Seismic data decomposition using sparse dictionary

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University of Alabama Libraries

Spectrum decomposition methods map 1D seismic trace into 2D plane of time and frequency. The decomposed frequency components of seismic trace are widely used to quantitatively predict the thickness of thin layers. The current popular time-spectrum analysis methods include the Short Time Fourier transform (STFT), Continuous Wavelet Transform (CWT), S-transform (ST), and Matching Pursuit (MP), among which MP is the most tolerant of window/scalar effect. However, the traditional wavelet library is a set of user defined wavelet which does not consider the seismic event interfering of thin layer. As a result, it is very difficult for MP based algorithms to obtain an accurate wavelet in each decomposition iteration for thin layer reservoirs. The improved MP (IMP) algorithm assumes that the seismic reflection response of thin layers can be simulated by the convolution between wavelet and a thin-layer cake model. The parameters of wavelet library of MP algorithm include wavelet type, the dominant frequency of wavelet, and the phase of the wavelet. The parameters of my new “wavelet” library include wavelet type, the dominant frequency of wavelet, the phase of the wavelet, and the time thickness of thin layer model. I applied IMP to three examples to demonstrate the effectiveness of IMP. The first example is a synthetic seismic trace generated using a layer-cake model. The second example is a synthetic seismic trace computed using well logs. The third example is the real seismic data. The first synthetic example indicates that the reflectivity set obtained using IMP accurately points out the interface of thin layers. The second synthetic example indicates that the impedance computed using reflectivity of IMP has higher correlation coefficient when compared to that of MP. The real seismic data example indicates that reflectivity set obtained using IMP can identify the top and base of thin layers whose two-way time thickness are great than T/5, where T is the period corresponding to the dominant frequency of seismic data.

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