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.
出处
《吉林大学学报（地球科学版）》
EI
CAS
CSCD
北大核心
2005年第4期520-524,共5页
Journal of Jilin University：Earth Science Edition
基金
国家自然科学基金项目(49874029)
教育部高等学校博士学科点专项基金项目(97018705)
关键词
波场模拟
褶积微分算子
傅氏变换
最优权系数
wave field modeling
convolution differentiator
Fourier transform
optimal weighting coefficients
