Geophysical Prospecting 37,875-892, 1989
AUTOMATIC E D I T I N G O F NOISY SEISMIC DATAR I C H A R D G. A N D E R S O N and G E O R G E A. M c M E C H A N
ABSTRACTANDERSON, and MCMECHAN, R.G. G.A. 1989. Automatic editing of noisy seismic data. Geophysical 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-versusoffset 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.
INTRODUCTIONSeismic 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) ratiosPaper 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.
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
(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 normalized 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 significant 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 traces S/N ratio, but on the relation between the traces 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
AUTOMATIC NOISY-TRACE EDITING
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 A L G O R I T H M SA 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 measurements 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.
R I C H A R D 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
DespikingThe first algorithm, which implements the single-channel despiking process, is similar to Evanss (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