Deconvolution Based On Sparse Transform And High Precision Wavelet Extraction Methods

With the increasingly exploration of seismic, the simple structure of reservoirexploration has finished. It is difficult to find complex geological structure, smallerand buried deep hydrocarbon reservoirs based on the conventional the resolution ofseismic data. We need to improve the resolution of seismic data, and through thehigh resolution seismic data can effective to horizon calibration, identify smallstructure or faults. So we studied the deconvolution methods to improve the seismicvertical resolution and for the wavelet extraction restrictive conditions we studied thewavelet extraction methods based on higher order statistics.Firstly, the paper summarized the current research situation of deconvolutionmethods and wavelet extraction methods at home and abroad, and then analyzeddisadvantages of these methods. Deconvolution as one of the main methods toimprove seismic vertical resolution, mainly traditional methods are least squaredeconvolution(LSD),spike deconvolution(SD),predictive deconvolution（PD）,sparsespike Deconvolution(SSD) and so on, these methods must under some assumptions,and they were seriously interfered by noise, when enhanced the interesting signal italso made noise increased. Conventional deconvolution methods processed seismicdata though single trace cycle; it destroyed the continuity of seismic profile. Forthese, by analysis of the characteristics of multiscale transformation, we proposeduse Curvelet transform to describe seismic reflected signals, the method didn’t needto assume reflected signals was sparse. We expressed the reflected signals sparsecharacteristic by sparse Curvelet coefficients. And deconvolution based onmulti-dimensional space transform instead of the traditional single channeldeconvolution by multi-dimensional deconvolution, it maintained the continuity ofseismic signal in theoretically.On this basis, we make the deconvolution problem into al1norm optimizationproblem, and introduced the method to solve the problem; finally we chose the soft threshold iteration (IST) algorithm to calculate the problem. The paper usedtheoretical data to analyze the limit resolution of sparse deconvolution based onCurvelet transform, it showed that the method under weaker noise interference canaccurately calculate more than8ms stratum thickness, and under seriously interferedby noise situation the method can also obtain satisfactory result. For the stratumthickness less than8ms, the calculated stratum thickness was slightly less than thereal thickness of strata, but the result was better than seismic apparent thickness. Inaddition, we also used theoretical data to analyze the ability of maintain seismicprofile continuity and the sensitivity of the noise for sparse deconvolution based onCurvelet transform method, and compared with traditional sparse spikedeconvolution method, the result showed that the deconvolution method based onCurvelet transform can effectively maintain the continuity of seismic profile, when itimproved the resolution it suppressed the noise at the same time. Finally, we verifiedthe deconvolution method based on Curvelet transform’s effectiveness based onpractical seismic data, the results showed that the method had a good applicationvalue.For the problem of how to choose soft threshold iteration (IST) algorithm’sparameters, we made the theoretical data test, and gave a reference principle forparameters choose. It was that when chose the iteration number, if iteration numberwas small, the resolution of profile would be lower, increase the iteration times canbe improved, but it would increase the calculation time, when iteration numberreached a certain value, the profile of the resolution won’t be improved; when chosethe threshold value, we can choose the threshold value according to noise intensityof seismic data, if the noise was strong then set keep less Curvelet coefficients, if thenoise was weaker then set keep more Curvelet coefficients.The purpose of seismic deconvolution was to eliminate seismic waveletinfluence, if we can accurately extract wavelet, then we can better eliminate theinfluence of wavelet and improve the seismic resolution. The traditional way wasbased on assuming seismic wavelet was minimum phase and the reflectioncoefficient was white noise sequence, then we can use seismic trace autocorrelationto instead wavelet autocorrelation to get deconvolution operator, but it was notaccurate, or separated the wavelet and reflection coefficient in cepstrum domain.With the higher order statistics widely application in seismic data processing, the seismic wavelet extract method based on higher order statistics was also greatlydeveloped. We can use higher order statistics to extract wavelet in time domain orfrequency domain, this paper mainly studied the method to extract wavelet based onhigher order statistic’s cepstrum, focusing on the complex cepstrum of bispectrumand complex cepstrum of trispectra. Firstly, we decomposition the wavelet tominimum phase component and maximum phase component, then using therelationship between higher order cumlant of seismic signal and wavelet to make asystem of equations, calculated the wavelet minimum phase and the maximum phasecomponent, and then can obtain the seismic wavelet. The method didn’t need toassume wavelet was minimum phase; it can extract any phase wavelet, so as to shakeoff the wavelet minimum phase constraint. The paper also discussed the influence ofgaussian noise for the complex cepstrum of bispectrum and complex cepstrum oftrispectra, and the theoretical experiments showed that because of the gaussian noisehigher order cumulant is zero, this method can inhibit any intensity the gaussiannoise.Considered the wavelet was attenuation in propagating processing in a certaintime, wavelet function was different, accordingly, we need to extract wavelet bysubsection seismic data. This will require the wavelet extraction methods under dataquantity were small can also extract wavelet accurately. We proposed a smoothwindow function to improve the cumulant estimate, and then discussed the influenceof data length. Theoretical experiments showed that when data was small it can alsoaccurately extract wavelet by smooth window function.Finally, we dealt with the real data based on the two methods, and verified theeffectiveness of the two methods.