Research On Identification And Elimination Method Of MonoFrequency Interference

During seismic data acquisition, there would be a strong monofrequency interference ( MFI ) around 50Hz in seismic records if a high-tension line crosses over the seismic lines. Traditional MFI suppression methods include the frequency domain suppression and the notched-frequency filtering. The former only suppresses on the amplitude spectrum of seismic data, nor on the phase spectrum. Therefore, the suppression amount is not easily controlled. If the suppression amount is too small, the strong residual MFI exists in seismic records. On the contrary, the effective signal could be injured if the suppression amount is too large. Additionally, since the interference frequency is not exactly at 50 Hz, the choice of computed window length is so difficult that the method itself is hard to implement effectively. Similarly, the notched-frequency filtering method could injure the frequency components of effective signals around the monofrequency. In order to decrease the injury, this kind of methods usually narrows the suppression frequency bands. Thus the corresponding time domain operator is so long that the computation time is also long. It results in the low computation efficiency and the severe boundary effect. Consider that the length of time domain operator would not be unlimited, the suppressed band must have a limited width. Hence, the frequency components of effective signals must be injured.In the seismic records, the amplitude, frequency and phase can be considered as basically invariable from the shallow to the deeper layer. Thus a MFI would be approximated by a cosine function or a combination of a cosine with a sine function in the time domain. Following that, the MFI is subtracted from the seismic record to eliminate the interference. For the cosine function approximation, there are three parameters such as amplitude, frequency and time-delay. The MFI has a linear relation with the amplitude, so it is directly computed according to a formula. The computational formula of the cosine function amplitude is first derived, and the frequency and time-delay estimation algorithms based on this formula are also proposed for the first time. At the same time, the MFI has nonlinear relations with the frequency and the time-delay, so these two parameters are estimated by a variety of algorithms. These estimation methods include scanning algorithm, steepest descent algorithm, and adaptive algorithm. For the cosine function adaptive algorithm, the computational formula of the time-delay is first derived, and the time-delay parameter is also computed according to it. Furthermore, we also propose and apply the identification and elimination methods of the cosine function MFI based on these frequency and time-delay estimation algorithms.In the sine-cosine function approximation, there are also three parameters: frequency, sine amplitude, and cosine amplitude. The sine and cosine amplitudes are directly computed according to their formulas for these two parameters are linearly proportional to the MFI. We first derive the computational formulas of the sine-cosine function amplitudes, and we also propose the frequency estimation algorithms for the first time, as well as the FMI identification and elimination methods based on these amplitude formulas. The frequency is estimated by a variety of algorithms. These methods include scanning algorithm, steepest descent algorithm, adaptive algorithm, and linear frequency-modulation spectrum algorithm ( LFMS ). Additionally, the LFMS algorithm is first proposed, too, as well as first applied to the frequency estimation algorithm and the method of identifying and eliminating the MFI. Furthermore, the identification and elimination methods of the sine-cosine function MFI based on these frequency estimations are first proposed, as well as first applied.We also propose two kinds of methods on identification and elimination of the MFI based on an autocorrelation and an autocorrelation-convolution algorithm. For the autocorrelation algorithm, the cosine function of a MFI is directly estimated by the autocorrelation operation of the seismic data. After that, the MFI is eliminated by the cosine function adaptive subtraction algorithm. Similarly, in the autocorrelation-convolution algorithm, by the autocorrelation and convolution operations of the seismic data, the sine and cosine functions of a MFI are directly estimated, and the MFI is eliminated by the sine-cosine function adaptive subtraction algorithm. However in these two algorithms, it is not necessary to estimate the three parameters of the MFI.A detailed and profound analysis is first performed about the FMI estimation error induced by three parameter estimation errors. The error of the amplitude estimation has a huge influence on the MFI. Even though the frequency and phase estimations are exact, it can bring a very strongly residual MFI in the seismic records. Additionally, the errors of the frequency and phase estimations can not only bring ones of the amplitude and MFI computations, but they can also make the MFI change in the time direction. In order to estimate the amplitude and MFI exactly and precisely, the accuracy of the frequency should not be less than 0.01Hz, and one of the time-delay should be 0.1 for the cosine function approximation. The synthetic data examples illustrate that the errors of the parameter estimations would truly affect the identification and elimination of the MFI.During the real seismic processing, the data analysis must be performed to confirm the initial frequency of the MFI. Using the method on an automatic identification of the MFI data trace, the operation efficiency eliminating the MFI could be greatly improved. At the same time, the estimated precision of three parameters and the MFI can be also enhanced by estimating the MFI in the shallow first-arrival or deep time zone. For multiple MFIs, the frequencies ( and time-delays ) are estimated one by one, and the amplitudes are computed by a system strategy.In the sine-cosine function approximation, the MFI only has a nonlinear relation with the frequency parameter. Therefore, the computational efficiency of this method is higher than that of the cosine function approximation within the same kinds of estimation methods. The distinguished merit of these methods is that the MFI can be effectively eliminated in the time domain. Meanwhile, the useful signals around the interference have not been injured. Consequently, the signal-to-noise ratio has been improved in the vicinity of monofrequency component. The synthetic and real data examples illustrate that the proposed methods are feasible and effective.The real data processing examples also illustrate that the computational time of the linear frequency-modulation spectrum method is shortest, and the operational efficiency is highest. So it adapts the application of the great capacity seismic data, and is the most effective method of eliminating the MFI.