Study Of Time-frequency Analysis With Matching Pursuit Algorithm And Its Application In Seismic Interpretation

This paper introduces the principle and the flow of matching pursuit in detail. I comparethe two methods of time frequency distribution: Wigner distrbution and the improvedanalytical expression of Liu’s, and derive the Wigner distrbution of Ricker wavelet. The peakfrequency of matching wavelet is based on instantaneous frequency and is searched within asubdictionary. Compared with the way of searching a better peak frequency around a bigfrequency range one by one, my method is much better for that it has a better precised peakfrequency, converges faster and has a better efficiency. Next this paper introduces theprinciple of Short-time Fourier Transform, Wavelet Transform and S Transform. I built asimple test model to test these methods and lead to the heir advantages and disadvantages.This paper introduces the detail and the disadvantages of RGB display technique, FromRGB displays of a synthetic example and a real seismic data example, we can see it exploitthe information extremely. Since channel may have different spectral response among itsdifferent thickness parts, RGB display technique help to map the channel clearly and see thechange of the thickness of the channel, just as show in this paper the light color correspondingto the thick part of the channel and the heavy color corresponding to the thin part of thechannel. It’s clearly to distinguish low frequency shadow below the gas reservoir.Based on Time-frequency analysis using matching pursuit technique which has a muchbetter resolution,I present a new method to predict the thickness of thin bed using evencomponent.First, it proves that the even component and the odd component of seismic signalconvolution of reflection coefficients and zero phase wavelet is equivalent to the convolutionof zero phase wavelet and the corresponding even component and the odd component of thereflection coefficients. After even component attained, we find that the one-to-onecorrespondence of thin bed thickness and peak frequency in the theoretical formulation, so it’sconvenient to build a moldboard to predict the thickness of thin bed. I build a test model toverify the feasibility of the method and summarize the shortcomings of the method.