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| Seismic surface wave interpolation method based on optimistic wavelet basis |
| Zhi-Nong WANG1, Cheng-Yu SUN1, Dun-Shi WU2 |
1. School of Geosciences,China University of Petroleum,Qingdao 266580,China
2. PetroChina Research Institute of Petroleum Exploration and Development-Northwest,Lanzhou 730020,China |
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Abstract The surface wave in the real seismic data can be used to invert near surface shear velocity.If the trace interval is large and the spatial sampling rate is not enough,there will be spatial aliasing.This can not only decrease the signal-to-noise ratio of frequency-velocity spectra but also affect the accuracy of dispersion curves and the result of inversion.So it is necessary to do the interpolation of surface wave.This paper presents a seismic surface wave interpolation method based on optimistic wavelet basis.The optimistic wavelet basis bior6.8 which is suitable for interpolation processing can be selected among many wavelet bases commonly used in seismic data processing through the theoretical analysis and the comparison of experimental error.The use of optimistic wavelet basis bior6.8 will increase the accuracy of interpolation.Because the events of surface wave are linear and the slopes of them are larger,this paper uses the linear normal moveout to level the events of surface wave firstly,then carries out the wavelet transform interpolation,and finally uses the inverse linear normal moveout to recover the surface wave.The effectiveness of the proposed method is verified by the interpolation result of theoretical model and real seismic data.After the interpolation,the waveform of the interpolated surface wave records is well recovered. It can improve the signal-to-noise ratio of frequency-velocity spectra,and solve the aliasing problem effectively caused by the undersampling of the surface wave data.
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Received: 04 June 2018
Published: 20 February 2019
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Corresponding Authors:
Cheng-Yu SUN
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Sketch of second level wavelet transform
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Flow chart of surface wave interpolation
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Interpolation result using optimistic wavelet basis bior6.8
a—original record;b—track record;c—interpolation record;d—interpolation error
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Interpolation error comparison
a—db wavelet basis error;b—sym wavelet basis error;c—bior wavelet basis error
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Wavelet basis bior6.8
a—decomposition of scaling function;b—decomposition of wavelet function;c—reconstruction of scaling function;d—reconstruction of wavelet function
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Filters corresponding to wavelet basis bior6.8
a—decomposition low pass filter;b—decomposition high pass filter;c—reconstructing low pass filter;d—reconstructing high pass filter
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Seismic records and dispersive images before and after extracting traces
a—original record;b—frequency wavenumber spectrum corresponding to the original record;c—track record;d—frequency wavenumber spectrum corresponding to the track record
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Four sub-bands used in 2D wavelet inverse transformation
a—low frequency approximation part;b—high frequency estimation of horizontal direction;c—high frequency estimation of vertical direction;d—high frequency estimation of diagonal direction
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Interpolation result and its FK spectrum
a—interpolation results;b—frequency wavenumber spectrum
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The 61st trace waveform comparison between original record and interpolation result
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Dispersion images comparison
a—frequency velocity spectrum of original recording;b—frequency velocity spectrum of track recording;c—frequency velocity spectrum of interpolation results
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Seismic records before and after interpolation
a—original record;b—interpolation results
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Dispersion images comparison
a—frequency velocity spectrum of original recording;b—frequency velocity spectrum of interpolation results
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