Sinusoidal noise often contaminates seismic data. When this noise is large compared to seismic signals, it adversely affects prestack seismic processing and subsequent interpretation. We develop a digital least‐squares filtering algorithm for canceling stationary sinusoidal noise in seismic data. The method effectively cancels sinusoidal noise when the noise is stationary, which is typical for recordings of a few seconds in length. This procedure differs from the usual notch‐filtering techniques because the sinusoidal noise is canceled without notching the signal spectrum. Since the method requires that the line frequency be accurately known, the algorithm can automatically search the trace spectrum to find the exact sinusoidal frequency value needed for filter design. The algorithm is highly automated and requires no input parameters when the interference comes from power lines or generators. We use model and field data to quantify the algorithm’s performance.
The use of normal modes to represent the propagation of elastic waves at large horizontal offset is well known. By addition of the relevant leaky modes, the mode theory is shown to be useful for representation of the seismograms at shorter range. A theoretical model consisting of a 2‐cm brass layer over a steel half‐space is considered. Dispersion curves and excitation functions are computed for the first four normal modes and the first three PL modes. Attenuation as a function of frequency also is computed for the PL modes. A suite of seismograms is computed for the distance range 50–70 cm, showing each mode individually and their sum (the total seismogram). It is found that, for the distances used, the individual modes do not approximate transients with a definite “arrival” time. Only their sum is required to exhibit this physical behavior. In addition, at short distances, the dispersion of a single mode is not visually obvious although the dispersion curve may be recovered by use of Fourier transform methods. Determination of the dispersion curves from the total seismogram is more difficult and requires some seperation of the modes, as they overlap in frequency and velocity. This work shows the preponderance of the leaky modes in the early part of the seismogram and indicates their importance in the later part of the seismogram for short horizontal offset.
Primary reflections in seismic records are often obscured by coherent noise making processing and interpretation difficult. Trapped water modes, surface waves, scattered waves, air waves, and tube waves to name a few, must be removed early in the processing sequence to optimize subsequent processing and imaging. We have developed a noise canceling algorithm that effectively removes many of the commonly encountered noise trains in seismic data. All currently available techniques for coherent noise attenuation suffer from limitations that introduce unacceptable signal distortions and artifacts. Also, most of those techniques impose the dual stringent requirements of equal and fine spatial sampling in the field acquisition of seismic data. Our technique takes advantage of characteristics usually found in coherent noise such as being localized in time, highly aliased, nondispersive (or only mildly so), and exhibit a variety of moveout patterns across the seismic records. When coherent noise is localized in time, a window much like a surgical mute is drawn around the noise. The algorithm derives an estimate of the noise in the window, automatically correcting for amplitude and phase differences, and adaptively subtracts this noise from the window of data. This signal estimate is then placed back in the record. In a model and a land data example, the algorithm removes noise more effectively with less signal distortion than does f-k filtering or velocity notch filtering. Downgoing energy in a vertical seismic profile (VSP) with irregular receiver spacing is also removed.
A general least‐squares, time‐domain filter design methodology has been developed that is easy to use for a variety of seismic filtering applications. The 1-D finite‐impulse response frequency filter can efficiently provide the noise attenuation and selectivity needed in modern data processing. Flexibility of design allows a choice of all basic types of single‐channel filters commonly used in processing. These include low‐pass, high‐pass, band‐pass, band‐reject, and notch filters. In addition, multiple bands may be passed or rejected using a single operator design without increasing the length of the filter. The ability to reject multiple noise bands with one filter is convenient and also reduces data processing costs. The filter can be viewed as a minimum‐phase Wiener‐Levinson predictive deconvolution filter designed to reject specified frequency bands. The filter is designed from an exact mathematical description of the specified stop bands that provide an explicit expression for the required autocorrelation lags in the normal equations. The filter’s desired frequency response (transition zone width and rejection level) is simply related to two input parameters—operator length and white noise level.
Estimation and removal of near‐surface effects in common‐depth‐point (CDP) data have been frequently discussed in the literature. A common problem with many automated statics techniques is their inability to extract statics whose spatial wavelengths are longer than a spread length. This, of course, can result in false structural anomalies. This paper describes an approach which extends the useful static estimation bandwidth to wavelengths of the order of 4 to 8 spread lengths. Traveltimes from one or more reflecting horizons are picked at each depth point and CDP offset. The time profiles are then decomposed into source static, receiver static, structure, and residual normal moveout (RNMO) estimates, and the process is iterated if required. A suite of analytical displays provides the user with direct QC measures of the traveltime picking performance. The technique will be demonstrated on model data to illustrate the theoretical performance over slowly changing near‐surface weathering anomalies. In addition, field examples will be shown from the Mackenzie Delta where permafrost variability in the near‐surface can create large traveltime anomalies.
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