地震波场模拟中的褶积微分算子法
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摘要
褶积微分算子是将偏导数算子的带限傅氏谱进行反傅氏变换得到的,具有对称或反对称和衰减速度快的特点。根据频谱分析理论,选用序列在结束时能光滑趋于零的截断窗口将褶积算子截断,结合考虑微分算子守恒定律,将褶积算子中心值进行修正,得到适合于波场模拟的最优权系数。给出用褶积微分算子模拟声波波场的实现途径与实例。理论分析与模型试算证明了褶积微分算子法的正确性与有效性。
Convolutional differentiator (CD) is obtained by inverse Fourier transform of band-limited Fourier spectra of partial derivative operator. CD is symmetric or antisymmetric and decays rapidly. According to spectral analysis theory, the authors use a window function whose sequences taper smoothly toward zero at the end of the sequences to truncate the CD and modify the central term of the operator by the law of conservation of energy for the differentiator. Thus the optimal weighting coefficients of CD suitable for wave field modeling are obtained. Finally, the realizing approach and examples for acoustic wave field modeling using CD are given. The theoretical analysis and numerical results show the accuracy and validity of the CD.
Convolutional differentiator (CD) is obtained by inverse Fourier transform of band-limited Fourier spectra of partial derivative operator. CD is symmetric or antisymmetric and decays rapidly. According to spectral analysis theory, the authors use a window function whose sequences taper smoothly toward zero at the end of the sequences to truncate the CD and modify the central term of the operator by the law of conservation of energy for the differentiator. Thus the optimal weighting coefficients of CD suitable for wave field modeling are obtained. Finally, the realizing approach and examples for acoustic wave field modeling using CD are given. The theoretical analysis and numerical results show the accuracy and validity of the CD.
引文
[1]王山山,邓玉琼.弹性波正演模拟的混合算法[J].石油地球物理勘探,1997,32(6):804808.WANG Shan-shan, DENG Yu-qiong. Hybrid algo-rithm for forward modeling of elastic waves[J]. OGP,1997,32(6):804808.
[2]滕吉文,张中杰,杨顶辉,等.各向异性介质中褶积微分算子法三分量地震资料的数字仿真[ J].石油物探,1995,34(3):1422.TENG Ji-wen, ZHANG Zhong-jie, YANG Ding-hui,et al. Digital emulation of tricomponent seismic data inanisotropic media through convolution differential op-erator [ J ]. Geophysical Prospecting for Petroleum,1995,34(3):1422.
[3]张中杰,滕吉文,杨顶辉.声波与弹性波场数值模拟中的褶积微分算子法[ J].地震学报,1996,18(1):6369.ZHANG Zhong-jie, TENG Ji-wen, YANG Ding-hui.The convolutional differentiator method for numericalmodeling of acoustic and elastic wave-field [ J]. ActaSeismological Sinica,1996,18(1):6369.
[4] Zhou B, Greenhalgh S. Seismic scalar wave equationmodeling by a convolutional differentiator[J]. Bulletinof the Seismological Society of America,1992,82:289303.
[5] Holberg O. Computational aspects of the choice of op-erator and sampling interval for numerical differentia-tion in large-scale simulation of wave phenomena[ J].Geophysical Prospecting,1987,35:629655.
[2]滕吉文,张中杰,杨顶辉,等.各向异性介质中褶积微分算子法三分量地震资料的数字仿真[ J].石油物探,1995,34(3):1422.TENG Ji-wen, ZHANG Zhong-jie, YANG Ding-hui,et al. Digital emulation of tricomponent seismic data inanisotropic media through convolution differential op-erator [ J ]. Geophysical Prospecting for Petroleum,1995,34(3):1422.
[3]张中杰,滕吉文,杨顶辉.声波与弹性波场数值模拟中的褶积微分算子法[ J].地震学报,1996,18(1):6369.ZHANG Zhong-jie, TENG Ji-wen, YANG Ding-hui.The convolutional differentiator method for numericalmodeling of acoustic and elastic wave-field [ J]. ActaSeismological Sinica,1996,18(1):6369.
[4] Zhou B, Greenhalgh S. Seismic scalar wave equationmodeling by a convolutional differentiator[J]. Bulletinof the Seismological Society of America,1992,82:289303.
[5] Holberg O. Computational aspects of the choice of op-erator and sampling interval for numerical differentia-tion in large-scale simulation of wave phenomena[ J].Geophysical Prospecting,1987,35:629655.
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