The Application Research Of Spectrum Focus In Seismic Data Processing

Finite length discrete Fourier transform and finite length discrete cosine transform are widely used in the spectrum analysis and signal to noise ratio of seismic data processing.However,the relationship between the spectrum of the two transformations and the true spectrum of the seismic data,the relationship between the filter data of the two transformation methods and the same frequency components of seismic data are little research.This paper discusses the content of two aspects.One is the relationship between the spectrum of Finite length discrete Fourier transform spectrum and the true seismic spectrum,and the relationship between the spectrum of finite cosine transform spectrum and the true seismic spectrum.The other is the relationship between the spectrum's the variation of the low frequency resonance noise and its wave characteristics.The first aspect is to discuss and verify the relationship between the finite length Fourier transform spectrum and the true seismic spectrum,and the relationship between the finite long cosine transform spectrum and the true seismic spectrum.From theoretical derivation,model verification and application of actual data,it is concluded that the spectrum of the two transformations is not the true spectrum of seismic spectrum.And the filter data of the two transformations is not the same frequency components of seismic data.The mixed wave method can improve the signal to noise ratio of the seismic data and reduce the effect of the distortion caused by the two transform methods.It is feasible method which tested by the theoretical data and the seismic data.The second aspect is content based on the wave characteristics of low frequency resonance noise.By using formula deduction and demonstration,put forward a fixed length window to sliding scan the low frequency resonance noise to estimate amplitude attribute and spectrum attribute of low frequency resonance noise.Though the mathematical deduction conclude the relationship between the energy of the different window and the first sample of these window,and the relationship between monochromatic wave energy of the spectrum of the different window and the first sample of these window.Through the verification of theoretical model and seismic data,the law of mathematical deduction is proved.The change law of the monochromatic wave by sliding window scan for the the monochromatic wave of spectrum of low frequency resonance noise,and using the change of single frequency to reflects the variation of low frequency resonance noise,this process is the change rule of focusing on a monochromatic wave changes in the resonant frequency interference,so the the method is called spectrum focusing method.