Abstract: 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.

Key words: wave field modeling, convolution differentiator, Fourier transform, optimal weighting coefficients