the data are high fold and, more importantly, when trace equalization is applied before stack, the S/N ratio of the stacked data is insensitive to errors in trace editing. The penalty (reduction in S / N ratio) for making a type 2 error (failing to delete a noisy trace) is usually greater than the penalty for making a type 1 error (deleting a non- noisy trace). As the fold of the data decreases, the penalty for making a type 1 error increases.

The fundamental limit to the effectiveness of noisy-trace editing is the fact that the S/N ratio of the traces cannot be usefully estimated at the beginning of processing, where noisy-trace editing is applied. A controlled experiment with human trace editors shows considerable disagreement about which traces should be deleted. Thus, noisy-trace editing is inherently an interpretive process. The fold of the data and whether or not trace equalization will be applied should be considered when making editing decisions.

As innovations in artificial intelligence and parallel processing are implemented in seismic processing, more sophisticated and accurate methods for automatic noisy- trace editing will be developed. However, except for detailed prestack amplitude analysis, the point of diminishing returns will quickly be reached. This state has already been achieved in field acquisition, where it is doubtful that any process will ever surpass the simplicity and cost-effectiveness of diversity stacking.

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ACKNOWLEDGEMENTS This research was supported by the National Science Foundation under grant EAR- 8816176, the UT-Dallas Geophysical Consortium, and Cray Research, Inc. We thank Dr J. Wiorkowski for providing a mathematical perspective during several discussions. J. Nation provided systems support for the Convex C 1 computer and D. Stephenson provided secretarial support. We thank J. P. Rickett and Sun Explo- ration and Production for providing the seismic data in Fig. 6. The noise strip used to construct the synthetic seismic lines was recorded during a 1985 field experiment in southern Oklahoma sponsored by Amoco, ARCO, Conoco, Enserch, Gus, Philips, Santa Fe Minerals, Schlumberger-Doll Research, Sohio and Texaco. This paper is Contribution No. 629 from the Program in Geosciences at The University of Texas at Dallas.

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