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Fractional Fourier Transform in Seismic Data Processing Applications

Author: ChenXu
Tutor: LiuCai；Feng
School: Jilin University
Course: Solid Earth Physics
Keywords: the Fractional Fourier Transform Wigner-Ville distributio Chirp signals frequency Examination
CLC: P631.4
Type: Master's thesis
Year: 2009
Downloads: 173
Quote: 1
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Abstract

Along with high-tech development increasing,request of people or the ignals analysis is more and more complicated,analytic signal objects are ore and more wide.In the past people mainly process and analyze the tationary signals.The main investigative tool is Fourier analysis method.People even also suppose nonstationary signals as linearity,Gaussian feature and stationary objects to process.These methods have more and more localizations.People regard nonlinearity、no-Gaussian feature and nonstationary signals as objects of modern nonstationary signals.In analyzing signals,analysizing and processing the nonstationary signals methods not only are the new technique in the development and applying of information science and technology numerous courses,but also cause extensive research and application interest in physics,mechanics,earth physics,living creature medical science, astronomy, hydrology etc。In practical application,such as correspondence signals,some radar signals,seismic wave,sonar etc,all are nonstationary signals.The traditional Fourier analysis is a full domain transformation in time or frequency domain,it can’t describe time domain and frequency domain characteristics at the same time,namely it can’t describe the relation between different time with different frequency.However,this kind of relation property justly is the most important and key property of the nonstationary signals.Fractional Fourier transform is a kind of improved method of the classic Fourier analysis method.Fractional Fourier transform is found on the rotation of coordinate axis.It can manifest time and frequency property of signals at the same time,and it makes up Fourier analysis that can’t manifest time and frequency property at the same time. V.Namias first put forward Fractional Fourier transform at 1980’.Several years of Recent,Fractional Fourier transform has applying Extensively in differential calculus,quantum mechanics theories and optics deliver,optical system and optical signals processing,filter wave of time varying and deliver along many roads,filter of scanning frequency, artificial nerve network,small wave transform,time-frequency analysis etc.It is emerging vaster applied foreground.In the thesis,the main aim is discussing the frequency separation filter and the application of Fractional Fourier transform.The research objects are chirp signals in the nonstationary signals. chirp signal is a kind of typical nonstationary signals that is the most suitable for making the frequency gathering evaluation,this kind of signals is used extensively in radar,sonar and seismic signals etc exploring systems. The FRFT has a chirp element in the kernel function,so it was especially propitious to deal with Linear Frequency-Modulated signal. This thesis researches the following aspects and obtains some valuable results:Firstly,this thesis introduces the basic theories principle of Fractional Fourier transform, So it shows that Fractional Fourier transform is another improvement method of the classic Fourier analysis through diagram,and Fractional Fourier transform can manifest signals and frequency property at the same time.The main property of Fractional Fourier transform is to provide the synthesize describing of the researched object from time domain to frequency area during whole process.Along with the rank from 0 continue to increase 1,Fractional Fourier transform manifests property of the researched object gradually changing om pure time domain to frequency domain. Fourier transfor- m provides more processing and analyzing data methods to be chosen than Fourier analysis.Secondly,this thesis proves that Fractional Fourier transform is a special linearity signals time-frequency analysis method from time-frequency analysis aspect,it has good time-frequency gathering Property for chirp signals,and it can manifest mutually with Wigner-Ville distribution and Radon-Wigner transform among typical time-frequency analysis methods, Fractional Fourier transform is a good time-frequency analysis tool to process nonstationary signals.Then,it can prove that if z(t)is chirp signals, Wigner-Ville distribution is an inclined line on the(t,ω)plane,while rotating coordinate axis appropriately,this inclined line may become a line parallelism or perpendicularity on the(u ,v)plane of Wigner-Ville distribution in new u axial system,namely Fractional Fourier transform of z(t)is single harmonic wave or shock wave function.Also it can prove that prank Fractional Fourier transform modulus-square of chirp signalsz z(t)is Radon-Wigner transform exactly.Namely Radon-Wigner transform manifests peak at (ω0,m)of chirp signals,then Fractional Fourier transform manifests peak at p = 1 ? 2arctan( m )/π, u =ω0 sin( pπ/ 2)So,it proves that Fractional Fourier transform has good time-frequency gathering property to chirp signals.Therefore,many analytical methods using Radon-Wigner transform to process time varying signals can consider to apply Fractional Fourier transform.In the thesis,there is an example that it gains frequency and inclined rate of chirp signals with parameters not known using Fractional Fourier transform.To calculation quantity,the calculation complication of WVD is 0(N2logN)but the calculation complication of Fractional Fourier transform is 0(NlogN).Generally,scanning example number of Fractional Fourier transform is smaller than adopted example number,moreover,this kind of many components signals with not known parameters analysis method using Fractional Fourier transform need not to consider cross items in twain transform,(But cross items of Wigner-Ville distribution and Radon-Wigner distribution will affect seriously the distinguishing rate of the signals),and it don’t need pole coordinate converting to Right angle coordinate in WVD method,making process simplify consumedly.Therefore making use of Fractional Fourier transform to analyze and process many components chirp signals has more advantages.This thesis gains frequency of chirp signals with not known parameters using Fractional Fourier transform and obtains good result.Finally, this article discussed the use of fractional Fourier transform of the actual seismic data processing.ata processing to some extent to improve the SNR, However, due to the method of calculating parameters and band-pass filter on the selection of weights is not perfect, because it remains to be further improved.

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