Dissertation > Astronomy,Earth Sciences > Geophysics > Earth ( rock circles ) physics ( geophysics ) > Seismology > Seismometry > The interpretation and processing of seismic observations

Reduction Methods of Seism Data Random Noise Based on Higher-Order Statistics

Author ZhangWenXue
Tutor WangZhongRen
School Jilin University
Course Applied Mathematics
Keywords higher-order statistics bispectra Yule—Walker of equation dual partition the Finite Volume Method
CLC P315.63
Type Master's thesis
Year 2007
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Random noise is unavoidable in seismic exploration.In the random noise re-duction,the method of prognose filter in space-frequency was initiated by Luis Canales in 1984. The method firstly commits a Fourier transform to each of the seism data in one of the time windouw. Swing energy of signal is predictalbe for every frequency. It is the linear combination of border upon seism The distribution of noise energy is random. So, in the light of least mean square error,a prognose error filter is determined, the output is the estimate of the unpredictalbe portion from each of primal seism. The output of signals can be obtained by detracting the prediction error from each of primal seism, again commits a inverse Fourier transform to each of primal seism,it find prognose output of signals.M.K.Chase extend f-x space diviable filter to 3-Din 1992 ,it come true diviable filter which 3-D form of 3-D seismic data.ZhongRen.Wang uinged 2-D AR model to reducte random noise in t-x,y space.The most methods mentioned above based on gaussian white noise are limited, because, A great many noise generally is gaussian colored noise or non-gaussian colored noise.The main mathematic tool in treating non-minimum phase signals,nonlinear signals and non-Ganssian signals is higher-order cumulants or higher-order spectra. During 1960s, researchers in mathematics, statistics, hydrokinetics, signal treating and other fields began to research higher-order cumulants. But it is fully developing after 1980s, After a few yeas research, higher-order cumulants is obtained lots of application in radar, sonar, communication, oceanography, astronomy, electromag-netism, plasma,physical geography, biomedicine and other fielde. Higher-order spectra have been given lots of attention lately due to their ability to preserve information of non-Gaussian stationary random processes. Higher-order cumulants have more advantage than correlation function. Hence,all the signals treated by correlation without satisfied results can be treated by higher-order cumnlants.Swami A and Mendel J M are firstly lodge modified Yule-Walker equations[16] based on higher-order statistics(HOS),three-order comulant is zero for gaussian white noise.so it able to reduce the noise.This article research reduce random noise in data of seism based on higher-order statistics,at first using conventional time sequence methods reduce random noise, withal the article advance news Yule-Walker equation based on three-order moment,using the equation to foundation AR model to reduce random noise, lastly the article reduce random noise based on bispectra Yule-Walker equations.above arithmetic all is implemented in MATLAB6.5.This article first commits a fourier transform to every seism data with random noise. withal Foundation AR models for every row, withal, Make certain order and quotiety of AR models,comeback aboriginal signals by the AR models.so inverse fourier transform to every seism data,gained reduced signals.The article time after time experimentation order of AR model for conventional time sequence methods and mend Yule-Walker equation methods,attain optimal effect.It explain the two method which agility and operable.when there is no input of unconventional wave, this article gained the following conclusionslf noise is gaussian white noise,all methods able reduce random noise,conventional time sequence methods is good than modified Yule-Walker equation and mend Yule-Walker equation methods ;If noise is gaussian-colored noise,modified Yule-Walker equation is had best,conventional time sequence methods is flooey;If noise is non-gaussian-colored noise,conventional time sequence methods unable reduce random noise,modified Yule-Walker equation is had best,but time is long.

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