Study On The Method Of Frequency Spectrum Imaging In Fractional Domain For Seismic Signal And Its Application

Fractional Fourier transform (FrFT) can be seen as a rotation in the time-frequencyplane. It can break through the restriction of the time-frequency-bandwidth product.This thesis extends the normal frequency spectrum image into the fractional frequencyspectrum image which can describe the time-frequency distribution of seismic signalmore accurately. Seismic signal is a kind of non-stationary signal. When the seismicsignal spreads in the oil and gas layer, the frequency characteristic will be different fromother mediums. So we can use the frequency spectrum technology to find the oil andgas layer. In this thesis, we combine the concept of FrFT with the normaltime-frequency technology to propose the fractional time frequency analysis (FractionalTime-Frequency Analysis, FrTFA) and adaptive optimal Gabor transform in fractionaldomain (Adaptive Optimal Gabor Transform in Fractional Domain, AOGTFD). Also,we research the fast algorithm of FrTFR and the extraction of seismic signal’s frequencyproperties. The related work is as follows,（1） The thesis summarized the definitions、 properties and numericalcomputations，then compare two kind of numerical computations and simulate thealgorithms.（2）The thesis combined the traditional time frequency analysis technology withFrFT, and propose the fractional time frequency analysis.（3）The thesis proposed the fractional Cohen Distribution(FrCD) for the firsttime，and research how to reduce the crossterms in fractional domain,then operator thesimulation of FrCD.（4）The thesis researched the relation between FrFT and Gabor transform,andpropose AOGTFD for the first time, then simulate the algorithm.（5）The thesis proposed the optimum proposal of FrTFA for the first time, whichwill deduce the complexity of FrTFA dramatically.（6）We research the extraction of seismic signal’s frequency properties includingcentered frequency property、root mean square frequency property、single frequencyproperty and energy attenuation gradient.