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《Chinese Journal of Geophysics》 2015-02
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Optimized finite-difference operators based on Chebyshev auto-convolution combined window function

WANG Zhi-Yang;LIU Hong;TANG Xiang-De;WANG Yang;Key Laboratory of Petroleum Resources Research,Institute of Geology and Geophysics, Chinese Academy of Sciences;University of Chinese Academy of Sciences;  
The finite-difference method has been widely utilized in seismic wave numerical modeling,seismic imaging and full waveform inversion.The accuracy of finite-difference numerical solutions directly affects results of seismic imaging and inversion.Using an autoconvolution combined window function to truncate spatial convolutional counterpart of the pseudospectral method,optimized explicit finite-difference operators are derived.The truncated window function method is used to get optimized finite-difference operators.Firstly,we analyze the influence on the accuracy of finite-difference operators caused by the properties of main lobe and side lobe in the amplitude response of truncated window functions.Secondly,based on the methods of auto-convolution and weighted combination,a window function which has narrower main lobe and larger attenuation of side lobe is designed,correspondingly bringing higher accuracy of finite-difference approximation.Finally,we use the window function to get optimized finite-difference operators.From the analysis of window functions,the factors that affect the accuracy of finitedifference approximation can be summarized in two aspects:(1)The width of main lobe of window functions.(2)The attenuation of side lobe of window functions.The window functions which have narrower main lobe and larger attenuation of side lobe can yield higher accuracy of finite-difference approximation.The Chebyshev window function has appropriate width of main lobe and attenuation of side lobe to get better stability of accuracy error on the premise of maintaining the appropriate wave number coverage range.Furthermore,the auto-convolution method will increase the attenuation of side lobe,however,widen the main lobe.Weighted combination can remedy the defect,choose different weight coefficients to reduce the width of main lobe.Combining the two methods,a specific window function named Chebyshev autoconvolution combined window is designed.Compared with the accuracy curves of approximation between the finite-difference operators truncated by Chebyshev auto-convolution combined window and the conventional operators,the former lead to great accuracy in a bigger frequency region.Tests on a homogeneous model and the Marmousi model show that the dispersion caused by the operators based on the Chebyshev auto-convolution combined window is quite weak under the same order of the conventional operators.Further comparison with the finite-difference operators truncated by improved binomial window,our operators still have a bigger frequency coverage range and smaller fluctuation of accuracy error.The finite-different operators based on the Chebyshev auto-convolution combined window have higher accuracy than that of the conventional operators and operators based on the improved binomial window.Our optimized eighth-order and twelfth-order operators can respectively reach,even exceed the accuracy of the conventional twelfth-order and twenty-fourth-order finitedifference operators,and the maximum deviation of absolute error is within [0,0.0004].For higher-order operators,the accuracy increase becomes more obvious.The results of elastic wavefield numerical modeling demonstrate that the operators based on the Chebyshev autoconvolution combined window can efficiently suppress the numerical dispersion and has greater modeling accuracy under the same discretizations without extra computing costs.In addition,through adjusting parameters of the auto-convolution combined window,we can adjust the accuracy of finite-difference approximation as required,visually and intuitively.
【Fund】: 中石油新技术新方法项目“GPU/CPU加速弹性介质全波形反演研究”;; 中国石油天然气集团公司科学研究与技术开发项目“弹性波地震成像技术合作研发与应用”;; 国家油气重大专项(2011ZX05008-006-50);; 国家高技术研究发展计划(863)项目“高精度可控震源技术”(2012AA061202)联合资助
【CateGory Index】: P631.4
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