| In seismology exploration, it is very important that seismic wavelets are estimated accurately. This is fundamental work for seismic traces deconvolution, migration, feature extraction, and geophysical interpretation. Higher order statistics (HOS), which has been applied in seismic wavelets estimating and processing, generalizes the seismic data processing used to be the 2nd order to higher order. For this, it not only may get rid of hypothesis that seismic wavelets are minimum-phase, recover the real wavelets from the HOS, improve the resolution of the seismic data; but can also eliminate the noise interference and enhance the effective wave in the wavelets processing, according to the powerful anti-color-noise ability of the HOS, which is also over others.In seismic signal processing, diminution of noise and improving of resolution is very important work. For the better purpose of seismic wavelets estimation, enhancement of signal-to-noise ratio (SNR) and elimination of coherent interference and random noise is absolutely necessary before seismic wavelets estimation. Therefore the main research of this paper will be focused on the surface wave and random noise diminution, effective wave events extraction and seismic wavelets estimation.In this paper, the HOS (4th order cumulants, bispectrum and trispectrum), singular value decomposition (SVD), wavelet transform and local SVD are adopted, the synthetic single trace seismogram, synthetic single shot seismic records and field single shot seismic records are analyzed. The main conclusions and innovations as follows:(1) Let the Ricker wavelet be the wavelet of seismic convolutional model (namely, it should be the parameter of a MA model), work out the autocorrelation, 3rd order cumulants, 4th order cumulants of the seismogram and also corresponding power spectrum, bispectrum and trispectrum. Construct the 2-D and 3-D Parzen window; improve the frequency resolution of bispectrum and trispectrum estimation. Compare the traditional power spectrum and power spectrum reconstructed by the bispectrum and trispectrum; reveal the latter has more suppression effect to color noise and is better than the former. While the signal has a symmetric distribution, the power spectrum reconstructed by the bispectrum proves failure, but the power spectrum reconstructed by the trispectrum is still better than the traditional one.(2) When the signal is random, the high order spectrum reconstruction will recover the amplitude and phase of system transfer function. As to the seismic convolutional model, it will recover the seismic wavelets. In this paper, using the fact that bispectrum contains amplitude and phase information of seismic wavelets and its super powerful anti-noise ability, adopt seismic wavelets estimation method based on amplitude and phase reconstruction with bispectrum; recover the wavelets totally. Because of BMU algorithm being unsteady with different initial value, improve the BMU algorithm; propose a new initial value determination method, which has been proved more efficient in the improvement of algorithm steadiness. The cases of synthetic seismic records with zero-phase Ricker wavelets and mixed-phases wavelets are simulated to prove the improved BMU algorithm has more steadiness than the former one by comparing the wavelets estimation results and spectrum errors of both.(3) According to the fact that high order cumulants (HOC) retain the phase information of signals and HOC of Gaussian color noise is always equal to zero, provide a new method of wavelet reconstruction based on 4th order cumulants of non-Gaussian seismic signals. Regard the seismic wavelets w( n ) as the parameters of a MA model. Considering that w( 1) is always very small, assume the first parameter value of MA is an arbitrary nonzero constant, improve the 4th order cumulants matrix equations, soften the assumption conditions of w( 1) to make it more applicable to seismic records processing. The feasibility of this method is demonstrated by the simulation of wavelet estimation for synthetic and field seismic records. Therefore, nonminimum-phase wavelets discrimination has more practical value.(4) Theoretically, as signal obeys a symmetric distribution, its 3rd order cumulants and bispectrum is zero, but the 4th order cumulants and trispectrum is not. The real reflectivity sequence almost obeys a symmetric non-Gaussian distribution. For estimating wavelets from a symmetrically distributed signal, introduce the least square method (LS) and discrete Fourier transform (DFT) for trispectral amplitude and phase reconstruction on the basis of LS and DFT for bispectral amplitude and phase reconstruction.(5) Aiming at those synthetic and field seismic records where the power of the surface waves is obviously ampler than the effective ones, first of all, reconstruct every surface wave events by SVD. While eliminating surface waves from the seismic records, according to the dominant frequencies of the effective waves are different from the interference ones, if there are no effective signals existing in some frequency range, set the wavelet coefficients corresponding to the frequency range to zero, and low-frequency and high-frequency random noise will be eliminated. Then piecewise linearize those seismic records, use the local SVD for suppressing partial random noise, the effective wave events are ultimately extracted. The synthetic and field single shot seismic records processing adequately indicate that the method combining SVD and wavelet transform is very effective in suppressing the surface waves and random noise in seismic records.Comparing the high order spectrum reconstructing power spectrum of the seismic records in each step mentioned above, indicate the surface waves and random noise are well suppressed. The dominant frequencies of the seismic records are centralizing to the neighborhood of the effective waves. For synthetic seismic records, respectively intercept two subsets from seismic records nearby the reflection wave events (in original records, one subset contains strong surface waves, the other mainly contains random noise), use the amplitude and phase reconstruction method with bispectrum to estimate the wavelets of records in each processing step, comparing the waveforms and spectrum, demonstrate the validity of extracting reflection wave events from noise with the methods mentioned above.(6) The key entrance of surface wave events retrieving is locating their directions. According to the fact that the surface-wave time-distance curves are almost beeline, find out the relationship between slopes of surface wave events and the singular value of SVD. Put forward that at which the first singular value or difference of the first and the second singular value or difference of the first two and the three singular value gets the maximum, the optimal slopes will be find out. According to the optimal slopes, rotate the surface wave events to level, these events will be reconstructed with SVD. From a large mount of simulations, in situation of lots of surface wave existence, their speed approaching each other, their dominant frequency increasing and the SNR decreasing will influence effect of reconstructing surface wave events by SVD.(7) Enhancing the gain twice, the deep information of field seismic records is revealed. Considering the concrete situations of different subsets of the real seismic records, put forward measures when using SVD to rebuild the surface wave events, for instance, reduce the surface wave event slope search range appropriately, extract the main surface wave event preferentially, use the first or the first two singular value to rebuild the surface wave events, intercept the records subsets reasonably, expand the application range of optimal slope appropriately while find out an optimal slope in a smaller range. These measures will improve the effect of surface wave events extraction, and then suppress those strong surface waves in field seismic records effectively.
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