地震波场模拟中的褶积微分算子法

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。

Seismic Wave Field Modeling with Convolutional Differentiator Algorithm

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.