• journal_title：Geophysics
• Contributor：Chunlei Chu ; Paul L. Stoffa
• Publisher：Society of Exploration Geophysicists
• Date：2012-
• Format：text/html
• Language：en
• Identifier：10.1190/geo2011-0336.1
• journal_abbrev：Geophysics
• issn：0016-8033
• volume：77
• issue：3
• firstpage：W17
• section：Tutorials and Expository Discussions

The finite-difference method evaluates a derivative through a weighted summation of function values from neighboring grid nodes. Conventional finite-difference weights can be calculated either from Taylor series expansions or by Lagrange interpolation polynomials. The finite-difference method can be interpreted as a truncated convolutional counterpart of the pseudospectral method in the space domain. For this reason, we also can derive finite-difference operators by truncating the convolution series of the pseudospectral method. Various truncation windows can be employed for this purpose and they result in finite-difference operators with different dispersion properties. We found that there exists two families of scaled binomial windows that can be used to derive conventional finite-difference operators analytically. With a minor change, these scaled binomial windows can also be used to derive optimized finite-difference operators with enhanced dispersion properties.